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Optical sensors for spacecraft attitude determination
Optical sensors for spacecraft attitude determination J. R. COLDRICK”
This article sets out the physical principles of operation of several types of optical sensor for spacecraft attitude determination. These include sensors which detect solar radiation, reflected sunlight (albedo) from the earth or moon, the infrared radiation contrast between earth and space, or the radiation from stars. Practical details of selected sensors which have been successfully flown in space are given.
Accurate orientation of a spacecraft or some of its on-board systems with respect to the earth, the sun, a star, or one of the planets poses one of the most challenging problems in space technology. For example, the current interest in earth orbiting ccmmunications, meteorological and earth resource survey satellites is accelerating developments in accurate determination and control of satellite attitude since these, and other applications satellites, generally require their antennae and sensors to be maintained in accurate orientation with respect to the earth for effective operation Disturbing torques which can affect the angular momentum of an earth satellite are caused by such phenomena as gradients in the earth’s gravitational field, the interaction of the satellite with its particle and radiation environment, and the earth’s geomagnetic field. It is essential to establish directional references to determine the satellite’s attitude and thus achieve and maintain the desired orientation in the presence of disturbing torques by an on-board control system. This article is concerned with methods of sensing and measuring attitude but before these are discussed, it would be relevant ot review briefly some non-optical methods.
Non-optical
attitude
sensors
Both single and two degree-of-freedom gyros can provide an internal inertial reference by detecting change in attitude from a pre-set direction or by sensing angular velocity. However, gyro drift tends to cause long-term errors unless some means of resetting the gyro or in-flight calibration is provided. Hence, inertial sensors have often been used with sounding rockets and other short-term missions or as memories in long-term missions, regularly updated by other types of sensors which measure the direction to an external reference such as the sun or stars.
* British Aircraft
Corporation
The earth’s magnetic field, detected by such sensors as fluxgate magnetometers, can provide an attitude reference for satellites in nearearth orbit. However, magnetic sensors tend to be severely limited in accuracy by field inhomogeneities, geomagnetic storms and magnetic fields in the satellite itself. An earth satellite can also be oriented with respect to the earth by sensing the gravity gradient with accelerometers and using a passive control system.
Optical attitude
sensors
It is possible to use an optical sensor to establish the direction to an external reference such as the sun, the earth or one of the stars. The sun presents an excellent reference target and a sun sensor is capable of high accuracy. In addition, it can be robust, small and comparatively light. A coarse sun sensor used in conjunction with a fine or digital one may obtain a sun-pointing accuracy of arc-minute order. For eccentric orbits and space flight the presence of the sun cannot be ignored and may as well be used to advantage as an attitude reference. However, for satellites which remain in the earth’s shadow for an appreciable time, some alternative to the sun sensor must be considered. A sensor which detects the infra-red radiation contrast between the earth and the cold space background may be used to achieve an earth pointing accuracy of the order of several arc-minutes. The main drawback of infra-red sensors is their inability (with present day detectors) to detect when at a distance of more than about 8 earth radii from earth. The albedo sensor, which detects sunlight which has been reflected from the earth (or the moon), will operate as well for circular as for highly eccentric orbits or interplanetary flight. The albedo target does not always constitute a welldefined reference however, and sensor accuracies of about 1o of arc are typical. When there is a need for high accuracy, or when other sensors are inoperable, then star tracking or star mapping
Optics and Laser Technology
June 1972
129
of the earth’s orbit, which means that the determination 01through cos (Yis not very accurate.
comes to the fore. Axis-pointing accuracy for satellites of arc seconds may be obtained and it seems that fraction of arc-second accuracy may soon be obtainable. It should of course be pointed out that in practical attitude measurement systems, two or more sensor types are often combined to enable satellite attitude to be determined from directional measurements made with respect to two or more external references, e.g. the sun and the earth. A discussion of complete attitude measurement systems is beyond the scope of this article, as is a discussion of methods used to process measurement information on the ground, including filtering techniques which are used to improve the accuracy of attitude reconstitution. The aim of the present paper is to outline the principles of operation of each type of optical sensor referred to above and to highlight problem areas and performace capabilities as appropriate.
of
The mask-type sensor depicted in Fig. 1b makes use of the fact that the effective incident intensity depends on the area of the photo-detector that is illuminated. If L is the length of the photo-detector (assumed to be rectangular), u is the illuminated length of photo-detector and d is the distance between mask and detector, then the output I is given by: 1 = K2 PA cosa where K2 is a constant = KZ P (L -. d tano) = KS costi - Kq sina,
7
where K3 and Kq are constants. By changing the shape of the mask opening and of the photo-dector, other relationships between I and o can be
Sun sensors Characteristics
of the sun
The sun presents a high intensity target to an optical sensor and subtends an angle of approximately 32 minutes of arc at the earth distance. Hence the sun constitutes one of the best references in our solar system and is widely used as a target for optical sensors flown on space vehicles. The solar irradiance received at the earth distance is approximately 140mWcm-2 and the radiation has a spectral distribution similar to that of a black-body at 5800 K, peaking at about 0.5 pm. Hence a great deal of the radiation is in the visible region of the spectrum and silicon photo-detectors may be used. The radiance of the solar disc decreases and the colour reddens wjth increasing distance from the centre (through the photo-sphere, the chrome-sphere and the corona); but these radiance and spectral variations do not affect a sensor whose objective is to find the centre of the solar disc because the sun has essentially perfect spherical symmetry.
a
[&/’
I=K,
PA cosa
A
Sun spots in the photo-sphere give rise to radiance inhomogeneities but the maximym sensor error introduced by sun spots has been estimated to be approximately 0.75 seconds of arc which is negligible compared with other error sources. The characteristics of the sun are discussed at length by Kuiper’ who deals in some detail with the make up of the photo-sphere, the chrome-sphere and the solar corona and with the characteristics and occurrence of sun spots.
Mask /
Analogue
sun sensors using shadows
or masks
This class of sun sensor makes use of the fact that the output from a photo-detector (e.g. a silicon cell) is proportional to the intensity of incident sunlight. This effect can be utilized in two ways as illustrated by Figs la and lb. The sensor depicted in Fig. la uses the fact that the effective incident intensity depends on the angle of incidence. If A is the photo-detector area,P the solar power per unit area and 01the angle of incidence, then the output I is given by: I = K, PA cosa,
where K, is a constant
Hence 01can be resolved, but it should be noted that the rises and falls *3.4% due to the eccentricity
solar irradiance
130
Optics
and Laser Technology
June 7972
I=K3cos aK,slna b
1 Fig. 1
--L
a: Analogue with mask
sun sensor;
b: analogue
sensor
obtained. The two basic principles outlined above can be used in a wide range of variations and combinations.
Bendix Corporation have developed and space flown several sun sensors based on the quadrant photo-detector. For initial sun acquisition, a typical sensor has a total field of view of f 90” (using peripheral detectors) and a field of view of 210” for subsequent tracking. In the tracking region, the output is a d.c. analogue function of pitch and yaw, linear to t10”.
One disadvantage of analogue sun sensors is that they are always affected by sunlight reflected from the earth (the albedo). In digital sun sensors, described below, the signal must reach a threshold before the detector will give a ‘one’ and thus there is no error below this threshold. It is usually possible in digital sensors to arrange to set the threshold well above the largest signal level occasioned by the earth albedo.
The same manufacturer has also produced fine angle sun sensors based on the above principle. High pointing accuracy (1 arc second) is achieved by using a long focal distance (50cm) and a small field-of-view (40 arc-minutes). This
Analogue sun sensors have been flown in space on several sounding rockets and satellites. Typical units (as manufactured by Ball Brothers) have a fieldof-view of t90” coarse, 15” fine and an accuracy of +5” coarse *0.02” fine. Analogue
sun sensors with quadrant
Gel I elements B
photo-detectors
In this class of sun sensor, an image of the sun, or the shadow of a mask is projected onto a quadrant photodetector as shown in Figs 2a and 2b. When the pointing error is zero, the image is situated symmetrically and all the detectors are equally illuminated. When a pointing error appears, the illumination of the elements is no longer equal and the error angles on 2-axes can be calculated by taking the following signals from the detectors: Pitch error
= (A+B)
Yaw error
= (A +
-
3
(c+D)
c) - (B+ D)
The linearity of the ouput signal depends upon the image 4 shape and a square image gives a _ (as in Fig. _ 2b) generally _ more linear sensor characteristic. Peripheral silicon detectors are frequently used for sun acquisition purposes.
~_ICell
i
I\\
\_
Mask
elements
b
&/QUadront
photo-detector
Lens
Solar cell
Optics
\
~~
/ /./, /,.,jj,j,/.,,,/
,,,,,,_
,,,,.,
C
Fig. 2
Reflecting wedge a: Quadrant
photo-detector
optics; b: quadrant a
I
[
mask; c: split-field Quadrant
photc-detector
sensor with
photo-detector
imaging
sensor with
sun sensor using a reflecting
wedge
Optics and Laser Technology
June
197.2
131
particular sensor’s output is an analogue (but not linear) function of the pointing error and can be used in sun-tracking systems as a null-detector. RAE have also developed several sun sensors based on quadrant photo-detectors. Fig 2c shows an RAE developed split-field device which uses a lens to form an image of the sun onto a reflecting wedge which splits the light between two silicon cells. The difference signal between the two cells gives pointing error on one axis. The total field of view is 28” X lo”, and accuracy is + 10 arc-seconds. Slit/reticle
type
large photo-detectors is used instead of a Gray code shadow mask combined with smaller detectors. The primary advantages of digital sun sensors are: 1 the output is a digital number that can be telemetred directly 2 earth albedo effects can be eliminated by careful selection of the threshold level at which the detectors trigger. 3 low power consumption, low mass, small size 4 can be used in spinning and j-axis stabilized vehicles.
sun sensors
This class of sun sensor uses slits or retitles to produce specially shaped fields of view, often very narrow. The most frequent application of such sensors is in spinning vehicles to determine spin-rate, the angle between the spin-axis and the sun vector or the roll angle. An example of this class is sensors is the Skylark V-beam sun sensor developed by RAE. This comprises two narrow vanes 1o X 180” crosed at an angle 8. Each field is formed by a narrow slit cut in a hemispherical shell over a silicon photo-diode. Each slit defines a plant in the vehicle and the presence of the sun in that plane is indicated when the vehicle rotates. Each slit produces an output pulse when the sun is present and the time between pulses can be transformed to the spin angle $.
2
Illuminated 3
lllumtnated
-dto Ides
Sunlight
3 Bit Gray
Code shadow mask
The angle between the sun vector and the spin axis 4 is given by cot 4 The accuracy
=
sin $ cot 0
of this sensor is 0.25” or better.
Various sun sensors have been developed with slit configurations which are more complex than the simple V-beam sensor described above. It is not possible to discuss these here.
a
3 Bit code
3 Bit Gray binary
code
Digital sun sensors The principle of operation of a digital sun sensor is illustrated in Fig. 3a. Solar radiation is incident on a 3 bit Gray code shadow mask placed in front of three photo-detectors. Opaque separators are placed between the photo-detectors so that each detector sees only the portion of the mask directly in front of it. The amplifier following each detector produces either an on or an off signal depending on the pattern on the shadow mask and the sun’s elevation angle. The particular combination of photo-detectors illuminated provides a digital measurement of the elevation angle of the sun. The accuracy depends on how many bits are used ; a fan field of view can be quantized into ;LS nail)’ ;IS In 1. segments with n binary detectors, so that if the total sensor field of view is 8” and there are II photo-detectors (i.e. n bits), the sensor resolution is f3”/(2” - I). A Gray code system is used rather than the regular binary code since the former requires a decision from only one detector for each transition between quantized segments. The regular binary code often requires simultaneous decisions from several detectors, giving rise to the possibility of errors in the transition region. In some types of digital sun sensor, an entrance slit combined with a Gray code reticle in front of quite
132
Optics
and Laser Technology
June 1972
Entrance
/
slit
elevation
code
b
Fig 3
a: Three shadow
bit digital
sun sensor with
mask; b: practical
a Grey
7 bit Adcole
code
sun sensor
A practical 7-bit digital sun sensor manufactured by Alcole Corporation is illustrated in Fig. 3b. The field of view is f 64”) the angular resolution 1o and the accuracy at transition + 0.25”. Dimensions of the optics/ detector configuration are 2% X 2% X y16 in and mass is 112g. The output from the sensor is processed in an electronic package to a desired form which may be serial Gray code, serial binary code or quantized analogue staircase voltage, depending on the telemetry requirements. Earth sensors Characteristics
of the earth
The albedo
Earth albedo sensors depend for their operation on detecting sunlight reflected from the earth. The reflected sunlight has approximately the same spectral characteristics as direct solar radiation. The term albedo is generally accepted to refer to the fraction of the total incident energy which is reflected by the body throughout the entire band between the ultra-violet and the far infra-red. Referring to the earth‘s albedo usually implies the earth and its atmosphere. The visual albedo of the earth is taken to mean the ratio of the amount of light diffusely reflected in all directions by the earth/atmosphere system to the amount of visual light incident upon the system. Often the term albedo is used in this latter context only. Radiometry calculations of irradiance received at particular points above the earth’s surface are usually based on a mean value of earth albedo, normally between 30% and 40% and the earth is considered to be a perfect Lambertian emitter. Unfortunately, the earth albedo is very irregular (as witnessed by photographs taken from TIROS, NIMBUS etc.) The earth albedo shows considerable variations over the various earth and atmospheric features that reflect light. The albedo varies from a low value over water surfaces to very high values recorded from certain types of cloud coverage. The main variations in earth surface figures are derived from: 1 2 3 4 5 6
variations in type of terrain, from desert to thick woodland to sea optical thickness of atmospheric gases and the consequent variations in absorption the sun’s elevation angle the Nadir angle the azimuth angle of the point of observation with respect to the sun seasonal variations (e.g. deciduous forsets becoming defoliated in winter, snowfields melting in summer etc .).
The 6th Edition of the Smithsonian Metrological Tables list the following albedo figures based on measurements taken in the visible spectrum from aircraft: deep ocean 3 to 5% ; inland water 5 to 10% ; green forest 3 to 6%~; bare ground IO to 20% ; desert 25% ; dry grass 15 to 25% ; snow fields 70 to 86%) ; dense opaque clouds 55 to 78% ; thin clouds 36 to 40%. Mean albedo figures for the whole earth have been measured by several people and values vary from 39% (visible spectrum measurements made by Danjon) to between 29 and 3 1% for the whole spectrum using measurements
taken by Nimbus 2.3 It is estimated that a mean albedo figure of 35% would be made up of 2 to 3% from the earth’s surface, 23 to 26% by clouds and 6 to 9% by the earth’s atmosphere. The effect of cloud on the mean albedo figure is very significant. The effect of latitude on the earth’s albedo is also to be noted. A recent report from ESTEC4 says that earth albedo varies from 55% at 90” to 10% on the equator. Finally, it is worth noticing that only under very rare conditions can the albedo figure fall below a value of 10%. This is because the earth’s atmosphere reflects from 6 to 9% of the incident sunlight. Hence the facts that the earth’s materials give poor albedo figures, that nearly half the earth’s surface is not covered by cloud at any time, and that latitude variations are considerable, still imply that an albedo figure of at least about 10% should always be available. One other important consideration is that the target shape is a crescent, except for the special case where the spacecraft-target-sun angle (or phase angle) is 0”. Changes in the phase angle vary the area of the illuminated earth that is visible to the spacecraft. For example, as the spacecraft approaches the earth’s surface, the total area of the earth that can be seen from the spacecraft is reduced. This consideration is important in designing earth albedo sensors. The infra-red
horizon
The target to be sensed in this case is the radiation discontinuity between the cold (4K) space background and the warm edge of the earth. The spectral characteristics of the self-emitted earth radiation depends strongly on the earth temperature. The effective temperature of the earth’s surface is about 300K giving a peak emission at a wavelength of around 9.6 pm. However, the effective temperature of the earth’s atmosphere is about 220K corresponding to peak emission at 13 .I/J~. Unfortunately, the radiation discontinuity at the horizon due to the earth’s atmosphere is not always very sharp. The relative sharpness depends quite markedly on the wavelength of observation. Earth horizon scanners were flown in space as early as 1958 and the data obtained showed that the earth’s profile is extremely complex when viewed in the broad infra-red spectrum from 2 to 20pm. In this spectral region, reflections and scattering of solar radiation coupled with radiation from ‘cold clouds’ can produce radiance variations in excess of 5 : 1 in a smgle earth scan. In the atmospheric window region from 8 to 12pm, the effect of reflected or scattered sunlight is removed (since there is a very little solar energy above 8~). but large radiance variations are still encountered due to cold clouds and pole-equator temperature differences. This last effect is particularly enhanced in the 8 to 12pm region since, in the atmospheric window, the sensor essentially views the earth’s surface. More recently, a number of studies and experiments have been conducted in order to obtain a better understanding of the earth’s radiation profile in
Optics and Laser Technology
June
1972
133
various parts of the spectrum. Wark et al’ ; Hanel et a16; Bandeen et al’ and Ehlers8 have presented data which indicates that in the 14 to 16pm CO* absorption band the earth’s horizon looks uniform and is devoid of the cloud effects which are so troublesome when a broad range of the9ifbfra-red spectrum is used. Two NASA publications t present extensive data on the analysis and synthesis of 15pm infra-red horizon radiance profiles.
Instantaneous
In the 14 to 16pm region, the earth irradiance is of the order of 1mW cm-’ at geostationary altitude. It is worth noticing that while the sun subtends an almost constant %” at the earth distance (there is a slight + 1.7% variation due to the eccentricity of the earth’s orbit), and the stars subtend constant angles of only a fraction of an arcsecond, the earth subtends quite large angles, especially at close range. For example, the earth subtends 150” at an altitude of 150 miles and 17.3’ at geostationary altitude (22,300 miles). Thus for eccentric orbits and non-orbital missions, the angular size of the earth changes rapidly with time. This problem is not encountered in the design of sun or star sensors for earth satellites but may be encountered in sun sensors for spacecraft which do not orbit the earth (e.g. Mariner or Viking) or which are in highly eccentric orbit (e.g. Heos). Earth albedo sensors Due to the problems of varying phase angle and nonuniform reflectance mentioned previously, the use of earth albedo sensors is somewhat limited. However, this class of sensor can be used for particuhrr missions where the orbital parameters are such that the earth is almost completely illuminated or where continuous attitude infor mation is not essential. In such situations fairly simple earth albedo sensors can often be designed since conventional visual range detectors and optics can be used. For angular earth sizes from about 0.2” to 12”, shadow mask albedo sensors may be used. Similarly, albedo sensors of the null type based on quadrant photo-detectors have also been developed.
Fig. 5
Blinker /
Fig. 4
734
sensor
As an example, Fig. 4 shows the slit-based earth albedo sensor designed and developed by BAC for the spinning Heos satellite. The sensor has two slits, the meridian slit aligned parallel to the satellite spin-axis. and the oblique slit tilted at 30” to the meridian slit. Three cylindrical spectrosil lenses image the earth albedo onto silicon photo-diode detectors. The field of view of the lens-diode combination is 120” X 1’ and the accuracy is approximately + 0.5”. The sensor is capable of detecting signals down to about 0.06nW cm -2 in the band 0.35 to I .I pm. Blinkers are attached which limit the angle through which the sun will be seen to a maximum of 60” for elevation angles of less than f 15”. BAC is currently investigating a new albedo sensor concept based on reflecting rather than refracting optics scanning sensors
In horizon scanning sensors, a rotating sensor field of view is used to develop a scan pattern, usually conical.
detector ,Oblique sensor assembly
BAC earth albedo sensor for Heos satellite
Optics and Laser Technology
scan horizon
For spin-stabilized vehicles. earth albedo sensors based on slits and retitles and based on digital techniques have been developed. These are similar to sun sensors described previously.
Horizon Silicon photo-diode
Conical
June 1972
Fig. 5 illustrates such a sensor designed for a non-spinning satellite where a rotating optical component is used to generate the conical scan. For two-axis attitude information i.e. pitch and roll, two optical heads are required and these are normally installed in the spacecraft so that they look out of opposite sides. A rectangular pulse is generated when the earth is traversed by the optical scan of each head. A reference:e pulse is also generated as the scan passes through the spacecraft pitch position. The signal processing circuits of the sensor compare the earth signals from the two heads to determine roll and phase-detect each head’s output in combination with its reference pulse to determine pitch. This type of sensor is useful over a wide range of spacecraft altitudes and is operationally characterized by wide acquisition angles and fast response times. The need to have high speed, rotating optical components oper-ating reliably in the space environment is their major drawback.
Fig. 6 shows how a wide angle conical scan can be generated in a spin stabilized satellite using the motion of the vehicle itself. Such sensors are often called horizon crossing indicators and have the advantage of not containing moving parts. In general, the best infrared detectors for use in horizon scanning sensors are thermistor bolometers and pyroelectric detectors. These are characterized by fast time constants (e.g. 1 to 5 ms) and low noise equivalent powers at the typical operating modulation frequency (e.g. 1.5 X 10-t’ W at 15Hz). Thermopile detectors are generally too slow for applications in scanning sensors. A typical wide-angle horizon sensor of the type shown in Fig. 5 is manufactured by Barnes Engineering Company and uses a rotating germanium prism driven by a synchronous motor to generate the field-of-view scan pattern. The field of view of 2” X 8” is scanned conically through an angle of 110”. The prism rotates at 30 revolutions per second and an immersed thermister bolometer detector is used. Typical operating accuracy is + 0.5” and the sensor has a mass of 1 Skg and a power consumption of 4 W (including scanning motor). Horizon crossing indicators of the type shown in Fig. 6 have been manufactured and proved in space by several companies including Barnes. These are generally more reliable (no moving parts), lighter and smaller than the typical scanning sensor described above. Horizon
tracking
sensors
Tracking sensors incorporate a number of edge or horizon trackers. Each tracker locates and locks onto the horizon. The angle between the line of sight of the tracker and a reference axis is measured and the roll and pitch attitude computed. In some instances the edge-trackers are positioned at fixed azimuth intervals (e.g. three at 120” intervals), and in others the trackers also scan in azimuth and follow the earth’s outline. One type of tracking sensor, as shown in Fig. 7, uses a detector with a small field of view (typically 1.5” X 1.5”) which is scanned through an arc of a few degrees peak-to-peak at a frequency of around 20Hz. This is called‘dithering’. The field of view can also be scanned at a low rate through an arc of about 80”. The tracker acquires the horizon by scanning slowly from space towards earth. When the dither
Instantaneous
Fig.7
Edge tracking
However, horizon tracking sensors have also been developed which use thermopile detectors and elimate the dither scan. In these sensors, the single bolometer normally used in edge-tracking sensors, is replaced by two thermopile detectors with their fields of view separated by a fixed angle. The two fields of view are servo-positioned within a scan plane so as to measure the declination angle to the horizon relative to the spacecraft. Horizon edge-tracking is accomplished by applying a fixed downward drive to the servoed assembly to direct the lower field of view into the horizon by an amount sufficient to generate a signal termed the ‘buck out’ signal equivalent to this fixed downward drive. During tracking the lower field of view rides on the horizon edge. This technique eliminates the requirement for high-speed optical chopping or scanning. A typical horizon edge tracker as shown in Fig. 7 has a field of view of 1” X 1” scanned through 5” peak to peak at 2OHz, and a total scan angle of 90”. The typical accuracy is 0.15” or better with a mass of 6 kg and power consumption of8 W.
nstantaneous
Bis&tor Horizon satellites
crossing indicator
sensor
scan intersects the horizon, an a.c. output appears which is used to terminate the slow scan and to provide tracking information to position the dither scan centrally on the horizon gradient. The position of the centre of the dither scan is read by a position transucer. The basic purpose of the dither is to modulate the incoming energy in a way which provides the required angular information. Hence thermistor bolometers and pyroelectric detectors can be used.
Horizon
Fig. 6
horizon
’
for spin stablized
sensors of the radiation
balance type
Fig. 8a shows the basic configuration of a static horizon sensor of the radiation balance type. The principle of operation involves comparing the radiation received from opposite portions of the earth. Typically an image of the earth is projected onto an array of infrared detectors and attitude information is obtained by taking the difference in radiant power received by opposite fields of view, i.e. (Pa - P>) gives pitch error and (Pa - PA) gives roll error. This should be compared with formulae 3,4 for quadrant photo-detector sensors. If all the detectors have equal sensitivity, the outputs of opposite detectors are equal, for a uniform earth when the pointing error is zero. Errors can be introduced by differences in detector sensitivities (matching of both
Optics and Laser Technology
June
1972
135
Pitch
have been introduced to measure the radiance of the earth at points adjacent to the areas observed by the main detectors. This information is used to compensate the sensor output for any radiance variation found.
OXIS I
IR detector’s field-of-view
The main advantages of horizon sensors of the radiation balance type is that they essentially involve no moving parts and have low power consumption, low weight and very high reliability. Since thermopile detectors generate their own voltage in an active sense and are ideally suitable for use in direct coupled (or unchopped) applications, they are generally used in this class of horizon sensor. The pro!lem of trying to identify a small change (typically 1 in 10 ) in a large bias voltage is encountered if one attempts to use thermistor bolometers in direct-coupled systems and it is normally essential to modulate the radiation with these detectors. However, with thermopiles, the only voltage that appears is the signal itself and thermopile sensors can be unchopped systems with no moving parts, resulting in increased reliability in the space environment. Pyroelectric detectors are not suitable for direct -coupled applications since the surface charge on which detector operation depends is not permanent and leaks away.
17.3’eorth
horizon
from geastationary
A typical sensor of this type as manufactured and proven in space by Barnes Engineering Company is based on antimony-bismuth thermopiles and has a field of view of 15” X IS” and an accuracy of 4 0.3”. Mass is I .5 kg and power consumption 3W. Other sensors working on these principles are currently under development in Europe and elsewhere and accuracies of + 0.1’ or better should become available. Solid-backed thertnopiles with improved responsivity for use in this type of sensor are also under devolopment at BAC and elsewhere.
i
Star sensors
/
field-of- v.tezw
Characteristics Rod iance compensotlon detectorb field-of-view
b
Fig. 8
a: Basic static horizon b: Tangent
sensor configuration;
field configuration
compensation
with
radiance
detectors
absolute responsivity and of temperature coefficient of responsivity is important) and also by the non-uniform radiance of the earth. For constant orbit satellites (e.g. geostationary), the so-called tangent field configuration can be used to reduce the earth radiance variation error to near zero pointing error. This is illustrated in Fig. 8b where the detector’s field of view extends below the earth horizon, this error is zero for zero pointing error. It is clearly only possible to maintain this field tangency condition when the earth’s image is of constant size. Fig. 8b also shows four extra detectors which
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Optics and Laser Technology
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1972
of the stars
To an optical sensor the stars present essentially point source targets since they subtend angles of fractions of an arc-second e.g. 0.0068 arc-seconds for Sirius and 0.041 arc-seconds for giant Antares. To describe the relative brightness of stars, it is necessary to introduce some astronomical terminology. Stellar magnitude is the astronomical unit of star intensity and a star having a magnitude of one has been arbitrarily defined as being 100 times brighter than a star of magnitude six. Stars of tnagnitude six are generally considered to be barely on the threshold of unaided vision. A difference of one tnagnitude is equivalent to a facor of 5dlO0, or 2.5 12, in intensity. The tnagnitude scale is defined in terms of a set of standard stars and is based on an assumed spectral response for the detector, for example, on the visual magnitude scale. Some typical KilUeS are :Sirius
- 1 .44 (the brightest star)
Canopus
_ 0.72
Polaris
+ 2.02
On this same scale, the sun has a magnitude of --26.$&, and is thus 25.36 magnitudes (or a factor of (2.5 12) = 1.39 X 1O1‘) brighter than Sirius (at the earth’s distance from the sun and from Sirius).
Table 1 gives an indication stars.
of the density of background
Table 1. Density of background Visual magnitude M
+8 +7 +6 +5 +4 +3 +2
stars 2
Stars/degree brighter than M
1.o 0.34 0.12 0.04 0.013 0.0014 0.0009
Calculation indicates that the integrated effect from the background radiation is approximately equivalent to one +3 visual magnitude star per square degree. To convert the star magnitudes given above into effective irradiance on a detector, it is necessary to know the spectral characteristics of the stars. Stars are divided into seven clases (0, B, A, F, G, K, and M) on the basis of absorption lines in their spectra. These classes are also in order of decreasing effective temperature, assuming that the star’s radiation is approximately blackbody. Thus 0 type stars are hottest and appear blue while M type stars are cooler and appear red. The sun is a yellow L type star (effective temperature S,SOOK), Vega is a blue A type star (effective temperature 1 1 ,OOOK), and Betalgeuse is a red M type star with an effective temperature of about 3,lOOK. Canopus is an F type star, slightly bluer than the sun with a temperature of 7,600K. Thus, the wavelengths for peak radiation output vary from 0.18 to 1.Opm and the ideal detector for use in star sensors should, therefore, respond to radiation from the near ultra-violet through to the near infra-red range of the spectrum. In practice, however, it may prove advantageous to limit the spectral response of the detector at the longer wavelengths to suppress the detection of the undesirable radiation from background stars. The spectral irradiances from some of the brightest stal ‘S as seen from above the earth’s atmosphere are as follows: Sirius:
4 X 0-l’ W cm-’ pm-’ , peaking at - 0.3pm
Canopus:
3 X O-“W cm-’ pm-’ , peaking at - 0.6pm
Antares:
8 X O-l3 W cm-’ pm-’ , peaking at - 1.3ym
Ramsey”
gives more detailed information
desired guide star. The width of the lock-on band is determined by the magnitude of the competing targets in the scan zone and by the accuracy of sensor calibration. For colour discrimination, the star light can be passed through two or more pass-band filters (e.g. a blue pass and a red pass). The ratio of energy in the two bands uniquely determines the colour temperature of the star. This method can be used in conjunction with magnitude discrimination to further limit the chance of acquiring the wrong target. Star sensors based on automatic threshold systems as described above involve a requirement for precise sensor calibration. This is difficult due to the current lack of extensive star spectral data, the effects of the earth’s atmosphere and drifts in the sensor itself. Hence, practical star sensors are normally based on star mapping modes (see next section) and/or auxilliary sensors instead of or in conjunction with automatic threshold systems. The use of an auxiliary sensor, e.g. an earth sensor, serves to limit the area in which the guide star can be located by supplying information on the position of another body, e.g. the earth, whose relationship to the desired guide star is known. A more sophisticated version of the auxiliary sensor technique involves the use of two or more star sensors, each set at an angle to intercept a different guide star and roughly calibrated to respond only to stars in a desired magnitude range. There is in general only one star combination which will result in simultaneous lock-on of all sensors. One class of sensor determines the direction to a star by using a rotating reticle onto which an image of the Star image Photo detector
Field lens
I
0 E
.
=
-
-
lEk
-_
..:,..:,:::,::~:~ ‘F
5
-
.:g:.:+.:
Processing electronics
-
a
A Rotation axis
on this subject.
Optical imagmg system
Rotating mirror _
Star trackers The method used for,star acquisition is influenced by the position and magnitude of the chosen guide star. Acquisition of the correct star is perhaps one of the most serious problems encountered in star tracker design since there are often many competing targets (other stars, planets and moons). Star magnitude and/or spectral characteristics may be used as methods of star identification. For magnitude discrimination the sensor is designed to produce a lock-on signal whenever the input energy lies within a range centred around the expected level from the
Star
image
Stationary
reticle
b Fig. 9
a: Rotating
reticle sun sensor; b: nutating
image star sensor
Optics and Laser Technology
June
1972
737
star is projected or by nutating the projected image by means of a rotating optical element. Fig. 9a illustrates the principle of the rotating reticle method. An optical system projects an image of the star (effectively a point source) onto a rotating reticle. The radiation transmitted by the reticle comprises alternating transparent and opaque segments which are coded in a special way so that the light is modulated by the reticle and the detector output consists of pulses. Processing electronics enables the position of the star image on the reticle to be derived. Then from a knowledge of the focal length of the optical system, the angle between optical axis and line of sight (i.e. the pointing error) can be obtained. The reticle shape determines the relationship between sensor output and pointing error. In many cases a linear relationship is not essential since the output is often used to drive a servo system to point the star sensor at the star, i.e. star tracker. Fig. 9b shows how the light passing the reticle can be modulated by nutating the star image rather than by rotating the reticle. In such a system, the image of the reticle is translated into a circular pattern by the rotation of a mirror. When there is no pointing error, the circular image trace is concentric with the reticle and the modulated signal has a constant frequency. When a pointing error exists, however, the image trace and the reticle are eccentric and the signal is frequency modulated in relation to the eccentricity. The processing electronics derives the eccentricity and thus the pointing error. The output signal can again be used directly as a measure of an angle or it can be used in a servo system to point the sensor at the star, i.e. a star tracker. Fig. 10 shows the principle of a vibrating reed star sensor. The vibrating reed has an aperture that is deflected in front of a photo-detector. An image of the star is projected by an optical system onto the reed. Thus the light from the star is transmitted by the aperture for a time interval that is determined by the reed vibration frequency and the position of the star image on the reed. When the star is at the centre of the scan field (i.e. on-axis) the detector signal comprises almost entirely the second harmonic of the reed vibration frequency, and the fundamental frequency is zero. When a pointing error appears, the signal at the fundamental frequency increases and is proportional to the pointing error for a great part of the scan field. Hence this can be used as the error signal for the star tracker. It is possible, and often preferable on the grounds of reliability, to use electronic rather than mechanical scanning to detect star pointing error. A quadrant photomultiplier, as shown in Fig. 1 1a, consists of an electron multiplier the front end of which has four photo-cathodes each in the shape of a quadrant of a circle. Electronic switching enables the amplified photo current from each quadrant to be read out sequentially at the anode. When used as a star sensor, the position of a defocussed star image on the photocathode plane is derived from the output currents (I,, I*, II, 1,) caused by emission from each of the four photocathode segments. Fig. I I. shows the defocused star image at the null position, i.e. exactly 011 axis, where I, = f, = IJ = I,. The output display shows the anode current
from the respective
photo-cathode
segments.
When the star is slightly removed from the null position, as
738
Optics and Laser Technology
June
1972
shown in Fig. 1 lc, the output from the four quadrants is no longer equal. The signal currents related to the x and v positions of the star image are: ;
1, = II + I, - Ia -1,
I, = I, f I, - Iz ~ I,
1, representing roll axis pointing error and I, representing pitch axis pointing error. Limits
of deflection Aperture
opening
Photo detector
Vibration sense
Imaging lens Fig. 10
Vibrating
reed star sensor
Front end assembly
Photo-cathode seqment 2
a
Focusm electro c? 4
De-focused star image I
Null
2 Output
3 display
4
posrtron
b
n 4 3
2
@ Off-null posrtron
Output
display
C
d
Fig. 11
a: Quadrant
photomultiplier;
image at null position; slightly
b: output
c: output
off null; d: output
for star
for star image
characteristics
for I.,.
When the star image is well removed from the vicinity of null, it is no longer possible to determine precise position information. Figure 1 l(d) shows that within the region 2x0 the star image impinges on one or two quadrants on both sides of the y axis and Z, is a function of x, i.e. x position information is available. 2x0 is the star image diameter. When the star image impinges on one or two quadrants on only one side of they axis, I, is constant and the only information obtained is that the image displacement is greater than x0. The region of the star position information area is at the option of the system designer; the larger the defocused star image, the greater the area of position information. This wider latitude is obtained at the expense of some loss of precision. This type of star tracker has the advantage of no moving parts but suffers from the drawback of needing high voltages. It is also possible to use an image dissector tube to act as photo detector as well as scanning device. As shown in Fig. 12, an optical system focuses the field of view onto the photo-cathode of an image dissector tube. The optical axis defines the reference axis and angular deviation of the line of sight from this axis may be resolved by electronic processing into two orthogonal planes which provide 2-axis attitude information. The image dissector tube comprises a photo-cathode which converts the optical image focused on the tube windows to an electron image which is electrostatically focused and accelerated towards an aperture plate. External electrostatic plates or electromagnetic coils are employed to sweep the electron image across the aperture. Thus the total sepjor field of view is scanned and this enables the angular position of the star to be detected. When the electron image of the star is focused on the aperture, the electron multiplier section of the tube thus provides a signal output at the collector electrode which, when compared with a sweep signal reference, gives the angular position of the star relative to the optical axis. Finally, star trackers can be based on an optical system which projects an image of the star onto the photoconductive target of a vidicon. The electron beam of the vidicon scans the photo-conductive target and a pulse is generated at the output whenever it crosses the star image. The position of the star image is then derived in the processing electronics. Having outlined the principles of operation of several classes of star tracker, it is now appropriate to examine briefly a few trackers that have been developed for space missions. RAE has developed a frequency modulated star sensor based on a nutating reticle which comprises 36 linear pairs of transparent and opaque sectors. A reflecting optical system is used to image the star, having a Scm aperture and a 75~111 focal length. The field of view is 0.5” and accuracy is of the order of 3 arc-seconds or better for a second magnitude star. Kollsman Instrument Corporation have developed several star trackers based on vibrating reeds. One such system developed for the Apollo mission, uses refracting optics and a miniature photo-multiplier detector. The field of view is 0.5” and tracking accuracy is 8 arc-seconds for stars of second magnitude. Another similar system developed for the OAO project uses a silicon photo-voltaic detector (with all the attendant advantages over a photo-multiplier, namely, no high voltage power supply, less prone to solar radiation
Optical system Photo-cathode,
, Ekctron multiplier sect ion Multtple dynodes
-Vacuum
Image dissector
Fig. 12
tube
star-sensor
damage, small size). With a field of view of 1” X 1O, tracking accuracy of the order of 10 arc-seconds is typical but the penalty of using a solid state detector is that sensitivity limits the system to stars of magnitude +I .I (detector magnitude, not visual magnitude). Honeywell has developed a Canopus star-tracker based on a quadrant photo-multiplier. With a field of view of 2” X 2”, the null accuracy is + 27 arc-seconds. One feature of this and many other star sensors which use photo-multipliers is a sun shutter to protect the sensitive photo-cathode from radiation damage. The sun shutter is activated by an auxiliary sun sensor with a 5” field of view, boresightcd with the star tracker. The use of a sun shutter is to be avoided whenever possible due to reliability problems. In practice this means using a solid state detector (with its associated lower sensitivity) rather than a photo-multiplier. Solid state detectors are, however, being developed and improved performances can be expected. Of particular interest for star sensor appli4tions are silicon pin photo-diodes, and silicon avalanche photo-detectors. Barnes Engineering Company in association with Jet Propulsion Laboratories developed a single-axis Canopus star tracker based on an image dissector tube for the Mariner spacecraft. This used an f/l reflecting optical system of 2.5cm aperture. The field of view was O.@ X IO” and tracking accuracy was 0. lo for Canopus. An external sun shutter was used. Star mappers The derivation of attitude information from stars can be achieved in a spinning satellite by means of a star mapper. The star mapper scans the celestial sphere and maps the star pattern intercepted by its field of view. A pattern of light-transmitting slits is placed in the focal plane reticle of an optical system and the magnitudes and transit times of stars passing across the slit-pattern are measured and telemetred to ground. A computer on the ground is used to compare the sensor information with catalogued star position information and attitude determination and reconstitution then becomes possible. The scanning is
Optics
and Laser Technology
June
1972
139
readily achieved by the rotation of a spinning satellite but for a 3-axis stabilised vehicle, it is still possible to employ star-mapping as a means of identifying and acquiring the desired guide star for tracking. In this latter case, it is necessary to achieve scanning by means of a reticle drive. Fig. 13 shows schematically a star mapper for use in a spinning satellite in order to determine spin-axis attitude. Light from a star passes through a focusing optical system from which stray light is barred by a baffle. In the focal plane there is a slit system which can contain one, two or more slits, which limit the field of view seen by the sensor. #en the satellite rotates, the star image passes over one of the slits and light from the star passes through to the cathode of a photo-multiplier tube placed immediately behind the slits. The star transit gives rise to a current pulse which may either be transmitted directly to the ground for analysis, or converted to a square pulse, stored on board and transmitted at a time interval determined by the spin period of the satellite. Using an on-board memory, it is possible to average information over several satellite revolutions before transmission to ground. As the satellite rotates, the angular separation of two or more stars may be obtained from their times of transit across a particular slit, and, subject to the identification of these stars with a ground level comparison, this information may be used in the determination of attitude. If a two slit system is used, as shown in Fig. 13, the timing of a single star as it crosses the two slits then gives an immediate fix for the spin axis with respect to the star direction, and only one further reference is required to give the satellite attitude. It should, however, be noted that a double slit causes confusion when two stars are very close together because four signals will be produced and it will be doubtful which allocation of signals to the appropriate star is the correct one. Another advantage of a single slit is that background noise is minimized. Against these advantages, however, it must be remembered that a single slit provides no immediate information as to vehicle attitude. For example, if only one detectable star is present in the band swept on the celestial sphere, the single slit gives no useful result since the transit time information is only helpful when related in time (and hence angle) to the transit of another. The double slit arrangement gives information
External
baffle
I
Detector
lens
/
A? Reticle
140
Typical
Fig. 14
a: Reticle
configuration
showing multi characteristic
for project
slit arrangement; trace obtained
scanner
b: Idealized
when a genuine
star image crosses the slit pattern
of Fig. 14a
on the angle between satellite spin-axis and the star line immediately, with only one detectable star per sweep. Even allowing for the fact that two slits involve an increased background noise (twice as large an instantaneous area marked on the celestial band), on balance the gain of information using two slits generally outweighs the loss occasioned by increased noise. One final point to consider is the spacecraft spin rate. Because of quantum mechanical effects, stars nominally detectable, may not be observed as the spacecraft rotates. The more slowly it does so, the longer the star stays in the sensor field of view and the greater the probability of the star being detected. It is not easy to make a precise calculation for this since it depends on the signal-to-noise ratio. However, consider as an example the problem of detecting a fourth magnitude star using a 5 cm apcriure objective lens. The irradiance is of the order of 6 X IO photons s-l and assuming an optical efficiency of 75% and a quantum efficiency of 20%, then to ensure 30 photoelectrons (when the question of detection seems critical), 200 photons are required to impinge on the objective lens during each scan. Thus the time required for a star 200 seconds = 0.33 ms. With a slit 6 x IO5 width of 0.15”. the maximum spin rate for detection of a to be seen is
4th magnitude
0.15
star is 0.33
x
_a degrees s-r IO
~75 r.p.m.
We conclude that for any reasonable satellite spin rates, third magnitude stars can be detectected with reasonable certainty, using currently available photo-multiplier tube performances. However, for fourth magnitude stars, satellite spin rate is limited to around 75 r .p.m. to ensure a reasonable probability of detection. In practice, this is not an unreasonable limitation.
Objective
Fig. 13
a
star-mapper
optical
Optics ano Laser Technology
Condenser kns system
(not to scale)
June 1972
Several star mappers have either been flown or are currently under development. ATS III (a technological satellite) was equipped with an experimental star mapper with a 12” useful field of views, an aperture of 8.8cm and a focal length of 7.6cm. The reticule comprised 3 slits of width 7.6 arc-minutes and a photo-multiplier was used as detector. Attitude reconstitution accuracy was of the order of 1 minute of arc. Another star mapper was flown on a sounding rocket (Project SCANNER) and had a field of view of 6” and a reticle comprising two systems of slits, one vertical and one
Table 2. Summary of sensor types Class of
Angular
Typical
of target
region (pm)
Typical detector irradiance (Wcm-‘1
Type of
sensor
detector
accuracy
Sun
0.53”
0.2 to 1.1
10-I
Silicon
+0.03”
size
Operating
spectral
sensor
solid-state Earth albedo
0.2 to 1 .I
100” to 2”
1o-2 to 1o-6
Silicon
+0.5”
solid-state
(depending on altitude) Earth
150” to IO0
Usually
1O-3
infra-red
(depending
14to
(at geostationary
16
altitude)
on altitude)
Star
Thermistors, pyroelectrics or solid-backed
17.3”
thermopiles
(geostationary)
(dx.
0.04 to 0.005
0.15 to 1.4
arc-seconds (deoending
lo-”
20.2”
to lo-l4
application)
Photomultiplier
+0.003”
(depending on star)
inclined as shown in Fig. 14a. The slit widths varied from 0.015” to 0.03” as shown and were unevenly spaced. This slit arrangement reduces the probability of false identification of a star since a genuine star now produces a characteristic trace as shown in Fig. 14b. An on-board logic system can then reject signals not of this characteristic form. This refinement of the double slit system is really of use only for weaker stars but then there is the serious chance that a weak star will only be detected at two of the slits. It is possible to add a logic device which will involve all six slits that a star may encounter but then the advantages of the refined system appear to be balanced by the drawbacks of having to incorporate additional electronic processing. Ball Brothers have also developed a star mapper for use on the OSO-H satellite. This has a 10” field of view and a 1Ocm2 receiving aperture. A double slit reticle is used, with 0.03” slit widths. Attitude reconstitution accuracy is approximately 0.02”. Conclusion
Table 2 summarises the main feature of each major class of attitude sensor described in this article.
on star)
References 1
8
9
10 11
Spotts J. H., Optical attitude sensors for space vehicle appbcation, M. SC. Thesis, University of California, Los Angeles, Oct. 1965, p.6 Kuiper G. P., The Sun, University of Chicago Press, 1953. Journal of Applied Meteorology, April 1970 Atzei A., ESRO TN-103, April 1970 Wark D. Q.,et al, Variation of the infra-red spectral radiance near the limb of the earth, Applied Optics, 3, 221,1964. Hanel R. A. et al, The infra-red horizon of the planet earth, J. Atmospheric Science, 20, 73, March, 1963 Bandeen W. R., Experimental Confirmation from the Tiros VII Meteorological Satellites of the theoretically calculated radiance of the earth within the 15~ band of carbon dioxide, J. Atmospheric Science, 20, 609, 1963. Ehlers E. E., Temperature measurement of earth and clouds from a satellite, 2nd Symposium on remote sensing of the environment, University of Michigan, Ann Arbor, 1964 Thomas J. R.,et al, The analysis of 15~ IR horizon radiance profiles variations over a range of meteorological, geographical and seasonal conditions, NASA CR-725,1967 Bates J. C.,et al, The synthesis of 15~ IR horizon radiance profiles from meteorological data inputs, NASA CR-724.1967 Ramsey R. C., Spectral irradiance from stars and planets above the atmosphere, from 0.1 to 100.0~ Applied Optics, 1, (41, July, 1962
Received
12th November
197 1
Optics and Laser Technology
June
7972
747
This article sets out the physical principles of operation of several types of optical sensor for spacecraft attitude determination. These include sensors which detect solar radiation, reflected sunlight (albedo) from the earth or moon, the infrared radiation contrast between earth and space, or the radiation from stars. Practical details of selected sensors which have been successfully flown in space are given.
Accurate orientation of a spacecraft or some of its on-board systems with respect to the earth, the sun, a star, or one of the planets poses one of the most challenging problems in space technology. For example, the current interest in earth orbiting ccmmunications, meteorological and earth resource survey satellites is accelerating developments in accurate determination and control of satellite attitude since these, and other applications satellites, generally require their antennae and sensors to be maintained in accurate orientation with respect to the earth for effective operation Disturbing torques which can affect the angular momentum of an earth satellite are caused by such phenomena as gradients in the earth’s gravitational field, the interaction of the satellite with its particle and radiation environment, and the earth’s geomagnetic field. It is essential to establish directional references to determine the satellite’s attitude and thus achieve and maintain the desired orientation in the presence of disturbing torques by an on-board control system. This article is concerned with methods of sensing and measuring attitude but before these are discussed, it would be relevant ot review briefly some non-optical methods.
Non-optical
attitude
sensors
Both single and two degree-of-freedom gyros can provide an internal inertial reference by detecting change in attitude from a pre-set direction or by sensing angular velocity. However, gyro drift tends to cause long-term errors unless some means of resetting the gyro or in-flight calibration is provided. Hence, inertial sensors have often been used with sounding rockets and other short-term missions or as memories in long-term missions, regularly updated by other types of sensors which measure the direction to an external reference such as the sun or stars.
* British Aircraft
Corporation
The earth’s magnetic field, detected by such sensors as fluxgate magnetometers, can provide an attitude reference for satellites in nearearth orbit. However, magnetic sensors tend to be severely limited in accuracy by field inhomogeneities, geomagnetic storms and magnetic fields in the satellite itself. An earth satellite can also be oriented with respect to the earth by sensing the gravity gradient with accelerometers and using a passive control system.
Optical attitude
sensors
It is possible to use an optical sensor to establish the direction to an external reference such as the sun, the earth or one of the stars. The sun presents an excellent reference target and a sun sensor is capable of high accuracy. In addition, it can be robust, small and comparatively light. A coarse sun sensor used in conjunction with a fine or digital one may obtain a sun-pointing accuracy of arc-minute order. For eccentric orbits and space flight the presence of the sun cannot be ignored and may as well be used to advantage as an attitude reference. However, for satellites which remain in the earth’s shadow for an appreciable time, some alternative to the sun sensor must be considered. A sensor which detects the infra-red radiation contrast between the earth and the cold space background may be used to achieve an earth pointing accuracy of the order of several arc-minutes. The main drawback of infra-red sensors is their inability (with present day detectors) to detect when at a distance of more than about 8 earth radii from earth. The albedo sensor, which detects sunlight which has been reflected from the earth (or the moon), will operate as well for circular as for highly eccentric orbits or interplanetary flight. The albedo target does not always constitute a welldefined reference however, and sensor accuracies of about 1o of arc are typical. When there is a need for high accuracy, or when other sensors are inoperable, then star tracking or star mapping
Optics and Laser Technology
June 1972
129
of the earth’s orbit, which means that the determination 01through cos (Yis not very accurate.
comes to the fore. Axis-pointing accuracy for satellites of arc seconds may be obtained and it seems that fraction of arc-second accuracy may soon be obtainable. It should of course be pointed out that in practical attitude measurement systems, two or more sensor types are often combined to enable satellite attitude to be determined from directional measurements made with respect to two or more external references, e.g. the sun and the earth. A discussion of complete attitude measurement systems is beyond the scope of this article, as is a discussion of methods used to process measurement information on the ground, including filtering techniques which are used to improve the accuracy of attitude reconstitution. The aim of the present paper is to outline the principles of operation of each type of optical sensor referred to above and to highlight problem areas and performace capabilities as appropriate.
of
The mask-type sensor depicted in Fig. 1b makes use of the fact that the effective incident intensity depends on the area of the photo-detector that is illuminated. If L is the length of the photo-detector (assumed to be rectangular), u is the illuminated length of photo-detector and d is the distance between mask and detector, then the output I is given by: 1 = K2 PA cosa where K2 is a constant = KZ P (L -. d tano) = KS costi - Kq sina,
7
where K3 and Kq are constants. By changing the shape of the mask opening and of the photo-dector, other relationships between I and o can be
Sun sensors Characteristics
of the sun
The sun presents a high intensity target to an optical sensor and subtends an angle of approximately 32 minutes of arc at the earth distance. Hence the sun constitutes one of the best references in our solar system and is widely used as a target for optical sensors flown on space vehicles. The solar irradiance received at the earth distance is approximately 140mWcm-2 and the radiation has a spectral distribution similar to that of a black-body at 5800 K, peaking at about 0.5 pm. Hence a great deal of the radiation is in the visible region of the spectrum and silicon photo-detectors may be used. The radiance of the solar disc decreases and the colour reddens wjth increasing distance from the centre (through the photo-sphere, the chrome-sphere and the corona); but these radiance and spectral variations do not affect a sensor whose objective is to find the centre of the solar disc because the sun has essentially perfect spherical symmetry.
a
[&/’
I=K,
PA cosa
A
Sun spots in the photo-sphere give rise to radiance inhomogeneities but the maximym sensor error introduced by sun spots has been estimated to be approximately 0.75 seconds of arc which is negligible compared with other error sources. The characteristics of the sun are discussed at length by Kuiper’ who deals in some detail with the make up of the photo-sphere, the chrome-sphere and the solar corona and with the characteristics and occurrence of sun spots.
Mask /
Analogue
sun sensors using shadows
or masks
This class of sun sensor makes use of the fact that the output from a photo-detector (e.g. a silicon cell) is proportional to the intensity of incident sunlight. This effect can be utilized in two ways as illustrated by Figs la and lb. The sensor depicted in Fig. la uses the fact that the effective incident intensity depends on the angle of incidence. If A is the photo-detector area,P the solar power per unit area and 01the angle of incidence, then the output I is given by: I = K, PA cosa,
where K, is a constant
Hence 01can be resolved, but it should be noted that the rises and falls *3.4% due to the eccentricity
solar irradiance
130
Optics
and Laser Technology
June 7972
I=K3cos aK,slna b
1 Fig. 1
--L
a: Analogue with mask
sun sensor;
b: analogue
sensor
obtained. The two basic principles outlined above can be used in a wide range of variations and combinations.
Bendix Corporation have developed and space flown several sun sensors based on the quadrant photo-detector. For initial sun acquisition, a typical sensor has a total field of view of f 90” (using peripheral detectors) and a field of view of 210” for subsequent tracking. In the tracking region, the output is a d.c. analogue function of pitch and yaw, linear to t10”.
One disadvantage of analogue sun sensors is that they are always affected by sunlight reflected from the earth (the albedo). In digital sun sensors, described below, the signal must reach a threshold before the detector will give a ‘one’ and thus there is no error below this threshold. It is usually possible in digital sensors to arrange to set the threshold well above the largest signal level occasioned by the earth albedo.
The same manufacturer has also produced fine angle sun sensors based on the above principle. High pointing accuracy (1 arc second) is achieved by using a long focal distance (50cm) and a small field-of-view (40 arc-minutes). This
Analogue sun sensors have been flown in space on several sounding rockets and satellites. Typical units (as manufactured by Ball Brothers) have a fieldof-view of t90” coarse, 15” fine and an accuracy of +5” coarse *0.02” fine. Analogue
sun sensors with quadrant
Gel I elements B
photo-detectors
In this class of sun sensor, an image of the sun, or the shadow of a mask is projected onto a quadrant photodetector as shown in Figs 2a and 2b. When the pointing error is zero, the image is situated symmetrically and all the detectors are equally illuminated. When a pointing error appears, the illumination of the elements is no longer equal and the error angles on 2-axes can be calculated by taking the following signals from the detectors: Pitch error
= (A+B)
Yaw error
= (A +
-
3
(c+D)
c) - (B+ D)
The linearity of the ouput signal depends upon the image 4 shape and a square image gives a _ (as in Fig. _ 2b) generally _ more linear sensor characteristic. Peripheral silicon detectors are frequently used for sun acquisition purposes.
~_ICell
i
I\\
\_
Mask
elements
b
&/QUadront
photo-detector
Lens
Solar cell
Optics
\
~~
/ /./, /,.,jj,j,/.,,,/
,,,,,,_
,,,,.,
C
Fig. 2
Reflecting wedge a: Quadrant
photo-detector
optics; b: quadrant a
I
[
mask; c: split-field Quadrant
photc-detector
sensor with
photo-detector
imaging
sensor with
sun sensor using a reflecting
wedge
Optics and Laser Technology
June
197.2
131
particular sensor’s output is an analogue (but not linear) function of the pointing error and can be used in sun-tracking systems as a null-detector. RAE have also developed several sun sensors based on quadrant photo-detectors. Fig 2c shows an RAE developed split-field device which uses a lens to form an image of the sun onto a reflecting wedge which splits the light between two silicon cells. The difference signal between the two cells gives pointing error on one axis. The total field of view is 28” X lo”, and accuracy is + 10 arc-seconds. Slit/reticle
type
large photo-detectors is used instead of a Gray code shadow mask combined with smaller detectors. The primary advantages of digital sun sensors are: 1 the output is a digital number that can be telemetred directly 2 earth albedo effects can be eliminated by careful selection of the threshold level at which the detectors trigger. 3 low power consumption, low mass, small size 4 can be used in spinning and j-axis stabilized vehicles.
sun sensors
This class of sun sensor uses slits or retitles to produce specially shaped fields of view, often very narrow. The most frequent application of such sensors is in spinning vehicles to determine spin-rate, the angle between the spin-axis and the sun vector or the roll angle. An example of this class is sensors is the Skylark V-beam sun sensor developed by RAE. This comprises two narrow vanes 1o X 180” crosed at an angle 8. Each field is formed by a narrow slit cut in a hemispherical shell over a silicon photo-diode. Each slit defines a plant in the vehicle and the presence of the sun in that plane is indicated when the vehicle rotates. Each slit produces an output pulse when the sun is present and the time between pulses can be transformed to the spin angle $.
2
Illuminated 3
lllumtnated
-dto Ides
Sunlight
3 Bit Gray
Code shadow mask
The angle between the sun vector and the spin axis 4 is given by cot 4 The accuracy
=
sin $ cot 0
of this sensor is 0.25” or better.
Various sun sensors have been developed with slit configurations which are more complex than the simple V-beam sensor described above. It is not possible to discuss these here.
a
3 Bit code
3 Bit Gray binary
code
Digital sun sensors The principle of operation of a digital sun sensor is illustrated in Fig. 3a. Solar radiation is incident on a 3 bit Gray code shadow mask placed in front of three photo-detectors. Opaque separators are placed between the photo-detectors so that each detector sees only the portion of the mask directly in front of it. The amplifier following each detector produces either an on or an off signal depending on the pattern on the shadow mask and the sun’s elevation angle. The particular combination of photo-detectors illuminated provides a digital measurement of the elevation angle of the sun. The accuracy depends on how many bits are used ; a fan field of view can be quantized into ;LS nail)’ ;IS In 1. segments with n binary detectors, so that if the total sensor field of view is 8” and there are II photo-detectors (i.e. n bits), the sensor resolution is f3”/(2” - I). A Gray code system is used rather than the regular binary code since the former requires a decision from only one detector for each transition between quantized segments. The regular binary code often requires simultaneous decisions from several detectors, giving rise to the possibility of errors in the transition region. In some types of digital sun sensor, an entrance slit combined with a Gray code reticle in front of quite
132
Optics
and Laser Technology
June 1972
Entrance
/
slit
elevation
code
b
Fig 3
a: Three shadow
bit digital
sun sensor with
mask; b: practical
a Grey
7 bit Adcole
code
sun sensor
A practical 7-bit digital sun sensor manufactured by Alcole Corporation is illustrated in Fig. 3b. The field of view is f 64”) the angular resolution 1o and the accuracy at transition + 0.25”. Dimensions of the optics/ detector configuration are 2% X 2% X y16 in and mass is 112g. The output from the sensor is processed in an electronic package to a desired form which may be serial Gray code, serial binary code or quantized analogue staircase voltage, depending on the telemetry requirements. Earth sensors Characteristics
of the earth
The albedo
Earth albedo sensors depend for their operation on detecting sunlight reflected from the earth. The reflected sunlight has approximately the same spectral characteristics as direct solar radiation. The term albedo is generally accepted to refer to the fraction of the total incident energy which is reflected by the body throughout the entire band between the ultra-violet and the far infra-red. Referring to the earth‘s albedo usually implies the earth and its atmosphere. The visual albedo of the earth is taken to mean the ratio of the amount of light diffusely reflected in all directions by the earth/atmosphere system to the amount of visual light incident upon the system. Often the term albedo is used in this latter context only. Radiometry calculations of irradiance received at particular points above the earth’s surface are usually based on a mean value of earth albedo, normally between 30% and 40% and the earth is considered to be a perfect Lambertian emitter. Unfortunately, the earth albedo is very irregular (as witnessed by photographs taken from TIROS, NIMBUS etc.) The earth albedo shows considerable variations over the various earth and atmospheric features that reflect light. The albedo varies from a low value over water surfaces to very high values recorded from certain types of cloud coverage. The main variations in earth surface figures are derived from: 1 2 3 4 5 6
variations in type of terrain, from desert to thick woodland to sea optical thickness of atmospheric gases and the consequent variations in absorption the sun’s elevation angle the Nadir angle the azimuth angle of the point of observation with respect to the sun seasonal variations (e.g. deciduous forsets becoming defoliated in winter, snowfields melting in summer etc .).
The 6th Edition of the Smithsonian Metrological Tables list the following albedo figures based on measurements taken in the visible spectrum from aircraft: deep ocean 3 to 5% ; inland water 5 to 10% ; green forest 3 to 6%~; bare ground IO to 20% ; desert 25% ; dry grass 15 to 25% ; snow fields 70 to 86%) ; dense opaque clouds 55 to 78% ; thin clouds 36 to 40%. Mean albedo figures for the whole earth have been measured by several people and values vary from 39% (visible spectrum measurements made by Danjon) to between 29 and 3 1% for the whole spectrum using measurements
taken by Nimbus 2.3 It is estimated that a mean albedo figure of 35% would be made up of 2 to 3% from the earth’s surface, 23 to 26% by clouds and 6 to 9% by the earth’s atmosphere. The effect of cloud on the mean albedo figure is very significant. The effect of latitude on the earth’s albedo is also to be noted. A recent report from ESTEC4 says that earth albedo varies from 55% at 90” to 10% on the equator. Finally, it is worth noticing that only under very rare conditions can the albedo figure fall below a value of 10%. This is because the earth’s atmosphere reflects from 6 to 9% of the incident sunlight. Hence the facts that the earth’s materials give poor albedo figures, that nearly half the earth’s surface is not covered by cloud at any time, and that latitude variations are considerable, still imply that an albedo figure of at least about 10% should always be available. One other important consideration is that the target shape is a crescent, except for the special case where the spacecraft-target-sun angle (or phase angle) is 0”. Changes in the phase angle vary the area of the illuminated earth that is visible to the spacecraft. For example, as the spacecraft approaches the earth’s surface, the total area of the earth that can be seen from the spacecraft is reduced. This consideration is important in designing earth albedo sensors. The infra-red
horizon
The target to be sensed in this case is the radiation discontinuity between the cold (4K) space background and the warm edge of the earth. The spectral characteristics of the self-emitted earth radiation depends strongly on the earth temperature. The effective temperature of the earth’s surface is about 300K giving a peak emission at a wavelength of around 9.6 pm. However, the effective temperature of the earth’s atmosphere is about 220K corresponding to peak emission at 13 .I/J~. Unfortunately, the radiation discontinuity at the horizon due to the earth’s atmosphere is not always very sharp. The relative sharpness depends quite markedly on the wavelength of observation. Earth horizon scanners were flown in space as early as 1958 and the data obtained showed that the earth’s profile is extremely complex when viewed in the broad infra-red spectrum from 2 to 20pm. In this spectral region, reflections and scattering of solar radiation coupled with radiation from ‘cold clouds’ can produce radiance variations in excess of 5 : 1 in a smgle earth scan. In the atmospheric window region from 8 to 12pm, the effect of reflected or scattered sunlight is removed (since there is a very little solar energy above 8~). but large radiance variations are still encountered due to cold clouds and pole-equator temperature differences. This last effect is particularly enhanced in the 8 to 12pm region since, in the atmospheric window, the sensor essentially views the earth’s surface. More recently, a number of studies and experiments have been conducted in order to obtain a better understanding of the earth’s radiation profile in
Optics and Laser Technology
June
1972
133
various parts of the spectrum. Wark et al’ ; Hanel et a16; Bandeen et al’ and Ehlers8 have presented data which indicates that in the 14 to 16pm CO* absorption band the earth’s horizon looks uniform and is devoid of the cloud effects which are so troublesome when a broad range of the9ifbfra-red spectrum is used. Two NASA publications t present extensive data on the analysis and synthesis of 15pm infra-red horizon radiance profiles.
Instantaneous
In the 14 to 16pm region, the earth irradiance is of the order of 1mW cm-’ at geostationary altitude. It is worth noticing that while the sun subtends an almost constant %” at the earth distance (there is a slight + 1.7% variation due to the eccentricity of the earth’s orbit), and the stars subtend constant angles of only a fraction of an arcsecond, the earth subtends quite large angles, especially at close range. For example, the earth subtends 150” at an altitude of 150 miles and 17.3’ at geostationary altitude (22,300 miles). Thus for eccentric orbits and non-orbital missions, the angular size of the earth changes rapidly with time. This problem is not encountered in the design of sun or star sensors for earth satellites but may be encountered in sun sensors for spacecraft which do not orbit the earth (e.g. Mariner or Viking) or which are in highly eccentric orbit (e.g. Heos). Earth albedo sensors Due to the problems of varying phase angle and nonuniform reflectance mentioned previously, the use of earth albedo sensors is somewhat limited. However, this class of sensor can be used for particuhrr missions where the orbital parameters are such that the earth is almost completely illuminated or where continuous attitude infor mation is not essential. In such situations fairly simple earth albedo sensors can often be designed since conventional visual range detectors and optics can be used. For angular earth sizes from about 0.2” to 12”, shadow mask albedo sensors may be used. Similarly, albedo sensors of the null type based on quadrant photo-detectors have also been developed.
Fig. 5
Blinker /
Fig. 4
734
sensor
As an example, Fig. 4 shows the slit-based earth albedo sensor designed and developed by BAC for the spinning Heos satellite. The sensor has two slits, the meridian slit aligned parallel to the satellite spin-axis. and the oblique slit tilted at 30” to the meridian slit. Three cylindrical spectrosil lenses image the earth albedo onto silicon photo-diode detectors. The field of view of the lens-diode combination is 120” X 1’ and the accuracy is approximately + 0.5”. The sensor is capable of detecting signals down to about 0.06nW cm -2 in the band 0.35 to I .I pm. Blinkers are attached which limit the angle through which the sun will be seen to a maximum of 60” for elevation angles of less than f 15”. BAC is currently investigating a new albedo sensor concept based on reflecting rather than refracting optics scanning sensors
In horizon scanning sensors, a rotating sensor field of view is used to develop a scan pattern, usually conical.
detector ,Oblique sensor assembly
BAC earth albedo sensor for Heos satellite
Optics and Laser Technology
scan horizon
For spin-stabilized vehicles. earth albedo sensors based on slits and retitles and based on digital techniques have been developed. These are similar to sun sensors described previously.
Horizon Silicon photo-diode
Conical
June 1972
Fig. 5 illustrates such a sensor designed for a non-spinning satellite where a rotating optical component is used to generate the conical scan. For two-axis attitude information i.e. pitch and roll, two optical heads are required and these are normally installed in the spacecraft so that they look out of opposite sides. A rectangular pulse is generated when the earth is traversed by the optical scan of each head. A reference:e pulse is also generated as the scan passes through the spacecraft pitch position. The signal processing circuits of the sensor compare the earth signals from the two heads to determine roll and phase-detect each head’s output in combination with its reference pulse to determine pitch. This type of sensor is useful over a wide range of spacecraft altitudes and is operationally characterized by wide acquisition angles and fast response times. The need to have high speed, rotating optical components oper-ating reliably in the space environment is their major drawback.
Fig. 6 shows how a wide angle conical scan can be generated in a spin stabilized satellite using the motion of the vehicle itself. Such sensors are often called horizon crossing indicators and have the advantage of not containing moving parts. In general, the best infrared detectors for use in horizon scanning sensors are thermistor bolometers and pyroelectric detectors. These are characterized by fast time constants (e.g. 1 to 5 ms) and low noise equivalent powers at the typical operating modulation frequency (e.g. 1.5 X 10-t’ W at 15Hz). Thermopile detectors are generally too slow for applications in scanning sensors. A typical wide-angle horizon sensor of the type shown in Fig. 5 is manufactured by Barnes Engineering Company and uses a rotating germanium prism driven by a synchronous motor to generate the field-of-view scan pattern. The field of view of 2” X 8” is scanned conically through an angle of 110”. The prism rotates at 30 revolutions per second and an immersed thermister bolometer detector is used. Typical operating accuracy is + 0.5” and the sensor has a mass of 1 Skg and a power consumption of 4 W (including scanning motor). Horizon crossing indicators of the type shown in Fig. 6 have been manufactured and proved in space by several companies including Barnes. These are generally more reliable (no moving parts), lighter and smaller than the typical scanning sensor described above. Horizon
tracking
sensors
Tracking sensors incorporate a number of edge or horizon trackers. Each tracker locates and locks onto the horizon. The angle between the line of sight of the tracker and a reference axis is measured and the roll and pitch attitude computed. In some instances the edge-trackers are positioned at fixed azimuth intervals (e.g. three at 120” intervals), and in others the trackers also scan in azimuth and follow the earth’s outline. One type of tracking sensor, as shown in Fig. 7, uses a detector with a small field of view (typically 1.5” X 1.5”) which is scanned through an arc of a few degrees peak-to-peak at a frequency of around 20Hz. This is called‘dithering’. The field of view can also be scanned at a low rate through an arc of about 80”. The tracker acquires the horizon by scanning slowly from space towards earth. When the dither
Instantaneous
Fig.7
Edge tracking
However, horizon tracking sensors have also been developed which use thermopile detectors and elimate the dither scan. In these sensors, the single bolometer normally used in edge-tracking sensors, is replaced by two thermopile detectors with their fields of view separated by a fixed angle. The two fields of view are servo-positioned within a scan plane so as to measure the declination angle to the horizon relative to the spacecraft. Horizon edge-tracking is accomplished by applying a fixed downward drive to the servoed assembly to direct the lower field of view into the horizon by an amount sufficient to generate a signal termed the ‘buck out’ signal equivalent to this fixed downward drive. During tracking the lower field of view rides on the horizon edge. This technique eliminates the requirement for high-speed optical chopping or scanning. A typical horizon edge tracker as shown in Fig. 7 has a field of view of 1” X 1” scanned through 5” peak to peak at 2OHz, and a total scan angle of 90”. The typical accuracy is 0.15” or better with a mass of 6 kg and power consumption of8 W.
nstantaneous
Bis&tor Horizon satellites
crossing indicator
sensor
scan intersects the horizon, an a.c. output appears which is used to terminate the slow scan and to provide tracking information to position the dither scan centrally on the horizon gradient. The position of the centre of the dither scan is read by a position transucer. The basic purpose of the dither is to modulate the incoming energy in a way which provides the required angular information. Hence thermistor bolometers and pyroelectric detectors can be used.
Horizon
Fig. 6
horizon
’
for spin stablized
sensors of the radiation
balance type
Fig. 8a shows the basic configuration of a static horizon sensor of the radiation balance type. The principle of operation involves comparing the radiation received from opposite portions of the earth. Typically an image of the earth is projected onto an array of infrared detectors and attitude information is obtained by taking the difference in radiant power received by opposite fields of view, i.e. (Pa - P>) gives pitch error and (Pa - PA) gives roll error. This should be compared with formulae 3,4 for quadrant photo-detector sensors. If all the detectors have equal sensitivity, the outputs of opposite detectors are equal, for a uniform earth when the pointing error is zero. Errors can be introduced by differences in detector sensitivities (matching of both
Optics and Laser Technology
June
1972
135
Pitch
have been introduced to measure the radiance of the earth at points adjacent to the areas observed by the main detectors. This information is used to compensate the sensor output for any radiance variation found.
OXIS I
IR detector’s field-of-view
The main advantages of horizon sensors of the radiation balance type is that they essentially involve no moving parts and have low power consumption, low weight and very high reliability. Since thermopile detectors generate their own voltage in an active sense and are ideally suitable for use in direct coupled (or unchopped) applications, they are generally used in this class of horizon sensor. The pro!lem of trying to identify a small change (typically 1 in 10 ) in a large bias voltage is encountered if one attempts to use thermistor bolometers in direct-coupled systems and it is normally essential to modulate the radiation with these detectors. However, with thermopiles, the only voltage that appears is the signal itself and thermopile sensors can be unchopped systems with no moving parts, resulting in increased reliability in the space environment. Pyroelectric detectors are not suitable for direct -coupled applications since the surface charge on which detector operation depends is not permanent and leaks away.
17.3’eorth
horizon
from geastationary
A typical sensor of this type as manufactured and proven in space by Barnes Engineering Company is based on antimony-bismuth thermopiles and has a field of view of 15” X IS” and an accuracy of 4 0.3”. Mass is I .5 kg and power consumption 3W. Other sensors working on these principles are currently under development in Europe and elsewhere and accuracies of + 0.1’ or better should become available. Solid-backed thertnopiles with improved responsivity for use in this type of sensor are also under devolopment at BAC and elsewhere.
i
Star sensors
/
field-of- v.tezw
Characteristics Rod iance compensotlon detectorb field-of-view
b
Fig. 8
a: Basic static horizon b: Tangent
sensor configuration;
field configuration
compensation
with
radiance
detectors
absolute responsivity and of temperature coefficient of responsivity is important) and also by the non-uniform radiance of the earth. For constant orbit satellites (e.g. geostationary), the so-called tangent field configuration can be used to reduce the earth radiance variation error to near zero pointing error. This is illustrated in Fig. 8b where the detector’s field of view extends below the earth horizon, this error is zero for zero pointing error. It is clearly only possible to maintain this field tangency condition when the earth’s image is of constant size. Fig. 8b also shows four extra detectors which
136
Optics and Laser Technology
lune
1972
of the stars
To an optical sensor the stars present essentially point source targets since they subtend angles of fractions of an arc-second e.g. 0.0068 arc-seconds for Sirius and 0.041 arc-seconds for giant Antares. To describe the relative brightness of stars, it is necessary to introduce some astronomical terminology. Stellar magnitude is the astronomical unit of star intensity and a star having a magnitude of one has been arbitrarily defined as being 100 times brighter than a star of magnitude six. Stars of tnagnitude six are generally considered to be barely on the threshold of unaided vision. A difference of one tnagnitude is equivalent to a facor of 5dlO0, or 2.5 12, in intensity. The tnagnitude scale is defined in terms of a set of standard stars and is based on an assumed spectral response for the detector, for example, on the visual magnitude scale. Some typical KilUeS are :Sirius
- 1 .44 (the brightest star)
Canopus
_ 0.72
Polaris
+ 2.02
On this same scale, the sun has a magnitude of --26.$&, and is thus 25.36 magnitudes (or a factor of (2.5 12) = 1.39 X 1O1‘) brighter than Sirius (at the earth’s distance from the sun and from Sirius).
Table 1 gives an indication stars.
of the density of background
Table 1. Density of background Visual magnitude M
+8 +7 +6 +5 +4 +3 +2
stars 2
Stars/degree brighter than M
1.o 0.34 0.12 0.04 0.013 0.0014 0.0009
Calculation indicates that the integrated effect from the background radiation is approximately equivalent to one +3 visual magnitude star per square degree. To convert the star magnitudes given above into effective irradiance on a detector, it is necessary to know the spectral characteristics of the stars. Stars are divided into seven clases (0, B, A, F, G, K, and M) on the basis of absorption lines in their spectra. These classes are also in order of decreasing effective temperature, assuming that the star’s radiation is approximately blackbody. Thus 0 type stars are hottest and appear blue while M type stars are cooler and appear red. The sun is a yellow L type star (effective temperature S,SOOK), Vega is a blue A type star (effective temperature 1 1 ,OOOK), and Betalgeuse is a red M type star with an effective temperature of about 3,lOOK. Canopus is an F type star, slightly bluer than the sun with a temperature of 7,600K. Thus, the wavelengths for peak radiation output vary from 0.18 to 1.Opm and the ideal detector for use in star sensors should, therefore, respond to radiation from the near ultra-violet through to the near infra-red range of the spectrum. In practice, however, it may prove advantageous to limit the spectral response of the detector at the longer wavelengths to suppress the detection of the undesirable radiation from background stars. The spectral irradiances from some of the brightest stal ‘S as seen from above the earth’s atmosphere are as follows: Sirius:
4 X 0-l’ W cm-’ pm-’ , peaking at - 0.3pm
Canopus:
3 X O-“W cm-’ pm-’ , peaking at - 0.6pm
Antares:
8 X O-l3 W cm-’ pm-’ , peaking at - 1.3ym
Ramsey”
gives more detailed information
desired guide star. The width of the lock-on band is determined by the magnitude of the competing targets in the scan zone and by the accuracy of sensor calibration. For colour discrimination, the star light can be passed through two or more pass-band filters (e.g. a blue pass and a red pass). The ratio of energy in the two bands uniquely determines the colour temperature of the star. This method can be used in conjunction with magnitude discrimination to further limit the chance of acquiring the wrong target. Star sensors based on automatic threshold systems as described above involve a requirement for precise sensor calibration. This is difficult due to the current lack of extensive star spectral data, the effects of the earth’s atmosphere and drifts in the sensor itself. Hence, practical star sensors are normally based on star mapping modes (see next section) and/or auxilliary sensors instead of or in conjunction with automatic threshold systems. The use of an auxiliary sensor, e.g. an earth sensor, serves to limit the area in which the guide star can be located by supplying information on the position of another body, e.g. the earth, whose relationship to the desired guide star is known. A more sophisticated version of the auxiliary sensor technique involves the use of two or more star sensors, each set at an angle to intercept a different guide star and roughly calibrated to respond only to stars in a desired magnitude range. There is in general only one star combination which will result in simultaneous lock-on of all sensors. One class of sensor determines the direction to a star by using a rotating reticle onto which an image of the Star image Photo detector
Field lens
I
0 E
.
=
-
-
lEk
-_
..:,..:,:::,::~:~ ‘F
5
-
.:g:.:+.:
Processing electronics
-
a
A Rotation axis
on this subject.
Optical imagmg system
Rotating mirror _
Star trackers The method used for,star acquisition is influenced by the position and magnitude of the chosen guide star. Acquisition of the correct star is perhaps one of the most serious problems encountered in star tracker design since there are often many competing targets (other stars, planets and moons). Star magnitude and/or spectral characteristics may be used as methods of star identification. For magnitude discrimination the sensor is designed to produce a lock-on signal whenever the input energy lies within a range centred around the expected level from the
Star
image
Stationary
reticle
b Fig. 9
a: Rotating
reticle sun sensor; b: nutating
image star sensor
Optics and Laser Technology
June
1972
737
star is projected or by nutating the projected image by means of a rotating optical element. Fig. 9a illustrates the principle of the rotating reticle method. An optical system projects an image of the star (effectively a point source) onto a rotating reticle. The radiation transmitted by the reticle comprises alternating transparent and opaque segments which are coded in a special way so that the light is modulated by the reticle and the detector output consists of pulses. Processing electronics enables the position of the star image on the reticle to be derived. Then from a knowledge of the focal length of the optical system, the angle between optical axis and line of sight (i.e. the pointing error) can be obtained. The reticle shape determines the relationship between sensor output and pointing error. In many cases a linear relationship is not essential since the output is often used to drive a servo system to point the star sensor at the star, i.e. star tracker. Fig. 9b shows how the light passing the reticle can be modulated by nutating the star image rather than by rotating the reticle. In such a system, the image of the reticle is translated into a circular pattern by the rotation of a mirror. When there is no pointing error, the circular image trace is concentric with the reticle and the modulated signal has a constant frequency. When a pointing error exists, however, the image trace and the reticle are eccentric and the signal is frequency modulated in relation to the eccentricity. The processing electronics derives the eccentricity and thus the pointing error. The output signal can again be used directly as a measure of an angle or it can be used in a servo system to point the sensor at the star, i.e. a star tracker. Fig. 10 shows the principle of a vibrating reed star sensor. The vibrating reed has an aperture that is deflected in front of a photo-detector. An image of the star is projected by an optical system onto the reed. Thus the light from the star is transmitted by the aperture for a time interval that is determined by the reed vibration frequency and the position of the star image on the reed. When the star is at the centre of the scan field (i.e. on-axis) the detector signal comprises almost entirely the second harmonic of the reed vibration frequency, and the fundamental frequency is zero. When a pointing error appears, the signal at the fundamental frequency increases and is proportional to the pointing error for a great part of the scan field. Hence this can be used as the error signal for the star tracker. It is possible, and often preferable on the grounds of reliability, to use electronic rather than mechanical scanning to detect star pointing error. A quadrant photomultiplier, as shown in Fig. 1 1a, consists of an electron multiplier the front end of which has four photo-cathodes each in the shape of a quadrant of a circle. Electronic switching enables the amplified photo current from each quadrant to be read out sequentially at the anode. When used as a star sensor, the position of a defocussed star image on the photocathode plane is derived from the output currents (I,, I*, II, 1,) caused by emission from each of the four photocathode segments. Fig. I I. shows the defocused star image at the null position, i.e. exactly 011 axis, where I, = f, = IJ = I,. The output display shows the anode current
from the respective
photo-cathode
segments.
When the star is slightly removed from the null position, as
738
Optics and Laser Technology
June
1972
shown in Fig. 1 lc, the output from the four quadrants is no longer equal. The signal currents related to the x and v positions of the star image are: ;
1, = II + I, - Ia -1,
I, = I, f I, - Iz ~ I,
1, representing roll axis pointing error and I, representing pitch axis pointing error. Limits
of deflection Aperture
opening
Photo detector
Vibration sense
Imaging lens Fig. 10
Vibrating
reed star sensor
Front end assembly
Photo-cathode seqment 2
a
Focusm electro c? 4
De-focused star image I
Null
2 Output
3 display
4
posrtron
b
n 4 3
2
@ Off-null posrtron
Output
display
C
d
Fig. 11
a: Quadrant
photomultiplier;
image at null position; slightly
b: output
c: output
off null; d: output
for star
for star image
characteristics
for I.,.
When the star image is well removed from the vicinity of null, it is no longer possible to determine precise position information. Figure 1 l(d) shows that within the region 2x0 the star image impinges on one or two quadrants on both sides of the y axis and Z, is a function of x, i.e. x position information is available. 2x0 is the star image diameter. When the star image impinges on one or two quadrants on only one side of they axis, I, is constant and the only information obtained is that the image displacement is greater than x0. The region of the star position information area is at the option of the system designer; the larger the defocused star image, the greater the area of position information. This wider latitude is obtained at the expense of some loss of precision. This type of star tracker has the advantage of no moving parts but suffers from the drawback of needing high voltages. It is also possible to use an image dissector tube to act as photo detector as well as scanning device. As shown in Fig. 12, an optical system focuses the field of view onto the photo-cathode of an image dissector tube. The optical axis defines the reference axis and angular deviation of the line of sight from this axis may be resolved by electronic processing into two orthogonal planes which provide 2-axis attitude information. The image dissector tube comprises a photo-cathode which converts the optical image focused on the tube windows to an electron image which is electrostatically focused and accelerated towards an aperture plate. External electrostatic plates or electromagnetic coils are employed to sweep the electron image across the aperture. Thus the total sepjor field of view is scanned and this enables the angular position of the star to be detected. When the electron image of the star is focused on the aperture, the electron multiplier section of the tube thus provides a signal output at the collector electrode which, when compared with a sweep signal reference, gives the angular position of the star relative to the optical axis. Finally, star trackers can be based on an optical system which projects an image of the star onto the photoconductive target of a vidicon. The electron beam of the vidicon scans the photo-conductive target and a pulse is generated at the output whenever it crosses the star image. The position of the star image is then derived in the processing electronics. Having outlined the principles of operation of several classes of star tracker, it is now appropriate to examine briefly a few trackers that have been developed for space missions. RAE has developed a frequency modulated star sensor based on a nutating reticle which comprises 36 linear pairs of transparent and opaque sectors. A reflecting optical system is used to image the star, having a Scm aperture and a 75~111 focal length. The field of view is 0.5” and accuracy is of the order of 3 arc-seconds or better for a second magnitude star. Kollsman Instrument Corporation have developed several star trackers based on vibrating reeds. One such system developed for the Apollo mission, uses refracting optics and a miniature photo-multiplier detector. The field of view is 0.5” and tracking accuracy is 8 arc-seconds for stars of second magnitude. Another similar system developed for the OAO project uses a silicon photo-voltaic detector (with all the attendant advantages over a photo-multiplier, namely, no high voltage power supply, less prone to solar radiation
Optical system Photo-cathode,
, Ekctron multiplier sect ion Multtple dynodes
-Vacuum
Image dissector
Fig. 12
tube
star-sensor
damage, small size). With a field of view of 1” X 1O, tracking accuracy of the order of 10 arc-seconds is typical but the penalty of using a solid state detector is that sensitivity limits the system to stars of magnitude +I .I (detector magnitude, not visual magnitude). Honeywell has developed a Canopus star-tracker based on a quadrant photo-multiplier. With a field of view of 2” X 2”, the null accuracy is + 27 arc-seconds. One feature of this and many other star sensors which use photo-multipliers is a sun shutter to protect the sensitive photo-cathode from radiation damage. The sun shutter is activated by an auxiliary sun sensor with a 5” field of view, boresightcd with the star tracker. The use of a sun shutter is to be avoided whenever possible due to reliability problems. In practice this means using a solid state detector (with its associated lower sensitivity) rather than a photo-multiplier. Solid state detectors are, however, being developed and improved performances can be expected. Of particular interest for star sensor appli4tions are silicon pin photo-diodes, and silicon avalanche photo-detectors. Barnes Engineering Company in association with Jet Propulsion Laboratories developed a single-axis Canopus star tracker based on an image dissector tube for the Mariner spacecraft. This used an f/l reflecting optical system of 2.5cm aperture. The field of view was O.@ X IO” and tracking accuracy was 0. lo for Canopus. An external sun shutter was used. Star mappers The derivation of attitude information from stars can be achieved in a spinning satellite by means of a star mapper. The star mapper scans the celestial sphere and maps the star pattern intercepted by its field of view. A pattern of light-transmitting slits is placed in the focal plane reticle of an optical system and the magnitudes and transit times of stars passing across the slit-pattern are measured and telemetred to ground. A computer on the ground is used to compare the sensor information with catalogued star position information and attitude determination and reconstitution then becomes possible. The scanning is
Optics
and Laser Technology
June
1972
139
readily achieved by the rotation of a spinning satellite but for a 3-axis stabilised vehicle, it is still possible to employ star-mapping as a means of identifying and acquiring the desired guide star for tracking. In this latter case, it is necessary to achieve scanning by means of a reticle drive. Fig. 13 shows schematically a star mapper for use in a spinning satellite in order to determine spin-axis attitude. Light from a star passes through a focusing optical system from which stray light is barred by a baffle. In the focal plane there is a slit system which can contain one, two or more slits, which limit the field of view seen by the sensor. #en the satellite rotates, the star image passes over one of the slits and light from the star passes through to the cathode of a photo-multiplier tube placed immediately behind the slits. The star transit gives rise to a current pulse which may either be transmitted directly to the ground for analysis, or converted to a square pulse, stored on board and transmitted at a time interval determined by the spin period of the satellite. Using an on-board memory, it is possible to average information over several satellite revolutions before transmission to ground. As the satellite rotates, the angular separation of two or more stars may be obtained from their times of transit across a particular slit, and, subject to the identification of these stars with a ground level comparison, this information may be used in the determination of attitude. If a two slit system is used, as shown in Fig. 13, the timing of a single star as it crosses the two slits then gives an immediate fix for the spin axis with respect to the star direction, and only one further reference is required to give the satellite attitude. It should, however, be noted that a double slit causes confusion when two stars are very close together because four signals will be produced and it will be doubtful which allocation of signals to the appropriate star is the correct one. Another advantage of a single slit is that background noise is minimized. Against these advantages, however, it must be remembered that a single slit provides no immediate information as to vehicle attitude. For example, if only one detectable star is present in the band swept on the celestial sphere, the single slit gives no useful result since the transit time information is only helpful when related in time (and hence angle) to the transit of another. The double slit arrangement gives information
External
baffle
I
Detector
lens
/
A? Reticle
140
Typical
Fig. 14
a: Reticle
configuration
showing multi characteristic
for project
slit arrangement; trace obtained
scanner
b: Idealized
when a genuine
star image crosses the slit pattern
of Fig. 14a
on the angle between satellite spin-axis and the star line immediately, with only one detectable star per sweep. Even allowing for the fact that two slits involve an increased background noise (twice as large an instantaneous area marked on the celestial band), on balance the gain of information using two slits generally outweighs the loss occasioned by increased noise. One final point to consider is the spacecraft spin rate. Because of quantum mechanical effects, stars nominally detectable, may not be observed as the spacecraft rotates. The more slowly it does so, the longer the star stays in the sensor field of view and the greater the probability of the star being detected. It is not easy to make a precise calculation for this since it depends on the signal-to-noise ratio. However, consider as an example the problem of detecting a fourth magnitude star using a 5 cm apcriure objective lens. The irradiance is of the order of 6 X IO photons s-l and assuming an optical efficiency of 75% and a quantum efficiency of 20%, then to ensure 30 photoelectrons (when the question of detection seems critical), 200 photons are required to impinge on the objective lens during each scan. Thus the time required for a star 200 seconds = 0.33 ms. With a slit 6 x IO5 width of 0.15”. the maximum spin rate for detection of a to be seen is
4th magnitude
0.15
star is 0.33
x
_a degrees s-r IO
~75 r.p.m.
We conclude that for any reasonable satellite spin rates, third magnitude stars can be detectected with reasonable certainty, using currently available photo-multiplier tube performances. However, for fourth magnitude stars, satellite spin rate is limited to around 75 r .p.m. to ensure a reasonable probability of detection. In practice, this is not an unreasonable limitation.
Objective
Fig. 13
a
star-mapper
optical
Optics ano Laser Technology
Condenser kns system
(not to scale)
June 1972
Several star mappers have either been flown or are currently under development. ATS III (a technological satellite) was equipped with an experimental star mapper with a 12” useful field of views, an aperture of 8.8cm and a focal length of 7.6cm. The reticule comprised 3 slits of width 7.6 arc-minutes and a photo-multiplier was used as detector. Attitude reconstitution accuracy was of the order of 1 minute of arc. Another star mapper was flown on a sounding rocket (Project SCANNER) and had a field of view of 6” and a reticle comprising two systems of slits, one vertical and one
Table 2. Summary of sensor types Class of
Angular
Typical
of target
region (pm)
Typical detector irradiance (Wcm-‘1
Type of
sensor
detector
accuracy
Sun
0.53”
0.2 to 1.1
10-I
Silicon
+0.03”
size
Operating
spectral
sensor
solid-state Earth albedo
0.2 to 1 .I
100” to 2”
1o-2 to 1o-6
Silicon
+0.5”
solid-state
(depending on altitude) Earth
150” to IO0
Usually
1O-3
infra-red
(depending
14to
(at geostationary
16
altitude)
on altitude)
Star
Thermistors, pyroelectrics or solid-backed
17.3”
thermopiles
(geostationary)
(dx.
0.04 to 0.005
0.15 to 1.4
arc-seconds (deoending
lo-”
20.2”
to lo-l4
application)
Photomultiplier
+0.003”
(depending on star)
inclined as shown in Fig. 14a. The slit widths varied from 0.015” to 0.03” as shown and were unevenly spaced. This slit arrangement reduces the probability of false identification of a star since a genuine star now produces a characteristic trace as shown in Fig. 14b. An on-board logic system can then reject signals not of this characteristic form. This refinement of the double slit system is really of use only for weaker stars but then there is the serious chance that a weak star will only be detected at two of the slits. It is possible to add a logic device which will involve all six slits that a star may encounter but then the advantages of the refined system appear to be balanced by the drawbacks of having to incorporate additional electronic processing. Ball Brothers have also developed a star mapper for use on the OSO-H satellite. This has a 10” field of view and a 1Ocm2 receiving aperture. A double slit reticle is used, with 0.03” slit widths. Attitude reconstitution accuracy is approximately 0.02”. Conclusion
Table 2 summarises the main feature of each major class of attitude sensor described in this article.
on star)
References 1
8
9
10 11
Spotts J. H., Optical attitude sensors for space vehicle appbcation, M. SC. Thesis, University of California, Los Angeles, Oct. 1965, p.6 Kuiper G. P., The Sun, University of Chicago Press, 1953. Journal of Applied Meteorology, April 1970 Atzei A., ESRO TN-103, April 1970 Wark D. Q.,et al, Variation of the infra-red spectral radiance near the limb of the earth, Applied Optics, 3, 221,1964. Hanel R. A. et al, The infra-red horizon of the planet earth, J. Atmospheric Science, 20, 73, March, 1963 Bandeen W. R., Experimental Confirmation from the Tiros VII Meteorological Satellites of the theoretically calculated radiance of the earth within the 15~ band of carbon dioxide, J. Atmospheric Science, 20, 609, 1963. Ehlers E. E., Temperature measurement of earth and clouds from a satellite, 2nd Symposium on remote sensing of the environment, University of Michigan, Ann Arbor, 1964 Thomas J. R.,et al, The analysis of 15~ IR horizon radiance profiles variations over a range of meteorological, geographical and seasonal conditions, NASA CR-725,1967 Bates J. C.,et al, The synthesis of 15~ IR horizon radiance profiles from meteorological data inputs, NASA CR-724.1967 Ramsey R. C., Spectral irradiance from stars and planets above the atmosphere, from 0.1 to 100.0~ Applied Optics, 1, (41, July, 1962
Received
12th November
197 1
Optics and Laser Technology
June
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