An Optical Sensor for the Drag-Free Satellite

R, De Hoff & D, Powell

AN OPI'ICAL SENSOR FOR THE DRAG-FREE SATELLITE R, L, De Hoff, SYSTEMS CONTROL, INC"

Research Engineer Palo Alto, Calif"

J, D, Powell, As s istant Professor Dept, Aeronautics and Astronautics STANFORD UNIVERSITY, Stanford, Calif"

94306

94305

An optical sensor for drag-free satellites [Ref, 1 ] is described, It is based on using fluorescent reemission from the proof mass excited by a pulsed ultraviolet source, a technique that separates the frequencies of the excited and excitant light fluxes, A theoretical analysis of the performance and linearity of the sensor was verified by the results on a laboratory prototype, The sensor provided a meassure of the position of a 4 cm radius proof mass in a 10 cm cavity to an accuracy of 1 mm, Null drift and thermal gradients caused errors less than 0,05 mm,

INTRODUCTION A drag-free satellite consists of a small, spherical proof mass housed within a satellite, While in orbit, the proof mass floats freely inside a cavity in the outer satellite, A suitable control system on the external satellite senses the position of the internal proof mass and causes appropriate thrust actuation on the external satellite to keep the proof mass centered in the cavity, The system is constrained to follow the proof mass regardless of the surface forces which might act on it, Hence, the system is drag-free in the sense that external forces such as aerodynamic drag or solar pressure have no effect on its orbit, The possible missions of the drag-free satellite include navigation, geodesy, aeronomy, and verification of the theory of RelatiVity; all of which benefit by an orbit unaffected by drag forces, In an actual satellite, the accuracy of the drag-free system is limited by small perturbation forces on the proof mass arising from the presence of the external satellite, Such forces are due to the vehicle mass attraction field, magnetic and electric fields, and the effects due to sensing the position of the proof mass, The largest perturbation force in designs carried out to date is the mass attraction o f the outer satellite, This perturbation can be reduced by keeping asymmetric mass distributions far from the proof mass, A large cavity will insure this,

351

R, De Hoff & J, Powell

ESRO (European Space Research Organization) has presented a study for a large cavity deep space probe [2], The proof mass is sensed optically. There is a very small linear region near the center of the cavity using a shadowing technique, and the proof mass is captured using several discrete, crossed beams which are interrupted as the proof mass passes through them, Kundt [3], in conjunction with this study, has presented a catalog of the practical limitations on the performance, including the effects of vehicle gravity, This paper describes an optical sensor based on a single light source which uniquely yields the proof mass position at any location in the cavity,

DESCRIPTION An important consideration in the deSign of spinning drag-free satellite systems is the attenuation of disturbing forces and gradients to acceptably low levels, Most of the disturbances fall off rapidly with the distance from the proof mass and cavity wall, For this reason, a large ball-to-wall separation is desirable, In a capacitive position sensor, the linearity is degraded by a small ball-to-cavity aspect ratio [4 ] , Also, the larger electric fields necessary for this type of system may cause unacceptable force levels [1], An alternate position sensing system has been devised, The system uses an optical semiconductor sensor to detect the position of the proof mass, It has the advantage of detecting the three-dimensional position of the proof mass anywhere within the cavity with a single light source, The measured output from the sensors is a slightly nonlinear function of the position, However, acceptable performance can be achieved for the entire range of the proof mass, Also, the large cavity allows a lower tolerance on the center of mass position within the cavity and looser restrictions on the center of mass drift during a miSSion. Figure I shows the sensor system, The sensor housing is a conducting cylinder with its axis parallel to the angular velocity of the vehicle, The proof mass is spherical and fabricated from a reasonably dense conductor with a tolerably low magnetic susceptance, One end of the housing is closed, The other end contains a light source and spin plane sensor strips, The light source consists of a quartz covered xenon flash tube, The two electrode type tube is used to eliminate the optical asymmetry inherent in tubes with a third triggering conductor, There is a spherical or parabolic mirror to roughly collimate the light from the xenon source. The short arc of the xenon lamp is located at the focus of the mirror, The flash tube emits a nearly point source of luminescent energy whose frequency distribution has a broad spectrum but is rich in ultraViolet, The tube is operated at high instantaneous power outputs, but at low duty cycles, The pulse length is typically from I to 250 ~sec, The electrical circuitry consists of a large storage capacitor and some electrical triggering and starting pulse· components, The emitted

352

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light is collimated into a wide beam and transmitted through the cylinder housing. At the top of the mirror assembly is the spin plane position sensor and optical filters. The optical filter is fabricated from a glass plate infused with absorbing material which w,ill pass optical radiation with wavelengths shorter than 450 nanDmeters. In the large cavity sensor, it is assumed that the proof mass is coated with a luminescent coating which is excited by the incid'ent ultraviolet and emits in the low red_ Luminescence is defined as the ~mission of radiation in excess of thermal radiation due to some phys-

lcal process. Luminescence of solids caused by the stimulation by exciting photons or electrons is typically divided into two categories, fluorescence and phosphorescence, depending on the persistence of the luminescent radiation. The position sensor consists of four detectors. These silicon devices are operated as Schottky barrier diodes with a long, optically sensitive junction. An incident luminescent flux distribution on the junction of the device causes a current from each end which is the sum of incremental currents generated along the junction. The currents are resistively divided by the sheet resistance of the silicon

353

R. De Hoff & D. Powell device. The currents from each end of the sensor strip can be subtracted to produce a signal which is proportional to the centroid of the light flux distribution. The sum of the currents from each end is proportional to the total energy absorbed by the device. If a division is made by the sum of the currents, a signal proportional to the centroid location and independent of the wotal flux magnitude is obtained. Figure 2 shows the energy spectra used by each component of the sensor.

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SYSTEM PERFORMANCE DESIGN An estimate of the power and sizing constraints can be determined if the overall conversion efficiencies are analyzed. An important area of interest is the fluorescent emission from the ball. For a fine grained coating, the intensity of emission from an elemental area on the ball follows Lambert's law close ly [6J . Thus, if 6r L = total flux emitted from an element of surface area, then (see Fig. 4):

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The nondimensional flux distribution may be written as a funct ion of the distance above the sensor, Figure 5 shows this distribution, From the standpoint of cavity sizing, the total luminescent flux distribution of the sensor is important, This may be quantitatively expressed by calculating the integral of the flux distribution a long a sensor strip. This cumulative distribution is shown i n Fig, 6 as a function of the upper limit of the integration and the hei ght above the sensor plane, As an example, consider the following set of nominal parameters (more detail on design tradeoffs is contained in Ref, 7); RB = 4 cm, x = 15 cm, and d = 15 cm, Now if the sensor requires at least 20 ~W o~ incident power for reasonable signal levels, then t'Ji' IN/ RB > 5 ~W/cm,

355

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FIG, 4

DIFFERENTIAL LUMINESCENCE GEOMETRY,

'1'ne required radiant lamp output power can be determined to be la W, Assuming a 0,1% duty cycle (100 ~ec pulse at la Hz), this would require an average input power of 0,1 W to the illumination source, The effect of variation in desi~n oarameters can be established in this wav. -rne ortnogonal array shown in Fig, 1 will yield an output proport·ional to the planar position of the projection of the proof mass center onto the sensor plane, The position output from the x axis is a function of the proof mass height above the sensor and the y position, These functional relations must be taken into account to predict behavior within the entire cavity volume, The analytical relations will be developed below, The integral expression derived from Fig, 4 is not practical for use in the evaluation of the sensor performance because of its complexity, A useful approximation can be made, It could be assumed that the ball is far above the sensor plane, i,e" d» I, For the case, ~« 1, the ball appears as a hemisphere, and the line of sight constraint can be dropped, The integration can be carried out exactly if it is assumed that and

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see Fig, 7, The centroid can then be calculated by substituting into the flux distribution,

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The axial symmetry of the flux distribution at the sensor plane makes the centroid a function only of the perpendicular distance to the sensor strip. Also, any dependence on height, which is manifested by a dependence on the total amount of incident flux, divides out of the centroid expression. The linearized gain or slope of the inputoutput curve near the center of the sensor is a function only of d, the distance from the sensor strip to the center of the ball and the length of the sensor strip. This slope is

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Figure 9 shows the single axis transfer functions. The most apparent nonlinearity is due to the variation of the slope with the height above the sensor plane. It should be noted, however, that the linearity is quite good throughout the sensor cavity.

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361

R. De Hoff & D. Powell The behavior of the large cavity sensor has been developed. Such a device can sense the three-dimensional location of the proof mass within a large cavity with great prec :· ·. ,}R using a single light source and simple optical system. The nonlinearity of the sensor output has been derived for all three axes using a typical configuration of physical components. Shadowing from structural members and other nonidealities have not been included in the development because their effect can be minimal with proper design. The analysis shows that the device is capable of nearly linear performance over a wide dynamic range and is suitable for large cavity drag-free satellite missions. EXPERIMENI'AL RESULTS FOR THE LARGE CAVITY SENSOR A large cavity se nsor was built and mounted on a spinning simulator at Stanford University [7 ] . The lower section of the sensor contained the pulsed light source, and the upper section housed the optical sensors and proof mass. The sensor was mounted on a pedestal support which was structurally integrated with the vehicle simulator. The proof mass was supported from above on a threaded rod for vertical adjustment. The top of the sensor was closed by a double light baffle allowing three centimeters of motion in the planar directions. The lowe r portion of the sensor housed the mirror assembly and the xenon arc lamp. A spherical mirror was installed with a 72 mm focal length and 20 cm in diameter. It was front surfaced with a 200 nm sputtered silver coating and a thin silicon monoxide layer for protection against oxidation. The mirror was mounted on a three-dimensional flex support which provided 2 mm of position adjustment in any direction. The flex support allowed the arc to be placed at the focal point and the mirror axis to be adjusted to the vertical. The xenon arc lamp produced a short, wide spectrum light pulse which was collimated by the mirror and directed upward through an ultraviolet glass filter. The filter, 20 cm in diameter and 4 mm thiCk, was fabricated from U-360 ultraviolet transmitting glass with a 100 nm pass-band centered at 360 nm. The filter separated the two halves of the sensor. Directly above the filter, a cross-member beam mounted the sensor strips. The upper section of the sensor contained the proof mass and position sensor. In addition to the four horizontal sensor strips, a vertical strip was mounted to produce signals measuring the vertical position of the ball. The cavity was 26 cm in diameter and 20 cm high. It was internally coated with an optically absorbent paint which limited the reflection of the ultraviolet excitation and the reemitted fluorescent energy. Figure 12 shows the measured time history of the current sums and differences for various ball radii and heights above the sensor plane.

362

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Each experimental point is the mean value of 1,000 measurements taken at that time instant. The light pulse shape is predicted very accurately by the theoretical analysis. Although the arc does not extinguish until nearly 400 ~ec after initiation, the light levels produced after 200 ~ec are negligible. This behavior is explained by the increased resistance of the arc at lower current levels and the resulting increase in the RC decay time constant. The inductance in the circuit causes the light pulses to rapidly peak at 75 ~ec after initiation with the behavior approximated by the l / JUC time constant of the circuit. The predicted time history indicates that the peak power output should be nearly 600 watts. The incident radiation produces widely differing current sums and differences for various ball radii and heights. However, the quotient of the difference over the sum reaches a constant value for reasonable light levels over a wide range of measurements. This behavior produces the extremely large dynamic range of the sensor. The optimal time instant to sample the signal is determined by the variance in the signal as discussed below. Finally, the measurements taken at the top of the cavity, h = 15 cm, show a larger ball-to-ball variation in the ratioed output than those at the nominal height, h = 8 cm •

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Figure 13 shows the measurement error of the current sums, differences, and ratio, R, for various ball radii, heights above the sensor strip and planar offset position of three centimeters from the center, These were calculated according to the following formula:

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Figure \4 shows the results of a sensor output survey for various positions within the cavity, The 3,5 cm radius proof mass was moved parallel to the x sensor axis offset either zero or 3 cm in the y direction and at various heights, The effect of differing ball size on the output was to cause the current to increase nearly proportionally to the square of radius change, The 3,5 cm radius ball was used for the remainder of the sensor tests, The figure shows some rather significant deviations from the results of the theoretical analysis of the idealized sensor discussed above, In this analysis, shadowing of the incident illumination by the sensor strip was ignored, The basis for this assumption was that a nearly parabolic mirror with a light source slightly behind the focal point will provide a slightly uncollimated beam of incident radiation, This will have a tendency to eliminate shadowing effects at a reasonable distance from the sensor strip, This behavior is prominent in the results shown in Fig, 14, The sensor strip shadow causes a significant decrease in the total incident flux when the ball surface is 5 mm above the sensor (h = 4cm) and a small decrease at the nominal operating point, h = 8 cm, The difference current is also affected, The slope at the origin increases due to the effect of decreasing total incident light flux, These effects are barely visible at h = 12 cm and h = 16 cm because the light beam is not sufficiently collimated to propagate the shadow that far from the sensor plane,

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Figure l~ illustrates a more subtle effect of sensor strip shadowing. In the figure, the unnormalized error in the output is plotted as a function of proof mass positions corresponding to the points shown in Fig. 14. The unnormalized error deviation is defined as

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Figure 16 shows the sensor output for a large number of positions within the cavity. Measurements of a matrix of points covering the entire cavity reg ion reachable by the proof mass were made. The current ratio was converted to centroid position, or equivalently. the units were changed to measured centimeters. This scale is shown in the figure The linearity of the sensor at the positions within the 3 cm operating region is quite satisfactory. Nonlinearities become important near the wall and near the sensor plane as expected. The gain change with height is significant as predicted. The characteristic is quite acceptable for applications within the designed 3 cm operating zone. Figure 11 shows a comparison of the linearized gain measured at the experimental points shown in Fig. 16. The horizontal scale is the reduced heig ht above the sensor plane as discussed above. Also plotted on the figure are the theoretical linearized g a ins developed. The figure indicates that shadowing tends to increase the gain over the theoretical values at the lower positions as was discussed a bove. The correspondenc e of the experimental values and the theoretical values is better at higher proof mass positions. This gain variation is perhaps the most important effect of the large cavity sensor. It is apparent that a linear relationship of height and gain might approximate the gain curve throughout a large portion of the cavitv.

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CONCLUSIONS A new technique for measuring the proof mass position was developed, An optical sensor was designed and built using the principle of fluorescence to separate excitation frequencies from sensed frequencies, A theoretical analysis of the performance and linearity of the sensor was Verified by the results on the laboratory prototype, The technique allows three axis measurements with a single excitation source and a simple optical deSign, Large semiconductor light sensors provide a measure of pOSition throughout the 10 cm radius cavit y accurate to within 1 mm , The natural behavior of the system increases the gain near 'the center which tends to produce lower errors in this region, Sensor linearity within the cavity is good, Sensor measurement accuracy near the cent er was better than ± 0. 5 mm, The sensor was operated in a pulsed mode, Improved accura~y was obtained by averaging over a number of pulses, A xenon arc lamp provided large instantaneous light flux densities at an extremely low average power consumption, Null bias offsets produced errors less than 0,05 mm because the sensor dark current was subtracted from the Signal current, Scale factor change caused by temperature gradients within the cavity caused errors less than 0,05 mm,

368

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ACKNOWLEDGMENTS The authors wish to thank the NASA-Goddard Space Flight Center for their support of this research under Contract NAS 5-21960.

REFERENCES 1.

Lange, B. O. , "The Control and Use of Drag-Free Satellites," Ph.D. Dissertation, Dept. Aeronautics and Astronautics, Stanford University, Stanford, Calif., 94305, SUDAAR No. 194, Jun. 1964.

2.

O.N.E.R.A. (Office National d'Etudes et de Recherches Aerospatiales), "Controle des Forces non Gravitationnelles," 29 Avenue de la Division Leclerc-92-Chatillon, Paris, France, Technical Note No. 1/1594 S4, Dec. 1969.

3.

Kundt, Wolfgang , "Drag-Free Space Probe," Science, Vol. 30, PP. 455-461, 1974.

4.

DeBra, D.B., '.'Drag-Free Satellite Control System Technology," Conf. on Experimental Tests of Gravitation Theories. California Institute of Technology and the Jet Propulsion Lab., Nov. 11-13, 1970 (Dr. DeBra is with Stanford University.)

5.

Markiewic z, J.D., and J.L. Emmet, "Design of Flashlamp Driving Circuits," J. of Quantum Electronics, Vol. QE-2, No. 11, Nov. 1966.

6.

Astrophysics and Space

Leverenz, Humbolt N., An Introduction to the Luminescence of Dover Publications, Inc., New York, N.Y., 1968.

~,

7.

De Hoff, Ronald, "Minimum Thrustors Control of a Spinning DragFree Satellite, Including Design of a Large Cavity Sensor," Ph.D. Dissertation, Dept. Aeronautics and Astronautics, Stanford University, Stanford, Calif ., 94305, SUDAAR No . 497, Dec. 1975.

369