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An optically coupled thermal imager
Infrared Phys. Vol. 28. No. 2, PP. 113-127. 1988 Printed in Great Britain
OOZO-0X91/88$3.00 + 0.00 Pergamon Press plc
AN OPTICALLY
COUPLED
R. G. HUMPHREYS RSRE,
Malvern, (Received
THERMAL
IMAGER
and H. A. TARRY Worcestershire,
I5 Oclober
U.K.
1987)
Abstract-A novel scheme for thermal imaging is proposed, using a thermal IR detector whose temperature is sensed using a thermo-optic property, and the image is read electronically using a conventional television chip. As with other thermal IR detectors, the image is mechanically chopped, and the difference between fields calculated electronically. The particular scheme discussed uses a liquid crystal as the thermo-optic medium. Calculations of signal and measurements of noise are presented to deduce what the performance of such a thermal imager would be.
INTRODUCTION
Thermal IR detectors in a staring array must be interfaced in some way with multiplexing electronics, and it is the properties of this interface-thermal and electrical-which usually limit the imaging performance of the array. This paper describes a novel form of imager which avoids the interface problems by using optical coupling between the detecting elements and multiplexing circuits: the thermal image is converted to a visible-light image which is then detected by a conventional TV camera chip. The essential signal processing can then be done before the image is displayed in a CRT. Optically read thermal detectors have been described before, (I) but early schemes were intended for direct viewing by the eye, and therefore had to present an image with a high contrast. Because the systems were d.c. coupled this could only be achieved by stabilising the temperature of the whole focal plane to a very high accuracy and by requiring a very high degree of uniformity in its response. However, once the image is available in electronic form, a.c. coupling can be done by subtracting successive “clear” and “opaque” fields while the scene is chopped; also the essential correction for non uniformity of response can be carried out. In this paper we discuss in detail the performance of a proposed imager of this type and the factors likely to limit its thermal and spatial resolution; these include the thermal properties of the focal plane, its optical properties and how they interact with the TV chip, and the noise mechanisms both in the focal plane and in the readout. We have chosen the temperature-dependent birefringence of a nematic liquid crystal to convert the thermal image to an optical image, and we present a theoretical and experimental study of its sensitivity and noise. Measuring or making reasonable assumptions of the properties of all the components allows the NET of the imager to be predicted. Figure 1 shows the layout of an imager with optical coupling. (‘I) The IR scene is focussed on to a focal plane which converts it to an image in visible (or near IR) light. Many schemes for this conversion exist in principle but for simplicity of construction we have chosen to use a system whose transmission of light depends on its temperature. Light from a separate source allows the image to be formed on a TV chip (e.g. a CCD array). If used in this way the detector will eventually reach thermal equilibrium with severe loss of spatial resolution, giving an image dominated by the non-uniformity of its responsivity to the mean background temperature. Introducing a chopper before the focal plane allows a degree of a.c. coupling: fields from the TV chip corresponding to “open” and “closed” chopper states can be subtracted electronically giving an image more uniform by several order of magnitude; the background pedestal and non-uniformity of response to it will have been removed. THE
FOCAL
PLANE
Very many materials can in principle be used to make the focal plane. transmission to temperature is required to give a signal exceeding potential 113
A high responsivity of noise mechanisms; this
II4
R. G. HUMPHREYS and H. A. TARRY TEMPERATURE CONTROLLED ENCLOSURE CHOPPER J
X14PLATE \ TV CHIP
r
It
SUBTRACTION
B+ / FOURlEd TRANSFORM PLANE
POLkRISER
I
‘.
FOCAL PLANE
7.t VISIBLE LIGHT SOURCE
VIDEO Fig. 1. Diagram
of optically
coupled
imager.
responsivity must also be maintained over the range within which the focal plane temperature can be stabilised. These conditions led us to choose a liquid crystal, in which co-operative forces between molecules give rise to a range of optical properties with large dependence on temperature. Since 1960 the selective reflection of a narrow wavelength band from a cholesteric liquid crystal has been used to sense temperature in direct-view imaging devices; (2)however this effect has a very limited dynamic range and requires accurate temperature stabilisation. Cholesterics of a much longer pitch give a rotation of the plane of polarisation of light which is highly temperature sensitive, and have also been proposed for imagingc3’ but because macroscopic realignment of the structure is involved the response could be slow especially if a liquid of high viscosity is involved. The necessary surface alignment is also difficult to achieve and maintain uniformly as it must allow free rotation of the local optic axis while maintaining its alignment with respect to the containment walls. If the alignment is not ideal, elliptically polarised light (with an unspecified axis) will be transmitted. More attractive candidates for the focal plane are the nematic liquid crystals. These have uniaxial birefringence An( = n, - no) _ 0.1 which is sensitive to temperature because of the temperature dependence of the microscopic order of the molecules. The optic axis is unaffected and it can therefore be fixed accurately in the plane of the film by the use of aligning films, which are already in common use in cheap display devices. Because the optic axis is known, the birefringence can be converted to a light intensity by the use of a quarter-wave plate aligned with the optic axis (see Fig. 2). Light (wavelength A) entering the film polarised at n/4 to the optic axis emerges from the where t is the quarter-wave plate again plane polarised and rotated through an angle y = (xAnt)/i film thickness. I
Fig. 2. Alignment of optical components in a nematic axis for extinction. D nematic director.
A
liquid crystal imager. P polariser axis. A analyser L optic axis of quarter-wave plate.
An optically
An analyser
aligned
coupled
at an angle 0 with respect
thermal
to the polariser
i.e. it is at an angle $ = 8 + y + (z/2) from extinction, temperature of the transmitted intensity is:
The value of $ used is a compromise
between
115
imager
transmits
an intensity
of:
and for small values of $ the variation
maximum
signal (large $) and maximum
with
contrast
(low $). The upper limit of $ is set by the dynamic range of the TV chip; a lower limit is set by non-uniformity in the position of extinction y caused by non-uniformity of thickness t and temperature in the nematic film. Between these limits II/ can be set to optimise the imager performance. This function could be performed by an electro-optic device with feedback. Dispersion of An can be corrected to a large extent by a second birefringent film, allowing the use of non-monochromatic light. The theory of Maier and Saupec4’ predicts the variations with temperature of the order parameter S of a nematic. S describes the mean-square angular displacement of the molecular axis, and is related to the birefringence by 2nA.n - NIX,,,S where N is the number of molecules per unit volume and LX,,,is the molecular polarisability. A universal curve of S falling with temperature is predicted, and there is a first order phase transition when S has fallen to 0.43. This is the nematic-isotropic transition at TN,. Our measurements of An for a range of nematic materials”’ confirm the general shape of the curve, showing the largest value of d/dT (An) within 1°C of TN, but as with all other similar measurements the precise values of d/dT (An) differ significantly from the theory. We are therefore unable to predict a maximum attainable value or any systematic way of achieving it. For this work we have chosen the cyanobiphenyl nematics; these have the highest value we have found of d/dT (An), of about 0.02”C’ nearly independent of temperature within 1°C of TNT, and also have the advantage of being chemically stable and available in a wide range of eutectic mixtures for use in display devices. In contrast to display requirements, we want a large temperature dependence of optical properties at a temperature not far above room temperature: we have therefore used mixture El (TN, = 41°C) for most of the measurements and theory.
Fig. 3. Measured
variation
T (‘c) of extinction angle y as a function of temperature the nematic mixture 24% PC296 polymer in El.
for a 10 pm thick film of
R. G. HUMPHREYS and
I16
H. A. TARRY
IR BLACKENING
PELLICLES ~~~~ENT
J INSULATOR
Fig. 4. Diagram
showing
(VACUU
the components
of the liquid crystal
focal plane
Figure 3 shows a typical measured variation of 7 with temperature for a 10 pm thick film. The IR focal plane must contain and align a uniform thin film of liquid crystal using a minimum of temperature insensitive material; it must absorb IR and transmit visible light efficiently; and it must be thermally isolated while at the same time maintaining a temperature uniform to t0.01 C to maintain uniformity of ;‘. The cell is illustrated in more detail in Fig. 4. The liquid is confined between thin (probably plastic) pellicles coated with alignment layers. The cell thickness is maintained accurately uniform by spacer pillars. The lower pellicle is supported by a rigid high thermal conductivity heat sink (a thermal “ground plane”) from which it is nearly thermally isolated. We envisage spacers being placed at the corners of each pixel which is about 70 pm square. The cell also has a layer designed to absorb the IR, which is illustrated in the figure as being on top of the front surface, but may be elsewhere. Although the design of the focal plane is complex, it should be possible to manufacture it cheaply in large areas by standard photolithographic techniques. The thermal analysis of this structure is described below. READOUT
OPTICS
AND
DETECTION
The most promising choice of readout light source is a high efficiency GaAs LED, having a relatively narrow spectral bandwidth. It is switched on for a period during both “light” and “dark” fields of the cheaper. While the LED is on, the TV chip is integrating the signal, so that any high frequency noise sources are averaged out and noise bandwidth is low. Two lenses are shown in Fig. 1 to focus and demagnify the image on to the chip; this arrangement makes available a Fourier transform plane for optical signal processing although a single lens or even proximity focussing could be considered. The chopper and objective lenses are conventional components, and the beam splitter is a dichroic plate with multilayer coatings for transmission of IR and reflection of visible light. The TV chip can be a CCD or MOS switched array; since we want it to work close to the shot (photon) noise limit, the only parameter that concerns us is the well saturation level, which we take to be 5 x 11 ‘I carriers cm 2. Available chips usually have high quantum efficiencies and fill factors. The output of this chip must be stored in a framestore capable of accommodating the full dynamic range of the chip (less any constant pedestal that could be skimmed beforehand), and an analogue to digital converter of at least 12 bit accuracy would be needed. The chip and processing electronics will not be described here in any more detail. The noise in a state-of-the-art solid state TV chip operating near full well is mainly shot noise, equivalent to photon noise on the readout light. Equations (1) and (2) give a signal/noise ratio for small $ of: (3)
An optically
coupled
thermal
117
imager
requiring Z, to be as large as possible. Although the ratio is independent of II/, saturation of the CCD wells in the TV chip puts a limit on the detected intensity I. In order to reduce I to this value Ic/ must be correspondingly reduced [equation (l)] moving the analyser closer to extinction. Any non-uniformity in the focal plane, e.g. of thickness, will give non-uniformity of the transmitted intensity Z, whose highest values must not exceed the saturation value of the chip, further restricting the choice of $. These non-uniformities are likely to be of low spatial frequency. We now consider briefly how the transfer function of the read out optics can be modified to minimise the damaging effects of non-uniformity. Before the analyser the signal and non-uniformity both appear as electric fields ES and E, polarised perpendicular to the pedestal field E,. An analyser $ from extinction therefore transmits a field: E,,sinII/
+(E,+E,)coscC/
(4)
with intensity: E~sin2~+E~~~s21C/+E~~~s2~+2sin~cos~(E,E,+E,E,)+2cos’~E,E,. (41 (2) (3) (1)
(5) (5)
Term 1 is the pedestal, terms 2 and 3 should be small and terms 4 and 5 represent the signal (E,E,), and the non-uniformities of the pedestal (l&E,) and of the signal (E, ES). Since the information of interest in the scene tends to be at relatively high spatial frequency (objects a few pixels wide) while the nonuniformity will be dominated by variations on the scale of the array size (e.g. detector thickness and temperature) the possibility exists to attenuate the non-uniformity (l&E,) without significantly reducing the signal of interest by using an annular stop in the Fourier plane. This form of bandpass filtering has not been investigated in detail in the present work, and there is some doubt that the scheme could be made workable without undue microphony, but it remains a unique potential advantage of the optically read detector scheme. Further possibilities like recognition aids could also be considered. THE
THERMAL
CIRCUIT
In order to estimate the magnitude of the signal to be detected, we have performed calculations of the response of a liquid crystal focal plane like that depicted in Fig. 4 to a chopped thermal scene. The calculations are somewhat idealised, but contain the essential features. The liquid crystal problem differs from the more usual IR detector in two respects. Firstly, the thermal conductivity of the liquid crystal is much lower than that of materials normally considered (e.g. pyroelectrics), so that reticulation is much less important. Secondly, being a liquid, the liquid crystal must be contained, so that reticulation is much more difficult: the thermal conductivity of liquid crystals is comparable to that of plastics, so that gas or vacuum is the only major reticulation possible. We therefore choose not to reticulate the focal plane, and we shall now calculate the performance which will result. The calculation makes two simplifying assumptions. The first is that the thermal properties of the materials comprising the focal plane are all the same. If the liquid is contained between plastic pellicles, and the spacers between the pellicles are also organic (e.g. photoresist) then this approximation is not serious. The specific heats of organic materials do not differ much, and the thermal conductivity of a liquid crystal perpendicular to the director appears (on the basis of limited data@‘) to be comparable to that of good plastics. Parallel to the director it is rather larger, but we shall ignore this complication. The second assumption is that the cell is thermally isolated from its surroundings on the time scale of a chopper cycle, while being sufficiently well linked to a heat sink to be sufficiently uniform in temperature to fix the operating point. This can be achieved by making the spacers between the cell and heat sink sufficiently small to give rise to a thermal conductance which is small compared to the lateral thermal spread within the cell, and to the capacitance term due to the heat capacity of the cell. We now calculate the change in temperature of a thermally isolated cell of thickness I, and volume specific heat c and thermal conductivity o in response to a chopped scene which gives a
R. G. HUMPHREYS and H. A. TARRY
IIS
power $I (4, w) incident on the detector. frequency. The heat diffusion equation is:
Here q is a spatial wavevector
and o is the chopper
dT ~7 = _ V2T, dt c We expand
the solutions
in terms of spatial
angular
(6) (q), and the temperature
wavevector
is given by:
i-(~+ql~‘;),
T=T,exp(nr)exp(iq.r)exp(
where v is a position vector in the plane of the detector and z is perpendicular to it. The quantity c1 is imaginary (r = iw) for solutions oscillatory in time, and the z-dependence can then be expressed in terms of:
This is a straightforward extension of the formulation of Holeman”’ whose approach we adopt, with the exception that the re-radiation of heat from the detector surface is ignored as small compared to the losses by conduction. The co-ordinate system adopted measures z within the cell from the surface closest to the heat sink. The solution is: (9) and the mean
detector
temperature
is: T
M For a sinusoidal
chopper,
=4(4d4
(10)
op1
and a single frequency
scene:
Rorl
$(q,w)=---TJq)cosqrcosot 2F’
(11)
where T,(q) is the temperature variation in the scene of wavevector q and the factor 2 derives from the chopper duty cycle. R, is the scene contrast in the 8-14pm band in F/l (5 x lo-’ W/cm2 modified by the atmospheric transmission) and q is the system quantum efficiency including the lens transmission and detector absorption; F is the focal ratio of the objective lens. The fundamental noise process in a thermal detector is due to spontaneous temperature fluctuations. These can be quantified by expanding in spatial frequency in the same way as with signal. The solutions of the heat diffusion equation [equation (6)] appropriate to noise are decaying irr rime. Equation (7) still applies, with a = - y, and equation (8) becomes: fl
Matching
these solutions
=
to the boundary
T = T,exp(-yt
j
( 1l/2. F _ qf
conditions
+ iq.r)cosT,
dT/dz
(12) = 0 at z = 0 and z = 1, (13)
where y
=;(!c$+q2>~2,
(14)
and II is an integer. These solutions are standing waves, and are normal modes of the temperature distribution. Only values of q which are integer multiples of rc/L, where L is the array dimension, are allowed. Of these modes, only that with n = 0 contribute to the noise on the detected light. A.211others give zero net temperature change when averaged through the cell thickness.
119
An optically coupled thermal imager
By calculating the entropy, and hence the internal energy of a temperature fluctuation, applying equipartition (U = ;kT), the mean square mode amplitude is found to be
and
(15) Spectrally
resolved,
this gives:
(16) as the mean square noise amplitude at specified spatial and temporal frequencies. We shall express our results as the Fourier transform of the NETD (noise equivalent temperature difference). This is equal to the more usual single pixel NETD at low spatial frequency, it increases with spatial frequency as the system MTF falls, and it includes the correlation in the noise between adjacent pixels. To obtain the temperature fluctuation limited NETD it is necessary to replace L by the pixel size a in equation (16). We now have expressions for the signal and the temperature fluctuation noise in the detector. The extent to which these are transmitted optically to the readout circuit is determined by the spatial and temporal band pass functions of the readout process. The finite pixel size requires that signal and noise be averaged over a pixel area. With a chopper field time rr and a read time rr during which the readout light is switched on, the noise is multiplied by: 4 Psin,,in~)(2sin~)($sin~). 2
( a
(17)
qxqr
The signal is multiplied by the same factors for pixel size and read time, but since the signal is phase coherent with the chopper the second bracket now becomes a factor of 2. With this filter function, the noise is integrated in quadrature over all temporal frequencies and then summed in quadrature over all aliased spatial frequencies. In this way, we obtain the thermal fluctuation noise of an optically read detector, not in thermal contact with a support, in a chopped system: (T;)
The integral 8y 7X; --s
y ~ o’+y2
= g
dw 27c’
(18)
over w is:
“1 1 -~ 0 0202+y2
sin2 Otr sin2 Ozr dw 2 2 = -+
r
Cyrl
-
1 + exp(-v,) - bp(rW>
- exp(-7GY
exp(- 74 2
1(19
and the summation over aliased spatial frequencies must be carried out numerically. It is possible to consider a number of other signal processing functions more complicated than the simple subtraction of successive frames. We shall not go through further calculations for these: they are straightforward extensions of the above analysis. The thermal fluctuation noise is shown in Fig. 5 in comparable units to those of the signal calculations. The calculation is based on equation (I 8), summed over aliased spatial frequencies. It is clear that this fundamental limit is low: if all other noise sources could be eliminated, we should have an excellent device performance. We take a specific heat c = 1.8 J/cm3/K, a thermal conductivity of r~ = 2 x 10-3/K, a 25 Hz chopper frequency, a pixel angular subtense of 0.5 mr and a 70 mm diameter lens. This translates into a 50 pm pixel for an f/l.4 objective or a 70 pm pixel in f /2. The signal phase with respect to the chopper is a function of spatial frequency, because large spatial frequencies decay more rapidly, and we choose to optimise the phase at a spatial frequency of 0.5 cycles/mr. The read out light is switched on for half a field time (10 ms). The magnitude of the signal as a function of spatial frequency is shown in Fig. 6 in units of the
120
R. G. HUMPHREYS and H. A. TARRY
0
0
I
I
I
I
I
I
1
2
3
4
5
6
I
(cycles
I mm ) of spatial
frequency
Spatial Fig. 5. Temperature
fluctuation
Frequency
noise in the detector calculated 10 pm thick detector.
as a function
for a
temperature change of the focal plane (chopper open minus chopper closed). The quantum efficiency is taken as unity in this calculation, but the filtering effect of the chopper and the finite read time are included. The signal rolls off significantly with spatial frequency, but the effect is not so serious as to rule out the use of an unreticulated focal plane. It is straightforward but slightly more complicated to include some thermal conductance through the spacers to the heat sink if they are considered to be uniformly distributed over the focal plane
40
30
5
20
IS 3 1c
0
I
I
I
I
I
I
1
2
3
4
5
6
Spatial Fig, 6. Chopped
temperature
Frequency
(cycles
I mm
1
difference in the detector for a 1 K scene temperature frequency for a 10pm thick detector.
as a function
of spatial
An optically
coupled
thermal
imager
121
rather than concentrated at the corners of the pixels. This procedure is only valid at low spatial frequencies and has negligible effect on the signal for spacers 7 pm square at the corners of 70 pm pixels and 2pm thick. Similarly the contribution of the radiation loss from the detector surface can be shown to be negligible. The use of gas filled encapsulations (rather than vacuum as this calculation has assumed) has also been examined. A Xenon filled encapsulation requires that the pillars between the detector and heat sink be about 5 pm or greater in thickness. Finally we consider briefly the properties required of the thermal ground plane. This should have a much higher thermal conductivity than the liquid crystal and support structure, and a much higher thermal mass. It should also be rigid, to suppress microphony. If the enclosure is evacuated and the surround of the ground plane is uniform, the non-uniformity in temperature is due entirely to radiation coupling. For example, it is necessary for an IR detector to work over a range of different scene temperatures; perhaps + 20°C. The heat diffusion equation for a uniform static scene is: V2T=
_k od
where 4 is the difference between emitted and absorbed power and d is the thickness of the heat sink and 0 its thermal conductivity. The solution of this equation for a circular disc of radius R is:
(21) and for R = 1 cm, 4 = 2.5 x 10m4 W/cm2 (20°C 8814/l,f/2), the temperature difference across the disc is 3 x 10-j K if the heat sink is 2 mm thick BaF, (cr = 0.12 W/cm/K). This conclusion is perhaps somewhat optimistic: it is unlikely that perfect radiation shielding would be possible, and the radiation reaching the detector might very well be in a wider range of wavelengths. The temperature would be an order of magnitude less uniform if the detector saw f/l in a wide bandwidth of wavelengths or if glass were used as the heat sink. We shall see later that a uniformity near lo- ’ K is required. The quick calculation suggests that this can be achieved without too much difficulty if a single crystal high thermal conductivity material is used. Glass is marginal as a material, but it should not be necessary to go to extreme materials such as copper or silicon which would have to operate in reflection.
FLUCTUATION
NOISE
IN
LIQUID
CRYSTALS
It is superficially rather surprising that there seems to be no discussion of noise in liquid crystal devices in the literature. There are three reasons for this absence. Firstly, the noise is low: if it were a problem, it would have been studied. Secondly, most liquid crystals are used in an essentially digital way, rather as analogue transducers for quantitative information. Thirdly, they tend to be viewed directly by the eye, which integrates over comparatively large areas and in a low temporal bandwidth. In the present study, we are much more demanding and liquid crystal noise is found to be significant. The noise observed in cells is associated with fluctuations of the director orientation within the cell. Director fluctuations have been extensively studied, but mainly as a means of determining the elastic constants and viscosity parameters of liquid crystals. We have discussed elsewhere”) a simple theory of the fluctuations which are observed when light is incident polarised parallel to the director and analysed at some angle from extinction. The application of the same theory to the present case of interest (light incident polarised at 45” to the director. and analysed after passing through a quarter wave plate) yields a prediction that the noise should vanish. We have extended the theory to second order terms, but this fails to explain the observed results. We do not therefore have a good theoretical understanding of the noise process. However, the form of the experimental noise spectra is the same for the two cases, and it is highly probable that the same dominant fluctuations are responsible for both. These are fluctuations in which the director twists in the plane of the cell. The dominant contribution comes from fluctuations with wavelength i/An where 3. is the optical wavelength and n the liquid crystal
R. G. HUMPHREYSand H. A. TARRY
122 birefringence.
Their
spectrum
is Lorenzian,
with
a characteristic
decay
time:
(22) where y, is the viscosity and k,, a liquid crystal elastic constant. We now summarise a wide range of noise measurements carried out both to characterise the nematic film and to test predictions of the evolving theory. Fluctuations of the type analysed by the theory can be easily observed in a nematic film viewed with a polarising microscope set close to extinction: there is an overall shimmer that appears to have a scale of a few microns. The noise due to those fluctuations has been measured in apparatus similar to the layout of Fig. 1, in which the nematic film was placed between polarisers with the correctly aligned I/4 plate, and illuminated by a stable monochromatic light source, intensity I,. The intensity fluctuations from a defined area of the film were measured using an FFT spectrum analyser. We express RMS fluctuation noise as a fraction of incident intensity I,. For these measurements the nematic film was held between flat glass plates (thereby ensuring stability and freedom from temperature fluctuations) and the nematic director was aligned by the reliable technique of coating the glass surfaces with SiO evaporated at 60” incidence.“’ Films of very good microscopic uniformity were made, although the use of very viscous nematics required care to realise a uniform alignment over the cell area. The use of a monochromatic light source (a laser) avoided the problems of compensating for birefringent dispersion, but the results were checked with less coherent sources and compensation to show that the observed noise was not a characteristic of a long coherence length. The lower noise measured when a longer wavelength was used was largely compensated by a similar reduction in responsivity. All optical surfaces were anti-reflection coated to avoid multiple paths through the birefringent components, and the apparatus was mechanically rigid and vibration free; even so at measurement frequencies below 1 Hz extraneous noise was never satisfactorily removed. Cell temperatures were maintained to within O.l”C. As described in Ref. (8) measurements made with the light polarised parallel to the cell director
-6 10 1
I
I
10
100 FrQCjUQnCy(Hz
1
Fig. 7. Measured noise spectra for a 12 km film of liquid crystal El in a glass cell li/ = 10’ pixel size a 70 pm. (a) 45” configuration (see Fig. 2). (b) Cell turned to put director parallel to incident polarisatlon. The dashed line (c) shows the theoretically predicted noise for the parallel configuration [Ref. (8)] using 5’, 0.13, k,, 8.7 x 10-12, k,, 4.6 x 10-12, k,, 1.23 x IO-“, An 0.192 (I = 6.33 nm).
An optically coupled thermal imager
123
agreed very well with the theory of twist modes in its dependence on pixel size, frequency. cell thickness t and analyser azimuth $. Changing the optical configuration to the one required in an imager (input polarisation at 45’ to the director) consistently gave values of noise higher than those predicted by the second order extension of the theory in Ref. (8) despite many experimental refinements. For ((/ = 10, the measured noise was only a factor of 3 lower than that for the parallel configuration. Figures 7-10 illustrate same experimental properties of fluctuation noise defined as (AZ,,/Z,). Its spectrum is l/f above a “knee” frequency of -20 Hz for El (Fig. 7) identical to that of the parallel configuration, given by equation (22); also identical is the dependence on cell thickness between 0.1 and 50 pm (approximately t ‘j2) and on pixel diameter a. For the smallest pixels optical aberrations limited the actual sampled area. The dependence of noise on analyser azimuth was qualitatively different from the “parallel” configuration, and varied as sin II/ rather than sin 214, (0 < $ < 90”); however as shown in Fig. 8 at the smallest values of $ a few degrees from extinction a constant noise value was measured; the extinction was also not perfect partly due to the time-averaged noise. The measured noise was largely independent of temperature, rising only by a factor of less than 1.5 as TN1 was approached. For II/ = 90”, removing the analyser does not reduce AZ/Z,,. The only mechanism which could then give rise to noise is scattering of light through a large angle, so that it is outside the collection aperture of the optics. Since the theory of Ref. (8) ruled out such effects in its formulation, it is not surprising that it is unable to explain the results. However, our observations do not appear to be wholly consistent with theories of wide angle scattering, as the dependence on wavelength observed was less than the L4 variation predicted.““’ In summary the measured noise in El or a similar cyanobiphenyl nematic at 20°C above 20 HZ is given empirically by:
ACms __ = &-If-l
Af
‘P
sin($
+ g)t
I:‘>,
(23)
T
where B =O.l and g =0.08 for El. It will be shown below that the magnitude of this fluctuation noise can be the main factor restricting the performance of an imager, but in the absence of a satisfactory theory to explain equation (23) it is difficult to predict changes in the nematic that could reduce the noise. However,
(c) Tmnsmitted
light
RMS Noise
(b) Parallel
configuration
iWrry X
I x t
t
X
(a)
X
45”configumtion
1:: -2
0
2
4
6
8
10 3
(degrees)
Fig. 8. Dependence of fluctuation noise U, at 70Hz on low values of the analyser azimuth $. (a) 45 configuration (Fig. 2). (b) Parallel configuration. Also shown in the intensity of transmitted light I.
124
R. G.
-6
10
HUMPHREYS and H. A. TARRY
,
I
1
I
I
10
100
1000
FrQqUQnCy
(Hz
)
Fig. 9. Measured noise spectra for IOpm glass cells containing nematic mixtures of PG296 and El illuminated in the 45’ configuration (Fig. 2). The lines represent (a) El (b) 24% PG296 in El (c) 44% PG296 in El (d) 60% PC3296 in El. $ = lo” (I = 70pm. Graph (e) shows the noise spectrum of the measuring apparatus.
t-l<
Diameter
( b)
Parallel
Of Fourier
configuration
p(anQ
apQrtUrQ
(mm)
Fig. IO. The effect of low-pass spatial filtering on fluctuation noise ~1,. Liquid E7 at 20 ‘C, film thickness 10 pm. pixel diameter a 70 grn, focal length of Fourier lens 100mm. The effect on the parallel configuration is also shown for comparison (b).
the noise measured in the parallel configuration is also described by equation (23) (with a higher B) for low values of II, and is accurately explained by the theory in Ref. (8). Assuming this link between the configurations is retained we anticipated from equation (22) that increasing the twist viscosity 7, should reduce the noise as filtered by the chopper. The use of polymer additives to increase y, had the desired effect of damping the fluctuations and reducing the noise; the knee .frequency was significantly reduced and values of B were those given in Table 1. In fact the noise was reduced by the same factor as that of the parallel
An optically
coupled
thermal
Table
imager
125
I
Percent 0 24
l.OxlO
’
2.8 x IO .'
44
1.0 x IO 2
60
35x10
3
configuration. The temperature sensitivity djdT (A/Z) was not significantly changed. Figure 9 shows a series of noise spectra for a range of polymer mixtures. A separate experiment using a thin cell verified that the response time of the most viscous films to a heat pulse was less than 1 ms, as might be expected for the essentially microscopic nature of the optical change. If the elastic constant kzz of the nematic could be increased a corresponding reduction of noise could be obtained by giving a greater fraction of energy to modes at frequencies well above those sampled by the chopper. The improvement would be linear in kz2, rather than a square root law as is the case with viscosity. We were unable to test this argument experimentally, as liquids with high k,? were not available. It has already been suggested that optical signal processing at the Fourier Transform plane could improve the imager performance. It was also found experimentally that an aperture in the FT plane significantly reduced measured fluctuation noise. Figure 10 shows that a factor of 2 reduction can be given by filtering out spatial frequencies a factor of 2 higher than the pixel frequency. This is again consistent with wide angle scattering as the noise mechanism. In the absence of a satisfactory theory of fluctuation noise our predictions of imager performance have been based on the experimental observations.
IMAGER
PERFORMANCE
The preceding sections have given sufficient information to allow the performance of an optically read imager to be estimated although it should be emphasised that the choice of materials and techniques is not necessarily the optimum. We shall consider a “standard” imager with the following characteristics Objective lens .fi2 70 Frame rate 2.5 Hz Array size 128 x 256; Read out light pulsed Read out wavelength
mm diameter 70 pm pixels once per field for 0.5 of the field time 0.63 pm
Equation (3) requires 4 to be a minimum. We choose $ to be 3” from extinction, because the contrast falls at lower $ (Fig. 8). Detailed study of the components of the imager allows us to estimate the following properties: Taking the maximum size of the TV chip to be about 1 cm, implies the use of pixels 50 pm square with a maximum well capacity of 1.3 x 10’ carriers; for the best performance we would need the received pedestal intensity / to nearly fill the wells, but some reduction of the average filling must be made to allow for the non-uniformity of I due to non-uniformity of cell thickness and temperature. For a well to be half-filled by an average pixel for $ = 3”, a non-uniformity in thickness or temperature giving $ = 4.2 will fill the well; the corresponding minimum of II/ = 1.8” will only fill the well by 18%. These limits imply that the thickness of the cell must be maintained uniform to better than 0.04 pm in 10 pm and its temperature to 0.02-C (for a responsivity of dy /dT = 5O’/‘C). With these assumptions, we can now calculate the predicted performance of an imager based on the liquid crystals we have studied. Figure 11 shows the contribution of the three noise sources (liquid crystal, photon and temperature fluctuation) and the signal that we wish to detect, plotted as functions of spatial frequency. The vertical scale is in terms of the temperature in the liquid crystal cell, and the horizontal axis covers the range of spatial frequencies detected with a 70pm
R. G. HUMPHREYSand H. A. TARRY
126
20
Signal
Photon Liquid _--_-_
.-.-.-.-.crystal
----
x zl I6
lo-
g
Temperature ________-_-_------_____
0
0
---we_-_,
I
1
I
I
I
I
1
2
3
4
5
6
Frequency
(cycles
Spatial
I mm
)
Fig. 11. Signal and noise as functions of spatial frequency for a 10 pm thick liquid crystal cell, with 2 pm thick pellicles, 70 pm pixels. The scene is viewed in f/2,chopped at 25 Hz and 70% of the power in the scene is reckoned as being transmitted by the lens, beam splitter, and enclosure windows and absorbed by the liquid. The encapsulation is evacuated and the cell is supported on 10 pm high pillars comprising 1% of the pixel area. The readout wavelength is taken to be 633 nm although the results would be very similar at another wavelength. The analyser is 3” away from extinction, and the 50 pm pixels of the TV chip are run at half full well on average. The liquid crystal is the highest viscosity mixture studied, assumed to have a responsivity ofSO”/“C as in Fig. 3. The overall mean power required in the readout light is 3 mW, and it is on for 10 ms in each 20 ms field. The vertical scale is in units of the temperature of the liquid crystal cell. For these parameters, 10-6K in the cell corresponds to 200 carriers in one pixel of the TV chip. The horizontal scale is in units of spatial frequency up to the maximum frequency faithfully sensed by an array with 70lm pixels. The signal is that corresponding to 1 K in the scene and the noise contributions are in comparable units.
pixel. We have not attempted to include the pixel to pixel correlation of the liquid crystal noise, which is expected to be negligible, so both liquid crystal noise and photon noise are independent of spatial frequency. The signal phase chosen optimises the signal at 4 cycles/mm, and the liquid crystal is the best material we have studied, i.e. the 60% polymer mixture. The result shows that with f /2 optics we have an imager NETD of 1.4 K at 0.5 cyclesimradian; reducing the f number to 1.4 and the pixel size to 50 pm reduces this to 1.O K. POTENTIAL
FOR
IMPROVEMENT
The noise shown in Fig. 11 has almost equal components of liquid crystal fluctuation noise and photon noise. Reduction of the NETD can therefore not be achieved by further reduction of fluctuation noise alone; and it is unlikely that the limitations of photon noise can easily be overcome. We therefore require a larger signal from a focal plane of similar dimensions, and this implies the use of a detector with a higher responsivity dZ/dT. In the case of the nematic liquid crystal a material with higher d/dT (An) is needed, while non-uniformity limitations do not allow An to be much higher. As discussed earlier other liquid crystal effects have the potential of giving higher responsivity at the cost of more severe problems of focal piane construction. We believe that of the many liquid crystal effects we have studied the variable birefringence nematic is unique in the lack of coupling
An optically
coupled
thermal
imager
127
between the signal mechanism (microscopic) and the dominant noise mechanism (macroscopic). We are unaware of any other class of materials in which such a high temperature sensitivity is associated with a broad temperature range over which it is observed; these characteristics ideally require a second order phase transition. If a solid with these properties were found, presumably the “liquid crystal” noise would be absent, and one constraint on system design would be eliminated. CONCLUSION
We have shown that an IR imager using optical coupling of its focal plane to a TV chip”‘) can give a useful imaging performance, with NET of 1.4 K at 0.5 cycles per radian. For comparison, described in the same way (also with f /2 optics) the pyroelectric vidicon has an NET of 5 K. None of the practical problems involved in constructing the imager is severe and all the components apart from the focal plane are readily obtainable; the focal plane itself could be made in large areas cheaply using developments of standard photolithography and plastic film processing techniques. Copyright 0 Controller
HMSO London
1987,
REFERENCES 1. C. Hilsum 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
and W. R. Harding, I&red Phys. 1, 67 (1961). J. L. Fergason, T. P. Vegl and M. Garbuny, U.S. Patent, 3 114836 (1963). Y. B. Andre, J. P. Chambaret, M. A. Franc0 and B. S. Prade, Appl. Opf. 18, 2607 (1979). W. Maier and A. Saune. 2. Naturforsch. 149. 882 (1959): Z. Naturforsch. 16a. 816 (1961).I M. Bradshaw (RSRE) Unpublished measurements.. ” ” F. Rondelez, W. Urbach and H. Hervet, Phys. Rev. Left. 41, 1058 (1978); I. C. Khoo and R. Normandin, IEEE J. quantum Electron. QE-21, 329 (1985); R. Vilanove, E. Guyon, C. Mitescu and P. Pieranski, J. Phys. 35, 153 (1974). B. R. Holeman, Infrared Phys. 12, 125 (1972). R. G. Humphreys, H. A. Tarry and M. Bradshaw, Liquid Crystals (To be published). E. Guyon, P. Pieranski and M. Boix, Left. appi. Engng Sci. 1, 19 (1973). M. I. Miraldi, L. Trossi, P. Taverna Valabrega and C. Oldano, II Nuouo Cimento 6OB, 165 (1980); D. Langevin and M. A. Bouchiat, J. Phys. Coil. Cl.. Suppl. 3, 197 (1975). C. T. Elliott, R. G. Humphreys and R. Watton, U.K. Patent Application No GB2 150 387A.
OOZO-0X91/88$3.00 + 0.00 Pergamon Press plc
AN OPTICALLY
COUPLED
R. G. HUMPHREYS RSRE,
Malvern, (Received
THERMAL
IMAGER
and H. A. TARRY Worcestershire,
I5 Oclober
U.K.
1987)
Abstract-A novel scheme for thermal imaging is proposed, using a thermal IR detector whose temperature is sensed using a thermo-optic property, and the image is read electronically using a conventional television chip. As with other thermal IR detectors, the image is mechanically chopped, and the difference between fields calculated electronically. The particular scheme discussed uses a liquid crystal as the thermo-optic medium. Calculations of signal and measurements of noise are presented to deduce what the performance of such a thermal imager would be.
INTRODUCTION
Thermal IR detectors in a staring array must be interfaced in some way with multiplexing electronics, and it is the properties of this interface-thermal and electrical-which usually limit the imaging performance of the array. This paper describes a novel form of imager which avoids the interface problems by using optical coupling between the detecting elements and multiplexing circuits: the thermal image is converted to a visible-light image which is then detected by a conventional TV camera chip. The essential signal processing can then be done before the image is displayed in a CRT. Optically read thermal detectors have been described before, (I) but early schemes were intended for direct viewing by the eye, and therefore had to present an image with a high contrast. Because the systems were d.c. coupled this could only be achieved by stabilising the temperature of the whole focal plane to a very high accuracy and by requiring a very high degree of uniformity in its response. However, once the image is available in electronic form, a.c. coupling can be done by subtracting successive “clear” and “opaque” fields while the scene is chopped; also the essential correction for non uniformity of response can be carried out. In this paper we discuss in detail the performance of a proposed imager of this type and the factors likely to limit its thermal and spatial resolution; these include the thermal properties of the focal plane, its optical properties and how they interact with the TV chip, and the noise mechanisms both in the focal plane and in the readout. We have chosen the temperature-dependent birefringence of a nematic liquid crystal to convert the thermal image to an optical image, and we present a theoretical and experimental study of its sensitivity and noise. Measuring or making reasonable assumptions of the properties of all the components allows the NET of the imager to be predicted. Figure 1 shows the layout of an imager with optical coupling. (‘I) The IR scene is focussed on to a focal plane which converts it to an image in visible (or near IR) light. Many schemes for this conversion exist in principle but for simplicity of construction we have chosen to use a system whose transmission of light depends on its temperature. Light from a separate source allows the image to be formed on a TV chip (e.g. a CCD array). If used in this way the detector will eventually reach thermal equilibrium with severe loss of spatial resolution, giving an image dominated by the non-uniformity of its responsivity to the mean background temperature. Introducing a chopper before the focal plane allows a degree of a.c. coupling: fields from the TV chip corresponding to “open” and “closed” chopper states can be subtracted electronically giving an image more uniform by several order of magnitude; the background pedestal and non-uniformity of response to it will have been removed. THE
FOCAL
PLANE
Very many materials can in principle be used to make the focal plane. transmission to temperature is required to give a signal exceeding potential 113
A high responsivity of noise mechanisms; this
II4
R. G. HUMPHREYS and H. A. TARRY TEMPERATURE CONTROLLED ENCLOSURE CHOPPER J
X14PLATE \ TV CHIP
r
It
SUBTRACTION
B+ / FOURlEd TRANSFORM PLANE
POLkRISER
I
‘.
FOCAL PLANE
7.t VISIBLE LIGHT SOURCE
VIDEO Fig. 1. Diagram
of optically
coupled
imager.
responsivity must also be maintained over the range within which the focal plane temperature can be stabilised. These conditions led us to choose a liquid crystal, in which co-operative forces between molecules give rise to a range of optical properties with large dependence on temperature. Since 1960 the selective reflection of a narrow wavelength band from a cholesteric liquid crystal has been used to sense temperature in direct-view imaging devices; (2)however this effect has a very limited dynamic range and requires accurate temperature stabilisation. Cholesterics of a much longer pitch give a rotation of the plane of polarisation of light which is highly temperature sensitive, and have also been proposed for imagingc3’ but because macroscopic realignment of the structure is involved the response could be slow especially if a liquid of high viscosity is involved. The necessary surface alignment is also difficult to achieve and maintain uniformly as it must allow free rotation of the local optic axis while maintaining its alignment with respect to the containment walls. If the alignment is not ideal, elliptically polarised light (with an unspecified axis) will be transmitted. More attractive candidates for the focal plane are the nematic liquid crystals. These have uniaxial birefringence An( = n, - no) _ 0.1 which is sensitive to temperature because of the temperature dependence of the microscopic order of the molecules. The optic axis is unaffected and it can therefore be fixed accurately in the plane of the film by the use of aligning films, which are already in common use in cheap display devices. Because the optic axis is known, the birefringence can be converted to a light intensity by the use of a quarter-wave plate aligned with the optic axis (see Fig. 2). Light (wavelength A) entering the film polarised at n/4 to the optic axis emerges from the where t is the quarter-wave plate again plane polarised and rotated through an angle y = (xAnt)/i film thickness. I
Fig. 2. Alignment of optical components in a nematic axis for extinction. D nematic director.
A
liquid crystal imager. P polariser axis. A analyser L optic axis of quarter-wave plate.
An optically
An analyser
aligned
coupled
at an angle 0 with respect
thermal
to the polariser
i.e. it is at an angle $ = 8 + y + (z/2) from extinction, temperature of the transmitted intensity is:
The value of $ used is a compromise
between
115
imager
transmits
an intensity
of:
and for small values of $ the variation
maximum
signal (large $) and maximum
with
contrast
(low $). The upper limit of $ is set by the dynamic range of the TV chip; a lower limit is set by non-uniformity in the position of extinction y caused by non-uniformity of thickness t and temperature in the nematic film. Between these limits II/ can be set to optimise the imager performance. This function could be performed by an electro-optic device with feedback. Dispersion of An can be corrected to a large extent by a second birefringent film, allowing the use of non-monochromatic light. The theory of Maier and Saupec4’ predicts the variations with temperature of the order parameter S of a nematic. S describes the mean-square angular displacement of the molecular axis, and is related to the birefringence by 2nA.n - NIX,,,S where N is the number of molecules per unit volume and LX,,,is the molecular polarisability. A universal curve of S falling with temperature is predicted, and there is a first order phase transition when S has fallen to 0.43. This is the nematic-isotropic transition at TN,. Our measurements of An for a range of nematic materials”’ confirm the general shape of the curve, showing the largest value of d/dT (An) within 1°C of TN, but as with all other similar measurements the precise values of d/dT (An) differ significantly from the theory. We are therefore unable to predict a maximum attainable value or any systematic way of achieving it. For this work we have chosen the cyanobiphenyl nematics; these have the highest value we have found of d/dT (An), of about 0.02”C’ nearly independent of temperature within 1°C of TNT, and also have the advantage of being chemically stable and available in a wide range of eutectic mixtures for use in display devices. In contrast to display requirements, we want a large temperature dependence of optical properties at a temperature not far above room temperature: we have therefore used mixture El (TN, = 41°C) for most of the measurements and theory.
Fig. 3. Measured
variation
T (‘c) of extinction angle y as a function of temperature the nematic mixture 24% PC296 polymer in El.
for a 10 pm thick film of
R. G. HUMPHREYS and
I16
H. A. TARRY
IR BLACKENING
PELLICLES ~~~~ENT
J INSULATOR
Fig. 4. Diagram
showing
(VACUU
the components
of the liquid crystal
focal plane
Figure 3 shows a typical measured variation of 7 with temperature for a 10 pm thick film. The IR focal plane must contain and align a uniform thin film of liquid crystal using a minimum of temperature insensitive material; it must absorb IR and transmit visible light efficiently; and it must be thermally isolated while at the same time maintaining a temperature uniform to t0.01 C to maintain uniformity of ;‘. The cell is illustrated in more detail in Fig. 4. The liquid is confined between thin (probably plastic) pellicles coated with alignment layers. The cell thickness is maintained accurately uniform by spacer pillars. The lower pellicle is supported by a rigid high thermal conductivity heat sink (a thermal “ground plane”) from which it is nearly thermally isolated. We envisage spacers being placed at the corners of each pixel which is about 70 pm square. The cell also has a layer designed to absorb the IR, which is illustrated in the figure as being on top of the front surface, but may be elsewhere. Although the design of the focal plane is complex, it should be possible to manufacture it cheaply in large areas by standard photolithographic techniques. The thermal analysis of this structure is described below. READOUT
OPTICS
AND
DETECTION
The most promising choice of readout light source is a high efficiency GaAs LED, having a relatively narrow spectral bandwidth. It is switched on for a period during both “light” and “dark” fields of the cheaper. While the LED is on, the TV chip is integrating the signal, so that any high frequency noise sources are averaged out and noise bandwidth is low. Two lenses are shown in Fig. 1 to focus and demagnify the image on to the chip; this arrangement makes available a Fourier transform plane for optical signal processing although a single lens or even proximity focussing could be considered. The chopper and objective lenses are conventional components, and the beam splitter is a dichroic plate with multilayer coatings for transmission of IR and reflection of visible light. The TV chip can be a CCD or MOS switched array; since we want it to work close to the shot (photon) noise limit, the only parameter that concerns us is the well saturation level, which we take to be 5 x 11 ‘I carriers cm 2. Available chips usually have high quantum efficiencies and fill factors. The output of this chip must be stored in a framestore capable of accommodating the full dynamic range of the chip (less any constant pedestal that could be skimmed beforehand), and an analogue to digital converter of at least 12 bit accuracy would be needed. The chip and processing electronics will not be described here in any more detail. The noise in a state-of-the-art solid state TV chip operating near full well is mainly shot noise, equivalent to photon noise on the readout light. Equations (1) and (2) give a signal/noise ratio for small $ of: (3)
An optically
coupled
thermal
117
imager
requiring Z, to be as large as possible. Although the ratio is independent of II/, saturation of the CCD wells in the TV chip puts a limit on the detected intensity I. In order to reduce I to this value Ic/ must be correspondingly reduced [equation (l)] moving the analyser closer to extinction. Any non-uniformity in the focal plane, e.g. of thickness, will give non-uniformity of the transmitted intensity Z, whose highest values must not exceed the saturation value of the chip, further restricting the choice of $. These non-uniformities are likely to be of low spatial frequency. We now consider briefly how the transfer function of the read out optics can be modified to minimise the damaging effects of non-uniformity. Before the analyser the signal and non-uniformity both appear as electric fields ES and E, polarised perpendicular to the pedestal field E,. An analyser $ from extinction therefore transmits a field: E,,sinII/
+(E,+E,)coscC/
(4)
with intensity: E~sin2~+E~~~s21C/+E~~~s2~+2sin~cos~(E,E,+E,E,)+2cos’~E,E,. (41 (2) (3) (1)
(5) (5)
Term 1 is the pedestal, terms 2 and 3 should be small and terms 4 and 5 represent the signal (E,E,), and the non-uniformities of the pedestal (l&E,) and of the signal (E, ES). Since the information of interest in the scene tends to be at relatively high spatial frequency (objects a few pixels wide) while the nonuniformity will be dominated by variations on the scale of the array size (e.g. detector thickness and temperature) the possibility exists to attenuate the non-uniformity (l&E,) without significantly reducing the signal of interest by using an annular stop in the Fourier plane. This form of bandpass filtering has not been investigated in detail in the present work, and there is some doubt that the scheme could be made workable without undue microphony, but it remains a unique potential advantage of the optically read detector scheme. Further possibilities like recognition aids could also be considered. THE
THERMAL
CIRCUIT
In order to estimate the magnitude of the signal to be detected, we have performed calculations of the response of a liquid crystal focal plane like that depicted in Fig. 4 to a chopped thermal scene. The calculations are somewhat idealised, but contain the essential features. The liquid crystal problem differs from the more usual IR detector in two respects. Firstly, the thermal conductivity of the liquid crystal is much lower than that of materials normally considered (e.g. pyroelectrics), so that reticulation is much less important. Secondly, being a liquid, the liquid crystal must be contained, so that reticulation is much more difficult: the thermal conductivity of liquid crystals is comparable to that of plastics, so that gas or vacuum is the only major reticulation possible. We therefore choose not to reticulate the focal plane, and we shall now calculate the performance which will result. The calculation makes two simplifying assumptions. The first is that the thermal properties of the materials comprising the focal plane are all the same. If the liquid is contained between plastic pellicles, and the spacers between the pellicles are also organic (e.g. photoresist) then this approximation is not serious. The specific heats of organic materials do not differ much, and the thermal conductivity of a liquid crystal perpendicular to the director appears (on the basis of limited data@‘) to be comparable to that of good plastics. Parallel to the director it is rather larger, but we shall ignore this complication. The second assumption is that the cell is thermally isolated from its surroundings on the time scale of a chopper cycle, while being sufficiently well linked to a heat sink to be sufficiently uniform in temperature to fix the operating point. This can be achieved by making the spacers between the cell and heat sink sufficiently small to give rise to a thermal conductance which is small compared to the lateral thermal spread within the cell, and to the capacitance term due to the heat capacity of the cell. We now calculate the change in temperature of a thermally isolated cell of thickness I, and volume specific heat c and thermal conductivity o in response to a chopped scene which gives a
R. G. HUMPHREYS and H. A. TARRY
IIS
power $I (4, w) incident on the detector. frequency. The heat diffusion equation is:
Here q is a spatial wavevector
and o is the chopper
dT ~7 = _ V2T, dt c We expand
the solutions
in terms of spatial
angular
(6) (q), and the temperature
wavevector
is given by:
i-(~+ql~‘;),
T=T,exp(nr)exp(iq.r)exp(
where v is a position vector in the plane of the detector and z is perpendicular to it. The quantity c1 is imaginary (r = iw) for solutions oscillatory in time, and the z-dependence can then be expressed in terms of:
This is a straightforward extension of the formulation of Holeman”’ whose approach we adopt, with the exception that the re-radiation of heat from the detector surface is ignored as small compared to the losses by conduction. The co-ordinate system adopted measures z within the cell from the surface closest to the heat sink. The solution is: (9) and the mean
detector
temperature
is: T
M For a sinusoidal
chopper,
=4(4d4
(10)
op1
and a single frequency
scene:
Rorl
$(q,w)=---TJq)cosqrcosot 2F’
(11)
where T,(q) is the temperature variation in the scene of wavevector q and the factor 2 derives from the chopper duty cycle. R, is the scene contrast in the 8-14pm band in F/l (5 x lo-’ W/cm2 modified by the atmospheric transmission) and q is the system quantum efficiency including the lens transmission and detector absorption; F is the focal ratio of the objective lens. The fundamental noise process in a thermal detector is due to spontaneous temperature fluctuations. These can be quantified by expanding in spatial frequency in the same way as with signal. The solutions of the heat diffusion equation [equation (6)] appropriate to noise are decaying irr rime. Equation (7) still applies, with a = - y, and equation (8) becomes: fl
Matching
these solutions
=
to the boundary
T = T,exp(-yt
j
( 1l/2. F _ qf
conditions
+ iq.r)cosT,
dT/dz
(12) = 0 at z = 0 and z = 1, (13)
where y
=;(!c$+q2>~2,
(14)
and II is an integer. These solutions are standing waves, and are normal modes of the temperature distribution. Only values of q which are integer multiples of rc/L, where L is the array dimension, are allowed. Of these modes, only that with n = 0 contribute to the noise on the detected light. A.211others give zero net temperature change when averaged through the cell thickness.
119
An optically coupled thermal imager
By calculating the entropy, and hence the internal energy of a temperature fluctuation, applying equipartition (U = ;kT), the mean square mode amplitude is found to be
and
(15) Spectrally
resolved,
this gives:
(16) as the mean square noise amplitude at specified spatial and temporal frequencies. We shall express our results as the Fourier transform of the NETD (noise equivalent temperature difference). This is equal to the more usual single pixel NETD at low spatial frequency, it increases with spatial frequency as the system MTF falls, and it includes the correlation in the noise between adjacent pixels. To obtain the temperature fluctuation limited NETD it is necessary to replace L by the pixel size a in equation (16). We now have expressions for the signal and the temperature fluctuation noise in the detector. The extent to which these are transmitted optically to the readout circuit is determined by the spatial and temporal band pass functions of the readout process. The finite pixel size requires that signal and noise be averaged over a pixel area. With a chopper field time rr and a read time rr during which the readout light is switched on, the noise is multiplied by: 4 Psin,,in~)(2sin~)($sin~). 2
( a
(17)
qxqr
The signal is multiplied by the same factors for pixel size and read time, but since the signal is phase coherent with the chopper the second bracket now becomes a factor of 2. With this filter function, the noise is integrated in quadrature over all temporal frequencies and then summed in quadrature over all aliased spatial frequencies. In this way, we obtain the thermal fluctuation noise of an optically read detector, not in thermal contact with a support, in a chopped system: (T;)
The integral 8y 7X; --s
y ~ o’+y2
= g
dw 27c’
(18)
over w is:
“1 1 -~ 0 0202+y2
sin2 Otr sin2 Ozr dw 2 2 = -+
r
Cyrl
-
1 + exp(-v,) - bp(rW>
- exp(-7GY
exp(- 74 2
1(19
and the summation over aliased spatial frequencies must be carried out numerically. It is possible to consider a number of other signal processing functions more complicated than the simple subtraction of successive frames. We shall not go through further calculations for these: they are straightforward extensions of the above analysis. The thermal fluctuation noise is shown in Fig. 5 in comparable units to those of the signal calculations. The calculation is based on equation (I 8), summed over aliased spatial frequencies. It is clear that this fundamental limit is low: if all other noise sources could be eliminated, we should have an excellent device performance. We take a specific heat c = 1.8 J/cm3/K, a thermal conductivity of r~ = 2 x 10-3/K, a 25 Hz chopper frequency, a pixel angular subtense of 0.5 mr and a 70 mm diameter lens. This translates into a 50 pm pixel for an f/l.4 objective or a 70 pm pixel in f /2. The signal phase with respect to the chopper is a function of spatial frequency, because large spatial frequencies decay more rapidly, and we choose to optimise the phase at a spatial frequency of 0.5 cycles/mr. The read out light is switched on for half a field time (10 ms). The magnitude of the signal as a function of spatial frequency is shown in Fig. 6 in units of the
120
R. G. HUMPHREYS and H. A. TARRY
0
0
I
I
I
I
I
I
1
2
3
4
5
6
I
(cycles
I mm ) of spatial
frequency
Spatial Fig. 5. Temperature
fluctuation
Frequency
noise in the detector calculated 10 pm thick detector.
as a function
for a
temperature change of the focal plane (chopper open minus chopper closed). The quantum efficiency is taken as unity in this calculation, but the filtering effect of the chopper and the finite read time are included. The signal rolls off significantly with spatial frequency, but the effect is not so serious as to rule out the use of an unreticulated focal plane. It is straightforward but slightly more complicated to include some thermal conductance through the spacers to the heat sink if they are considered to be uniformly distributed over the focal plane
40
30
5
20
IS 3 1c
0
I
I
I
I
I
I
1
2
3
4
5
6
Spatial Fig, 6. Chopped
temperature
Frequency
(cycles
I mm
1
difference in the detector for a 1 K scene temperature frequency for a 10pm thick detector.
as a function
of spatial
An optically
coupled
thermal
imager
121
rather than concentrated at the corners of the pixels. This procedure is only valid at low spatial frequencies and has negligible effect on the signal for spacers 7 pm square at the corners of 70 pm pixels and 2pm thick. Similarly the contribution of the radiation loss from the detector surface can be shown to be negligible. The use of gas filled encapsulations (rather than vacuum as this calculation has assumed) has also been examined. A Xenon filled encapsulation requires that the pillars between the detector and heat sink be about 5 pm or greater in thickness. Finally we consider briefly the properties required of the thermal ground plane. This should have a much higher thermal conductivity than the liquid crystal and support structure, and a much higher thermal mass. It should also be rigid, to suppress microphony. If the enclosure is evacuated and the surround of the ground plane is uniform, the non-uniformity in temperature is due entirely to radiation coupling. For example, it is necessary for an IR detector to work over a range of different scene temperatures; perhaps + 20°C. The heat diffusion equation for a uniform static scene is: V2T=
_k od
where 4 is the difference between emitted and absorbed power and d is the thickness of the heat sink and 0 its thermal conductivity. The solution of this equation for a circular disc of radius R is:
(21) and for R = 1 cm, 4 = 2.5 x 10m4 W/cm2 (20°C 8814/l,f/2), the temperature difference across the disc is 3 x 10-j K if the heat sink is 2 mm thick BaF, (cr = 0.12 W/cm/K). This conclusion is perhaps somewhat optimistic: it is unlikely that perfect radiation shielding would be possible, and the radiation reaching the detector might very well be in a wider range of wavelengths. The temperature would be an order of magnitude less uniform if the detector saw f/l in a wide bandwidth of wavelengths or if glass were used as the heat sink. We shall see later that a uniformity near lo- ’ K is required. The quick calculation suggests that this can be achieved without too much difficulty if a single crystal high thermal conductivity material is used. Glass is marginal as a material, but it should not be necessary to go to extreme materials such as copper or silicon which would have to operate in reflection.
FLUCTUATION
NOISE
IN
LIQUID
CRYSTALS
It is superficially rather surprising that there seems to be no discussion of noise in liquid crystal devices in the literature. There are three reasons for this absence. Firstly, the noise is low: if it were a problem, it would have been studied. Secondly, most liquid crystals are used in an essentially digital way, rather as analogue transducers for quantitative information. Thirdly, they tend to be viewed directly by the eye, which integrates over comparatively large areas and in a low temporal bandwidth. In the present study, we are much more demanding and liquid crystal noise is found to be significant. The noise observed in cells is associated with fluctuations of the director orientation within the cell. Director fluctuations have been extensively studied, but mainly as a means of determining the elastic constants and viscosity parameters of liquid crystals. We have discussed elsewhere”) a simple theory of the fluctuations which are observed when light is incident polarised parallel to the director and analysed at some angle from extinction. The application of the same theory to the present case of interest (light incident polarised at 45” to the director. and analysed after passing through a quarter wave plate) yields a prediction that the noise should vanish. We have extended the theory to second order terms, but this fails to explain the observed results. We do not therefore have a good theoretical understanding of the noise process. However, the form of the experimental noise spectra is the same for the two cases, and it is highly probable that the same dominant fluctuations are responsible for both. These are fluctuations in which the director twists in the plane of the cell. The dominant contribution comes from fluctuations with wavelength i/An where 3. is the optical wavelength and n the liquid crystal
R. G. HUMPHREYSand H. A. TARRY
122 birefringence.
Their
spectrum
is Lorenzian,
with
a characteristic
decay
time:
(22) where y, is the viscosity and k,, a liquid crystal elastic constant. We now summarise a wide range of noise measurements carried out both to characterise the nematic film and to test predictions of the evolving theory. Fluctuations of the type analysed by the theory can be easily observed in a nematic film viewed with a polarising microscope set close to extinction: there is an overall shimmer that appears to have a scale of a few microns. The noise due to those fluctuations has been measured in apparatus similar to the layout of Fig. 1, in which the nematic film was placed between polarisers with the correctly aligned I/4 plate, and illuminated by a stable monochromatic light source, intensity I,. The intensity fluctuations from a defined area of the film were measured using an FFT spectrum analyser. We express RMS fluctuation noise as a fraction of incident intensity I,. For these measurements the nematic film was held between flat glass plates (thereby ensuring stability and freedom from temperature fluctuations) and the nematic director was aligned by the reliable technique of coating the glass surfaces with SiO evaporated at 60” incidence.“’ Films of very good microscopic uniformity were made, although the use of very viscous nematics required care to realise a uniform alignment over the cell area. The use of a monochromatic light source (a laser) avoided the problems of compensating for birefringent dispersion, but the results were checked with less coherent sources and compensation to show that the observed noise was not a characteristic of a long coherence length. The lower noise measured when a longer wavelength was used was largely compensated by a similar reduction in responsivity. All optical surfaces were anti-reflection coated to avoid multiple paths through the birefringent components, and the apparatus was mechanically rigid and vibration free; even so at measurement frequencies below 1 Hz extraneous noise was never satisfactorily removed. Cell temperatures were maintained to within O.l”C. As described in Ref. (8) measurements made with the light polarised parallel to the cell director
-6 10 1
I
I
10
100 FrQCjUQnCy(Hz
1
Fig. 7. Measured noise spectra for a 12 km film of liquid crystal El in a glass cell li/ = 10’ pixel size a 70 pm. (a) 45” configuration (see Fig. 2). (b) Cell turned to put director parallel to incident polarisatlon. The dashed line (c) shows the theoretically predicted noise for the parallel configuration [Ref. (8)] using 5’, 0.13, k,, 8.7 x 10-12, k,, 4.6 x 10-12, k,, 1.23 x IO-“, An 0.192 (I = 6.33 nm).
An optically coupled thermal imager
123
agreed very well with the theory of twist modes in its dependence on pixel size, frequency. cell thickness t and analyser azimuth $. Changing the optical configuration to the one required in an imager (input polarisation at 45’ to the director) consistently gave values of noise higher than those predicted by the second order extension of the theory in Ref. (8) despite many experimental refinements. For ((/ = 10, the measured noise was only a factor of 3 lower than that for the parallel configuration. Figures 7-10 illustrate same experimental properties of fluctuation noise defined as (AZ,,/Z,). Its spectrum is l/f above a “knee” frequency of -20 Hz for El (Fig. 7) identical to that of the parallel configuration, given by equation (22); also identical is the dependence on cell thickness between 0.1 and 50 pm (approximately t ‘j2) and on pixel diameter a. For the smallest pixels optical aberrations limited the actual sampled area. The dependence of noise on analyser azimuth was qualitatively different from the “parallel” configuration, and varied as sin II/ rather than sin 214, (0 < $ < 90”); however as shown in Fig. 8 at the smallest values of $ a few degrees from extinction a constant noise value was measured; the extinction was also not perfect partly due to the time-averaged noise. The measured noise was largely independent of temperature, rising only by a factor of less than 1.5 as TN1 was approached. For II/ = 90”, removing the analyser does not reduce AZ/Z,,. The only mechanism which could then give rise to noise is scattering of light through a large angle, so that it is outside the collection aperture of the optics. Since the theory of Ref. (8) ruled out such effects in its formulation, it is not surprising that it is unable to explain the results. However, our observations do not appear to be wholly consistent with theories of wide angle scattering, as the dependence on wavelength observed was less than the L4 variation predicted.““’ In summary the measured noise in El or a similar cyanobiphenyl nematic at 20°C above 20 HZ is given empirically by:
ACms __ = &-If-l
Af
‘P
sin($
+ g)t
I:‘>,
(23)
T
where B =O.l and g =0.08 for El. It will be shown below that the magnitude of this fluctuation noise can be the main factor restricting the performance of an imager, but in the absence of a satisfactory theory to explain equation (23) it is difficult to predict changes in the nematic that could reduce the noise. However,
(c) Tmnsmitted
light
RMS Noise
(b) Parallel
configuration
iWrry X
I x t
t
X
(a)
X
45”configumtion
1:: -2
0
2
4
6
8
10 3
(degrees)
Fig. 8. Dependence of fluctuation noise U, at 70Hz on low values of the analyser azimuth $. (a) 45 configuration (Fig. 2). (b) Parallel configuration. Also shown in the intensity of transmitted light I.
124
R. G.
-6
10
HUMPHREYS and H. A. TARRY
,
I
1
I
I
10
100
1000
FrQqUQnCy
(Hz
)
Fig. 9. Measured noise spectra for IOpm glass cells containing nematic mixtures of PG296 and El illuminated in the 45’ configuration (Fig. 2). The lines represent (a) El (b) 24% PG296 in El (c) 44% PG296 in El (d) 60% PC3296 in El. $ = lo” (I = 70pm. Graph (e) shows the noise spectrum of the measuring apparatus.
t-l<
Diameter
( b)
Parallel
Of Fourier
configuration
p(anQ
apQrtUrQ
(mm)
Fig. IO. The effect of low-pass spatial filtering on fluctuation noise ~1,. Liquid E7 at 20 ‘C, film thickness 10 pm. pixel diameter a 70 grn, focal length of Fourier lens 100mm. The effect on the parallel configuration is also shown for comparison (b).
the noise measured in the parallel configuration is also described by equation (23) (with a higher B) for low values of II, and is accurately explained by the theory in Ref. (8). Assuming this link between the configurations is retained we anticipated from equation (22) that increasing the twist viscosity 7, should reduce the noise as filtered by the chopper. The use of polymer additives to increase y, had the desired effect of damping the fluctuations and reducing the noise; the knee .frequency was significantly reduced and values of B were those given in Table 1. In fact the noise was reduced by the same factor as that of the parallel
An optically
coupled
thermal
Table
imager
125
I
Percent 0 24
l.OxlO
’
2.8 x IO .'
44
1.0 x IO 2
60
35x10
3
configuration. The temperature sensitivity djdT (A/Z) was not significantly changed. Figure 9 shows a series of noise spectra for a range of polymer mixtures. A separate experiment using a thin cell verified that the response time of the most viscous films to a heat pulse was less than 1 ms, as might be expected for the essentially microscopic nature of the optical change. If the elastic constant kzz of the nematic could be increased a corresponding reduction of noise could be obtained by giving a greater fraction of energy to modes at frequencies well above those sampled by the chopper. The improvement would be linear in kz2, rather than a square root law as is the case with viscosity. We were unable to test this argument experimentally, as liquids with high k,? were not available. It has already been suggested that optical signal processing at the Fourier Transform plane could improve the imager performance. It was also found experimentally that an aperture in the FT plane significantly reduced measured fluctuation noise. Figure 10 shows that a factor of 2 reduction can be given by filtering out spatial frequencies a factor of 2 higher than the pixel frequency. This is again consistent with wide angle scattering as the noise mechanism. In the absence of a satisfactory theory of fluctuation noise our predictions of imager performance have been based on the experimental observations.
IMAGER
PERFORMANCE
The preceding sections have given sufficient information to allow the performance of an optically read imager to be estimated although it should be emphasised that the choice of materials and techniques is not necessarily the optimum. We shall consider a “standard” imager with the following characteristics Objective lens .fi2 70 Frame rate 2.5 Hz Array size 128 x 256; Read out light pulsed Read out wavelength
mm diameter 70 pm pixels once per field for 0.5 of the field time 0.63 pm
Equation (3) requires 4 to be a minimum. We choose $ to be 3” from extinction, because the contrast falls at lower $ (Fig. 8). Detailed study of the components of the imager allows us to estimate the following properties: Taking the maximum size of the TV chip to be about 1 cm, implies the use of pixels 50 pm square with a maximum well capacity of 1.3 x 10’ carriers; for the best performance we would need the received pedestal intensity / to nearly fill the wells, but some reduction of the average filling must be made to allow for the non-uniformity of I due to non-uniformity of cell thickness and temperature. For a well to be half-filled by an average pixel for $ = 3”, a non-uniformity in thickness or temperature giving $ = 4.2 will fill the well; the corresponding minimum of II/ = 1.8” will only fill the well by 18%. These limits imply that the thickness of the cell must be maintained uniform to better than 0.04 pm in 10 pm and its temperature to 0.02-C (for a responsivity of dy /dT = 5O’/‘C). With these assumptions, we can now calculate the predicted performance of an imager based on the liquid crystals we have studied. Figure 11 shows the contribution of the three noise sources (liquid crystal, photon and temperature fluctuation) and the signal that we wish to detect, plotted as functions of spatial frequency. The vertical scale is in terms of the temperature in the liquid crystal cell, and the horizontal axis covers the range of spatial frequencies detected with a 70pm
R. G. HUMPHREYSand H. A. TARRY
126
20
Signal
Photon Liquid _--_-_
.-.-.-.-.crystal
----
x zl I6
lo-
g
Temperature ________-_-_------_____
0
0
---we_-_,
I
1
I
I
I
I
1
2
3
4
5
6
Frequency
(cycles
Spatial
I mm
)
Fig. 11. Signal and noise as functions of spatial frequency for a 10 pm thick liquid crystal cell, with 2 pm thick pellicles, 70 pm pixels. The scene is viewed in f/2,chopped at 25 Hz and 70% of the power in the scene is reckoned as being transmitted by the lens, beam splitter, and enclosure windows and absorbed by the liquid. The encapsulation is evacuated and the cell is supported on 10 pm high pillars comprising 1% of the pixel area. The readout wavelength is taken to be 633 nm although the results would be very similar at another wavelength. The analyser is 3” away from extinction, and the 50 pm pixels of the TV chip are run at half full well on average. The liquid crystal is the highest viscosity mixture studied, assumed to have a responsivity ofSO”/“C as in Fig. 3. The overall mean power required in the readout light is 3 mW, and it is on for 10 ms in each 20 ms field. The vertical scale is in units of the temperature of the liquid crystal cell. For these parameters, 10-6K in the cell corresponds to 200 carriers in one pixel of the TV chip. The horizontal scale is in units of spatial frequency up to the maximum frequency faithfully sensed by an array with 70lm pixels. The signal is that corresponding to 1 K in the scene and the noise contributions are in comparable units.
pixel. We have not attempted to include the pixel to pixel correlation of the liquid crystal noise, which is expected to be negligible, so both liquid crystal noise and photon noise are independent of spatial frequency. The signal phase chosen optimises the signal at 4 cycles/mm, and the liquid crystal is the best material we have studied, i.e. the 60% polymer mixture. The result shows that with f /2 optics we have an imager NETD of 1.4 K at 0.5 cyclesimradian; reducing the f number to 1.4 and the pixel size to 50 pm reduces this to 1.O K. POTENTIAL
FOR
IMPROVEMENT
The noise shown in Fig. 11 has almost equal components of liquid crystal fluctuation noise and photon noise. Reduction of the NETD can therefore not be achieved by further reduction of fluctuation noise alone; and it is unlikely that the limitations of photon noise can easily be overcome. We therefore require a larger signal from a focal plane of similar dimensions, and this implies the use of a detector with a higher responsivity dZ/dT. In the case of the nematic liquid crystal a material with higher d/dT (An) is needed, while non-uniformity limitations do not allow An to be much higher. As discussed earlier other liquid crystal effects have the potential of giving higher responsivity at the cost of more severe problems of focal piane construction. We believe that of the many liquid crystal effects we have studied the variable birefringence nematic is unique in the lack of coupling
An optically
coupled
thermal
imager
127
between the signal mechanism (microscopic) and the dominant noise mechanism (macroscopic). We are unaware of any other class of materials in which such a high temperature sensitivity is associated with a broad temperature range over which it is observed; these characteristics ideally require a second order phase transition. If a solid with these properties were found, presumably the “liquid crystal” noise would be absent, and one constraint on system design would be eliminated. CONCLUSION
We have shown that an IR imager using optical coupling of its focal plane to a TV chip”‘) can give a useful imaging performance, with NET of 1.4 K at 0.5 cycles per radian. For comparison, described in the same way (also with f /2 optics) the pyroelectric vidicon has an NET of 5 K. None of the practical problems involved in constructing the imager is severe and all the components apart from the focal plane are readily obtainable; the focal plane itself could be made in large areas cheaply using developments of standard photolithography and plastic film processing techniques. Copyright 0 Controller
HMSO London
1987,
REFERENCES 1. C. Hilsum 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
and W. R. Harding, I&red Phys. 1, 67 (1961). J. L. Fergason, T. P. Vegl and M. Garbuny, U.S. Patent, 3 114836 (1963). Y. B. Andre, J. P. Chambaret, M. A. Franc0 and B. S. Prade, Appl. Opf. 18, 2607 (1979). W. Maier and A. Saune. 2. Naturforsch. 149. 882 (1959): Z. Naturforsch. 16a. 816 (1961).I M. Bradshaw (RSRE) Unpublished measurements.. ” ” F. Rondelez, W. Urbach and H. Hervet, Phys. Rev. Left. 41, 1058 (1978); I. C. Khoo and R. Normandin, IEEE J. quantum Electron. QE-21, 329 (1985); R. Vilanove, E. Guyon, C. Mitescu and P. Pieranski, J. Phys. 35, 153 (1974). B. R. Holeman, Infrared Phys. 12, 125 (1972). R. G. Humphreys, H. A. Tarry and M. Bradshaw, Liquid Crystals (To be published). E. Guyon, P. Pieranski and M. Boix, Left. appi. Engng Sci. 1, 19 (1973). M. I. Miraldi, L. Trossi, P. Taverna Valabrega and C. Oldano, II Nuouo Cimento 6OB, 165 (1980); D. Langevin and M. A. Bouchiat, J. Phys. Coil. Cl.. Suppl. 3, 197 (1975). C. T. Elliott, R. G. Humphreys and R. Watton, U.K. Patent Application No GB2 150 387A.