THERMOPHYSICAL

MEASUREMENTS

IMAGE CONVERTERS BASED ON LINEAR PYROELECTRIC DETECTOR ARRAYS M. D. Kladkevich, V. B. Samoilov, and L. V. Shchedrina

UDC 535.232.6.087.92

Pyroelectric radiation detectors are fast thermal detectors and represent the most general use of pyroelectric detectors at present; they operate at room temperature. They are widely used in image converters for the invisible spectral range to give visible conversion: in one-component detectors with two-dimensional scanning [i], in linear arrays with onedimensional scanning [2], in matrices without scanning [3], and in image converters containing temperature sensitive targets [4]. Linear arrays and matrices are the most promising image converters. Each element in a linear array on scanning by a mirror produces a column, and the entire linear array forms a line. No scanning is required with a matrix. Here a linear pyroelectric detector array is considered. The basic specifications for a multicomponent pyroelectric structure are high observing capacity in an element and high number of elements per unit area, with minimal coupling between elements and high filling factor, as well as identical elements, which should be easy to manufacture. A primary factor affecting the resolving power arises from the electrical and thermal coupling between the elements in the array, which is usually generated on a single crystal. One strives to increase the resolving power by increasing the number of elements per unit length and reducing the gaps between them, which increases the parasitic signals arising from the irradiation of adjacent parts. Reducing the gaps is accompanied firstly by increase in the capacitance between adjacent electrodes, which increases the signal division coefficient between the elements because of the capacitative coupling. Secondly, reducing the gap to a size comparable with the length of the temperature wave means that the heat flux heats not only the irradiated element but also adjacent ones because of the thermal coupling. It is therefore important to examine the effects of the electrical and thermal coupling on the resolving power. We begin with the thermal coupling. The heat-loss sources are firstly the radiation from each element and secondly the heat transfer from the irradiated element due to conduction through the faces. The latter is considered as transverse thermal conductance. Calculating the temperature response is complicated by t h e fact that the temperature is unevenly distributed in the transverse direction. To obtain high threshold sensitivity, the thickness t is made as small as possible. The best results at present are obtained with TGS crystals doped with L-e-alanine [5], but it is simpler to use lithium tantalate single crystals [6], which we employed here. At modulation frequencies below I00 Hz, the thickness of a sensing element is usually much less than the length IT of the temperature wave. In our case, t = 10-15 ~m, while IT = 150 ~m. This provides a uniform temperature distribution over the thickness, so the thermal processes can be calculated on the basis of the one-dimensional thermal conduction equation. Let the system be heated by a flux with intensity W 0 modulated at frequency ~. This corresponds to harmonic variation in the detector temperature: 8 - e imt. The incident flux is taken as spatially homogeneous and as uniformly irradiating the working area. Figure 1 shows the configuration. The number of detecting components was 32. The entire receiving area (width h = 2 mm, length 2L = 20 mm) is constituted by an alternation of two areas. The hatched parts in Fig. 1 are the electrodes, which form the sensitive elements. The width of a single electrode is 2d = 0.5 n~n. The second type of region consists of the gaps (width of an individual gap 2A = 0.i mm). The irradiated side was a single solid electrode coated with black. Transverse thermal diffusion transports heat between the elements and is responsible for the thermal coupling. The gap width is comparable with the thermal-diffusion distance and is the main factor governing the thermal coupling coefficient. Translated from Izmeritel'naya Tekhnika, No. 7, pp. 47-49, July, 1992.

836

0543-1972/92/3507-08365J12.50

9 1993 Plenum Publishing Corporation

Z

Fig. 1 We represent the system as a thin extended plate with thickness s and length 2L (Fig. i). The part -a ~ x ~ a is exposed to a heat flux with density Woe i~t. At the boundaries of the line, one assumes ideal heat transfer, and as the modulation frequency was 20 Hz, the array was heated uniformly throughout the thickness, so 8(z) = const, and 0 = e(x). To derive the spatially inhomogeneous distribution 8(x), one solves the thermal-conduction equation for a three-layer system:

aoi(x,t)/at=~2oa(x,t)lax2: ao~fx,t) a20~(x,t) Woe i~t at =~ Ox~ + pcl O03(x,t) at =~O20~(x't)lax~

(l)

with the boundary conditions

01(--oo,t)=O: s 0 t (--a,t)=O2(--a,t): ezra ,t')=O3(a ,t); aOl(x,t) ae2(x,t) [ . " Ox x--= = a--'-7----t~=-" ;

a0,tx t) I

aO,(x.t) I ~X

x:a

(2)

:

~

ax

x~a

In (i) and (2), the symbols are: K = K/pc the thermal diffusivity, K the thermal conductivity, and pc the heat capacity per unit volume. For lithium tantalate, < = 1.2.10 -6 m2/sec, 0c = 3.2"106 J/m3"K, and K = 3.85 W/m.K. The general solution to (i) is

O~(x,t)=Oi( x)e i~ . The coordinate-dependent

parts of the temperature

response are

]17 o

O1(x)= io~ocl eaXsh(ak); Wo O~(x)= io~cl

O:~fx)= ~

{l_e-akch(kx)}; eLkXsh(ak) '

(3) rl

in which k = /i--~K = (i + i)/IT; i T = /2K/(~pc) is the length of the temperature governs the thermal diffusion distance in the material.

wave, which

837

From the temperature response described by (3) for a three-layer system one can consider the thermal coupling. The thermal coupling coefficient between elements i and n is Kin=UinlUnn,

in which Uin is the thermal response of element i when element n is illuminated, is the signal arising at the illuminated element.

while Unn

In this case (Fig. i), the thermal coupling is described by

(4)

Kno=UnolUoo, n = 1 , 2 , 3 . . . . .

and is expressed as the ratio of the emf generated in element n Ulzo~ hy 2nb@d

c

~

(5)

%u.')~,

2nb--d

to that in the illuminated one Uoo= hy -~- [ d OJx)dx.

(6)

--d

Formulas (4)-(6) contain the pyroelectric coefficient ~ together with the capacitance of an element C and b = d + A. One calculates the temperature response of those elements from (5) and (6) via the expressions for the increases in temperature in the second and third parts of the three-layer system correspondingly from (3), from which we get the final expression for the thermal coupling coefficient of (4): ....

n~b

[

kd

__e_a k

I-'sh(ak).

(7)

This shows that the parasitic signals arising from adjacent illumination decrease exponentially as n increases, so the dependence of the thermal coupling coefficient on the gap width was examined, which is contained in b = d + A. However, importance here attaches not only to the negative exponential dependence of K n on A but also the relation between A and i T . Heating arises not only from the heat flux to the irradiated element but also from that to adjacent ones and give rise to the transverse thermal conductivity, which increases as the gap is reduced to a size comparable with the length of the temperature wave. This is the reason for the thermal coupling, which increases as A decreases. The theoretical and experimental results may be compared in detail on the basis of some simplifications. The lithium tantalate crystals had a temperature wavelength at the working frequency much less than the dimensions of an individual element, so we use the approximation ak > dk >> i, when (7) becomes Kn=eX(4dk--2e-(a-~}~] -I

(8)

in which ~ = (a + d - 2nb)k. Coefficient K n in (8) is complex. If synchronous detectors are used, the reference-voltage phase is that of the signal, and the total outputvoltage from an element will be dependent on the components of the parasitic signals in phase with the main signal and proportional to the real part of the coupling coefficient: ReKn=-~'e-X'(cosxl--sinxl), where

zl

= [d(2n

The modulus

of

1)

-

the

(9)

a + 2nA]/A T. coupling

coefficient

is

IKnl= 4V'2------7- e - ~ ' "

(10)

Consider the following situations. With complete illumination of the detecting area of an individual element, i.e., with a = d, the real part in (9) becomes

838

tKn],~

_

i~

a~

_

z

tO z

258

~0

200

I

20

tYg

] l# -t

liTO

R7 50

I I5" ,7

,,, 18

5

i

2oo

I09

Fig. 2

goo

t;, H z

Fig. 3 ~T

--%2 "

ReK.= S-d- e

<

'

"

~coz~2--sm%),

in which T= = [ 2 d ( n - i) + 2na]/a T. The modulus of the coupling coefficient k,

IK~I=4V---~7 e-~' is IKII

= 4.7"10 -2 when one considers adjacent elements;

for n = 2 we get IK=I = 6.1 '10-4.

Consider illumination of one element and half the gap, i.e., a = b = d + A. and (i0) become R e K n = "~~r e -

TS

Then (9)

(cosT3--sin%);

X, IK.I= 4 V f d

(n)

in w h i c h ~a = [ 2 d ( n - 1) + A(2n - 1 ) ] / A w. The (11) c o e f f i c i e n t can be e s t i m a t e d f o r l i t h i u m t a n t a l a t e n a t e d r e g i o n , w h i c h g i v e s a somewhat h i g h e r v a l u e . For e x a m p l e , c e n t e l e m e n t s and IK21 = 8 . 8 . 1 0 -4 f o r n = 2.

with the increased illumiIKxl = 6 . 8 " 1 0 -2 f o r a d j a -

One can e s t i m a t e t h e e f f e c t s from t h e e l e c t r i c a l c o u p l i n g s on t h e r e s o l v i n g power by c a l c u l a t i n g the c a p a c i t a n c e s between a d j a c e n t e l e m e n t s . We u s e t h e [7] r e s u l t s f o r two plates of unequal width on a dielectric layer. The electrical capacitance per unit length is obtained as C~=2q F ~

F'(qY

+(e2--q)

F1(ql)

PC(q,)

(12)

in which s and ~2 are the dielectric constants correspondingly of the surrounding medium and the pyroactive element, while F, F', Fl, and F I' are complete elliptic integrals with moduli q, q', ql, and q1', q= lr I~--(q' ) o-=d/ ( d4 A ) :

q1=Vl--(ql )==ft,--t~),'(q+t~);tt=(e ~---1)/(e ~ + 1 ) ; ~=,~.(2d+a)lt; ~ , - , , A / t . We use the corresponding expansions for the elliptic integrals with q2 << i and (qi')2 = 1 to reduce (12) to

This shows clearly how the capacitance between two adjacent elements is dependent on the gap width. The capacitance increases as the gap narrows, so the electrical coupling coefficient increases:

839

/fel= co

C* 2C'-f-C

d --[ 2 + ~ , ~ ]

-l. ,

in which C* = Chh is the capacitance between adjacent electrodes and C = s2dh/(2~s capacitance of one element.

is the

The electrical coupling coefficient between elements on a lithium tantalate single crystal does not exceed 1%, which is substantially less than the thermal coupling coefficient for realistic modulation frequencies. The couplings were measured by experiment as follows. The radiation flux was provided by an energy-calibrated lamp and was defined by a stop, being chopped by a disk modulator operating at 5-700 Hz. To provide illumination of an individual element, the stop was part of a mask used to deposit the elements. A lens system focused the beam on the element and provided equal dimensions for the stop and the image in the array plane. The electrical signals were measured with a Unipan type 237 tuned amplifier, which handled the synphase component of the signal corresponding to Re Kn, and the phase shift was recorded by a synchronous detector. The couplings distorted the amplitude distribution in the channels, so to recover t h e true picture one needs a complete set of coupling coefficients. We see from (7)-(11) that the coupling coefficients decrease rapidly (exponentially) away from the irradiated element. Figure 2 shows the modulus of the coupling coefficient (curve i) and the phase shift (curve 2) between the main and parasitic signals as functions of distance between the irradiated element (the ninth) and the others with a modulation frequency of 20 Hz. The numerical values of [Knl are similar to the calculated ones and decrease as n increases to 0.03%. The frequency dependence of K n reflects the large difference between these two coupling mechanisms (thermal and electrical). With thermal coupling, X T and correspondingly K n decrease as the modulation frequency rises. The electrical contribution to the coupling is determined only by the distribution of the signal between the capacitances and by the capacitance between components, being independent of the modulation frequency. Figure 3 shows frequency-dependence curves 1 and 2 for [KII and IK21. The thermal coupling mechanism predominates between adjacent elements up to 400 Hz. However, at the next element, the decline in the thermal waves is so great above a frequency of 50 Hz that the electrical coupling becomes predominant. LITERATURE CITED i,

2. 3. 4. 5. 6. 7.

840

V. K. Novik, N. D. Gavrilova, and N. B. Fel'dman, Pyroelectric Converters [in Russian], Soy. Radio, Moscow (1979). H. Blackburn, H. C. Wright, R. Eddington, and R. S. King, Radio Electron. Eng., 8, No. 12, 38 (1972). 0. V. Elfimov, L. S. Kremenchugskii, and S. K. Sklyarenko, Molecular Spectroscopy: Proceedings of the All-Union Spectroscopy Congress [in Russian], Minsk (1971), p. 90. R. M. Logan, Infrared Phys., 16, No. 1/2, 75 (1976). "Pyroelectric detector array (Spiricon)," Laser Focus., 14, No. 9, 75 (1978). C. B. Roundy, Infrared Phys., 19, No. 5, 507 (1979). Yu. Ya. lossel', E. S. Kochanov, and M. G. Strunskii, Capacitance Calculation [in Russian], Energoizdat, Leningrad (1981).