PHOTOMULTIPLIER SIGNAL SPECTRUM IN AN OPTICAL HETERODYNE SYSTEM

V. I. Vaitsel' and S. S. Khmelevtsov

Izvestiya VUZ. Fizika, Vol. 11, No. 6, pp. 87-88, 1968

UDC 586

The spectrum of the received signal in an optical heterodyne may be broadened by atmospheric turbulence, and allowance must be made for this in the design of distance ganges based on fringe counting, which may have an accuracy of the order of the wavelength.

On the other hand, optical heterodyne systems can be used to de- termine turbulence characteristics. The spatial-coherence function can [1, 2] be determined by a heterodyne method, and such experi- ments have been performed [8].

Here we consider measurement of the time-coherence function by a heterodyne method.

The spectral power density I(w) of the signal component is related to the autocorrelation function p(r) by a Fourier transformation:

oo ~-- (i) I(o,) = 2 p (r e d =,

o p (=) = < i ( t ) ~ ( t + ~) > - - ( t ( t ) ) ~ = ~ b-) - - ~ ( ~ ) . (2 )

Here i(t) is the photomultiplier current corresponding to the signal component at time t. Apart from a constant factor A, we can [1-8]

write i(t) as i (t) = A [ V (x, t) dS; in which V(x, t) is the complex S

amplitude for the field of the signal wave. The integration is carried over the surface S of the receiving aperture, which is taken as being a slit of length d whose width is much less than the wave correlation radius. Then the y(r) of (2) becomes

d d

( (, V(x, t) dx V*(x , t) dx (~) I

d d

2 2

We use the approximations

~ (r, O) 2 (0, ~), 2 ~ ( r ,~) ~- , ( 0 , % . ~ (r, 0) ~o

and put I < V ? I d = constant to get

1 -~ (~) ~ r (~) = 7 x

d

X 2 1-- e x p - - { a ~ [ l - - ~ , ( r , 0) G(0, z)] ~[1--

0

- : f (r, 0) ~ (0, el I } dr (a)

Here 7~(r , r ) and yxZ(r,r) are the correlation coefficients for the fluctu- at.ions in the phase and the logarithm of the amplitude at points in the aperture separated by a distance r at times separated by r , while the

a o~ ~are the variances of those quantities. Studies have been made [1-8] of I"(0) in relation to the dimen-

sions of the receiving aperture:

d r ,

r (o) = 2 i - 2,i x 0

2 ~ ~. [I 2 0 X e x p - - { % [ 1 - - ' ~ ( r , 0 ) l+ --7~(r, )]}dr.

it has been shown [4] that exp-{Ox 2 [1 - yxZ(r, 0)] + o~(r, 0)]} is the normalized spatial-coherence function for radiation that has passed through the atmosphere.

The atmospheric time-coherence function r d r ) = exp-{ox 2 [1 - - yxa ( r ) ] + @ [ 1 - y ~ ( r ) ] } can be de te rmined by experiment from the spectrum analyzer I(~o) via (1)-(8)i here T (~o) ~exp-{oa+ a ~ } mnstbe known from other measurements. If the turbulence is strong, i .e . ,

2 2 Ox,O~ >> 0, we have y(~o) ~ 0 and the time-coherence function is completely determined by the spectrum of the signal.

Fa(r) and F (r) coincide if d -+ 0. If d ~ r0 (radius of wave cor- relation), Fa(r) may be calculated from (8) via the measured F(r) , provided that the spatial correlation functions yx2(r, 0) and y~(r, 0).

REFERENCES

1. S. Gardner, IEEE,Int. Cony. Rec., 12, pt. 6, 1964. 2. D. L. Fried, TIIER, 55, no. 1, 1967.

t 8. Gotdstein, Miles, and Szabo, TIIER, 58, no. 9, 1888, 1965. 4. D. L. Fried, Journ. Opt. Soc. Am., 56, no. 10, 1966.

16 November 1967 Kuznetsov Siberian Pnysicotechnical Institute

EFFECTIVE CHARGE OF IONS IN WURTZITE ZINC SULFIDE

r A. Zhdanov and L. A. Brysneva

izvestiya VUZ. Fizika, Vol. 11, no. 6, pp. 88-89, 1968

UDC 689.01

In [1] we attempted the determination of the effective charge of ions in wurtzite zinc sulfide by constructing the diagram for the cal- culated elastic modulus closest to the diagram constructed from ex- perimental values. For the experimental elastic moduli we used the following values: cll = 11.89; c12 = 5.012; qa = 2.711; eaa = 12.70; c44 = 2.907, in units of 1011 dyn/cm 2, which we converted from [2];

s~l = 1.112 ~ 0.3~o s[2= - 0 . 4 8 6 , 4 % , G -- -0 .14~ 15Vo, s~ = 0.847 = 0.4fro, S~g = 8.44 • 0.7%, in units of 10 -u cmZ/dyn. For the mag-

5 2

nitude of the effective charge on the ions in wurtzite zinc sulfide we obtained e = 1.1%.

Use of experimental values for the elastic moduli which were ob- tained in [8] and which, as shown in [4], were more accurate, did not change our conclusion as to the magnitude of the effective charge

in wurtaite zinc sulfide (e = 1.1%), but the agreement between the diagrams of the calculated values and the experimental values became closer. In Fig. 1 the dashed line represents the calculated elastic