PHOTOELECTRO-OPTICAL AMPLIFIER

B. P. Kozyrev*)

1. INTRODUCTION

In a number of problems—for example, in work with low-inertia thermal indicators of radiation, thermoelements and bolometers—there arises a very acute need for a method of measuring very small emfs, of the order of several nanovolts \((10^{-9}\ \mathrm{V})\), and sometimes even fractions of a nanovolt. Such emf values cannot be registered directly either with the aid of vacuum-tube amplifiers or by means of a galvanometer, for in the cathode tube the noise level is much greater than several nanovolts and is often close to microvolts, while a good galvanometer, although it has a fluctuation threshold even smaller than \(10^{-9}\ \mathrm{V}\), nevertheless, because of ground vibrations and imperfections of the reading devices, permits in practice the measurement of only \(10^{-7}\ \mathrm{V}\), and in the extreme case \(3 \cdot 10^{-8}\ \mathrm{V}\) (system \(Z_c\)). Sometimes, however, the introduction into the input circuit of a tube amplifier of a step-up transformer, with the obligatory condition of interrupting the thermocurrent or modulating the radiation, can considerably improve the possibilities of measuring small emfs by the method of cathode amplification, bringing the limit of measurable emfs at times to \(10^{-9}\ \mathrm{V}\)¹. Nevertheless, the author² has shown the significant advantages of the galvanometric method of detecting extremely small emfs, based on the use, instead of a reading scale, of one or two photoelements. Such devices, often unsuccessfully called by the too general term “photo-relay,” are intended for registering microdisplacements of a shadow over the surface of a photoelement and have long since, beginning in 1926, been proposed by various investigators (more than 60 papers are analyzed in the above-mentioned work²).

*) This article is a brief exposition of works for which the author was awarded the Stalin Prize by a decree of the Council of Ministers (“Pravda,” March 4, 1950). — Ed.

At a cursory examination of such a scheme for recording small earthquakes, based on combining a galvanometer with a photocell, the whole apparatus appears extremely simple, and it has even sometimes been stated² that a photorelay can be made within one hour. Indeed, photoelectric amplifiers (PEA), as such photorelays are more properly called, are quite uncomplicated (although, for that matter, they cannot be made in one hour) and have such obvious advantages in sensitivity over cathode amplification that at first it seems simply incomprehensible why this method has not yet become widespread, despite being more than twenty years old.

The principal reason for the ineffectiveness of all work on PEA carried out up to the present time is the sharp dependence of the operation of the PEA circuit on the influence of ground vibrations. A certain, sometimes very considerable, instability of the zero position of the galvanometer is well known; it often changes continuously by monotonic drifting to one side or, still more unpleasantly, by small irregular jumps. The complete futility of using any PEA for recording signal displacements of the shadow boundary by hundredths or thousandths of a millimeter is entirely obvious if the displacements due to disturbances caused by ground vibrations are visible to the naked eye.

Only by protecting the galvanometer from ground effects through the use of a damping device, usually consisting of a suspended system with springs or rubber², can a sufficiently stable position of the galvanometer zero reading be obtained. In this case, however, the entire PEA installation for the most part usually acquires an extremely cumbersome, overly laboratory-like, and completely nonportable form. The author’s experiments, carried out over a number of years with PEA of various designs and with all sorts of shock absorbers, led to the conclusion that ordinary galvanometers with a moving frame mounted on a ribbon or wire suspension cannot produce a good effect and, at best, are suitable for realizing a bulky long-period device with an insufficiently stable zero and consequently not very sensitive. It became entirely clear that only a galvanometer having a well-balanced frame on taut suspensions can be used for an effective PEA, and that only after the development of special galvanometric designs can one create a photoelectric amplifier with good parameters and a technically finished design. Of decisive importance in the author’s work on PEA was the introduction of the principle of overcalming the input galvanometer and the rejection of operation in the critical regime.

2. THE PRINCIPLE OF OVERDAMPING THE INPUT SHORT-PERIOD GALVANOMETER OF THE PEA CIRCUIT AND ELIMINATION OF THE INFLUENCE OF GROUND OSCILLATIONS

It is known from galvanometry that the angle \(\theta\) of rotation of the movable frame is related to the dimensionless variable \(\tau\) by the following equation:

\[ \frac{d^{2}\theta}{d\tau^{2}}+2\alpha\frac{d\theta}{d\tau}+\theta=A\cdot \sin(\varkappa\tau+\delta), \tag{1} \]

where

\[ \varkappa=\frac{\omega_{1}}{\omega_{0}} \quad\text{and}\quad \tau=\omega_{0}t=\frac{2\pi}{t_{0}}\cdot t, \]

with \(\omega_{0}\) and \(\omega_{1}\) representing, respectively, the angular frequencies of the natural oscillations of the frame and of the alternating current flowing through it, and \(\alpha\) the damping coefficient; the quantity \(A\) is proportional to the amplitude value of the frame current. The solutions of equation (1) for various values of \(\alpha\) have the form:

\[ \theta=\frac{A}{N}\cdot \sin(\varkappa\tau+\delta+\chi)+ \begin{cases} c\cdot e^{-\alpha\tau}\cdot \operatorname{sh}(\beta\tau+\varphi), & \alpha>1,\\ (a+b\tau)\cdot e^{-\tau}, & \alpha=1,\\ c\cdot e^{-\alpha\tau}\cdot \sin(\varepsilon\tau+\varphi), & \alpha<1, \end{cases} \tag{2} \]

where

\[ \varepsilon=\sqrt{1-\alpha^{2}};\qquad \beta=\sqrt{\alpha^{2}-1} \]

and the constants \(c,\ \varphi,\ a,\ b\) are determined from the initial data.

Since the exponential term entering into the obtained expressions rapidly decays, it may be asserted that, for sufficiently large \(t\), the amplitude value of the forced oscillations of the frame is \(N\) times smaller than the quantity \(A\), with the resonance factor

\[ \frac{1}{N}=\frac{1}{\sqrt{(1-\varkappa^{2})^{2}+4\alpha^{2}\varkappa^{2}}}. \]

A different result is obtained when the movable system of the galvanometer is acted upon not by alternating currents, but by ground oscillations. Assuming the ground displacement to be harmonically varying as a function of \(\tau\):

\[ x=f(\tau)=C_{0}\cdot \sin(\varkappa\tau+\delta), \]

we obtain for the acceleration characterizing the disturbing force the expression:

\[ \frac{d^{2}x}{d\tau^{2}}=C_{0}\cdot \varkappa^{2}\cdot \sin(\varkappa\tau+\delta), \]

after which the basic equation for this case will have the following form:

\[ \frac{d^{2}\varphi}{d\tau^{2}}+2\alpha\frac{d\varphi}{d\tau}+\varphi=C\cdot \varkappa^{2}\cdot \sin(\varkappa\tau+\delta), \]

i.e., it will differ from equation (1) by the presence of the factor \(x^2\) on the right-hand side. Therefore the resonance factor will now be equal to

\[ \frac{1}{N'}=\frac{x^2}{N}=\frac{x^2}{\sqrt{(1-x^2)^2+4a^2x^2}} . \]

Figure 1 shows the dependences of the quantities \(\frac{1}{N}\) and \(\frac{x^2}{N}\) as functions of the values of \(x\), i.e., it gives a graphical interpretation of the behavior of the galvanometer frame under the action of alternating current or ground oscillations of different frequencies, with different curves corresponding to different damping coefficients. Fig. 1, a illustrates the well-known ability of the galvanometer to transmit, without distortion, only low-frequency oscillations \((x \ll 1)\), and shows a sharp “drop” in amplitude values at elevated \(x\) (especially if, in addition, \(a \gg 1\)). Of greater interest is Fig. 1, b, which is the mirror image of Fig. 1, a with respect to the value \(x=1\) and indicates the absence of deflections of the frame relative to the galvanometer case (the ground) at small values of \(x\), and equally almost small deflections at large \(x\), provided that \(a \gg 1\). Thus, the frame will not be displaced appreciably relative to the galvanometer case either at low \((x<1)\) or at elevated \((x>1)\) relative frequencies of ground oscillations, if this frame is strongly overdamped \((a \gg 1)\), “overcalmed.” Only at very large values of \(x\) does an increase in the damping coefficient give no effect, and the frame does not manage to follow the oscillations of the galvanometer case \((N' \approx 1)\), i.e., it gives displacements. However, under ordinary operating conditions such extreme components in the frequency spectrum of ground oscillations are almost never present.

As we see, the curves of Fig. 1, b and the reasoning given above open up a new and simple method for stabilizing the zero position of the input galvanometer of the FEU by abandoning the classical recommendations of the critical regime \((a=1)\) and passing to overdamping, i.e., to \(a \gg 1\). The main arguments in defense of the critical regime are the desire to obtain the highest possible voltage sensitivity for the given galvanometer and the least expenditure of time for setting the reading; moreover, upon more exact consideration it turns out that the fastest reading is obtained at \(a=0.83\), with some loss in sensitivity (10% relative to the critical regime).

If we now turn to the case \(a>1\), i.e., use the corresponding form of equation (2) and prescribe the usual initial data:

\[ \theta=0 \text{ at } \tau=0, \]

Fig. 11. Dependence of the resonance factor on the ratio of angular frequencies \(\chi\) under the action of current (a) and ground vibrations (b).

then, after transformations, we obtain:

\[ \theta=\theta_{\infty}\left[1-\frac{e^{-\alpha \tau}}{\beta}\cdot \operatorname{sh}(\beta \tau+\mu)\right], \tag{3} \]

where

\[ \operatorname{th}\mu=\frac{\beta}{\alpha}=\frac{\sqrt{\alpha^{2}-1}}{\alpha} \quad \text{and} \quad \operatorname{sh}\mu=\sqrt{\alpha^{2}-1}=\beta . \]

Assuming the accuracy of setting the reading to be, for example, \(1\%\), i.e. taking

\[ \frac{\theta}{\theta_{\infty}}=0.99, \]

we have

\[ e^{-\alpha\tau}\cdot \operatorname{sh}(\beta\tau+\mu)=0.01\beta \]

or

\[ e^{\mu-(\alpha-\beta)\tau}-e^{-[\mu+(\alpha+\beta)\tau]}=0.02\beta . \tag{4} \]

An exact computation of \(\tau\) from the transcendental equation (4) is impossible; an approximate value can be obtained by noting that for \(\alpha \gg 1\) one always has:

\[ e^{\mu-(\alpha-\beta)\tau}\gg e^{-[\mu+(\alpha+\beta)\tau]}, \]

since

\[ \beta=\sqrt{\alpha^{2}-1}\simeq \alpha \]

and, since

\[ \operatorname{th}\mu=\frac{\beta}{\alpha}\simeq 1, \]

then

\[ \mu \gg 1. \]

If we further take into account that \(\tau=\omega_{0}t=\frac{2\pi}{t_{0}}\cdot t\) for a short-period galvanometer will already, even for small \(t\), considerably exceed 1, then instead of equation (4) one may write

\[ e^{\mu-(\alpha-\beta)\tau}=0.02\beta, \]

whence

\[ \tau=\frac{\mu-\ln 0.02\beta}{\alpha-\beta}=\frac{2\pi}{t_{0}}\cdot t. \]

or

\[ \frac{t}{t_{0}}=\frac{1}{2\pi}\cdot \frac{\mu-\ln 0.02\beta}{\alpha-\beta}. \tag{5} \]

The relation obtained indicates how many times the time for setting the reading with an accuracy up to \(1\%\) exceeds the period of free oscillations.

From the known condition for the critical mode of operation of a galvanometer with a given moving coil,

\[ \frac{(HnS)^{2}}{2R_{k}\cdot 10^{9}\sqrt{KD}}=1, \tag{6} \]

PHOTOELECTROOPTICAL AMPLIFIER

where \(n\) is the number of turns, \(S\) is the area, and \(K\) is the moment of inertia of the frame; \(D\) is the specific opposing moment; \(H\) is the magnetic-field strength; and \(R_k\) is the critical resistance of the galvanometer circuit. It is evident that an over-damped state can be obtained in three ways: by increasing \(H\), by decreasing \(D\), and by decreasing \(R_k\). Assuming that, for a short-period galvanometer system, the magnetic-field strength \(H\) already has the limiting value attainable in practice, so that any further increase is impossible, and, moreover, rejecting a decrease of \(D\) because of the undesirability of impairing the ballistic properties of the moving system and the stiffness of the suspensions, which is so necessary for precision balancing, one must recognize as acceptable only the last way of over-damping the galvanometer—lowering the resistance \(R\) of the galvanometer circuit.

Since the damping coefficient \(\alpha\) is related to the design data of the galvanometer by the relation

\[ \alpha=\frac{(HnS)^2}{2R\cdot 10^9 \sqrt{KD}}, \]

then, recalling equality (6), we obtain

\[ R=\frac{R_k}{\alpha}, \]

i.e., in order to pass from the critical regime to a state with coefficient \(\alpha>1\), it is necessary to reduce the resistance of the galvanometer circuit by a factor of \(\alpha\). For various values of \(\alpha\), i.e., for different over-damped states, the ratios \(\dfrac{t}{t_0}\) can be calculated from equation (5). Taking the accuracy of setting the reading to be \(1\%\), \(5\%\), and \(10\%\), from the corresponding approximate equations analogous to (5), the values of \(\dfrac{t}{t_0}\) presented in Table 1 were calculated.

Table 1

From consideration of the data in Table 1 one may draw a very approximate, but practically useful, conclusion that the settling time of the reading to an accuracy of up to 5% exceeds the period \(t_0\) by approximately as many times as the resistance of the entire circuit is less than the critical resistance \(R_{\mathrm{k}}\). This circumstance immediately explains why the over-damped operating regime of a galvanometer is usually ignored—the reason for this is the inevitable slowness of action for ordinary galvanometers. Indeed, if, for example, one takes an MZG galvanometer having \(t_0 = 11\) sec.

\[ \left(R_g = 6\ \text{ohms};\ R_{\mathrm{k\ external}} = 6\ \text{ohms};\ S_{v\,\mathrm{cr}} = 4\ \frac{\text{mm}}{\text{m}\cdot\mu\text{A}}\right) \]

and overdamps it approximately twofold by closing it through \(1\ \text{ohm}\), then the time \(t_{0.95}\) for the reading to settle to within 5% will be about 22 sec., i.e. too large. In general, the majority of modern sensitive galvanometers have a frame on a suspension, and not on stretched fibers, and possess too large a period of free oscillations and, as was already noted above, an oscillating zero position. It is quite evident that practical use of the principle of overdamping for protecting the galvanometer frame from the action of ground interference is possible only for sufficiently short-period designs, in which, after an \(\alpha\)-fold reduction of the circuit resistance relative to \(R_{\mathrm{k}}\), the settling time of the reading (5%) \(\alpha t_0\) will not be too large. Since such galvanometer systems, suitable for the photoelectro-optical installations considered below, practically do not exist, the author carried out a special development of short-period, highly sensitive, and very stable galvanometers, which ensured the achievement of high efficiency in the FEOU.

Although, as is known, when the period \(t_0\) is shortened the fluctuation threshold increases, nevertheless it still proves to be considerably smaller than the interference inherent in the cathode tube and the inevitable thermal noise in the load resistance of the grid circuit. If, for example, \(R = 10^5\ \text{ohms}\), \(\Delta f = 5\ \text{cps}\), then even for such a comparatively narrow-band amplifier we obtain:

\[ U_{\mathrm{fl.}} = \sqrt{4KTR\Delta f} = 1.3\cdot 10^{-10}\sqrt{R\Delta f} \approx 1\cdot 10^{-7}\ \text{volts}. \]

According to Ising’s formula\(^4\),

\[ I_{\mathrm{fl.}} = \frac{1.12\cdot 10^{-10}}{\sqrt{\alpha t_0 R}}\ \text{amperes} \]

or

\[ U_{\mathrm{fl.}} = I_{\mathrm{fl.}}\cdot R = 1.12\cdot 10^{-10}\sqrt{\frac{R}{\alpha t_0}}, \]

after which, for \(R=R_t+R_g=4+1.4=5.4\) ohms,

\[ R_k=10.4\ \text{ohms};\quad t_0=0.13\ \text{sec};\quad \text{and}\quad \alpha=\frac{10.4}{5.4}\simeq 2 \]

we obtain

\[ U_{\mathrm{fl.}}=1.12\cdot 10^{-10}\sqrt{\frac{5.4}{2\cdot 0.15}} =4.7\cdot 10^{-10}\ \text{volts}. \]

It is useful to note that, as a result of decreasing the resistance of the galvanometer circuit by overdamping it and lengthening the time spent on the reading, the fluctuation threshold of voltages is decreased by a factor \(\alpha\) in comparison with \(U_{\mathrm{fl.}}\) corresponding to the same galvanometer, but operating in the critical regime.

There is, however, one substantial drawback in the method developed above for protecting the circuit of the photoelectric optical amplifier (FEOU) from ground disturbances by overdamping the input galvanometer: the difficulty of varying the resistance of the radiation indicator (thermoelement, bolometer) feeding this galvanometer; replacing one thermoelement by another having a different resistance will be accompanied by a change in the degree of overdamping, and hence also in the settling time of the reading. A transition, for example, to a very low-resistance thermoelement may extremely slow the action of the entire apparatus. To eliminate this defect, one may propose the method of a magnetic shunt—not implemented, however, in the experiments described below, but commonly used for this purpose; it is quite obvious that, when working with different thermoelements, in order to keep the damping coefficient and the settling time of the reading unchanged, it will be necessary to vary \(R_k\) by means of the magnetic shunt in such a way that the ratio

\[ \frac{R_k}{R_t+R_g} \]

in all cases remains unchanged and equal to the chosen value of \(\alpha\).

3. CALCULATION OF A TORSION AND TRANSVERSAL PHOTOELECTRIC OPTICAL AMPLIFIER

Although, as has already been indicated above, there exist more than sixty works dealing specifically with the investigation and application of various circuits of photoelectric optical amplifiers, a complete analysis of these circuits and a sufficiently accurate calculation were first carried out by the author\(^{2}\); the overwhelming majority of the above-mentioned studies usually contain a description of some experimental setup and of the results obtained with it. Such an empirical approach to the FEOU did not reveal a clear picture of the influence of the individual factors and gave effects determined by the parameters of the random parts of which the FEOU consisted.

From the optical point of view it is necessary to distinguish two basic types of photoelectric-optical amplifiers (FEOU):

1) torsional, based on the microdisplacement of the shadow boundary over the surface of the photocell under the influence of the rotation of a mirror reflecting the light flux onto the photocell (FE);

2) transverse, based on the variation of the light flux directed onto the photocell by intercepting this flux with some moving member, for example the pointer of a galvanometer.

In Fig. 2 the basic arrangement of the parts characteristic of a torsional FEOU is shown schematically. The condenser \(K\) projects onto the galvanometer mirror \(Z\) the image of the lamp filament \(L\); the objective \(O\) forms on the surface of the photocell an image of the grating diaphragm of the condenser. Since in front of the photocell there is fixed a stationary grating, geometrically exactly the same as the image of the condenser grating, but displaced in such a way that the transition boundaries from light to shadow fall at the positions of the slits in this grating, then upon the slightest rotation of the mirror \(Z\), and consequently upon displacement of the light–shadow boundaries, the current in the photocell circuit will change.

Fig. 2. Optical scheme of a torsional FEOU.

If it is assumed that the condenser and the objective are thin corrected lenses which cause no loss of light flux,

and if the luminous intensity of the lamp is taken to be equal to \(I\), then the illumination of the surface of the photoelement will be equal to:

\[ E'_1=E_1\cdot\left(\frac{r_0}{r}\right)^2 =\frac{I_1\cdot 10^4}{(X+f_1)^2}\cdot\left(\frac{r_0}{r}\right)^2 =\frac{I_1\cdot 10^4}{f_1^2(1+\beta_{\mathrm{k}})^2}\cdot\left(\frac{\beta_{\mathrm{k}}}{\beta_0}\right)^2, \tag{7} \]

or

\[ f_1+X=f_1\left(1+\frac{X}{f_1}\right) =f_1\left(1+\frac{1}{\beta_{\mathrm{k}}}\right) =\frac{f_1}{\beta_{\mathrm{k}}}(1+\beta_{\mathrm{k}}), \]

\[ \frac{r_0}{r}=\frac{1}{\beta_0}, \]

where \(\beta_{\mathrm{k}}\) and \(\beta_0\) are the linear magnifications given respectively by the condenser and the objective.

If the variation of the current intensity in the circuit of the input galvanometer \(G_{\mathrm{I}}\), whose mirror actuates the PEOA, is denoted by \(\Delta i_1\), and the change in current intensity in the circuit of the photoelement, into which the second (output) galvanometer \(G_{\mathrm{II}}\) is connected, is taken to be equal to \(\Delta i_2\), then one may write:

\[ \Delta i_2=\mu_1\cdot \Delta F_1=\mu_1\cdot 10^{-4}\cdot E'_1\cdot L_1\cdot \Delta x_1, \tag{8} \]

where \(\mu_1\) is the sensitivity of the photoelement in \(\dfrac{a}{\text{lm}}\); \(\Delta F_1\) is the change in the luminous flux falling on the photoelement, caused by displacement of the image of the condenser grating; \(L_1\) is the total length of all portions of the light–shadow boundary on the surface (the total length of the active apertures of the grating); \(\Delta x_1\) is the displacement of the image of the condenser grating over the surface of the photoelement, expressed in cm.

Denoting the sensitivities of \(G_{\mathrm{I}}\) and \(G_{\mathrm{II}}\), respectively, by \(S_{i1}\) and \(S_{i2}\), and assuming them, as is generally customary, to be expressed in

\[ \frac{\text{mm}}{\text{m}\cdot\mu\text{a}}, \]

we may write:

\[ \Delta x_1=\frac{S_{i1}\cdot 10^5\cdot \Delta i_1}{\dfrac{100}{l_1}} =\frac{S_{i1}\cdot 10^5\cdot \Delta i_1}{K_1}, \tag{9} \]

where \(l_1\) is the distance from the mirror of \(G_{\mathrm{I}}\) to the photoelement in the PEOA arrangement, i.e., according to Fig. 2, \(l_1=f_2+x'\).

After this, from relations (7), (8), (9) we obtain

\[ \frac{\Delta i_2}{\Delta i_1} =10^5\,\frac{I_1\mu_1L_1}{f_1^2(1+\beta_{\mathrm{k}})^3} \cdot\left(\frac{\beta_{\mathrm{k}}}{\beta_0}\right)^2\cdot \frac{S_{i1}}{K_1}. \tag{10} \]

But since

\[ f_2+x'=\beta_0(f_1+X') =\beta_0\left(f_1+\frac{f_1^2}{X}\right) =\beta_0\cdot f_1(1+\beta_{\mathrm{k}}), \]

then instead of (10) we have

\[ \frac{\Delta i_2}{\Delta i_1} =10^3\,\frac{I_1\cdot\mu_1\cdot L_1\cdot S_{i1}}{f_1(1+\beta_{\mathrm{k}})} \cdot\frac{\beta_{\mathrm{k}}^2}{\beta_0}. \tag{11} \]

The last formula indicates the advisability of using a short-focus condenser (small \(f_1\)) and obtaining from it the greatest possible linear magnification \(\beta_k\); however, because of the usually small dimensions of the mirror \(G_1\), the latter circumstance cannot be made use of, since a greatly enlarged image of the lamp filament (Fig. 2) cannot be accommodated on the area of this mirror.

In the case when, in practice, the illumination of the photocell \(E'_1\) is known, a more convenient formula is one derived from equalities (8) and (9), and also evident directly from Fig. 2:

\[ \frac{\Delta i_2}{\Delta i_1} = 10 \cdot \mu_1 \cdot E'_1 \cdot L_1 \cdot \frac{S_{i1}}{K_1}. \tag{12} \]

Usually, in reality, because of the small dimensions of the mirror \(G_1\) and for geometrical reasons, one has to take \(\beta_k=1\) and \(\beta_0=1\). Then

\[ l_1=f_2+x'=\beta_0 f_1(1+\beta_k)=2f_1 \]

and relation (11) takes the form:

\[ \frac{\Delta i_2}{\Delta i_1} = 10^3 \frac{\mu_1 I_1 L_1 S_{i1}}{2f_1}. \tag{13} \]

Instead of comparing the variations of the currents \(\Delta i_2\) and \(\Delta i_1\), one may compare with one another the corresponding linear deflections \(\Delta D_2\) and \(\Delta D_1\) on the scales of the galvanometers \(G_{\mathrm{II}}\) and \(G_{\mathrm{I}}\), reduced to one distance, remembering that

\[ \Delta D_2=\frac{S_{i2}\cdot 10^5 \cdot \Delta i_2}{K_2}; \qquad \Delta D_1=\frac{S_{i1}\cdot 10^5 \cdot \Delta i_1}{K_2}. \]

Then, according to (13) and (12),

\[ \frac{\Delta D_2}{\Delta D_1} = 10^3 \frac{\mu_1 I_1 L_1 S_{i1}}{2f_1}, \]

\[ \frac{\Delta D_2}{\Delta D_1} = 10 \cdot \mu_1 \cdot E'_1 \cdot L_1 \cdot \frac{S_{i2}}{K_1}. \tag{14} \]

The scheme of a transverse or transversal PhEOU, in general outline, is shown in Fig. 3: an incandescent filament of diameter \(2\rho_0\) (perpendicular to the drawing) is projected by the condenser \(K\) onto the plane in which the movable shielding index \(E\) of the galvanometer \(G_{\mathrm{I}}\) is placed, in turn projected by the objective \(O\) onto the photocell \(FE\). If we again assume that the illumination \(E'_1\) of the photocell is known from experiment (although it may also be calculated), then, analogously to the preceding, we obtain:

\[ \Delta i_2 = \mu_1 \cdot \Delta F_1 = \mu_1 \cdot 10^{-4} \cdot E'_1 \cdot 2r_1 \frac{S_{i1}\cdot 10^5 \cdot \Delta i_1}{K_1} = \]

\[ = 10\mu_1 E'_1 \cdot 2r_1 \frac{S_{i1}}{K_1}\cdot \Delta i_1, \]

whence

\[ \frac{\Delta i_2}{\Delta i_1} =10\mu_1 E'_1 2r_1\cdot \frac{S_{i1}}{K_1}, \qquad \frac{\Delta D_2}{\Delta D_1} =10\mu_1 E'_1\cdot 2r_1\cdot \frac{S_{i3}}{K_1}. \tag{15} \]

Since usually \(L_1 \gg 2r_1\), where \(2r_1\) denotes the diameter of the photocell, the torsion PEOA, other conditions being equal, is more effective than the transverse one.

Fig. 3. Optical scheme of a transverse PEOA.

It is quite obvious that schemes of a two- and three-stage PEOA may prove expedient, i.e., such devices in which the light pointer \(\Gamma_{\mathrm{II}}\), in the form of an image of a raster, falls not on a scale but on a second photocell, then the pointer \(\Gamma_{\mathrm{III}}\) on a third photocell, and so on.

The formulas for the current amplification coefficient \(\dfrac{\Delta i_3}{\Delta i_1}\) and the linear amplification coefficient \(\dfrac{\Delta D_3}{\Delta D_1}\) for a two-stage PEOA may be written, proceeding from (12), (13), (14), and (15), in the following way:

\[ \left. \begin{aligned} \frac{\Delta i_3}{\Delta i_1} &=10^2\mu_1\mu_2 E'_1E'_2 L'_1L'_2\, \frac{S_{i1}S_{i2}}{K_1K_2}; \\[0.8em] \frac{\Delta i_3}{\Delta i_1} &=10^6\,\frac{\mu_1\mu_2 I_1I_2L_1L_2S_{i1}S_{i2}}{4f_1^2}; \\[0.8em] \frac{\Delta i_3}{\Delta i_1} &=10^2\mu_1\mu_2 E'_1E'_2\,2r_1\,2r_2\, \frac{S_{i1}S_{i2}}{K_1K_2}; \\[0.8em] \frac{\Delta D_3}{\Delta D_1} &=10^2\mu_1\mu_2 E'_1E'_2L_1L_2\, \frac{S_{i2}S_{i3}}{K_1K_2}; \\[0.8em] \frac{\Delta D_3}{\Delta D_1} &=10^6\,\frac{\mu_1\mu_2 I_1I_2L_1L_2S_{i2}S_{i3}}{4f_1^2}; \\[0.8em] \frac{\Delta D_3}{\Delta D_1} &=10^2\mu_1\mu_2 E'_1E'_2\,2r_1\,2r_2\, \frac{S_{i2}S_{i3}}{K_1K_2}. \end{aligned} \right\} \tag{16} \]

For a three-stage FEOU, after introducing simplifying notation, the formulas take the following form:

Torsional type:

\[ \left. \begin{aligned} \frac{\Delta i_4}{\Delta i_1} &= 10^3 \prod_{m=1}^{m=3} \mu_m E'_m L_m \frac{S_{1m}}{K_m};\\ \frac{\Delta i_4}{\Delta i_1} &= 10^9 \prod_{m=1}^{m=3} \frac{\mu_m l_m L_m S_{1m}}{8 f_1^3};\\ \frac{\Delta D_4}{\Delta D_1} &= 10^3 \prod_{m=1}^{m=3} \mu_m E'_m L_m \frac{S_{12}S_{13}S_{14}}{K_m};\\ \frac{\Delta D_4}{\Delta D_1} &= 10^9 \prod_{m=1}^{m=3} \frac{\mu_m l_m L_m S_{12}S_{13}S_{14}}{8 f_1^3}. \end{aligned} \right\} \tag{17} \]

Transversal type:

\[ \left. \begin{aligned} \frac{\Delta i_4}{\Delta i_1} &= 10^3 \prod_{m=1}^{m=3} \mu_m E'_m 2 r_m \frac{S_{1m}}{K_m};\\ \frac{\Delta D_4}{\Delta D_1} &= 10^3 \prod_{m=1}^{m=3} \mu_m E'_m 2 r_m \frac{S_{12}S_{13}S_{14}}{K_m}. \end{aligned} \right. \]

It is quite clear that the totality of formulas (16) and (17) makes it possible, in the most varied cases, to estimate the degree of effectiveness of an FEOU, proceeding from the obvious proposition that the ratios \(\frac{\Delta D_3}{\Delta D_1}\), \(\frac{\Delta D_8}{\Delta D_1}\), etc., i.e. the linear amplifications, must always considerably exceed unity; the values of the current gains \(\frac{\Delta i_2}{\Delta i_1}\), \(\frac{\Delta i_3}{\Delta i_1}\), etc., generally speaking, must also be greater than unity, but in a multistage FEOU, in the first stage there may also be a departure from this rule, and it is sometimes permissible to have

\[ \frac{\Delta i_2}{\Delta i_1} < 1, \]

provided only that the subsequent stages compensate for the loss in current gain in the first stage. For example, one may take a very fast low-resistance and comparatively coarse galvanometer \(G_{\mathrm{I}}\), having a small \(S_{i1}\) and therefore leading to

\[ \frac{\Delta i_2}{\Delta i_1} < 1, \]

but introducing us into a comparatively high-resistance photoelement circuit of the first stage, into which it will be possible to include a high-resistance \(G_{\mathrm{II}}\), having high sensitivity to current and, consequently, giving a considerable deflection.

4. SPECIFIC PROPERTIES AND CALCULATION OF GALVANOMETERS FOR A PHOTOELECTRO-OPTICAL AMPLIFIER

The galvanometer is the basic element of the PEOA circuit, determining the sensitivity and speed of operation of the entire apparatus. As was already indicated at the beginning, the most expedient construction of a galvanometer for the PEOA appears to be a system with a rotating frame mounted on rigid short suspensions, allowing good balancing and having a firm zero position. In addition, from the principle of operation of the PEOA developed above, when the frame is over-calmed, there naturally follows the necessity of a short-period galvanometer, so that the time required to establish a reading in repeated over-calming should not be excessively large. In order that a short-period galvanometer on rigid suspensions should not have too low a sensitivity, in the present work, in contrast to ordinary rules, increased values of the magnetic-field intensity were used, reaching \(H = 4000—5000\) oersteds. As is known, very strong magnetic fields impose exceptional requirements on the purity and absence of magnetic impurities in the materials entering into the frame; moreover, the situation in this respect is to some extent facilitated by the use of a radial magnetic field when a core is introduced inside the frame. In addition, large magnetic fields, increasing the sensitivity, at the same time entail considerable values of the critical resistances \(R_k\) of the galvanometer, since the sensitivity is proportional to \(H\), while the resistance \(R_k\) is proportional to the square of \(H\).

However, the usual objections to large \(H\) because of the fear of magnetic impurities are relevant only when working with very small opposing moments \(D\), characteristic of designs with a frame on suspension, and not on stretched suspensions. It is very important to note that all galvanometer systems used by the author in the PEOA had unusually large \(D_1\), not less than \(10\ \dfrac{\text{dyne}\cdot\text{cm}}{\text{radian}}\) and sometimes reaching \(29\ \dfrac{\text{dyne}\cdot\text{cm}}{\text{radian}}\), whereas in the galvanometer system \(Z_c\) of the Kipp firm \(D = 0.003\), and in the Moll microgalvanometer \(D = 0.18\ \dfrac{\text{dyne}\cdot\text{cm}}{\text{radian}}\). The transition to sharply increased values of \(D\) freed one from any special measures for cleaning the frame wire of possible magnetic impurities and gave the short period necessary for the principle of over-calming, as well as a stability of the zero with respect to ground disturbances that is valuable for a highly sensitive PEOA.

For calculating the most important practical parameters of the galvanometer systems needed for the PEOA, it is sufficient to take

from theory³ the following usual formulas:

Period of free oscillations:

\[ t_0=2\pi\sqrt{\frac{K}{D}}. \]

Moment of inertia of the frame with the mirror:

\[ K=(1+\xi)\frac{n}{2}\cdot\pi\cdot r^2\delta l'(2D)^2\left(1+\frac{2l}{3l'}\right). \]

Moment of the forces counteracting the suspensions, in \(\dfrac{\text{dyne}\cdot\text{cm}}{\text{radian}}\):

\[ D=\frac{N\tau\rho^4}{2l_0}\quad(\text{wire})\quad\text{or}\quad D=\frac{Nab^3}{3l_0}\quad(\text{ribbon}). \]

Condition for the onset of periodicity:

\[ (HnS)^2=2R_k\cdot10^9\sqrt{KD}. \]

Sensitivity to current \(\left(\text{in }\dfrac{\text{mm}}{\text{m}\cdot\mu\text{A}}\right)\):

\[ S_i=2\cdot10^{-4}\frac{HnS}{D}. \tag{18} \]

The principal design data that one can dispose of in constructing a galvanometer are \(K\), \(D\), \(H\), and after choosing their values one can, by the formulas given above, calculate \(t_0\), \(R_k\), and \(S_i\). Since, in addition, in manufacturing a galvanometer it is important to know the relation between \(R_n\) (the resistance of the \(n\) turns of the frame) and \(R_k\), represented as \(\lambda=\dfrac{R_k}{R_n}\), then, after introducing into the formulas the quantity \(\lambda\) and the ratio \(\beta=\dfrac{2l}{l'}\), we obtain relations useful in design:

\[ R_k=\lambda\cdot R_n=\lambda\cdot n\cdot\rho_0\,\frac{2l'(1+\beta)}{\pi r^2}, \]

\[ KR_k=(nS)^2\delta\rho_0\lambda(1+\xi)(1+\beta)\left(1+\frac{\beta}{3}\right), \tag{19} \]

\[ H^2=\frac{4\pi\delta\rho_0\lambda(1+\beta)\left(1+\frac{\beta}{3}\right)(1+\xi)\cdot10^9}{t_0}. \]

However, in reality it is almost never necessary to vary the magnitude \(H\), and one must simply take the greatest attainable value of \(H\) for the selected alloy (magnico, alnico) and the given design of the radial field and magnetic circuit. Moreover, most often in calculation it is more convenient to take, as the initial quantities, the values \(S_i\), \(t_0\), \(R_k\), \(\lambda\) required by the FEOU circuit, and from them, for the chosen \(H\), determine from formulas (18) \(D\), \(K\), \(nS\), and finally to make concrete the design of the frame and the suspensions. Incidentally, special attention must be paid to the choice of the mirror, which in this case cannot be small (diameter not less than \(7\) mm), since in almost all FEOU systems it proves necess-

by projecting onto this mirror an image of the source filament, and the loss of luminous flux with excessively small mirror dimensions would be unavoidable.

Table II gives the principal design data and parameters of the galvanometers used in the single-stage FEОU-9 and the two-stage FEОU-10 described below.

Table II

For all the galvanometers indicated in Table II, \(\xi = 0.5\) was adopted, i.e., the additional moment of inertia due to the mirror, the balancing crosspiece, and the lacquer impregnating the frame was assumed equal to 50% of the moment of inertia of the frame turns; all magnets were cast from magnico alloy; the suspensions of all \(G_{\mathrm{I}}\) were made of beryllium bronze, 0.15 mm wide and 15 \(\mu\) thick \((D_1 = 6.8)\), while the suspensions of all \(G_{\mathrm{II}}\) and \(G_{\mathrm{III}}\) were made of phosphor bronze 50 \(\mu\) in diameter \(\left(D_1 = 24 \dfrac{\text{dyne}\cdot\text{cm}}{\text{radian}}\right)\); the mirrors of \(G_{\mathrm{I}}\) and \(G_{\mathrm{II}}\) in FEОU-9 are circular, 10 mm in diameter and 0.3 mm thick, while the mirrors of all FEОU-10 galvanometers have dimensions \(5\times 7\times 0.3\) mm. The FEОU-9 galvanometers have a double metallic

Fig. 4. Output galvanometer from FEU-9.

Fig. 5. Galvanometer from the FÉOU-10.

housing, between the walls of which a layer of cotton wool for thermal insulation is laid (protection against thermoe.m.f.).

Figs. 4 and 5 show photographs of the galvanometers of the FEOU-9 and FEOU-10.

5. SINGLE-STAGE AND TWO-STAGE PHOTOELECTRO-OPTICAL AMPLIFIERS FEOU-9 AND FEOU-10

A good illustration of formulas (12), (13), and (14) for a torsion single-stage photoelectro-optical amplifier is the system of the apparatus developed by the author in 1948 and reproduced in 1949, called FEOU-9 and schematically depicted in Fig. 6.

Fig. 6. Diagram of FEOU-9.

In order to reduce the influence of fluctuations in the current feeding the lamp, a two-beam optical channel was used, into which rasters were introduced for the purpose of increasing sensitivity. The condenser and the objective are relatively long-focus lenses (\(f_1 \simeq 20\ \text{cm}\), \(f_0 \simeq 40\ \text{cm}\)) and are selected in such a way that, owing to fulfillment of the condition \(f_0 = 2f_1\) and to the double passage through the objective lens by the rays going to the photocell, the distances from \(\Gamma_1\) to the photocells and to the projected gratings were identical and equal to the distance from the light source to these gratings, i.e. \(2f_1\). The photocells in FEOU-9 were taken with external photoeffect TsG-1 and connected into the arms of a bridge circuit, the other two arms of which consisted of coke resistances of \(3\ \text{M}\Omega\) each and a \(5\ \text{M}\Omega\) adjustable resistance connected between them for tuning the entire circuit and controlling galvanometer \(\Gamma_{II}\), which monitored the balance of the bridge, powered by a dry battery of \(300\ \text{V}\). There was no damper, for the input galvanometer \(\Gamma_I\) was overdamped, and the entire apparatus, protected by a Silumin casing, was fastened directly to the wall. Fig. 7 shows photographs of the frame on which the main parts of FEOU-9 were mounted;

PHOTOELECTRO-OPTICAL AMPLIFIER

illuminator with lamps and two prisms, two condensers with two gratings, galvanometer \(G_I\) with a projection objective, a camera with two TsG-1 photocells and two gratings. The output

a

b

Fig. 7. a — frame of the FEOU-9; b — general view of the FEOU-9.

galvanometer \(G_{II}\) could be located anywhere, while the circuit-control panel was placed on the housing, which was fastened to the wall and contained the above-mentioned frame with the components. The FEOU-9

does not contain cathode tubes and directly develops a sufficiently necessary amplification.

Since the lamp had \(I=10\) candles \((6v;\ 1.5a)\), then \(E'_1 \approx E'_2=\)

\[ =60\ \text{lux}; \]

with \(\mu=2\cdot 10^{-4}\ \dfrac{a}{mm}\) and \(L_1=25\ cm\), by formula (12) or (13), for \(S_{i1}=3.4\) (see Table II), we obtain:

\[ \frac{\Delta i_2}{\Delta i_1}\approx 4.5. \]

As we see, the current amplification turns out to be very small, but the amplified current \(\Delta i_2\) flows in a very high-resistance circuit of photocells, into which one can connect a galvanometer \(G_{\mathrm{II}}\) that is very sensitive to current and thereby obtain a large linear amplification, according to formulas (14):

\[ \frac{\Delta D_2}{\Delta D_1} = 10\cdot 2\cdot 10^{-4}\cdot 60\cdot 25\cdot \frac{590}{\dfrac{100}{40}} \approx 700. \]

Thus, if we suppose that in circuit \(G_{\mathrm{I}}\) there is connected a radiation thermoelement having a resistance of \(4\ \Omega\) and

Fig. 8. FEOU-9. Signals \(1.25\cdot 10^{-9}\ v;\ 1.7\cdot 10^{-9}\ v;\ 2.5\cdot 10^{-9}\ v.\)

sensitivity \(\varepsilon'=1\ \dfrac{v}{wt}\), then, when radiant power \(\Phi=4\cdot 10^{-9}\ wt\) falls on it, a current will appear in circuit \(G_{\mathrm{I}}\)

\[ \Delta i_1=\frac{4\cdot 10^{-9}}{6}\approx 6\cdot 10^{-10}\ a, \]

which is transformed into

\[ \Delta i_2=6\cdot 10^{-10}\cdot 4.5\approx 2.7\cdot 10^{-9}\ a, \]

easily measured by galvanometer \(G_{\mathrm{II}}\) (see Table II). In practice, however, the calculation will be considerably more complicated because of the processes in the bridge circuit, which will cause a certain depression of the deflection on the scale of \(G_{\mathrm{II}}\).

Figure 8 gives an oscillogram illustrating the exact observance of proportionality and the magnitude of the sensitivity to small emf’s in the FEOU-9 instrument. Independence from extraneous thermo-emf’s during the tests was achieved by closing \(G_{\mathrm{I}}\) on a bifilarly wound coil of red copper, which had a resistance of \(4\ \Omega\) and was included in the circuit of a double potentiometer. As is seen from Fig. 8, the FEOU-9 permits one to measure freely so small an emf as \(2\cdot 10^{-9}\ v\), for on the oscillogram three signals are quite distinguishable, obtained from the appearance in circuit \(G_{\mathrm{I}}\) of an emf of \(1.25\cdot 10^{-9}\ v\). Figure 9 shows a spectrogram obtained by N. G. Yaroslavskii in the laboratory of Academician A. N. Terenin at the State Optical Institute with an FEOU-9 and an infrared mirror monochromator ISP-14¹¹ in the region

about \(7\,\mu\), illustrating the rotational levels in \(H_2O\) molecules (absorption lines of water vapor contained in the air).

However, the FEOU-9 is relatively slow in operation because of the sharp over-damping of the galvanometer \(G_1\), and for the entire cycle of rise and fall of the current, i.e., for the measurement of one point on the spectral curve, no less than 18 sec are required. Since it is usually considered necessary, when measuring the whole spectrum from 0.7 to \(15\,\mu\), to measure 300 points, this entire cycle will require 1.5 hours; in practice the speed of rotation of the prism and of the drum with the photographic paper was set (with some margin) equal even to 2.5 hours. Although this interval of time is not excessively large, but, on the contrary, quite usual, and, for example, in the apparatus of the Perkin-Elmer firm there is a similar recording speed, it nevertheless seemed highly expedient, if possible, to shorten the recording time of the spectrogram, which was achieved by the author in 1949 after the development of the two-cascade FEOU-10.

Fig. 9. FEOU-9 and ISP-14 monochromator. Absorption lines of \(H_2O\) vapor near \(6.2\,\mu\).

In the FEOU-10 system, shown schematically in Fig. 10, it should be especially noted, in comparison with the FEOU-9, that there is a transition to short-focus optics \((f_1 = 6\ \text{cm};\ f_0 = 12\ \text{cm})\) and the use of granular-silver photoelements\({}^{10}\) with a blocking layer (FESS-10), having a large \(\mu\) of the order of \(2 \cdot 10^{-3}\ \dfrac{a}{\text{lm}}\) at a load resistance of about \(300\ \Omega\). Experience showed that these photoelements give stable operation in the FEOU only with

at not very great illuminances, and therefore usually one took \(E'_1 \simeq E'_2 \simeq 100\) lux. Since the working diameter of the condenser and of the photocell was equal to \(3.5\ \text{cm}\), then with seven slits in the raster of the first stage we have \(L_1 = 20\ \text{cm}\), and with four slits in the raster of the second stage we have \(L_2 = 12\ \text{cm}\), after which, using the data for \(\Gamma_I\), \(\Gamma_{II}\), and \(\Gamma_{III}\) from Table II, by formula (16) we obtain (remembering that \(K_1 = K_2 = \dfrac{100}{2f_0} = 8\))

\[ \frac{\Delta i_3}{\Delta i_1} = 10^2 \cdot (2 \cdot 10^{-3})^2 \cdot 100^2 \cdot 20 \cdot 12 \cdot \frac{1.15 \cdot 7.7}{8^3} = 132, \]

\[ \frac{\Delta D_3}{\Delta D_1} = 880. \]

If we assume that, as before, the radiation thermoelement connected into the circuit \(\Gamma_1\) has \(R_t = 4\ \Omega\) and \(\varepsilon' = 1\ \dfrac{v}{w}\), then, when

Fig. 10. Diagram of FEOU-10.

a radiant power \(\Phi = 4 \cdot 10^{-9}\ \text{W}\) falls on the thermoelement, we obtain

\[ \Delta i_1 = \frac{4 \cdot 10^{-9}}{1.3 + 4} = 7.5 \cdot 10^{-10}\ \text{A}, \]

after which

\[ \Delta i_3 = 7.5 \cdot 10^{-10} \cdot 132 = 1 \cdot 10^{-7}\ \text{A}. \]

Since the sensitivity of \(\Gamma_{III}\) (see Table II) is equal to \(S_i = 7.7\), the FEOU-10 scheme under consideration is quite capable of registering radiant powers as small as \(4 \cdot 10^{-9}\ \text{W}\).

a

b

Fig. 11. Internal (a) and external (b) views of the FEОU-10.

As is evident from Fig. 11, the FEOU-10, despite having two stages of photoelectrooptical amplification, is much more compact than the FEOU-9 and is a portable instrument \((350 \times 185 \times 285\ \mathrm{mm})\), operating directly on a table rather than on a bracket or wall, as does the FEOU-9. A substantial advantage of the FEOU-10 is also the absence of the need for a 300 V battery supplying the photoelement bridge in the FEOU-9.

However, the chief merit of the FEOU-10 system is its considerably higher speed of operation, illustrated by the curves in Fig. 12, which at the same time confirm the strict proportionality of the deflections in the region of very small emfs. The rise and fall of the current

Fig. 12. FEOU-10. Signals \(2.5 \cdot 10^{-8}\)—\(7.5 \cdot 10^{-8}\ \mathrm{V}\); paper speed
\(1\ \dfrac{\mathrm{mm}}{\mathrm{sec}}\)

in the circuit \(G_1\) now require no more than 3 sec., i.e., 300 points of the spectrogram can be recorded in 15 minutes; this recording speed exceeds the operating speed of all apparatus manufactured by various firms and is inferior only to the data of two literature references \(^{5,6}\).

6. CONCLUSION

The above results, obtained by the author as the outcome of prolonged work on varying the principle of photoelectrooptical amplification and on the specific investigation of galvanometric systems, are not limiting. From formula (17) for a three-stage FEOU it is quite obvious that, by adding a third stage, it is possible to use still faster galvanometers without detriment to the sensitivity of the entire installation, and such an investigation is now being carried out. It should be noted that in recent years in radiation metrology there have prevailed, in the author’s opinion, false tendencies toward the development of methods of interrupting the current or modulating the light flux \(^{7,8,9}\), which are merely a cumbersome, purely radio-engineering method of amplification, quite unnecessary for the essence of the process of radiation recording. The scattering by a modulator of the measured light flux into separate pulses is possible only with a very low-inertia indicator and is usually performed at a frequency not exceeding 10–20 Hz, and, for recording the presence of some-

any value of the luminous flux, it is evidently necessary to carry out several pulses (interruptions), i.e., the total duration of the time spent on the measurement will be considerably greater than 0.1 sec and usually reaches 1 sec or more. Therefore, variations of the luminous flux in the exit slit due to the rotation of the monochromator prism, occurring over time intervals of 0.1 sec, cannot be distinguished by means of these modulation methods, since the latter are based on an artificial sinusoidal variation of the luminous flux with approximately the same frequency.

The method developed by the author for single- and multistage photoelectro-optical amplification is free from any interference with the process of variation of the luminous flux being measured; it is based on the use of a galvanometer, which, as is known, has a very low fluctuation threshold, and, owing to the principle of reexposure and multistage operation, opens up exceptional prospects for rapid radiation metrology and has already shown superior results.

References

1. Aiken and Welz, Electronics, 124 (1947).
2. Kozyrev B. P., Registration of Extremely Small Radiations by Thermal Indicators. Doctoral dissertation (1948).
3. Strong D., Technique of the Physical Experiment. State Technical Publishing House, 318 (1948).
4. Ising, Ann. d. Phys. 5, 911 (1931).
5. Daly and Sutherland, Proc. Phys. Soc. 59, 77 (1947).
6. Backer and Robb, RSI 14, 356 (1943).
7. Liston, Quinn, Sargeant, Scott, RSI 17, 194 (1946).
8. Roes, RSI 16, 172 (1945).
9. Clark Jones, JOSA 39, 344 (1949).
10. Kosenko and Miselyuk, ZhTF 18, 1369 (1948).
11. Neumin G. G., Optical-Mechanical Industry, No. 1, 15 (1947).