NEW INSTRUMENTS AND METHODS OF MEASUREMENT

APPLICATION OF PHOTOMULTIPLIERS IN SPECTRAL ANALYSIS

N. O. Chechik

INTRODUCTION

Photoelectric cells with multiple amplification, based on the use of the phenomenon of secondary-electron emission and briefly called “electron multipliers” or “photomultipliers” 1,2,3,4, have in recent years found wide application in all kinds of scientific research in which one has to measure or detect weak and very weak light fluxes.

The reasons for this are not accidental. They are explained by the advantages that photomultipliers possess in comparison with photoelectric cells. In a number of cases such an advantage is the large amplification factor characteristic of photomultipliers. Whereas the sensitivity of vacuum photoelectric cells is 10–200 μA/lm, the integral sensitivity of photomultipliers is usually of the order of 1–10 A/lm. Such enormous sensitivity is not the limiting value for photomultipliers, and in individual cases (with improved focusing) it may reach thousands and tens of thousands of A/lm 5; the amplification may then be as high as \(10^8\) times 6.

The high integral sensitivity of photomultipliers makes it possible greatly to simplify the measuring apparatus, reducing the photoelectric part of the instrument to the photomultiplier itself, its power source, and the measuring device, which is usually a pointer or mirror galvanometer 7,8,9. The entire apparatus becomes extremely simple and convenient in operation. It should be noted that the problem of power supply, which several years ago could be regarded as one of the reasons limiting the use of electron multipliers 1, is at present practically insignificant, and photomultipliers can be used both under stationary and field (portable) conditions.

Modern photomultipliers have small dark currents 10, making it possible considerably to extend the working range of light-

characteristic, and compensation of the dark current makes it possible to move the sensitivity threshold approximately another 2 orders of magnitude.

In the case of using photoelements for analogous measurements, the use of current or voltage amplifiers with large amplification factors is unavoidable. Increasing the amplification factor of a direct-current amplifier and the need for considerable limitation of the spectrum of electrical fluctuations lead to a substantial increase in the time constant of the photoelectric instrument, which in a number of cases is completely inadmissible.

In the case of photomultipliers, an effective measure for reducing electrical fluctuations is a reduction of the dark current by lowering the temperature of the photomultiplier, and also, in turn, limitation of the spectrum of the amplified frequencies (narrowing of the pass band)6,13,14,15.

Electrical fluctuations in the photomultiplier, in the input circuits and in the first stage of the amplifier, as well as the time constant of the amplifier, are determining factors in establishing the sensitivity for measuring very weak light fluxes.

Photoelectric instruments using photomultipliers may have a sensitivity threshold several orders of magnitude below the sensitivity threshold of photoelectric instruments using photoelements. This is another essential advantage of employing photomultipliers in photometric measurements.

Photometric measurements based on the use of photomultipliers find their greatest application in spectral7,8,16,17,18,19,20,21 and colorimetric22,23,24,25 analyses, in work connected with the study of combination scattering of light26,27,28, in investigations in the field of luminescence and phosphorescence9,29,30,31,32, in various optical investigations33,34,35,36,37,38,39, in astronomy40,41,42,43, and in various works on atomic physics6,44,45,46,47,48,49,50,51,52,53.

Photoelectric photometers differ among themselves in the sensitivity and accuracy of measurements, the type of scale (linear or logarithmic), inertia, spectral sensitivity, and a number of other factors. The variety of requirements which in each particular case are imposed on photoelectric photometers excludes the possibility of producing universal photoelectric photometers.

In this article the general questions of the use of photomultipliers and certain methods of applying photomultipliers in spectral analysis are considered.

SOME LIMITATIONS ENCOUNTERED IN THE USE OF PHOTOMULTIPLIERS

The large integral sensitivity of photomultipliers, measured in amperes per lumen, by no means signifies that the maximum photocurrents which flow in the anode circuit of a photomultiplier can reach values of one or more amperes.

Studies carried out by Engstrom showed that, despite the pulsed measurement regime, the maximum anode current of the 931A photomultiplier could not exceed 45 ma. Moreover, the current was unstable.

The use of a photomultiplier for measurement purposes is limited by much smaller currents, whose magnitudes are determined by the fatigue of the photomultiplier, characterized by a decrease in its sensitivity. Different photomultipliers have different fatigue characteristics; however, the fact that fatigue exists is common to all photomultipliers.

Fig. 1. Fatigue curves of 931A photomultipliers.
(According to Engstrom.)

In Fig. 1 two typical fatigue curves of 931A photomultipliers are shown. The points of one curve correspond to measurements after 20 minutes had elapsed, and of the other—after 40 minutes had elapsed. During the measurement, the strength of the photomultiplier anode current was kept constant by regulating the luminous flux incident on the photocathode. Between measurements of two points an interval of at least one day was maintained, during which the sensitivity recovered approximately to its initial value. In those cases in which the current reached 1 ma, the recovery of sensitivity in one day was incomplete.

Kessler and Wolf \(^{20}\) investigated the fatigue of the 931A photomultiplier under continuous illumination of the photocathode for 20 hours, at photocurrent values of 3 and 23 μa. The results obtained by them are presented in Fig. 2.

Curve \(A\) shows the decrease in sensitivity of the photomultiplier (in relative units, expressed on a linear scale) at

at an average photocurrent of 3 μA. Curve C shows the decrease in sensitivity at a current of 23 μA. The level of sensitivity decrease that occurred in the case of curve C after 20 hours of measurement remained unchanged over the following 12 days.

Cessation of the action of light leads to a slow recovery of sensitivity along curve B (time scale in tens of hours); moreover, upon repeated illumination of the photomultiplier, in which the photocurrent again amounted to 23 μA, the sensitivity fell along curve D.

Fig. 2. Curves of decrease and recovery of the sensitivity of 931A photomultipliers. (After Kessler and Wolf.)

The decrease in the sensitivity of photomultipliers shown in Figs. 1 and 2 is due to a reduction in amplification in several of the last stages. The magnitude of the decrease in sensitivity increases as the light intensity (or, in the present case, equivalently, the photocurrent intensity) increases, and also depends on the previous state of the photomultiplier.

From the considered curves of sensitivity decrease it follows that the maximum operating photocurrent of the multiplier should not exceed 1 mA. In those cases where a decrease in sensitivity is inadmissible, the maximum current of the photomultiplier should not exceed 1 μA. It is also recommended to begin the measurement approximately half an hour after switching on the power supply and applying the light flux to the photomultiplier.

Another factor limiting the maximum photocurrent is the nonlinearity of the light characteristic of the photomultiplier, which is caused by the influence of space charge. According to the measurements of Rodionov^7, the nonlinearity of the light characteristic of the Kubetsky tube,

having an \([Ag—O—Cs]\) photocathode and \([Cu—S—Cs]\) emitters, beginning approximately at \(1\) mA.

The first factor limiting the photocurrent that can be recorded by a photomultiplier is the magnitude of the dark current.

The dark current of a photomultiplier consists mainly of the leakage current and the amplified thermal currents of the photocathode and of all stages of secondary-electron emission (emitters), and is a function of the voltage feeding the photomultiplier.

The dark current of a photomultiplier can be represented by the formula

\[ I_{\mathrm{t}} = I_{\mathrm{y}} + I_{\mathrm{tk}} M + I_{\mathrm{te}} \sum_{1}^{n} M_i, \tag{1} \]

where

\[ \sum_{1}^{n} M_i = M\left( \frac{1}{m_1} + \frac{1}{m_1 m_2} +\cdots +\frac{1}{m_1 m_2 \ldots m_n} \right). \]

Here \(I_{\mathrm{y}}\) is the leakage current, \(I_{\mathrm{tk}}\) is the thermal current of the photocathode, \(I_{\mathrm{te}}\) is the thermal current of an emitter, \(M = m_1 m_2 \ldots m_n\) is the total amplification factor of the multiplier, and \(m_1, m_2, \ldots, m_n\) are respectively the amplification factors of the 1st, 2nd, ..., \(n\)-th stages.

Fig. 3. Dependence of the dark current on the voltage per stage for RCA photomultipliers.

Labels in the figure: vertical axis—“Anode dark current in microamperes”; horizontal axis—“Volts per stage”; curves—“Sum of leakage current and amplified thermal current,” “Leakage current,” “Amplified thermal current”; shaded region—“Region of unstable regenerative ionization.”

In Fig. 3 the solid line shows the dependence of the dark current of a photomultiplier on the voltage per stage, which is typical for RCA photomultipliers. As can be seen from the figure, at low voltages the leakage current predominates. The cause of leakage is the deposition of cesium on the insulating gaps between the electrodes of the photomultiplier. In some cases leakage may increase as a result of the deposition of moisture on the outer surface of the bulb and the base of the photomultiplier. Beginning at \(60\) V per stage, the amplified thermal current of the photocathode acquires substantial importance in the total magnitude of the dark current. Its magnitude, according to da—

is, according to Engstrom\(^ {15}\), \(6 \cdot 10^{-15}\) a for the 931A multiplier with an \([\mathrm{Sb}—\mathrm{Cs}]\) cathode.

Beginning at approximately 110 V per cascade, there begins, in Engstrom’s terminology, the “region of regenerative ionization.” Within this region the dark current increases sharply and is very unstable. The exact cause of this phenomenon is unknown. One can only suppose that regenerative ionization is caused by feedback arising either as a result of secondary emission of positive ions (residual gas or cesium vapor), or as a result of photoemission from the excited gas or from the fluorescence of the glass and other insulators of the photomultiplier. Since the gain in this region reaches the order of \(10^{7} \div 10^{8}\), a very weak feedback from the anode to the photocathode leads to regenerative ionization, the consequence of which is complete breakdown and an uncontrolled discharge. For many RCA photomultipliers this discharge occurs between 140 and 160 V per cascade.

The phenomenon of regenerative ionization was observed by us in Kubetsky photomultipliers having an \([\mathrm{Sb}—\mathrm{Cs}]\) photocathode and improved focusing. Whereas, in Kubetsky photomultipliers focused in the usual way, the nature of the variation of the integral sensitivity and the dark current is represented respectively by curves 1 and 2 in Fig. 4, and regenerative ionization is not observed, with improved focusing, which is achieved by using an additional magnet and appropriate

Fig. 4. Dependence of the integral sensitivity and dark current on the voltage feeding the photomultiplier, for Kubetsky photomultipliers with an \([\mathrm{Sb}—\mathrm{Cs}]\) photocathode. 1 and 2—curves of integral sensitivity and dark current for a normally focused photomultiplier. 3 and 4—curves of integral sensitivity and dark current for a well-focused (additional magnet) photomultiplier.

by the choice of the magnetic field, the integral sensitivity and the dark current are expressed, respectively, by curves 3 and 4, and at a photomultiplier voltage equal to 1240 V (89 V per stage), a rapid increase of the dark current is observed. This voltage corresponds to an integral sensitivity of 1000 A/lm, which, for a photocathode sensitivity of 100 μA/lm, means an amplification of \(10^7\).

These observations confirm Engstrom’s conclusion, according to which the conditions for the occurrence of regenerative ionization exist for all photomultipliers when their amplification is substantially large. Clarification of the causes of the rapid increase of the dark current in Kubecký photomultipliers showed that, as a result of intense electron bombardment, the anode indeed becomes luminous and optical feedback arises.

For many photometric works, the magnitude and constancy of the dark current acquire the greatest importance. It follows from Fig. 3 that in 931A photomultipliers, when the stage voltage is lowered below 60 V, the leakage-current component predominates in the dark current; at 40 V per stage it has a value of \(10^{-8}\) A, with an insulation resistance of \(4 \cdot 10^9\) ohm.

The insulation resistance limits the maximum value of the input resistance of a direct-current amplifier and, consequently, also the amplification factor attainable with this amplifier. The insulation resistance also limits the minimum value of the constant component of the dark current, determined by the leakage current.

A reduction in the role of the leakage current can be achieved by increasing the insulation resistance and by using a guard ring between the anode and the last stage. Dobrovol’skii\(^{54}\), as early as 1938, made Kubecký photomultipliers in which the anode was separated from the last stage by a corrugated constriction. This measure reduced the possibility of cesium deposition on the glass between the anode and the last stage and made it possible to reduce the leakage current to \(10^{-10}\) A*).

Figure 5 shows the dependence of the dark current on the photomultiplier voltage for modern Kubecký photomultipliers. Curve 1 depicts the dark-current characteristic of a photomultiplier with an \([\mathrm{Ag}-\mathrm{O}-\mathrm{Cs}]\) photocathode, having an insulation resistance of \(2 \cdot 10^{11}\) ohm. Despite such a large insulation resistance, the dark current, even at a photomultiplier voltage equal to 400 V, is limited by the value \(5 \cdot 10^{-10}\) A.

A different picture is found when a guard ring is used. As is seen from curve 2, which represents a photomultiplier with an \([\mathrm{Sb}-\mathrm{Cs}]\) photocathode containing a guard ring between the anode and the last stage, when the supply voltage is lowered to 800 V,

*) It should be noted that the thermocurrent of these photomultipliers at room temperature reached \(10^{-5} \div 10^{-7}\) A.

where the dark current is equal to \(1\cdot 10^{-10}\) a, there is no characteristic bend in the dark-current curve that would indicate the presence of leakage current.

However, the guard ring introduced inside the photomultiplier does not protect against leakage current over its outer surface. If there are no surface leakages caused by moisture, then the leakage current is determined by the resistance of the glass between the anode and the last stage. The magnitude of this resistance depends on the geometrical dimensions of the glass gap between the two electrodes and on the value of the specific resistance of the glass. It should be assumed that the leakage current determined by the resistance of the insulating glass reaches, at a photomultiplier voltage of 800 v, a value of the order of \(10^{-11}\) a.

The appearance of surface leakages caused by moisture was observed by us simultaneously in a number of Kubetsky photomultipliers with an \([\mathrm{Sb}—\mathrm{Cs}]\) photocathode. It is interesting to note that, at a photomultiplier voltage of 800 v, in all the photomultipliers measured by us (5 specimens) the leakage current was approximately the same and was equal to \((1\div 2)\times 10^{-8}\) a. Measurements of the thermocurrent showed that its value remains the same as it was before the appearance of surface leakages.

Fig. 5. Curves of the dependence of the dark current on the supply voltage for Kubetsky photomultipliers: (1) with an \([\mathrm{Ag}—\mathrm{O}—\mathrm{Cs}]\) photocathode and without a guard ring; (2) with an \([\mathrm{Sb}—\mathrm{Cs}]\) photocathode in the presence of a guard ring.

Elimination of surface leakages is achieved by coating the glass of the photomultiplier and the supply cable with a thin film of molten paraffin or wax \(^{15}\), after preliminary washing of the surface to be coated with alcohol and subsequent drying. The mount in which the photomultiplier is enclosed must be hermetic, and a moisture absorber, for example phosphorus pentoxide, is placed in it. If the photomultiplier is cooled, then, in order to avoid fogging of the mount window, the latter is made of cellophane \(^{15,55}\).

The constancy of the dark current depends on the constancy of its components. In photomultipliers operating at comparatively low working voltages, changes in the dark current are determined by the instability of ohmic leakages and by the presence of ionic feedback, formed through residual gas or cesium vapor1. Together with S. M. Fainshtein we observed the process of formation of the insulation resistance of a group of Kubetsky photomultipliers with an \([ \mathrm{Sb}—\mathrm{Cs}]\) photocathode.

The results of the observations are given below in Table I.

Table I

Insulation resistance of the guard-ring—anode section in Kubetsky photomultipliers (in ohms)

Photomultiplier No.	After thermal and vacuum treatment	After cesiation	6 days after cesiation	18 days after cesiation
85	\(4\cdot 10^{11}\)	\(2\cdot 10^{11}\)	\(1.0\cdot 10^{11}\)	\(1.7\cdot 10^{11}\)
86	\(1.4\cdot 10^{11}\)	\(1.2\cdot 10^{11}\)	\(1.4\cdot 10^{10}\)	\(8\cdot 10^{7}\)*)
89	\(1.4\cdot 10^{11}\)	\(1.7\cdot 10^{11}\)	\(9\cdot 10^{9}\)*)	\(2.5\cdot 10^{7}\)*)
91 **)	\(1.8\cdot 10^{11}\)	\(2.6\cdot 10^{10}\)	\(1.5\cdot 10^{10}\)	—
96	\(1.0\cdot 10^{11}\)	\(1.4\cdot 10^{11}\)	\(5.2\cdot 10^{8}\)	\(2.6\cdot 10^{8}\)*)
99	\(1.6\cdot 10^{11}\)	\(1.3\cdot 10^{11}\)	\(1.4\cdot 10^{11}\)	\(1.0\cdot 10^{11}\)
101	\(2.0\cdot 10^{11}\)	\(1.0\cdot 10^{11}\)	\(5.4\cdot 10^{10}\)	\(5\cdot 10^{10}\)

) Instability of the insulation resistance was observed.
*) This photomultiplier had no photocathode.

From Table I it is seen that immediately after thermal and vacuum treatment the insulation resistance in all the photomultipliers is of the same order and sufficiently stable. After cesiation the insulation resistance decreases somewhat, while nevertheless remaining sufficiently high and stable. With time, the insulation resistance in some photomultipliers decreases noticeably and becomes unstable. This pattern is observed both for the “anode—guard ring” section and for the “guard ring—last dynode” section.

It may be supposed that the slow changes in insulation resistance are explained by the surface migration of cesium over the glass in the gaps between the electrodes.

On the other hand, even partial immersion of a Kubetsky photomultiplier (from the photocathode side) in liquid air leads to an immediate increase in the insulation resistance from values of the or-

on the order of \(10^8—10^9\) ohms to \((1 \div 2)\cdot 10^{11}\) ohms. This compels one to assume the presence of cesium vapor, which condenses when the photomultiplier is cooled.

Allen\(^{47}\) indicates that in photomultipliers with glass bulbs an instability of the amplification factor is observed (and consequently also an instability of the dark current). This phenomenon is explained by him as the appearance of charges on the inner surface of the glass bulb. Partial elimination of this drawback is achieved by applying an aquadag coating to the inner surface of the bulb, near the first three or four electrodes. The coating must have electrical contact with the first electrode. In photomultipliers with metal bulbs, the appearance of charges does not occur.

The thermionic current can, naturally, also be reduced by lowering the voltage of the photomultiplier. This entails a reduction of the amplification factor and, consequently, a reduction of the integral sensitivity. Such a method of reducing the dark current is permissible only in those cases where the integral sensitivity is sufficiently high or, in any case, exceeds the minimum permissible value. When comparing different photomultipliers with respect to dark current, it is necessary simultaneously to compare them with respect to efficiency, which is the ratio of the integral sensitivity to the dark current.

A comparison of the efficiency of Kubetskii photomultipliers with an \([\mathrm{Sb—Cs}]\) photocathode, carried out by Feinstein\(^{10,58}\), with the best RCA photomultipliers of type 1P21, which also have an \([\mathrm{Sb—Cs}]\) photocathode, showed that at identical values of the dark current the Kubetskii photomultipliers possess an efficiency approximately 5 times greater.

This is explained chiefly by the fact that the sensitivity of the photocathode of the 1P21 photomultiplier is on the order of \(20—25\ \mu\mathrm{A}/\mathrm{lm}\), whereas the sensitivity of the \([\mathrm{Sb—Cs}]\) photocathode of Kubetskii photomultipliers is on the order of \(100—125\ \mu\mathrm{A}/\mathrm{lm}\)\(^{10}\). By sensitizing the \([\mathrm{Sb—Cs}]\) photocathode with oxygen, Feinstein\(^{59}\) succeeded in increasing the efficiency of the Kubetskii photomultipliers still further, bringing the sensitivity of the photocathode to \(175\ \mu\mathrm{A}/\mathrm{lm}\).

ELECTRICAL FLUCTUATIONS

AND THE SENSITIVITY THRESHOLD OF A PHOTOMULTIPLIER

The sensitivity threshold of a photomultiplier is that smallest luminous flux \(F_{\mathrm{thr}}\) which can still be detected by it.

In photomultipliers the sensitivity threshold is limited primarily by electrical fluctuations of the thermionic current and of the photocurrent. Thermal fluctuations of the load resistance of the photomultiplier (or of its insulation resistance) are relatively small, and in measurements in spectral analysis they may be neglected. The nature

this phenomenon is sufficiently widely covered in the literature \(^{1,3,13,60,61,62}\), and therefore we shall not dwell on it here.

As is known \(^{60,61}\), the mean square of the electrical fluctuations of the anode current of a photomultiplier can be expressed by the formula

\[ \overline{I_{\phi\ell}^{\,2}}=2e\Delta f(1+B)(I_{\phi}+I_{\tau})M, \tag{2} \]

where \(e\) is the electron charge, \(\Delta f\) is the spectrum of the amplified frequencies, \((1+B)\) is a constant depending on the fluctuations of secondary-electron emission (according to Shockley and Pierce \(^{60,61}\), \(1+B\simeq 2.5\)), \(I_{\phi}\) is the photocurrent of the photomultiplier, \(I_{\tau}\) is the dark current of the photomultiplier, and \(M\) is the gain coefficient of the photomultiplier.

[In Fig. 6: vertical axis—“Signal-to-noise ratio in decibels”; horizontal axis—“Photocathode current in amperes”; curves/labels \(A\), \(B\), \(C\); reference markings \(1000\) c/s, \(100\) c/s, \(10\) c/s.]

Fig. 6. Dependence of the signal-to-noise ratio, expressed in decibels, on the photocathode current.

The minimal steady photocurrent that can still be distinguished against the background of noise produced by electrical fluctuations is usually taken to be equal to the noise current, i.e. \(\sqrt{\overline{I_{\phi\ell}^{\,2}}}\), and consequently the signal-to-noise ratio is \(\rho=1^{*}\), where

\[ \rho=\frac{I_{\phi}}{2e\Delta f(1+B)(I_{\phi}+I_{\tau})}. \tag{3} \]

Thus, in order to measure a photocurrent with an accuracy of \(1\%\), it is necessary that \(\rho=100\).

Expressing \(\rho\) in decibels and plotting graphically the dependence \(\rho_{\mathrm{db}}=\varphi(I_{\phi k})^{**}\), where \(I_{\phi k}=\dfrac{I_{\phi}}{M}\) is the photocurrent of the photocathode, we obtain the curve shown in Fig. 6.

The upper part of the curve corresponds to the case when \(I_{\phi}\gg I_{\tau}\), and the magnitude of the fluctuations of the dark current may be neglected. Conversely, the lower part of the curve occurs when \(I_{\phi}\ll I_{\tau}\).

To determine the true value of \(\rho_{\mathrm{db}}\) that applies when measuring a given photocurrent \(I_{\phi k1}\), it is necessary to measure in decibels the length of the ordinate enclosed between the curve at the value \(I_{\phi k1}\),

\[ \text{*} \]

In some cases, as for example in recording stellar transits \(^{12}\), for the reliable detection of the light of a star one takes \(\rho=3\).

\[ \text{**} \]

Let us recall that \(\rho_{\mathrm{db}}=10\lg(\rho^2)=20\lg\rho\). Thus, \(\rho_{\mathrm{db}}=20\,\mathrm{db}\) corresponds to measuring \(I_{\phi k}\) with an accuracy of up to \(10\%\), while \(\rho_{\mathrm{db}}=40\,\mathrm{db}\) corresponds to measur-

and a straight line parallel to the abscissa axis, corresponding to the frequency spectrum specified by the pass band \(\Delta f\).

Thus, for \(I_t = 1\cdot 10^{-9}a,\ \Delta f = 1\) cycle, \(M = 10^5\) and \(I_{\mathrm{ph}} \simeq 10^{-16}a\), we obtain \(p_{\mathrm{fb}} = 0\) or \(p = 1\). In real photomultipliers the dark current is usually of the order \(10^{-6} \div 10^{-10}a\).

When measuring weak light fluxes, the sensitivity threshold, limited by fluctuations of the dark current, is expressed by the formula

\[ F_{\mathrm{th}} = \frac{\sqrt{8\cdot 10^{-19}\Delta f I_t M}}{\gamma} \; {}^{*}). \tag{4} \]

In the case where the frequency band is not limited by the subsequent amplifying circuit, it may be expressed as \(\Delta f \simeq \dfrac{1}{2RC}^{12}\), where \(R\) is the resistance in the anode circuit of the photomultiplier, and \(C\) is the capacitance connected in parallel with \(R\). In the limiting case, the value of \(R\) is determined by the insulation resistance of the anode, and the value of \(C\) by the resultant capacitance of the photomultiplier structure, concentrated between the anode and the last stage (or the guard ring).

Expressing \(F_{\mathrm{th}}\) through the parameters of the photomultiplier, replacing in formula (4) \(\Delta f = \dfrac{1}{2RC}\) and \(M=\dfrac{\gamma}{\gamma_{\mathrm{ph}}}\), where \(\gamma_{\mathrm{ph}}\) is the photocathode sensitivity in \(a/lm\), we obtain

\[ F_{\mathrm{th}} = \sqrt{\frac{4\cdot 10^{-19} I_t}{RC\,\gamma_{\mathrm{ph}}\,\gamma}} . \tag{5} \]

Starting from this formula, let us consider two types of Kubetskii photomultipliers with average parameters:

1. A photomultiplier with an \([\mathrm{Ag}-\mathrm{O}-\mathrm{Cs}]\) photocathode:

\[ \gamma_{\mathrm{ph}} = 10\ \mu a/lm,\qquad \gamma = 2\ a/lm,\qquad I_t = 1\cdot 10^{-7}\ a,\qquad R_{\mathrm{ins}} = 10^9\ \Omega, \]

\[ C \simeq 10\ \mu\mu f. \]

Sensitivity threshold:

\[ F_{\mathrm{th}} = 1.4\cdot 10^{-9}\ lm. \]

1. A photomultiplier with an \([\mathrm{Sb}-\mathrm{Cs}]\) photocathode:

\[ \gamma_{\mathrm{ph}} = 100\ \mu a/lm,\qquad \gamma = 10\ a/lm,\qquad I_t = 1\cdot 10^{-8}\ a,\qquad R_{\mathrm{ins}} = 10^{11}\ \Omega, \]

\[ C \simeq 10\ \mu\mu f. \]

Sensitivity threshold:

\[ F_{\mathrm{th}} = 5.7\cdot 10^{-12}\ lm. \]

Thus, the sensitivity threshold of the newly developed in the USSR photomultiplier with an \([\mathrm{Sb}-\mathrm{Cs}]\) photocathode\(^{10,58}\) is more than

\({}^{*})\) Under the condition that \(I_{\phi} < I_t\) and \(I_{\mathrm{ins}} < I_t\).

2 orders of magnitude lower than in photomultipliers with an \([Ag—O—Cs]\) photocathode. It is interesting to note in this connection that the quantum yield of an \([Sb—Cs]\) photocathode in the visible part of the spectrum is 50 times greater than the quantum yield of an \([Ag—O—Cs]\) photocathode,⁶³ and, consequently, in this region of the spectrum photomultipliers with an \([Sb—Cs]\) photocathode considerably surpass, in absolute sensitivity, photomultipliers with an \([Ag—O—Cs]\) photocathode.

Sinitsyn⁶⁴ carried out measurements of \(\gamma\) and \(I_T\) for eight Kubetsky photomultipliers having an \([Ag—O—Cs]\) photocathode and \([Cu—S—Cs]\) emitters. For them he measured the values of the luminous flux \(\beta\) giving, at the output of the photomultiplier, a current equal to the noise of the dark current, that is,

\[ \beta=\frac{\sqrt{i_{\mathrm{fl}}^{2}}}{\gamma}. \]

The values of \(\beta\) obtained by him lay in the range from \(1\cdot10^{-7}\) to \(4.5\cdot10^{-9}\) lm.

Determining, on the basis of the data given by Sinitsyn, the values of \(\Delta f\) on the assumption that all the photomultipliers had a photocathode sensitivity \(\gamma_{\mathrm{phk}}\simeq 10\ \mu\mathrm{A}/\mathrm{lm}\), we obtain a frequency spectrum of the order of \(3\cdot10^{4}\) cps. Obviously, this spectrum was specified by the parameters \(R\) and \(C\) of the amplifier input used in the measurements, since the frequency spectrum determined by the parameters \(R_{\mathrm{in}}\) and \(C\) of the photomultiplier itself is of the order of 50 cps. Unfortunately, the values of the \(R\) and \(C\) used in Sinitsyn’s article are not given.

The sensitivity threshold of a photomultiplier can be lowered in the following ways:

1) by reducing thermionic emission,
2) by narrowing the frequency band,
3) by increasing the efficiency of the photomultiplier, primarily by increasing the sensitivity of the photocathode.

The most effective is the reduction of thermionic emission by cooling the photomultiplier. Cooling of photomultipliers has been used in a number of works.

Rank and his collaborators²⁶,²⁷,²⁸, in works on the combinational scattering of light, cooled photomultipliers 931, 931 A and 1P21 with dry ice. The combination of cooling with limiting the frequency band to 0.5 cps (\(R=10^{8}\ \Omega\), \(C=0.001\ \mu\mathrm{F}\)) allowed them to detect photocurrents \(I_{\mathrm{phk}}=(2\div5)\cdot10^{-17}\ \mathrm{A}\), which, for a photocathode sensitivity of these multipliers of \(20\ \mu\mathrm{A}/\mathrm{lm}\), corresponds to \(F_{\mathrm{thr}}=(1\div2.5)\cdot10^{-12}\ \mathrm{lm}\).

In Chechik’s work¹⁴ on photoelectric photometry of very weak luminous fluxes, cooling was applied to Kubetsky photomultipliers with an \([Ag—O—Cs]\) photocathode by using a cold conductor, one end of which was immersed in a Dewar vessel filled with liquid air, while the other had

close thermal contact with the photomultiplier on the photocathode side. With the frequency band limited to 0.08 cps \((R = 2 \cdot 10^9\ \Omega,\ C = 3200\ \mu\mu\mathrm{F})\), the measured sensitivity threshold was \(F_{\mathrm{thr}} = 1 \cdot 10^{-13}\ \mathrm{lm}\).

Bay\(^{6}\), using a photomultiplier with an \([\mathrm{Ag}—\mathrm{O}—\mathrm{Cs}]\) photocathode and similar emitters, which at room temperature had a dark current of \(1.75 \cdot 10^{-5}\ \mathrm{a}\), as a result of cooling the entire photomultiplier by immersing it in a Dewar vessel with liquid air, carried out counting of infrared photons.

Of great interest are the investigations of Engstrom\(^{15}\), who observed the dependence of the change in the integral sensitivity and the sensitivity threshold of 1P21 photomultipliers on temperature. These photomultipliers have \([\mathrm{Ag}—\mathrm{Mg}—\mathrm{O}]\) emitters which, according to Bay’s\(^{6}\) investigations, exhibit negligible thermionic emission. The main source of thermionic emission in 1P21 photomultipliers is the \([\mathrm{Sb}—\mathrm{Cs}]\) photocathode, deposited on a metallic substrate. According to Engstrom’s measurements, this photocathode has a thermionic current equal to \(6 \cdot 10^{-15}\ \mathrm{a}\) at room temperature.

Fig. 7. Dependence of the sensitivity threshold of a photomultiplier on temperature (after Engstrom). 1P21-type photomultiplier at 100 V per stage and pass band 1.8 cps. Photomultiplier load 1 megohm. Measured flux \(1.5 \cdot 10^{-10}\ \mathrm{lm}\). Color temperature 2870 K°. Modulation frequency 90 cps.

The results obtained by Engstrom are given in Fig. 7. The measurements were carried out with a resonant amplifier tuned to a frequency of 90 cps and having a pass band of 1.8 cps. The luminous flux used in the measurements of integral sensitivity was \(1.5 \cdot 10^{-10}\ \mathrm{lm}\) and was modulated by rectangular oscillations at a frequency of 90 cps. The signal and noise voltages (thermionic-current fluctuations), measured at the output of the amplifier and referred to its input, which had a resistance of \(10^6\ \Omega\), are expressed in Fig. 7 in decibels relative to a conventional voltage of 1 microvolt, at which the ratio of the measured voltage to the conventional voltage is zero decibels. On the right-hand ordinate axis is plotted the photomultiplier sensitivity threshold, corresponding to the noise curve, expressed in lumens.

As can be seen from Fig. 7, when the temperature is lowered from \(50^\circ\mathrm{C}\) to \(-175^\circ\mathrm{C}\), the integral sensitivity decreases; however, its change does not exceed a factor of 2–3. As for the sensitivity threshold (the noise curve), as a result of lowering the temperature from \(20^\circ\mathrm{C}\) to \(-175^\circ\mathrm{C}\) it decreases by two orders of magnitude (i.e., by 40 db).

Fig. 8. Dependence of the number of pulses caused by autoelectronic emission on the voltage feeding the photomultiplier (according to Bay).

The reasons for the distortion of the noise characteristic are not clear. It is assumed that the distortion is due to autoelectronic emission. This assumption is confirmed in Bay’s work, in which he observed the dependence of the number of pulses on the voltage feeding a 10-stage \([Ag—O—Cs]\) photomultiplier cooled to the temperature of liquid air. From Fig. 8, which shows Bay’s dependence of the number of pulses per minute on the feeding voltage, it follows that a noticeable increase in autoelectronic emission begins at 950–1000 V.

DEVELOPMENT OF PHOTOELECTRIC METHODS OF SPECTRAL ANALYSIS USING PHOTOMULTIPLIERS

Spectral methods for determining the chemical composition of a substance are at present widely used. For many years the principal method of measuring the intensity of spectral lines was the photographic method. Its main disadvantages are the slowness of the measurement process, laboriousness, considerable cost (in the case of mass measurements), and, finally, the errors inevitably inherent in photographic photometry (first of all those introduced by the graininess and nonuniformity of the photosensitive layer of the plate, as well as by other factors).

In connection with the need to eliminate the disadvantages of the photographic method, in recent years work has developed on the application of photoelectric methods in spectral analysis. Among them, the methods based on the use of photomultipliers have become most widespread.

The first in time was the work of S. F. Rodionov,⁷ in which an electrophotometer was described, intended for measuring absorption and based on the use of a Kubetsky photomultiplier. This work was published in 1939. In subsequent years works of this kind multiplied especially.

The advantages of using a photomultiplier as compared with a photographic plate can be seen very clearly, for example, from the work of Dieke and Crosswhite[^17].

Figure 9 shows a portion of the spectrum of iron. In the middle part of the figure is shown the ordinary spectrum obtained by photographic means—

Fig. 9. Portion of the spectrum of iron. In the middle is shown the spectrogram, at the top—the microphotogram, at the bottom the photoelectrogram.

spectrogram; in its upper part is its microphotogram. The short, chaotically shaped serrations in the lower part of the microphotogram are distortions caused by the graininess of the photographic emulsion on which the spectrogram was photographed.

In the lower half of the same figure is shown a photoelectrogram recorded with the aid of a photomultiplier. The recording amplitudes are propor-

tional intensities of the spectral lines, while distortions are entirely absent.

Figs. 10 and 11 illustrate the resolving power and sensitivity of this measurement method. The resolving power, determined by the dispersion of the spectrograph, remains the same as in photography. This is seen from the recording of the iron triplet at 3100 Å (Fig. 10), whose lines are separated from one another by 0.07 Å.

Fig. 10. Iron triplet 3100 Å (second order).

The possibilities of the method with respect to sensitivity are clearly seen from Fig. 11, which shows four photoelectric recordings of the mercury line 4358 Å at different levels of apparatus sensitivity. Records $A$ and $B$ were made without the use of an amplifier after the photomultiplier; $C$ and $D$—with an additional direct-current amplifier. The sensitivity in recording curve $D$ was 500 times greater than in recording $A$. Thus, by this method it is possible to record both the line 4358 Å and the line 4390 Å, although the latter is approximately 40,000 times weaker than the former. Similar sensitivity can be achieved by the photographic method only at the cost of very long exposures.

In addition to the advantages indicated, the speed and simplicity of analysis by the photoelectric method are of great practical importance. A degree of automation of the measurement process that is difficult to attain for the photographic method, and direct readout, are comparatively easy to realize in the photoelectric method.

In the following paragraphs we shall consider some general questions that arise in the application of photoelectric methods of spectral analysis, and shall describe some of the most interesting measurement techniques.

SHORTCOMINGS OF THE METHOD CAUSED BY THE LIGHT SOURCE, AND THEIR ELIMINATION

As is known, the concentration of the element under investigation $C$ in the sample is connected with the intensity $F$ of the lines of the element in the sample by the expression[^65]

\[ F = aC^b, \tag{6} \]

where $a$ is a constant characterizing the properties of the line, the rate of evaporation of the sample, and the rate of diffusion of the vapors; $b$ is a quantity depending on concentration, but over a certain interval of concentrations it may be considered constant. At low intensities $b = 1$. As the intensity increases, its value decreases.

The principal sources of excitation of the spectrum used in spectral analysis are the flame, the arc, and the spark. The flame is the oldest and sufficiently stable source of excitation for the purposes of spectral analysis; however, it has the lowest temperature and makes it possible to obtain only the brightest lines.

Fig. 11. Mercury line 4358 Å, recorded at different sensitivities.

A higher-temperature source is the arc. Depending on the electrodes used, the temperature of the arc lies within the range from 4100 to 7000° K. Recently the alternating-current arc has usually been used, in particular, the activated alternating-current arc.

Oscillographic recording of the intensity of the ZnI 4811 Å line, in parallel with recording of the current and voltage across the discharge gap, carried out for an alternating-current activated arc by Abramson and Mandelstam^36, showed that the intensity of lines in the arc spectrum changes, in general, in parallel with the change in the discharge current; however, at the same time, the presence of random irregular changes in line intensity is characteristic. An analogous pattern was observed for a direct-current arc by other investigators^35.

Fig. 12. Zonal characteristic of the photocathode of a type 931A photomultiplier.

As may be supposed, the changes in intensity are caused by vortex motions of the gas in the arc channel. In this process there is a displacement of the anode and cathode spots over the surface of the electrodes, leading to a change in the length and shape of the arc column. Instability of this kind, unpleasant also in the case of the photographic method, is an even more substantial source of interference in the photoelectric method.

The changes described in the arc lead to displacement of the light spot on the photocathode. If this spot is sufficiently small, the result will be changes in the photocurrent at the output of the photomultiplier, caused, on the one hand, by nonuniformities in the zonal sensitivity of the photocathode and, on the other hand, by the properties of the focusing optics of the photomultiplier. In photomultipliers having an electrostatic screen in the form of a grid in front of the photocathode window, the zonal characteristic of the photocathode receives additional distortions caused by the presence on the photocathode of shadows from the conductors of the electrostatic screen.

Figure 12 shows the zonal characteristic of the cathode of an RCA 931A photomultiplier with an electrostatic screen in front of the photocathode^20.

While the intrinsic zonal sensitivity of the photocathode is comparatively uniform, the presence of a zigzag screen grid in front of the photocathode window gives the curve a sawtooth character. It is obvious that the presence of such a zonal characteristic is a drawback, additionally complicating the problem of photoelectric registration of the intensity of spectral lines.

The “hottest” source of excitation of spectral lines is the condensed spark—in it, the lines of all the most difficultly ionized elements are excited. The temperature of the spark depends on the strength of the current flowing and is determined by the spark regime and by the parameters of the circuit. The spark temperature may reach 12000° K.

The high current density in the spark and the rapidity of its increase are the cause of the appearance of ejections of torches—luminous jets of vapor of the substance—which occur in the oscillatory stage of the discharge.

Oscillographic recording of the course of the intensity of various lines in the spark, carried out by a number of investigators20,35,36, shows that, despite the general reproducibility of the current from discharge to discharge, considerable fluctuations of line intensity occur. Only over a comparatively short period, of several seconds’ duration, can the mean value of the intensity be considered sufficiently constant.

The photoelectric method offers possibilities for partial neutralization of these factors.

A considerable weakening of the changes in line intensity, occurring both in the case of the spark and in the case of the arc, is achieved by averaging or integrating the pulses of photocurrent over a certain interval of time. By using an inertial current meter, such as, for example, a galvanometer with a large damping decrement, or by shunting a short-period galvanometer with a resistance and obtaining such a degree of damping that the oscillations of the galvanometer will be aperiodic, one obtains an averaging of the current pulses measured over a certain time \(\tau\), necessary for the attainment of the equilibrium position with the required degree of accuracy.

This method was applied in the work of Buttner and Brewington16, considered below, and gave good results. The short-period galvanometer used by them was shunted with an Ayrton shunt, the resistance of which was equal to half the external critical resistance of the galvanometer.

Another variety of the averaging method consists in increasing the time constant of the amplifier circuit connected to the output of the photomultiplier. In this case the section consisting of the resistance \(R\) and the capacitance \(C\), which determines the time constant \(RC\) of the circuit, may be inserted either at the input18, or at the output20, or in the intermediate stages of the amplifier circuit. The time during which the readings of the output meter become established depends on the required

accuracy of measurement. For example, the readings reach 95% of the true value in a time \(\tau=3RC\) seconds. Here \(R\) is expressed in ohms, and \(C\) in farads.

In a number of circuits for photoelectric measurement of the intensities of spectral lines \(^{19,21}\), a method is used in which the current is integrated over a certain interval of time. This method consists in the following: the photocurrent \(I_{\phi}\), flowing in the anode circuit of the photomultiplier, charges a capacitor of capacitance \(C\) connected into this circuit. If leakage of the capacitor and of the circuit elements shunting it is negligibly small, then after a time \(\tau\) has elapsed from the start of measuring the current \(I_{\phi}\), the voltage on the capacitor reaches the value

\[ U=\frac{I_{\phi}\tau}{C}. \tag{7} \]

In the case of interest to us the photocurrent \(I_{\phi}\) is a complicated function of time, determined as the integral value of all the individual photocurrent pulses over the time interval \(\tau\). With \(\tau\) of duration 10–20 seconds, the measurement can be carried out with an accuracy entirely satisfactory for practice. The measurement problem is reduced to determining the magnitude of the voltage \(U\), which is achieved by using a sensitive cathode voltmeter with a high-resistance input.

To eliminate the shortcomings caused by displacement of the arc column, a frosted quartz plate is sometimes used, placed in front of the photocathode window \(^{19}\). As a result of diffuse scattering of the light incident on the plate, the sensitivity curve becomes fairly flat; however, the sensitivity itself is substantially reduced.

Both the arc and the spark are powerful sources of electrical interference. The methods of combating this interference are the usual ones in such cases: maximum suppression of the intensity of the interference, limitation of it in the spectrum, the use of careful shielding both of the excitation source (interference) and of the photoelectric apparatus, as well as the use of filters in the power-supply circuits and the powering of the excitation source and the photoelectric apparatus from separate sources.

ELIMINATION OF THE INFLUENCE OF THE CONTINUOUS-SPECTRUM BACKGROUND

The background produced by the continuous spectrum limits the sensitivity and accuracy of analysis when working with lines of low intensity, i.e., it makes the determination of small concentrations difficult.

The role of the background in lowering the sensitivity of analysis can be illustrated by Fig. 13 \(^{21}\), where, on a semilogarithmic scale, the dependence of the instrument readings for the spark and for the arc on the concentration of molybdenum is shown.

From Fig. 13 it follows that, already beginning with concentrations of 0.1% and less, the dependence of the instrument readings on concentration acquires, for the spark, a nonlinear character, and the sensitivity of measuring concentrations below 0.1% falls sharply. A similar picture is also observed in the case of the arc, but in this case the nonlinearity of the curve begins at a concentration of 0.01%.

The nonlinearity of both curves is to a considerable degree due to the masking influence of the background of the continuous spectrum, the radiation of which falls on the photocathode simultaneously with the radiation of the spectral line being measured.

Fig. 13. Working curves for molybdenum contained in iron alloy. The curves show the role of the background when using a spark and an arc as excitation sources.

The decrease in the accuracy of measurements caused by the influence of the background is presented in Fig. 14²¹, where the mean error in measuring the percentage content of chromium in a sample is shown.

In the case of the spark, beginning with concentrations of several percent and approximately down to a concentration of 0.07%, the accuracy of measurement

Fig. 14. Error of analysis as a function of the concentration of the element being analyzed. Each point corresponds to the value of the mean error, determined from 20 measurements of one and the same sample.

is 2%, but with a further decrease in concentration the mean error rises sharply, and consequently the accuracy of measurement sharplyತ್ತ

drops. For an arc, the measurement accuracy at high concentrations is about 5%; when the concentration is lowered to 0.005%, it drops only slightly.

Thus, in measuring low concentrations, the advantage of the arc over the spark is obvious.

A reduction in the brightness of the background in comparison with the brightness of the line can be achieved by increasing the dispersion of the spectrograph, and also

Fig. 15. Details of the exit slit: a—without background compensation; b—with background compensation. Dimensions in millimeters.

by choosing the optimum slit width, at which the most advantageous ratio is obtained between the brightness and width of the lines and the brightness of the background^65.

Another way of reducing the influence of the background, applicable only in the case of the photoelectric method, consists in compensating the photocurrent caused by the background. For this the following procedure is used.

The exit slit, positioned with respect to the measured line as shown in Fig. 15, a, is doubled in size, and the line is placed in one half of the slit (Fig. 15, b). By using an optical shutter that makes it possible alternately to open one half of the slit and close the other, one can alternately direct to the photocathode either the radiation of the line and the background, or only the radiation of the background. Synchronously with the switching of the shutter, the polarity of the capacitor integrating the photocurrent is switched in the anode circuit of the photomultiplier; in this way, if not completely, then to a considerable extent, the influence of the background from both halves of the slit is compensated in installations for automatic spectral analysis^1,21.

The effectiveness of this method is evident from Fig. 16, which shows curves of the dependence of the instrument readings on the nickel concentration with background compensation and without compensation.

THE ROLE OF THE DARK CURRENT AND THE WEAKENING OF ITS INFLUENCE

The dark current of a photomultiplier, when measuring weak photocurrents, has the same masking effect as does a continuous spectral background. Reduction of the dark current by cooling, which gives radical results, as was already indicated above, is technically very inconvenient; moreover, for the tasks of spectral analysis it is usually sufficient to reduce the dark current by 1–2 orders of magnitude (photomultipliers with an \([{\rm Sb}—{\rm Cs}]\) photocathode are meant). Therefore, in apparatus for industrial or semi-production application, simple compensation or elimination of the constant component of the dark current is more often used.

The coupling capacitance prevents the constant component of the anode current of the photomultiplier, including the dark current, from reaching the grid of the input tube of the amplifier. Since, however, fluctuations of the dark current pass through the capacitor and are then amplified by the amplifier, to reduce their influence a limitation of the fluctuation spectrum is used by narrowing the passband of the amplifier.

Fig. 16. Working curves for nickel with and without background compensation. A 60% background compensation has been achieved.

The use of this method of eliminating the dark current, of course, presupposes that the luminous flux must be modulated. This latter circumstance in a number of cases is inconvenient or undesirable and, consequently, limits the possibility of applying the method under consideration. However, for example, in the case of using an alternating-current arc or spark as the excitation source, the luminous flux is already modulated by the excitation source itself. The modulation frequency in this case is equal to twice the frequency \(f\) of the alternating current feeding the arc.

To limit the fluctuation spectrum, any methods of selective low-frequency amplification may be applied. The simplest method is the use of ordinary resonant amplifiers,

tuned to the frequency \(2f\). However, circuits consisting of \(L\) and \(C\) have larger damping decrements at low frequencies; therefore better results are obtained by using amplifiers with negative feedback based on the application of parallel T-filters consisting of \(R\) and \(C\) \(^{20,66,67,68,69}\). Such amplifiers possess high selectivity and can be made for very low frequencies.

The schematic diagram of a single-stage amplifier of this type is shown in Fig. 17. The pass-band width thereby attained is approximately \(2\)–\(3\) cycles at a frequency of \(120\) cycles (Fig. 18).

When using a photomultiplier having a dark current of \(1\cdot 10^{-9}\) a, the presence of an amplifier pass band \(2\) cycles wide makes it possible to reduce the fluctuations of the dark current to a value of \(1.3\cdot 10^{-11}\) a (for \(M = 10^5\)).

Fig. 17. Schematic diagram of a single-stage amplifier with negative feedback, having a parallel T-filter of \(R\) and \(C\).

Fig. 18. Selectivity curve of an amplifier with negative feedback, having a parallel T-filter of \(R\) and \(C\), shown in Fig. 17.

A necessary condition for the effective use of such circuits is the requirement of sufficient stability of the frequency of the alternating-current mains.

Another type of resonant amplifiers are amplifiers based on the use of mechanical resonance. A tuning fork or the vibrator of a reed frequency meter is used here as the filtering element. Amplifiers with filters of this type make it possible to obtain very narrow pass bands. They have also found application in photoelectric apparatus for spectral analysis \(^{70}\).

Compensation of the constant component of the dark current with simultaneous limitation of the fluctuation spectrum is used in apparatus based on the recording or amplification of direct current.

Usually, in the simplest cases, two photomultipliers are used: one for the analyzed line, the other for the comparison lines (the internal-standard lines). Both photomultipliers are connected in such a way that the internal resistances of the “last cascade—anode” sections and the resistances of the anode load form the arms of a bridge.

If the photomultipliers have sufficiently identical parameters and, in particular, \(I_{t1}=I_{t2}\), then the balance of the bridge will not be disturbed

Fig. 19. Circuit for mutual compensation of the dark currents of two photomultipliers.

by the dark current. Since, however, in practice it is very difficult to select a pair of photomultipliers having the same dark current, equalization of the dark currents is achieved by adjusting the voltage applied to each photomultiplier. In doing so, of course, the identity of the sensitivities of the two photomultipliers must be impaired, and this must be taken into account.

One circuit of this kind is shown in Fig. 19.

As for fluctuations of the dark current and photocurrent, they are practically limited only by the inertia of the galvanometer connected in the diagonal of the bridge. The frequency band passed by the galvanometer system is characterized by the expression

\[ \Delta f \cong \frac{1}{T_0}, \tag{8} \]

where \(T_0\) is the natural period of oscillation of the moving system of the galvanometer in seconds, and \(\Delta f\) is the frequency band in hertz.

In those cases where a cathode voltmeter is connected into the diagonal of the bridge, the pass band is determined either by the period of oscillation of the output meter or, if this period is small, by the time constant \(RC\) of the input of the cathode voltmeter. In the latter case

\[ \Delta f \simeq \frac{1}{2RC}, \tag{9} \]

where \(\Delta f\) is in hertz, \(R\) in ohms, and \(C\) in farads. To obtain the required pass band, the necessary capacitance \(C\) is connected in parallel with the input of the cathode voltmeter.

Fig. 20. Circuit for compensating the dark current of a photomultiplier by means of an external direct-current source.

Another method of compensating the constant component of the dark current consists in having the dark current of the photomultiplier compensated by a constant current from some external source (Fig. 20).

A shortcoming of the compensation methods considered above is the dependence of the degree of compensation on the constancy of the dark current. Kubetskii \(^{11}\) carried out a method of compensating the dark current and measuring weak luminous fluxes, which he called the integral-balance method; close to it is also the method later applied by Saunderson et al. \(^{19,21}\) for eliminating the background of the continuous spectrum and the dark current. For this purpose Kubetskii uses two capacitors of equal capacitance, which integrate the dark current and the photocurrent (or the photocurrents from the measured and reference sources). The measurement is made by comparing the charges accumulated by the two capacitors. Saunderson uses one capacitor for this purpose.

Both in Kubetskii’s method and in Saunderson’s, the inconstancy of the dark current is eliminated to a certain extent.

The method using one capacitor, the circuit of which is shown in Fig. 21, has the advantage that the error due to nonidentity of the capacitors (inequality of capacitances and leakages) is eliminated. The intervals of time during which the capacitor is charged by the photocurrent of the line and (with the opposite sign) by the dark current, or by the dark current and the photocurrent of the background, alternate with sufficient frequency during one measurement. This achieves approximate equality of the influence of the dark current in the pro-

...in the process of charging the capacitor from the line and from the background. The number of alternations is equal to 10; the duration of each charging act is 1 second; the duration of charging during one measurement cycle is 20 seconds.

With proper accuracy of operation of the mechanical system and of the electrical contacts of the switches, this method should be considered considerably better than compensation by manual adjustment of the magnitude of the compensating current.

In photometric circuits of this kind, where the measure of the magnitude of the light flux being measured is the potential difference on a certain capacitor connected simultaneously into the circuit of the photomultiplier anode and the grid of the first amplifier tube, it is necessary, taking into account the high quality of the capacitor insulation, to short-circuit the storage capacitor after each measurement cycle, allowing the preceding charge to drain off completely. In those cases where direct-current amplification is used ^72, the quality of the insulation of the photomultiplier anode and the constancy of the leakage magnitude are very important.

Fig. 21. Circuit for automatic compensation of the dark current of a photomultiplier.

METHODS OF MEASUREMENT

Modern methods of quantitative spectral analysis are based on the measurement of the relative, and not the absolute, intensity of spectral lines. To determine the concentration of the analyzed element (impurity element), the ratio is measured of the intensity of the analyzed element to the intensity of the line of the comparison element (internal standard) contained in this same sample. As the comparison element, either the principal element of the sample is chosen, or an additional element specially introduced in the same quantities.

If, in such a method, the lines whose intensities are being compared are homologous, then a change in the excitation intensity of the spectrum, which occurs when using such sources as a direct-current or spark arc, will not affect the relative intensity of the lines being compared.

On the basis of expression (6), for the ratio of the mean intensity values of the analyzed line \(F_{\text{an}}\) and the comparison line \(F_{\text{cp}}\), we obtain:

\[ \frac{F_{\text{an}}}{F_{\text{cp}}}=\frac{a}{F_{\text{cp}}}C^b=a'C^b, \tag{10} \]

or

\[ \lg \frac{F_{\text{an}}}{F_{\text{cp}}}=b\lg C+\lg a'. \tag{11} \]

The logarithm of the concentration depends linearly on the logarithm of the intensity ratio of the lines being compared.

The concentrations of the elements being analyzed may differ from one another by several orders of magnitude. Therefore, the entire range of measurable concentrations for one and the same analyzed line is usually divided into several subranges; moreover, in order that the results of measuring intensity ratios be more accurate, homologous lines of the comparison element that are closest in intensity are used for comparison.

Although in practice it is possible to carry out not only the rapid alternate feeding of the compared lines to one and the same photocathode, but even their simultaneous feeding (using, for example, the method of modulating them at different frequencies), nevertheless a separate photomultiplier is usually used for each line. Thus, at a minimum, two photomultipliers are used simultaneously. When proceeding to the investigation of another analyzed element, or of another concentration of the same element that differs greatly in magnitude, the photomultiplier of the analyzed element and the photomultiplier of the comparison element are moved.

On the guides along which the photomultipliers move, slits are placed at the positions corresponding to the respective lines, the positions of which are determined in advance. Even so, a final precise adjustment of the photomultiplier in front of the slit by means of the corresponding adjusting screws is required. Therefore, in those cases where the speed of analysis is of primary importance, and the concentrations of the elements being analyzed lie within known limits, one photomultiplier is used for the comparison line and one photomultiplier each for all the analyzed lines. The measurement of the intensity of all lines takes place simultaneously.

The measurement of the intensity ratio is reduced to measuring the ratio of the corresponding photocurrents or voltages and introducing a correction for the spectral sensitivity of the photomultipliers.

The most widespread and simplest method is the method of direct reading. In this method the measuring instrument, connected, for example, analogously to the scheme in Fig. 19, may be directly calibrated for the concentration of the analyzed ele-

ment. An installation of this type is described, for example, by Nachtoll and Bryan[^18].

The circuit operates on the principle of bridge unbalance. The dependence of the bridge unbalance voltage \(U_{\mathrm{kv}}\), recorded by a cathode voltmeter (in the diagram of Fig. 19 denoted by the letter \(G\)), is expressed by the formula

\[ \lg \left(\frac{U_{\mathrm{kv}}}{R_{\mathrm{sr}} I_{\mathrm{fsr}}} + 1\right) = b \lg C + \lg a' - \lg \frac{\gamma_{\mathrm{sr}}}{\gamma_{\mathrm{an}}}, \tag{12} \]

where \(I_{\mathrm{fsr}}\) is the photocurrent of the photomultiplier for the comparison line,

\(\gamma_{\mathrm{sr}}\) and \(\gamma_{\mathrm{an}}\) are, respectively, the integral sensitivities of the photomultipliers for the comparison line and for the analyzed line,

\(R_{\mathrm{sr}}\) is the resistance in the anode circuit of the photomultiplier for the comparison line.

Transition from one analyzed element to another is carried out by moving the photomultiplier along the spectrum. The determination of 8 elements in one sample is performed with this instrument in 4 minutes.

Table II gives the maximum and mean deviations for 15 measurements made with this instrument over the course of two weeks.

Table II

	Maximum (%)	Mean (%)
Deviation from the mean value of the voltage at the instrument output	0.11	0.07
Deviation from the established percentage of aluminum (5.9%)	0.18	0.12
Percentage error	3.1	2.0

One of the disadvantages of the direct-reading method is the necessity of recalibrating the scale of the instrument when the photomultiplier is replaced. This is evident from formula (12).

Predominant application in the photoelectric apparatus of spectral analysis is found by the null method[^16,^19,^20,^21]. In the installation described by Buttner and Brivington[^16], the percentage concentration of the analyzed element is determined from the ratio of the inter-cathode voltages of two photomultipliers (for the analyzed line and the comparison line), which is established when the bridge is balanced by changing the voltage on one of the photomultipliers,

The dependence of the interstage voltages of the photomultiplier for the analyzed line \(U_{\rm an}\) and of the photomultiplier for the comparison line \(U_{\rm cp}\) on the concentration of the element being analyzed is expressed by the formula

\[ \lg \frac{U_{\rm cp}}{U_{\rm an}}=\frac{2}{n}\left(b\lg C+\lg a'\right), \tag{13} \]

where \(n\) is the number of stages of secondary-electron emission. The voltmeter measuring the interstage voltage can be calibrated directly in percent concentration of the element being measured.

According to the authors’ data, for samples containing aluminum with a concentration within the range \(0.009\text{—}0.18\%\), the mean measurement error (in comparison with the calibration curve) was \(7.2\%\), while for samples with a concentration of \(5.6\text{—}10.2\%\) the mean error was \(4.7\%\).

Kessler and Wolf \({}^{20}\) also constructed an instrument using the null method. Their circuit, shown in Fig. 22, is distinguished by high sensitivity and high accuracy of measurement. This has been achieved at the cost of complicating the apparatus, which, however, is fully justified both by the qualities mentioned above and by the simplicity of the measurements.

The circuit contains two symmetrical halves, each of which consists of a photomultiplier, a preamplifier with a voltage divider at the input, used when measuring intense lines (to avoid distortion), a calibrated voltage divider intended for measuring the ratio \(F_{\rm an}/F_{\rm cp}\), an amplifier with negative feedback and a pass band of the order of \(2\text{—}3\) cps at a frequency of 120 cps, a buffer amplifier, and a detector.

The circuit operates on alternating current, using modulation of the arc light at a frequency of 120 cps. The detected voltages of the two halves of the circuit are connected in opposition to one another and charge a capacitor of large capacitance, the voltage of which is fed to a cathode voltmeter. The cathode voltmeter is used as the null indicator. The constancy of the voltage feeding the photomultipliers (1263 V) is maintained with an accuracy of \(0.02\%\), which is necessary for obtaining high measurement accuracy.

The displacement of the calibrated voltage divider located in the channel measuring the investigated line is fixed by the zero position of the output indicator. The ratio

\[ p=\frac{R_{\rm an}}{R_{\rm cp}} \]

of the resistances of the calibrated dividers located in the channels of the analyzed line and the comparison line will be proportional to the ratio of the intensities of the analyzed line to the comparison line, i.e., \(F_{\rm an}/F_{\rm cp}\).

The dependence of the ratio \(R_{\rm an}/R_{\rm cp}\) on the concentration of the element being analyzed is expressed by the formula

\[ \lg \frac{R_{\rm an}}{R_{\rm cp}}=b\lg C+\lg a'-\lg \frac{\gamma_{\rm cp}K_{\rm cp}}{\gamma_{\rm an}K_{\rm an}}, \tag{14} \]

Fig. 22. Circuit for measuring the ratio of the intensities of the analyzed line and the comparison line, using alternating-current amplifiers with narrow-band filters. The values of \(R\) and \(C\) are given respectively in megohms and microfarads.

where \(K_{\mathrm{sr}}\) and \(K_{\mathrm{an}}\) are the amplification coefficients of the sections “amplifier input—resistance \(R\)” of each channel. In this circuit high demands are placed on the stability of operation of the amplifiers and on the constancy of the sensitivity of the photomultipliers.

The apparatus considered was used for the quantitative analysis of chromium in steel. As the excitation source an air, condensed, interrupted spark was used, supplied by a voltage of 14,000 V.

The authors note the large role of fatigue of the photomultipliers, entailing a change in their integral sensitivity. To reduce fatigue when measuring intense spectral lines, the light flux of the photomultipliers should always be weakened, limiting its maximum value to \(1\ \mu\text{A}\) by the use of neutral filters. Another measure recommended by the authors for reducing the influence of fatigue is preliminary illumination of the photomultiplier for several minutes with light from the spark source.

Comparison of the results of chemical analysis with analysis carried out by means of this apparatus showed that the difference in the results of the two analyses ranges from 1 to 2.8%, at chromium concentrations, respectively, from 2.95 to 0.82%.

As will be shown below, analysis of the errors when using photoelectric apparatus for spectral analysis leads one to believe that the principal causes of the errors lie not in the photoelectric apparatus, but in the excitation sources.

The shortcomings of the photoelectric apparatus considered above are the length of the measurements, the impossibility of simultaneously measuring the concentrations of all analyzed elements of the sample at once, and the inconveniences introduced by moving the photomultipliers.

The tasks of industry require further acceleration and simplification of the measurement technique. This is possible only as a result of maximum automation of the analysis process.

Saunderson et al.\(^{19}\) carried out an installation for automatic quantitative spectral analysis, intended for the investigation of magnetic alloys in a factory laboratory. The installation makes it possible to analyze simultaneously seven components of an alloy. The duration of the measurement is 40 seconds, and the entire interval of time from the moment the melt sample is sent from the shop until the result for seven elements is received back is no more than 5 minutes. The productivity of the installation is characterized by the figures: 4000 samples and 20,000 quantitative determinations per month.

The methods of compensation of background and dark current which are used in this installation have already been shown above. The basic technical principles of automation of the measurements can be clarified from Fig. 23.

\(S\) is a spectrograph with a concave grating. The light from the analyzed line and the comparison line passes through the exit slits and falls on the corresponding photomultipliers \(\Phi_{\mathrm{an}}\) and \(\Phi_{\mathrm{sr}}\). The photocurrents \(I_{\Phi\mathrm{an}}\) and \(I_{\Phi\mathrm{sr}}\) ...

charge the capacitors \(C_1\) and \(C_2\) during the time when the optical shutter, not shown in the drawing, admits light to the corresponding photomultiplier. After the excitation period ends, the switches \(B\) close simultaneously and the capacitors \(C_1\) and \(C_2\) begin to discharge through the resistances \(R_1\) and \(R_2\), which are the input resistances of two direct-current amplifiers (in the diagram the amplifiers are conventionally shown as two triodes). At the moment—

Labels in Fig. 23: source; analyzed line; comparison line; entrance slit; concave grating; exit slits; \(S\); \(\Phi_{\text{an}}\); \(\Phi_{\text{sr}}\); \(C_1\); \(C_2\); \(B\); \(B\); \(R_1\); \(R_2\); amplifier; amplifier; relay 1; relay 2; recording instrument.

Fig. 23. Schematic circuit for measuring the ratio of the intensities of two compared spectral lines \((^{19})\).

when the voltage at the input of the corresponding amplifier falls to some fixed value \(U_k\), for example to 1 volt, a relay located at the output of the amplifier operates. If such measurement conditions are provided under which \(I_{\text{sr}} > I_{\text{an}}\), then the voltage on the capacitor \(C_1\) reaches the value \(U_k\) earlier than the voltage on the capacitor \(C_2\).

Before the measurement begins, relay 1 is open and relay 2 is closed. Therefore, as a result of the operation of relay 1, the pen of the self-recording instrument begins to write, its tape moving at a constant speed. When relay 2 operates, recording ceases. As a result, a straight line is recorded on the tape, the length of which is proportional to the time interval \(\Delta t\) between the instants of operation of relays 1 and 2.

Since, on the basis of the formula for the discharge of a capacitor,

\[ U_k = Ue^{-\frac{t}{RC}} \]

(\(U\) is the initial voltage on the capacitor, equal to \(U_{\text{an}}\) for \(C_1\) and \(U_{\text{sr}}\) for \(C_2\)), the times elapsed before the capacitors reach the final potential \(U_k\) are equal to

\[ t_1=R_1C_1\lg\frac{U_{\text{an}}}{U_k} \quad\text{and}\quad t_2=R_2C_2\lg\frac{U_{\text{sr}}}{U_k}, \]

then, taking \(R_1=R_2=R\) and \(C_1=C_2=C'\), the segment \(\Delta t\) is equal to:

\[ |\Delta t|=RC'\lg\frac{U_{\text{an}}}{U_{\text{sr}}}. \tag{15} \]

Since

\[ \frac{F_{\text{an}}}{F_{\text{sr}}} = \frac{\gamma_{\text{sr}}}{\gamma_{\text{an}}}\cdot \frac{U_{\text{an}}}{U_{\text{sr}}}, \]

then

\[ |\Delta t|=RC'\lg \frac{F_{\text{an}}\gamma_{\text{an}}}{F_{\text{sr}}\gamma_{\text{sr}}}. \]

On the basis of formula (11) we obtain

\[ |\Delta t|=RC'\left(b\lg C+\lg a' + \lg\frac{\gamma_{\text{an}}}{\gamma_{\text{sr}}}\right). \tag{16} \]

The logarithm of the concentration of the element is proportional to the time, i.e., to the length of the traced straight line. According to this formula, calibration curves are constructed for each element.

It is seen from formula (16) that, when photomultipliers are changed or their sensitivity is altered, the graph \(|\Delta t|=f(\lg C)\) is displaced parallel to itself, while the angular coefficient \(bRC'\) remains unchanged and, consequently, the calibration of the instrument is easily restored. In practice the dependence \(|\Delta t|=f(\lg C)\) proves to be not entirely linear, which is explained by incomplete compensation of the background.

The complete layout of the installation is much more complicated than the schematic diagram given above. To amplify the photocurrents of eight photomultipliers, eight identical amplifiers with negative feedback are used. The electromechanical part consists of a complex system of relays and commutators. The entire installation, together with the spectrograph, is mounted as a single unit. Fig. 24 shows the system of arrangement of the optical components and photomultipliers. (In addition to the simultaneous analysis of seven elements, an analysis of three more elements can subsequently be made.)

Table III gives figures for the measurement errors obtained with this apparatus for various concentrations of certain elements.

The drawbacks of this installation are the difficulty of maintaining the constancy of the amplifier zero, the presence of a complex multi-contact elec-

tromechanical system, as well as the need to use rulers and calibration curves to determine the measurement results.

Fig. 24. Diagram of the arrangement of eleven photomultipliers, optical components, and the path of the rays in the installation[^19].

Carpenter et al.[^21] constructed an automatic installation for spectral analysis, making it possible to obtain the finished result of the analysis directly on the scale of the instrument in values of the element concentration. In this installation many essential

Table III

Element	Concentration, in %	Measurement error, in %
Mn	0.30	1.9
Si	0.008	15.4
Si	0.046	8.0
Si	0.13	2.7
Cu	0.008	5.4
Cu	0.04	3.1
Cu	0.21	3.5
Be	0.0001	21.1
Be	0.0025	5.8

features of Saunderson’s apparatus, such as, for example, the method of automatic compensation of the dark current and background; corrections for the influence of the uncompensated background are introduced directly into the graduation of the instrument scale.

Fig. 25. Schematic diagram of the measurement of the ratio of the intensities of two compared spectral lines in an apparatus with direct automatic readout\(^ {21}\).

The main difference lies in the manner of connecting the capacitors and in the method of indication. The capacitors \(C_1\) and \(C_2\), charged by the photocurrents \(I_{\mathrm{an}}\) and \(I_{\mathrm{sr}}\), are automatically switched on as shown in Fig. 25. The capacitor of the comparison element \(C_2\), whose voltage is higher than the voltage on capacitor \(C_1\), is discharged through the resistance \(R\). Simultaneously with the switching on of the capacitors, the disk carrying the scale of concentrations of the element being analyzed begins to rotate (Fig. 26). The speed of rotation of the disk is 1 revolution in 10 seconds.

When the difference between the voltages of the two capacitors reaches a certain value, the relay operates and the disk stops. By analogy with formula (15),

\[ |t| = RC_2 \lg \frac{U_{\mathrm{an}}}{U_{\mathrm{sr}}}, \]

whence, on the basis of formula (11),

\[ |t| = RC_2 \left(\lg C + \lg a' + \lg \frac{\gamma_{\mathrm{an}}}{\gamma_{\mathrm{sr}}}\right). \tag{17} \]

Fig. 26. Appearance of the graduation of the instrument scale, directly recording the concentration of the element being analyzed.

The angle of rotation of the disk is proportional to the discharge time of capacitor \(C_2\), which in turn is proportional to the concentration of the element, according to formula (17).

The discharge time of capacitor \(C_2\) makes it possible to record two logarithmic cycles of concentrations, i.e., the ratio \(C_{\max}\) to \(C_{\min}\) is \(100:1\). The correction for background is introduced into the calibration of the scale on the basis of experimental data.

Table IV gives figures characterizing the sensitivity and accuracy of this setup.

Table IV

Element	Line wavelength in Å	Spark: range of measured concentrations in %	Spark: measurement error in %	Arc: range of measured concentrations in %	Arc: measurement error in %	Arc: concentration recorded with an accuracy up to 25%
Ni	3414	0,05—5,0	2,0	0,01—0,2	7	0,004
Cr	4254	0,05—5,0	1,5	0,005—0,2	5	0,001
Si	2881	0,07—5,0	2,5	0,02—0,5	6	0,007
Mn	2933	0,05—5,0	3,0	0,02—2,0	9	0,01
Cu	3274	0,01—1,0	2,0	—	—	—
Mo	3864	0,04—5,0	2,5	0,002—0,2	6	0,001
Al	3944	0,04—5,0	2,5	0,005—0,1	5	0,002
Sn	3175	—	—	0,01—0,5	7	0,005

The principal factors determining the instrumental accuracy are the stability of the amplifier and the relay, the accuracy of the relay actuation time, the magnitude of the capacitor leakage, and the scale-reading error. In the authors’ opinion, the errors are distributed as follows: the error in determining the time (with a capacitor of \(0.1\) microfarad capacity and a leakage equal to \(50\,000\) megohms) is \(0.6\%\); the error due to instability of the circuit (zero drift of the amplifier) and instability of the amplification coefficient is \(0.6\%\); the delay time in relay actuation is \(0.01\) second; the scale permits readings with an accuracy of \(1\%\), i.e., it is the largest source of instrumental errors. However, the spectrochemical errors are still larger.

The spectrochemical accuracy of the analysis depends on the light source. The light sources used were a condensed spark fed by a voltage of \(25\,000\) V, and an alternating-current arc fed from a \(2200\) V transformer. The total magnitude of the experimental

errors was already given in Fig. 14 and makes it possible to consider that the accuracy of measurements carried out with an apparatus of this type is determined primarily by its spectrochemical accuracy.

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1. References visible in the source as \(1,5,6\). ↩