MULTI-SLIT SPECTROPHOTOMETRY

In recent times the field of application of infrared spectroscopy methods in research and factory laboratories has expanded considerably. The expansion of the field of application of these methods is due primarily to the significant improvement of both the instru-

spectral instruments—monochromators, as well as to progress in the design and manufacture of infrared-radiation receivers—thermoelements and bolometers; this also includes achievements in improving sources of infrared radiation. Alongside the problems already solved, new problems arise which, in turn, impose ever higher requirements on increasing the sensitivity of spectral apparatus. Since the best examples of modern thermal indicators are approaching, in their sensitivity, the theoretical limit set by the existence of thermal fluctuations, and at the same time increasing the radiation intensity of sources in the region of medium and long wavelengths encounters insurmountable difficulties, the only way to increase the effectiveness of infrared spectroscopy remains the search for new principles for improving spectral instruments. In this direction substantial progress has been achieved. It is known that it is always possible to obtain a considerable increase in the amount of radiation passing through a monochromator by widening the entrance and exit slits. However, this method of increasing sensitivity has its negative side, consisting in a reduction of the resolving power of the instrument, as a result of which it becomes unsuitable for studying the fine structure of absorption bands in the infrared region, which is of great scientific and practical significance.

An original method, making it possible to increase the sensitivity of spectral instruments without reducing the resolving power, was recently described by Golay*) using ideas expressed by Fellgett. Since this method may find application not only in infrared spectroscopy, where it makes it possible to increase the efficiency of instruments by more than an order of magnitude, but also in other fields of experimental physics, when it is necessary to record one or another distribution function, it seems advisable to set forth this new principle at least briefly.

Let us suppose that we have a monochromator at our disposal. We first set the width of the entrance and exit slits so as to ensure the desired resolving power of the instrument. Then we widen both slits by a factor of \(n\) compared with the original width. In this case, if the dimensions of the receiving device placed behind the exit slit are sufficiently large, then the readings of the instrument in the study of a continuous spectrum will increase by a factor of \(n^2\). Indeed, widening the entrance slit will increase the illumination in the plane of the exit slit by a factor of \(n\), and widening the exit slit will further increase by a factor of \(n\) the amount of radiation falling on the receiver. However, as a result of widening the slits, a significant deterioration in the purity of the spectrum will occur, since radiation of different wavelengths will be superposed on one another. Let us consider in somewhat greater detail how this obscuring of the spectrum arises, and show how it can be avoided by using the methods proposed by Golay.

Let us divide the entrance slit, widened \(n\) times, into parts \(a_1, a_2, a_3, \ldots, a_n\). The image of these partial slits in the exit plane of the monochromator, obtained with the aid of radiation of a specified wavelength, makes it possible to divide the exit slit of the monochromator likewise into \(n\) parts \(b_1, b_2, b_3, \ldots, b_n\). If radiation of only one specified wavelength falls on the monochromator, then the rays entering \(a_1\) will emerge through \(b_1\), and so on. When mixed radiation is incident, there will be a crossing passage of rays through slits of different numbers, which leads to a decrease in resolving power and to an obscuring of the spectrum by “undesir—

*) Golay, J. Opt. Soc. Amer. 39, 437 (1949).

... lateral radiation.” If it were possible in some way to exclude the passage of crossed beams, this would give an increase in the amount of energy passing through the monochromator, without loss in resolving power. It is obvious that this cannot be achieved by optical methods alone. However, by enlisting methods known from radio engineering and electronic automation, the desired result can be achieved.

One such method is as follows: let us modulate the radiation passing through the partial input slit \(a_m\) with frequency \(f_1 + m\Delta f\), and the radiation passing through the partial output slit \(b_m\) with frequency \(f_3 + m\Delta f\). In this case the radiation of a given wavelength, for which the slits \(a_m\) and \(b_m\) are conjugate, will, after passing through both slits, be modulated with frequency \(f_2 - f_1\), whereas radiation of other wavelengths passing (for a given position of the monochromator prism) through slits with different indices will be modulated with frequency \(f_3 - f_1 + (k-i)\Delta f\), where \(i\) and \(k\) are the indices of the input and output slits, respectively. By choosing \(f_2 - f_1\) so that this frequency does not coincide with any of the partial frequencies or with their sum, one can isolate the frequency \(f_2 - f_1\) in the readings of the instrument. Thus, the amplitude of oscillations of this frequency will correspond to the intensity of radiant energy of the given wavelength. The action on the measuring instrument of radiation of other wavelengths will be excluded, since they will be modulated by other frequencies. Thus, the resolving power of the instrument and the purity of the spectrum will correspond to the width of a slit equal to \(1/n\) of its full width, while the intensity will be considerably increased (in the ideal case, by a factor of \(n\)).

Table I

However, the implementation of this very general scheme in practice is rather difficult; therefore other, more effective modulation schemes have been proposed. First of all, in order to increase the amount of radiation it is advisable to replace sinusoidal modulation by rectangular modulation, i.e., such modulation in which, for part of the time, the radiation passes unattenuated, and for part of the time it is completely blocked. The nature of the modulation by means of which the crossed beams are blocked is most easily understood from consideration of Table I. This table is drawn up for the case when the expanded slit of the monochromator is divided into 6 parts, and the entire period of modulation

subdivided into 8 intervals of equal duration. The digits 1 and 0 in the table denote the passage and blocking of the light beam, i.e. the (relative) intensity of the beam passing through a given partial slit during the specified time interval.

Examination of the table shows that radiation passing through conjugate partial slits (i.e. partial slits of the same number) will in all cases be stopped during the first half-period either at the entrance or at the exit slit. During the second half-period it will be transmitted for half the time and stopped for half the time. Otherwise, radiation of other wavelengths, passing through partial slits with unequal numbers, will be modulated. For example, rays passing through the first and fourth or, conversely, the fourth and first partial slits will not be able to pass at all, since one of the slits will always be closed. The same will also occur for the combinations of slits 2—5, 5—2, 3—6, 6—3. Otherwise, radiation passing, for example, through slits 4—2 and 2—4 will be modulated. In this case the passage of rays will occur during one quarter of the duration of the first half-period and one quarter of the second half-period. It is not difficult to see that, for any combination of slits of different numbers modulated according to the scheme of Table I, the radiation will be either completely stopped or will pass partly in the first half-period and partly in the second. At the same time, radiation of the desired wavelength that has passed through conjugate slits will pass only during the second half-period. It presents no difficulty to separate the action of rays modulated by these two different methods. For this purpose it is necessary to connect the radiation indicator to a device that sums the difference of the indicator readings over both half-periods. Such an indicator may, for example, be a collector of two half-rings, rotating with the modulation period and transmitting current from the indicator to a galvanometer. Owing to such a device, radiation that has passed through slits with different numbers and is modulated so that the pulses fall into both half-periods will exert no effect on the recording instrument, whereas radiation that has passed through conjugate slits will act on the instrument.

The action of the device described can be expressed mathematically. Let \(f_m(t)\) represent the law of modulation of the \(m\)-th input partial slit. This function takes only the values 0 and 1. Let \(f_n^*(t)\) denote the modulation of the \(n\)-th output partial slit. Then the expression

\[ \int_{0}^{T} f_m(t) f_n^*(t) P(t)\,dt=\delta_{m,n}, \tag{1} \]

where \(\delta_{m,n}=\dfrac{1}{4}\) for \(m=n\) and \(\delta_{m,n}=0\) for \(m\ne n\), and the function \(P(t)\), defined by the equalities

\[ P= \begin{cases} -1 & \text{for } 0<t<\dfrac{T}{2},\\[4pt] +1 & \text{for } \dfrac{T}{2}<t<T, \end{cases} \tag{2} \]

determines the values of the functions \(f_m(t)\) and \(f_m^*(t)\). For the particular case

the six partial slits, the values of these functions are given in Table I. These conjugate “two-dimensional functions” possess the property of orthogonality with respect to the function \(P(t)\), defined by equalities (2). Owing to its properties, the function \(P(t)\) produces a summation of the effect caused by directly transmitted radiation, and the exclusion of interfering cross-transmitted radiation. It should be noted that the orthogonality property is preserved for each pair of slits separately, and therefore completely uniform illumination of the entrance slit is not necessary.

Let us now indicate a simple method for constructing the values of the function \(f_m(t)\) and its conjugate \(f_m^*(t)\). Consider the matrix \(\left|\begin{array}{l}00\\01\end{array}\right|\), and perform with it an iterative process consisting in writing it repeatedly in the four parts of a square \(\left|\begin{array}{|c|c|}\hline & \\ \hline & \\ \hline\end{array}\right|\), while in the lower right corner the matrix is “turned inside out,” i.e., 0 is replaced by 1 and 1 by 0; in other words, the operation that the matrix itself denotes is performed on it, if 0 is regarded as the sign of repetition and 1 as the sign of replacement (“turning inside out”). Performing this operation, we obtain:

\[ \begin{array}{cc|cc} 0&0&0&0\\ 0&1&0&1\\ \hline 0&0&1&1\\ 0&1&1&0 \end{array} \]

Repeating this operation with the newly obtained matrix, we obtain:

\[ \begin{array}{cccc|cccc} 0&0&0&0&0&0&0&0\\ 0&1&0&1&0&1&0&1\\ 0&0&1&1&0&0&1&1\\ 0&1&1&0&0&1&1&0\\ \hline 0&0&0&0&1&1&1&1\\ 0&1&0&1&1&0&1&0\\ 0&0&1&1&1&1&0&0\\ 0&1&1&0&1&0&0&1 \end{array} \]

Deleting the 1st and 5th rows in this matrix, we obtain the first part of Table I, i.e., the values of the function \(f_m\) for \(n=6\). The values of \(f_m^*\) are obtained if we make a replacement (“turning inside out”) of the first four columns of the matrix. Repeating the construction, we first obtain the matrix for 14 sub-slits, then for 30, and so on.

The modulation described above is most simply carried out by placing, in front of the widened entrance and exit slit of the monochromator, two rotating disks with spiral-shaped slots corresponding to the values of the functions \(f_m\) and \(f_m^*\). The manufacture of these disks presents a difficult technical problem, which was successfully solved by the authors in the following way. A plate made of a material transparent to infrared rays was coated, by sputtering, with a layer of an opaque metal (gold), which was scraped away in the required places. Since a substantial gain in resolving power without loss of sensitivity is possible only in the case of a large number of sub-slits, removal of the metal layer at the corresponding places of the disk is possible only with the aid of a special automatic, very

precisely acting device. The disk being processed was set in rotation through a worm gear (512:1) by a motor. In front of the disk, on a special carriage, a “pen” was mounted, which, by means of an electromagnet, could be pressed against the disk, removing thereby a layer of opaque metal. During rotation of the disk the carriage, together with the “pen” and the electromagnet, moved along the radius of the disk, so that in one revolution of the disk it shifted by the width of a partial slit. A strip of approximately the same width was cleaned by the “pen” when it was pressed against the disk. Thus, if the slit was subdivided into 62 parts (as was the case in reality), then in order to manufacture the modulating device the disk had to make 62 revolutions, and during one revolution the “pen” had to be pressed against the disk 32 times to obtain a transparent partial slit and move away from the disk 32 times to obtain an opaque partial slit. Consequently, to manufacture the disk, \(62 \times 64 = 3968\) switchings

Fig. 1.

and switch-offs of the electromagnet controlling the “pen” are required. The instants of switching the electromagnet on and off must be specified very accurately in accordance with the form of the functions \(f_m\) and \(f_m^*\).

It is quite impossible to carry out accurate manual control of the electromagnet; therefore it was necessary to create a special circuit for controlling the electromagnet. For simplicity, let us show the operation of such a circuit not for the case of 62, but only for 14 partial slits. The schematic diagram of such a device is shown in Fig. 1. The elements \(C_1, \ldots, C_8\) represent counters formed by trigger-tube circuits having two stable equilibrium positions. An impulse fed to the counter input transfers the counter from one state to the other. Two successive impulses return the counter to its initial state. In doing so, the counter sends an impulse to the next counter following it, and so on. The totality of such counters is nothing other than a counting device for the number of impulses in the binary system of numeration. The circuit elements \(G_1, G_2, G_3, G_4\) are called “gates”; their arrangement is such that when they simultaneously receive impulses from both counters to which they are connected, they transmit an impulse to the circuit element \(R\). If, however, only one impulse acts on a “gate,” they block it. The circuit element denoted by the letter \(R\) transmits an impulse to the electromagnet controlling the “pen” when an odd number of impulses passed by the “gates” acts upon it. It is not difficult to verify that the circuit arranged in this way will, when supplied to the first counter with successive

…of additional voltage pulses, generate at the output of element \(K\) pulses in accordance with the values of the function \(f_m\), if the absence of a pulse is taken as zero and a pulse as unity. The first sixteen pulses form the first row of the matrix. The second sixteen form the second, and so on. When pulses corresponding to the right lower quadrant of the matrix are supplied, counters \(C_4\) and \(C_8\) will be in the “one” state, and thus this fourth quadrant will be inverted in comparison with the other three quadrants. To obtain matrices with a large number of elements, it is only necessary correspondingly to increase the number of counters and “gates.” To put the entire device into operation, a photocell is used, which receives a light pulse at each revolution of the motor that rotates its modulation disk.

The disks made in this way are placed in front of the entrance and exit slits of the monochromator, a photograph of which is shown in Fig. 2.

Fig. 2.

The described monochromator device with 62 partial slits should theoretically have had a sensitivity 32 times higher than that of a simple monochromator with the same slit width. However, because it was necessary additionally to limit the height of the slit, which, besides this, was partly screened by the rotation of one of the disks, an increase in sensitivity of approximately 10 times was achieved, with a partial-slit width of \(0.126\) mm. It is intended in future to construct a monochromator with 126 partial slits, which will give an even greater gain in sensitivity.

The author points out that, for practical reasons, it proved expedient to make the modulation disks not on the basis of the simple matrix described above, but of a somewhat modified one, obtained from the first by interchanging individual columns. A more detailed description of the modified matrix and of the corresponding counting device is not given in the article.

K. Vul'fson