NEWS OF SPECTROPHOTOMETRY

1. Two-stage spectral sensitometry with a biprism

When studying rapid phenomena by optical methods—for example, in studying the spectra of explosions, sparks, exploding wires, etc.—it is sometimes necessary to obtain a whole series of data from a single photograph of the spectrum. In order to estimate the relative intensities of any lines in this spectrum, it is necessary, for each region of the spectrum, to establish the relation between the relative intensity of the parameters of the light and the blackening or transmittance of the developed image of the spectrum. If a single photograph is involved, then for these purposes the method of photographing the spectrum through a step attenuator placed on the slit of the spectrograph is suitable. However, the attenuator requires precise preliminary calibration, which is associated, in turn, with all the difficulties and errors of photographic spectrophotometry. Cady and Gordon*) have described a new method of photographic sensitometry that is convenient for these purposes. Its advantages consist not only in the fact that it uses a single photograph, but also

Fig. 1. 1—spectrograph slit, 2—collimator lens, 3—refracting prism, 4—biprism, 5—camera lens, 6—plate, S—image of the spectrum, a, b—zones obtained from the two halves of the biprism, ab—overlap zone.

in the fact that it requires neither intermittent illumination nor preliminary calibration, eliminates concern about the reproducibility of the results, and provides the possibility of self-checking.

The method consists in placing a biprism behind the refracting prism of the spectrograph (so that its edge is horizontal), and the photograph is obtained as two spectra superposed along the entire length of the spectrum (Fig. 1). As it passes through the biprism, the upper half of the entire light beam passes through the upper half of the biprism, and the lower half through the lower one. As a result, one half of the spectrum is displaced slightly downward, and the other upward. In Fig. 1, zone a is obtained from the upper half of the biprism, zone b from the lower half; zone ab is the overlap zone. In this zone the intensi—

*) W. M. Cady and G. Gordon, JOSA 39, 369 (1949).

FROM CURRENT LITERATURE

…of each line is twice as great as its intensity in the outer zones, the intensities of which must be equal. The latter is achieved by the corresponding adjustment of the diaphragm. For accurate sensitometry it is also necessary to have entirely uniform illumination of the spectrograph slit. This is usually achieved by focusing the light source onto the collimator lens by means of a lens placed in front of the slit.

The method of obtaining a curve relating the intensity of the lines \(I\) to the transmission \(T\) of the developed image is as follows: in each spectral region \(T\) is measured in all three zones \((a,\ ab,\ \text{and } b)\) for each of several lines of different intensity. Then a graph is constructed on which \(T_{ab}\) is plotted along the abscissa axis, and along the ordinate axis

\[ \frac{T_{a+b}}{2}, \]

i.e., the averaged transmission of the two outer zones. Since for each measured line we have the values \(T_{ab}\) and \(T_{\frac{a+b}{2}}\), as a result we obtain a series of points

\[ \left(T_{ab},\ T_{\frac{a+b}{2}}\right), \]

lying on some curve. Such a curve is shown in Fig. 2. Let us denote the intensity of the brightest line in the zone \(ab\) by \(I' = 100\). The corresponding transmission in the zone \(ab\) will be \(T'_{ab} = 1.5\%\) (according to the measurements), and in the outer zones

\[ T'_{\frac{a+b}{2}} = 3.7\%. \]

Fig. 2. Graph obtained by plotting the values \(T_{ab}\) and \(T_{\frac{a+b}{2}}\) for different lines in a certain spectral region.

Some imaginary line having intensity \(I'' = 50\) would give, in the central zone, the transmission

\[ T''_{ab} = T'_{\frac{a+b}{2}} = 3.7\%. \]

From the graph we find what \(T''_{\frac{a+b}{2}}\) corresponds to this \(T''_{ab}\). We obtain 8, etc. This stepwise process can be repeated further and a table obtained:

Thus, from a single double exposure one can obtain blackening curves for any regions of the spectrum.

FROM CURRENT LITERATURE

2. Application of the Féry prism in Beckman’s new spectrophotometer.

The Féry prism, first described in 19101, is an ingenious combination of a lens and a prism: it decomposes the beam of light incident upon it into a spectrum and itself focuses it.

Fig. 3. Diagram of the Féry spectrograph. \(S\) — slit, \(F\) — Féry prism, \(M\) — silvered side, \(P\) — curved plate.

In the Féry spectrograph (Fig. 3) the front and rear surfaces of the prism had a cylindrical form, as a result of which the image of the entrance slit was stretched in the vertical direction (the height of the image was about 2 inches), which adversely affected the intensity of the spectrum. Owing to such considerable astigmatism, the Féry prism could not be used in monochromators. In Beckman’s new spectrophotometer2, however, the Féry prism has found a successful application. It was found that replacing the front cylindrical surface of the prism with a spherical one leads to good optical qualities: the astigmatism is reduced, so that, for example, with a glass prism having \(F = 18\) inches, a luminous point is imaged as a line \(3/4\) inch high, which is already quite acceptable for a monochromator. However, as in the case of any other prism, the image of the entrance slit is curved. In this case astigmatism should greatly impair the image quality. This difficulty is removed by making the entrance slit in the monochromator of such a curvature that its image at the exit is straight. Strictly speaking, the required curvature of the entrance slit is a function of wavelength, but with a reasonable choice of this curvature it is possible to obtain a sufficiently sharp image over a fairly wide range of wavelengths.

Fig. 4. Diagram of the construction for moving the prism in Beckman’s monochromator. \(F\) — Féry prism, \(B\) — the platform carrying it, \(ff\) — rods, \(A\) — base, or wall of the instrument.

In the Féry spectrograph the prism is fixed immovably, and the spectrum is obtained on a certain curved surface (Fig. 3). In a monochromator the positions of the entrance and exit slits are fixed, so that the prism itself must somehow be moved in order that, at any wavelength, the image should be obtained in the plane of the exit slit. In Beckman’s instrument the prism rotates and at the same time moves translationally. This motion is effected by means of a special carriage. Fig. 4 gives a diagram of such a construction. The rods \(ff\) are fixed at the points \(aa\) and \(bb\). When the plate \(B\), carrying the prism, is moved, the prism will both rotate and undergo translational motion,

The construction of the entrance and exit slits is also unusual. The slits are placed side by side; their inner jaws are immobile, while the outer ones can be moved apart by greater or lesser pressure on a certain elastic plate connected with them.

The new spectrophotometer makes it possible to work in the region from 320 to 1000 mµ. It uses 2 photocells—one for the region 320–640 mµ, the other for 640–1000 mµ. As usual, in the region \(\lambda < 360\) mµ scattered or stray light is eliminated with the aid of an appropriate filter (in the present case, Corning filter 9863).

3. Application of a New Scale for Constructing Rectilinear Blackening Curves

To determine unknown intensities in quantitative photographic photometry, “blackening curves” are usually used. To construct these curves, the logarithms of the light intensities are plotted along the abscissa axis, and along the ordinate axis “blackening”

Table 1.
\(T\)—coordinates of the distances \(d\).

\[ \left(S=\lg\frac{I_0}{I}\right) \]

or the logarithm of transmission. Ordinary photographic materials give a well-known S-shaped curve, only an insignificant segment of which is rectilinear. The most accurate and convenient photometric operations are within this rectilinear part of the blackening curves. The light intensities for “blackening marks” are selected precisely so that the blackenings fall on this rectilinear part of the curve. The use of the curved portions of blackening curves is disadvantageous because of the much lower accuracy and the need for a larger number of points describing this section of the curve.

Hughes and Murphy\(^4\) proposed a convenient scale that makes it possible to obtain rectilinear characteristic curves of photographic materials within the limits from 2 to 97% transmission of the developed layer. The use of such straightened curves is very advantageous, since fewer blackening marks are needed to obtain these curves, and many intermediate stages of processing the data can be discarded.

Of the many functions investigated, the authors settled on the following expression:

\[ f(T)=\frac{\lg T}{1-T}-Ae^{T/\gamma}+B. \]

Here \(T\) is the transmission of the photographic layer, and \(A\) and \(B\) are arbitrary constants. The latter is chosen so that the curve passes through the origin of coordinates. Tests showed the suitability of this scale for different \(\gamma\) (from 0.9 to 3) and different spectral regions (from the visible to the ultraviolet).

Along the abscissa axis the authors plot the logarithms of the exposures, and along the ordinate axis a certain function of the transmission of the developed image \(f(T)\).

The most convenient way to construct these characteristic curves is to draw on millimeter paper the corresponding scales for $I$ and $T$ according to values calculated in advance.

For $T$ the authors give the following scale (see Table 1).

A. Il’ina

REFERENCES

1. C. Fery, J. de Phys. 9, 762 (1910).
2. A. O. Beckman et al., JOSA 39, 377 (1949).
3. S. L. Mandel’shtam, Introduction to Spectral Analysis. State Publishing House of Technical-Theoretical Literature.
4. H. K. Hughes and R. W. Murphy, JOSA 39, 501 (1949).