METHODS OF SPECTRAL SENSITOMETRY

Yu. N. Gorokhovskii, Leningrad

§ 1. Introduction

One of the most essential features of the modern progress of photography is the almost complete displacement of pure silver-bromide emulsions, sensitive only to the blue-violet and to part of the ultraviolet region of the spectrum (the inherent sensitivity of the bromide silver of the photographic emulsion), by emulsions whose sensitivity extends also to other parts of the spectrum, including its infrared part. This progress was achieved thanks to the successes of sensitization—imparting additional sensitivity to a photographic emulsion by means of the adsorption, on bromide (or, in general, haloid) silver, of various dyes (sensitizers). It should be noted, however, that the action of sensitizers is not limited to the creation of some additional region of sensitivity, but often also leads to an increase in the ordinary “blue” sensitivity.

The modern assortment of highly sensitive photographic materials consists almost exclusively of materials sensitized to one or another part of the spectrum, and nonsensitized materials are used only in special cases. Layers possessing additional sensitivity to yellow-green rays (520–580 mμ) are called orthochromatic; those sensitive to yellow-red rays (up to \(\lambda = 680\) mμ) are called panchromatic; and, finally, those sensitive to infrared rays (730–1200 mμ) are called infrared.

The extension of the spectral range of photographic sensitivity makes it possible to approach the solution of two most important problems:

1) obtaining correct color rendering, i.e. obtaining on a black-and-white photograph a gradation of tones corresponding to the visual brightnesses of the various parts of the photographed multicolored object;

2) increasing visibility—photographing an object in rays to which the human eye is only slightly sensitive or is not sensitive at all.

Parallel with the photochemical technology indicated above, sensitometry also naturally evolved—the science of the quantitative determination of photosensitivity. On the one hand, the requirements imposed on light sources for sensitometric testing increased considerably—with respect to the spectral composition of the light emitted by the source and to its constancy. The Hefner candle was replaced by an incandescent electric lamp with a known color temperature, and Davis and Gibson¹ developed a series of liquid light filters placed in front of a light source of any color temperature and bringing the spectral distribution of the energy incident on the plate close to the distribution of energy in midday daylight (the so-called daylight filters).

On the other hand, a special branch of sensitometry began to develop—spectral or color sensitometry, i.e. the science of determining sensitivity to light of a more or less narrow spectral composition. Depending on whether the sensitivity to monochromatic radiation or to polychromatic light (“color”) is determined, one should distinguish between spectral sensitometry proper and color sensitometry proper (Spektralsensitometrie and Farbensensitometrie). Since the concept of “color” from the point of view

from the standpoint of spectral sensitivity is sufficiently arbitrary, then it is obvious that the determination of spectral sensitivity (sometimes called monochromatic sensitivity) must, both on principled and methodological grounds, be preferred to the determination of color sensitivity, all the more since no other determination has meaning in the invisible parts of the spectrum (ultraviolet and infrared light). However, the complexity and lack of clarity of the laws governing the combined action of light of different wavelengths on the photographic layer (the law of additivity) make the determination of color sensitivity desirable for practical purposes in some cases as well.

The present article aims to consider the existing methods of spectral sensitometry. However, this must be preceded by a brief survey of the foundations of color sensitometry, which should explain the advantages and the necessity of developing precisely the method of spectral sensitometry, despite its relative complexity and its lesser “practicality” in comparison with color sensitometry.

§ 2. Color Sensitometry

The determination of color sensitivity may be carried out in two ways: either by the method of light filters, or by the method of color charts.

The method of light filters consists in the following. In front of the photographic layer a neutral-gray wedge is placed, i.e. a light filter whose absorption within the visible part of the spectrum is not selective in character and whose optical density changes uniformly in one direction; and on the wedge there are superimposed strips of colored light filters transmitting a more or less sharply cut-out portion of the spectrum. The layer is exposed to a certain standard light source and is developed (under strictly defined conditions, of course). On the photographic layer there are obtained strips with optical densities decreasing from one end of the strip to the other and reaching zero or some chosen density value. Numerically, color sensitivity is expressed in various ways: if the Eder-Hecht wedge sensitometer is used as the neutral-gray wedge, then the sensitivity to red, yellow, green, and blue colors is expressed in Eder-Hecht degrees (by threshold, i.e. by the minimum density of blackening above fog); if the ступенчатый wedge for sensitometry according to the DIN system (German industrial sensitometric standard) is used, then the sensitivity is expressed in DIN degrees (the ordinal number of the wedge step under which, on the layer, with an exposure of \(\frac{1}{20}\) second, a density of about 0.1 above fog is obtained).\(^{4}\)

For this latter case Egger\(^{5}\) proposes using a yellow Luther filter which cuts off the entire region of the spectrum corresponding to the intrinsic sensitivity of the emulsion (\(\lambda_0 \lambda = 490\ \mathrm{m}\mu\)); the difference between the sensitivity without the filter and the sensitivity under the filter (the so-called Gelbdifferenz) is the smaller the higher the degree of sensitization. Egger divides photographic layers, according to the magnitude of this difference, into 3 groups:

\[ \text{if the difference (in } \frac{1^\circ}{10}\ \text{DIN) is } \begin{cases} \sim 9 & \text{then the layer is weakly orthochromatic;}\\ \sim 6 & \text{the layer is highly orthochromatic;}\\ \sim 3 & \text{the layer is panchromatic.} \end{cases} \]

Gobbl\(^{6}\) proposed the following modification of the light-filter method. The photographic layer is exposed to daylight under a neutral-gray wedge with a known constant and under three filters—blue, yellow, and red (the absorption curves of the filters are given in Fig. 1). Thus

* The question of the addition of colors in photography is set forth in the interesting works of A. van Kreveld\(^{2}\), as well as of Uebbe\(^{3}\), on which we have not had the opportunity to dwell here.

...in this way three strips with variable density are obtained on the plate; the plate is cut into 3 parts and these parts are folded so that the mean densities coincide. From the displacement of the “yellow” and “red” strips relative to the “blue” strip, for a known wedge constant, one judges how many times \((n)\) the illumination must be increased in order, with the given exposure time, to obtain in yellow or red light the same mean densities as in blue light. The quantities \(\frac{1}{n}\) give the values of the relative “red” and “green” sensitivities \(v_r\) and \(v_g\)—the so-called Hübl numbers. The “green” sensitivity is the difference between the “yellow” and “red” sensitivities. Direct determination under a green filter is difficult, since green filters always have a sloping absorption curve.*

The method of color charts consists in photographing on the tested layer a color chart. Of the large number of charts proposed at different times, we shall describe the two most interesting.

Fig. 1.

1. The stepwise “Arca” color chart represents, surrounded by a black background, four colored strips—red, yellow, green, and blue. Next to each of them is a strip consisting of a series of gray steps of varying degree of “grayness”—from completely white to completely black. A certain step will, in a given light, possess the same brightness as the adjacent colored strip. Such a step is designated as 100%; darker steps are assessed by correspondingly smaller percentages, and lighter ones by larger percentages. If the photographic layer possesses the same sensitivity to the individual colors as the human eye, then on a negative image made on the tested material the steps designated 100%, at a certain exposure, will merge with the colored strips. In this case the given photographic layer will give correct color rendering. If, however, one or another colored strip merges with darker steps, this means that the sensitivity of the photographic layer to these colors is less than the sensitivity of the human eye and constitutes of it the percentage indicated on the merging gray step. In Fig. 2 a photograph of a color chart on panchromatic material is shown.

2. Lagorio’s chart\(^9\) is based on the same principle as the preceding chart, but contains 24 colored strips with maxima of diffuse reflection successively shifting from 400 to 700 mμ. Next to each colored strip are printed in all one and the same gray step wedge. The curve connecting the points at which the colored strips have the same visual brightness as the gray steps gives the relative visibility curve of the human eye over the spectrum, while the curve connecting the points of equal photographic densities of each colored strip and the gray wedge represents the relative color-sensitivity curve of the layer on which the chart was photographed.

The essential shortcomings of both methods described above are, on the one hand, the impossibility of obtaining pure spectral zones and the arbitrariness of their selection, and, on the other hand, the relative character of the obtained values of color sensitivity and the impossibility of obtaining absolute values.

In the method of light filters, even Hübl did not succeed in selecting filters that would cut out, with complete strictness, definite spectral regions (Fig. 1), but satis—

* A generally favorable critique of this method is given in the article by Heisenberg and Bilz.\(^7\)

...he was unable to find a satisfactory green filter at all, as a result of which, for the determination of “green” sensitivity, one has to resort to indirect methods. The situation is still worse in the method of charts. Bilys made measurements for the colored fields of the “Agfa” chart by means of spectral reflection curves, shown in Fig. 3. One can

Fig. 2. Stepped color chart “Agfa”.

see that the curves overlap one another to a considerable extent; the reflection at the maximum is far from reaching 100%, and the blue, and then the green, pigment is especially unsatisfactory. In the light reflected by the paper colored with pigments, the content of light of extraneous spectral zones reaches 80% for the blue pigment, and 33% for the red pigment.

The results obtained will depend strongly on the spectral composition of the source light; thus, Bilys gives correction coefficients for the “Agfa” chart in the case of electric lamps, which turn out to be quite significant. No less important is the composition of the source light in the method of light filters. It should also be borne in mind that reproduction of colored charts is a very difficult task, as a result of which, in order to obtain reliable results, one has to use charts made uniformly in one place.

Fig. 3.

But the most essential defect of the methods of color sensitometry is, of course, the relativity of the values obtained and the impossibility of expressing color sensitivity in absolute, for example energetic, units.

In defense of the definition of color sensitivity, the argument is usually advanced that in practice photographic shooting is almost always carried out over a wide range of wavelengths, and not in monochromatic light, and therefore the determination of color sensitivity should be made under equivalent conditions. However, this condition is very poorly observed in existing methods. Real colored objects usually have reflection not in a narrow spectral region, but over the entire spectrum, and the color of the object is determined by the region near the maximum on the reflection curve (according to Ostwald this corresponds to a considerable content of white

…in the given color). Moreover, a number of objects have two reflection maxima. Therefore, the choice of any pigment as a comparison object, or the use of a light filter, leads to conditional, unreliable results in practice. It may be said that in the methods of color sensitometry the spectral composition of the light is not sufficiently pure to draw any quantitative conclusions about sensitivity to narrow spectral regions, but at the same time it is not sufficiently mixed for the conditions of practical photography to be regarded as reproduced.

§ 3. Spectral Sensitometry

The measure of the spectral sensitivity of a photographic layer may be either the density of blackening obtained at a given exposure (i.e., at a given quantity of monochromatic radiation incident on the plate), or the quantity of energy of monochromatic radiation that produces a definite photographic effect (usually the formation of a definite density of blackening).

In ordinary sensitometry, for determining sensitivity, the second method is always used, i.e., the energetic expression of sensitivity. In spectral sensitometry, historically the earlier method was likewise the energetic expression of sensitivity. The first work devoted to determining spectral sensitivity in absolute energy units belongs to Leimbach¹¹ (1909); it contains very carefully measured energy curves of sensitivity in the interval from \(\lambda = 430\ \mathrm{m}\mu\) to \(\lambda = 680\ \mathrm{m}\mu\), at constant density values (1.0; 1.5 and 2.0). The measurements were carried out in a prismatic monochromator with a Nernst filament as the light source. For each wavelength, the amount of energy passing through the exit slit was determined by means of a bolometer. For all the materials investigated by Leimbach, the amount of energy necessary to obtain, after development, a density of 0.1 above fog (according to Bills’s recalculations) was, at \(\lambda = 450\ \mathrm{m}\mu\), in energy units, \(0.02\text{–}0.04\ \mathrm{erg}/\mathrm{cm}^2\) of energy of the same wavelength. In addition, it was established that the maximum of spectral sensitivity corresponds to wavelengths somewhat smaller than \(450\ \mathrm{m}\mu\).

Scheffer¹² used, as the source of monochromatic radiation, a mercury arc, from which a blue mercury line (\(\lambda = 436\ \mathrm{m}\mu\)) was isolated by a light filter, and measured the illumination produced by it in the plane of the plate. He determined the amounts of energy that, in the emulsion under investigation, produced the formation of various densities after development. If these data are recalculated, then the amount of energy producing a density of 0.1 above fog will be

\[ E^{\lambda = 436}_{D = 0.1} = 0.0064\ \mathrm{erg}/\mathrm{cm}^2 . \]

Helmick¹³, working with a monochromator and measuring, by means of a thermoelement, the energy incident on the plate, determined the amounts of ultraviolet radiation that gave minimal blackenings (thresholds). It turned out, for example, that for \(\lambda = 365\ \mathrm{m}\mu\)

\[ E^{\lambda = 365}_{D \simeq 0.1} = 0.028\ \mathrm{erg}/\mathrm{cm}^2 . \]

Harrison¹⁴ determined the sensitivity in the ultraviolet region of several types of English and American plates. The results he obtained, however, cannot be compared with other data, since the author coated the emulsion with fluorescent oils, which greatly increased the effective sensitivity to the short-wave part of the spectrum; thus, for example, the maximum sensitivity, contrary to the data of all other authors, proved to lie near \(\lambda = 250\ \mathrm{m}\mu\).

Jones and Sandvik\(^{15}\) constructed a spectrosensitometer consisting of a monochromator with double dispersion; in front of its slit there was placed a disk with sector-shaped cutouts, whose angular dimensions were the smaller the farther they were from the center of the disk (i.e., like ordinary sensitometers with a rotating disk). Such a device made it possible, for any wavelength, to obtain simultaneously a series of exposures successively increasing with time (i.e., a spectrosensitogram). The light source was a gas-filled lamp. From 700 to 360 \(m\mu\) the density of the light flux \(I_\lambda\) at the exit slit of the monochromator was measured with a thermoelement, and from 350 to 300 \(m\mu\) it was calculated according to Planck’s law for the radiation of an absolutely black body, taking into account reflections from all optical surfaces. Several identically exposed sensitograms

Fig. 4.

were developed for different times, obtaining different contrasts. As a result, for each wavelength a family of characteristic curves was obtained, i.e., curves on a graph where the logarithms of the exposures, i.e. \(\lg I_\lambda t\), are plotted along the abscissa axis, and the optical densities \(D\) along the ordinate axis (Fig. 4).

The longer the development, the greater the contrast
\(\gamma = \dfrac{dD}{d\lg E}\) (on the rectilinear portion of the characteristic curve)*.

Spectral sensitivity was expressed as the quantity reciprocal to the amount of illumination (exposure) \(I_\lambda t\) required to obtain, at \(\gamma = 1.0\), a density \(D = 1.0\); thus:

\[ S_\lambda=\left(\frac{1}{I_\lambda t}\right)_{D=1.0}. \tag{1} \]

Using this kind of calculation, Jones and Sandvik obtained, for a number of photographic materials, curves of spectral sensitivity (Fig. 5), whose maximum proved to lie near \(\lambda = 350\ m\mu\).

Leishman\(^{16}\), using an electric lamp in front of which light filters with a narrow transmission region (approximately \(50\ m\mu\)) were placed, determined, in quantum units, the amounts of energy with wavelengths of about 435, 550, and 615 \(m\mu\) that produce, in nonsensitized emulsions and in emulsions sensitized with erythrosine and pinachrome violet,

* In practice, the contrast \(\gamma\) is determined as the tangent of the angle of inclination of the rectilinear portion of the characteristic curve to the abscissa axis.

formation of the minimal density (threshold), density 0.5 and density 1.0. His data are given in Table 1.

Fig. 5.

TABLE 1

If these data are recalculated in \(\mathrm{erg}/\mathrm{cm}^2\), we obtain that \(E^{\lambda=435}_{D=0.1}=0.059\ \mathrm{erg}/\mathrm{cm}^2\) for both the unsensitized and the sensitized emulsions, whereas \(E^{\lambda=550}_{D=0.1}=43\ \mathrm{erg}/\mathrm{cm}^2\) for the unsensitized emulsion and \(1.1\ \mathrm{erg}/\mathrm{cm}^2\) for the sensitized emulsion.

Let us also mention the study by Weitzel and Gessler^17, who determined the spectral sensitivity of a large number of German plate types by the very questionable method of exposing a plate in a quartz spectrograph with a slit width variable over a very wide range (1:32), and expressing the sensitivity in conventional units relative to a single photographic material arbitrarily chosen as the standard.

Bilz^18, like Sheppard, illuminated the plate with a mercury lamp, in which filters isolated either the blue mercury line with \(\lambda = 436\) mµ or the green line with \(\lambda = 546\) mµ; the energy in the plane of the plate was determined with a thermoelement. To bring the conditions closer to those of ordinary sensitometry, in particular to those of the practical sensitometric system adopted in Germany (DIN), Bilz exposed the layer under test for \(\frac{1}{20}\) second through a neutral-gray step wedge. Spectral sensitivity was defined as the quantity reciprocal to the amount of energy which, after development, produced a density of 0.1 above fog, i.e.

\[ S_\lambda=\left(\frac{1}{E_\lambda}\right)_{D=0.1}. \]

A large number of German photographic materials was investigated; for all of them the sensitivity at \(\lambda=436\) mµ (“blue” sensitivity, characterizing the inherent sensitivity of silver bromide) ranged from 77 to 4 cm²/erg, while the sensitivity at \(\lambda=546\) mµ (“green” sensitivity, characterizing the average additional sensitivity) amounted, relative to the “blue,” to 0.3–0.6 for sensitized layers and 0.006 for nonsensitized layers.

We thus see that before 1932 only Leifbach and Jones and Sandvik measured the entire curve of spectral sensitivity in absolute energy units. However, both of them worked with a monochromator—an instrument not very convenient for practical work. Therefore, in subsequent years research thought quite naturally began to seek possibilities for using spectrographs in which the distribution of energy (the luminous-flux density) with wavelength is known in the caustic plane.

In this direction we should first of all note the study by Wildt^19, who used as a light source Alpha Lyrae (its color temperature is about 11000°K), whose spectrum is well known; however, the sensitivity data (for density 1.0) are expressed in relative energy units. To some extent this is also true of Stobbe’s work.^20 He used a diffraction spectrograph with a light source having a color temperature of 2700°K. The energy in the caustic plane was not measured, but was calculated from Planck’s equation on the assumption that a tungsten filament is a gray body; moreover, the author made an unfounded neglect of the absorption of the optical system. Exposures were varied by means of Nichols prisms placed in front of the spectrograph slit, and also by changing the slit width. In accordance with astrophotographic practice, Stobbe chose an exposure-duration interval from 30 to 240 sec. Sensitivity was expressed in logarithms of the quantities of energy giving a density of 0.1. Obviously, Stobbe’s method is to a considerable extent imperfect; nevertheless, the curves of spectral sensi-

TABLE 2

\[ \Delta \lg E^{546-436}_{D=0.1} \]

...sensitivities of a number of photographic materials are very interesting. It is curious to compare, for the same photographic materials, the data of Bilts ^18 and Stobbe. Table 2 gives the differences calculated by the latter between the sensitivities at \(\lambda = 426\) m\(\mu\) and at \(\lambda = 546\) m\(\mu\). We see that, on the average, the supplementary sensitivity according to Stobbe’s data amounts to a smaller fraction of the “blue” sensitivity than follows from Bilts’s data.

Fig. 6.

In 1935 there appeared a work by Bilts ^21 deserving of every attention. With a diffraction spectrograph (with dispersions on the average \(7\ \mathrm{m}\mu/\mathrm{mm}\)) and with great care, he was able to measure, by a thermoelement, the distribution of energy in the plane of the caustic in the interval from \(\lambda = 400\) m\(\mu\) to \(\lambda = 700\) m\(\mu\). The exposures were varied by changing the intensity of the incident light with the aid of a neutral-gray step wedge, with an exposure duration of only \(\frac{1}{1000}\) second. The wedge had 18 steps, chosen so that the ratio of the extreme exposures was \(1:50\). Development was carried out in DIN. According to the author’s calculations, after analysis of all possible errors, the mean square error of the determination of sensitivity (for a density of 0.1 above fog) was 19%. The newest photographic layers produced by “Agfa” were studied; the results are given in Fig. 6.

The comparison of spectral sensitivities \((\mathrm{erg}/\mathrm{cm}^2)\), carried out by Bilts, is interesting: on the one hand, those measured by him in 1933 by the old method for the materials then available, and on the other, those measured by the new method for the newest “Agfa” photographic materials (Table 3).

We see that the sensitivities increased very considerably; the author indicates that this is partly explained by the increase in development time from 7 to 15 min.; the latter was achieved owing to the lower fogging of the new emulsions in comparison with the old ones.

Finally, let us mention work carried out during 1934–1935 at the State Optical Institute in Leningrad ^22. A prism spectrograph was used, and a ribbon lamp as the light source. Owing to the considerably more favorable conditions for the distribution of energy in the spectrum and the much smaller amount of scattered light inside the instrument, the prism spectrograph should undoubtedly be preferred to the diffraction spectrograph. The exposures were changed on a time scale with the aid of a carefully graduated “Compur” shutter.

TABLE 3

Fig. 7.

Spectral sensitivity was determined in erg/cm² by a blackening density of 1.0 (after subtraction of fog). Various photographic materials were investigated; the results are given in Figs. 7 and 8.

It is curious that for all the photographic materials investigated in this work, sensitized to the visible parts of the spectrum, the “green” sensitivity ($\lambda = 546$ m$\mu$) amounted to 4–13% of the “blue” sensitivity ($\lambda = 436$ m$\mu$), i.e., a fraction much smaller than follows according to Biltsu (30–60%) and Stobbe (20–45%), who used diffraction spectrographs.

As was already indicated at the beginning of this paragraph, another method of expressing spectral sensitivity is also used—by the density obtained when the photographic material is illuminated with a given quantity of monochromatic radiation. In order to be able to compare sensitivities at different wavelengths, in this method one must have an “equalized” spectrum, i.e., a spectrum with the same surface density of luminous flux over its entire length. Most light sources (electric lamps) have a color temperature from 2000 to 3000°K, which corresponds

to the position of the energy maximum between \(\lambda = 1450\) and \(965\ \mathrm{m}\mu\). Thus the problem consists in introducing before the focal plane of the spectrograph an optical or mechanical device that weakens the rapidly increasing yellow-red part of the spectrum with wavelength. In practice

Fig. 8.

only one device of this kind is used—the energy equalizer according to Schmishek. Schmishek \(^{23}\) placed before the cassette of the diffraction spectrograph a disk similar to that used in sector photometers with a rotating disk. A shaped cut-out was made in the disk (Fig. 9).

Fig. 9.

Fig. 10.

The width of the cut-out at different distances from the center of the disk was inversely proportional to the density of the luminous flux at the point of the spectrum situated opposite that place of the cut-out. When the disk rotates, different illumination times are obtained at different distances from its axis, as a result of which the same amounts of energy for all wavelengths fall on the photographic plate. Fig. 10 gives curves of isoenergetic sensitivity for one of the materials investigated by Schmishek \(^{24}\); the three curves correspond to three different exposures. From these curves it is seen that they are not parallel to one another; with increasing difference in exposure this nonparallelism appears ever more sharply \(^{25}\), causing the complete change in the shape of the curve (Fig. 11), borrowed from the paper of Arens and Eggert \(^{26}\). This is explained by the fact that the mean densities

lie on the rectilinear portion of the characteristic curve, while the small and large densities lie on its gently sloping ends. This circumstance makes the isoenergetic curves \(D-\lambda\) of little use for the absolute expression of the spectral properties of photographic materials. In practice, however, this method is often used.

Fig. 11.

§ 4. SPECTRAL SENSITIVITY AND COLOR RENDERING

As we have already indicated at the beginning, one of the principal requirements imposed on a photographic material is the possibility of obtaining an image with correct color rendering.

Translated into the language of spectral sensitometry, this means that the curve of spectral sensitivity must coincide with the curve of the relative visibility of the human eye, taken on the appropriate scale. In Fig. 12 the visibility curve is shown, for which the basis is the ratio of relative visibility; such a visibility curve can be compared with the curves of spectral sensitivity presented in this article. The maximum of the curve lies at \(\lambda - 555\ \mathrm{m}\mu\). Meanwhile, the curves of spectral sensitivity, as we have already seen, even for the most highly sensitized emulsions have a maximum in the blue-violet part of the spectrum. Therefore, in photographic reproduction the yellow light filter must weaken the “cutting” excess of sensitivity in the blue part of the spectrum (usually a very large one), and in part also in other parts of the spectrum. The photographic material in combination with such a yellow filter will possess a sensitivity adequate to the sensitivity of the human eye; the curve in Fig. 10 therefore also represents the spectral sensitivity of an ideal photographic material giving correct color rendering.

Fig. 12.

To determine the character of color rendering by a photographic material, the following method of expressing spectral sensitivity is also proposed\({}^{26}\). One uses not the energy curve of spectral sensitivity, but the brightness curve, i.e., sensitivity is expressed as the reciprocal of the brightness of monochromatic radiation giving the given photographic effect. The brightness sensitivity \(S'_{\lambda}\) can be obtained by a simple recalculation of the energy sensitivity \(S_{\lambda}\) (let us note

for what follows, that in this case the different exposures on the spectrograms must be obtained by changing exclusively the illumination, and not the exposure time). If

\[ S_\lambda=\left(\frac{1}{E_\lambda}\right)_{D=\mathrm{const}}, \tag{2} \]

then

\[ S'_\lambda=\left(\frac{1}{B_\lambda}\right)_{D=\mathrm{const}} =\left(\frac{1}{E_\lambda V_\lambda}\right)_{D=\mathrm{const}}, \tag{3} \]

where \(E_\lambda\) and \(B_\lambda\) are the illumination in energy units (energy per unit area) and the brightness of monochromatic radiation, and \(V_\lambda\) is the relative visibility at the given wavelength. Figure 13 gives such a curve of spectral sensitivity with respect to brightness (on a logarithmic scale). We see that its form differs very substantially from the energy curve; moreover, toward the ends of the spectrum the sensitivity rises sharply (for the quantity of energy giving the given brightness increases), reaching infinity at the limits of the visible spectrum. It is obvious that a photographic layer which correctly renders colors must have a spectral-sensitivity curve with respect to brightness parallel to the axis of abscissae, i.e., equal brightnesses must give equal blackening densities at all wavelengths.

Fig. 13.

This method of expression cannot be denied rationality if the investigator is interested in the correctness of color rendition. In other cases it can hardly be recommended, since the brightness curve is obtained by recalculating the same energy curve, and, moreover, the curve beyond the limits of the visible part of the spectrum (sharp rises of the sensitivity curve near \(\lambda=400\ \mathrm{m}\mu\) and \(\lambda=700\ \mathrm{m}\mu\) already have no real meaning).

If one does not touch upon the question of the extent to which the action of light of different wavelengths is additive (a question that naturally arises whenever one deals with light of different spectral composition), it may be said that spectral sensitometry makes it possible to determine the character of color rendition by a given photographic material no worse than color sensitometry does.

§ 5. Particular Questions of Spectral Sensitometry

In spectral sensitometry, just as in general sensitometry, the question of the method of exposing the studied...

of the photographic layer under consideration. The exposure, or quantity of illumination, is the product of the illuminance \(I\) and the time of its action \(t\).

\[ E = It. \tag{4} \]

One and the same quantity of illumination can be obtained both over a short interval of time, with high illuminance, and over a long interval with low illuminance. It is also obvious that the exposure can be varied in two ways: either by changing the time \(t\) (the time scale), or by changing the illuminance (the illumination scale).

However, as Abney (1874), and subsequently a number of other authors, showed, one and the same exposure can give entirely different photographic effects depending on the relation between the magnitudes \(I\) and \(t\). Thus, the formation of the visible photographic image—the one obtained after development (we can say nothing about the latent image)—does not obey the photochemical law of the reciprocity of Roscoe and Bunsen. For the photographic image it turned out that the slower the action of a given quantity of light, the smaller the photographic effect.

Schwarzschild (1899) established that, for the process of forming the visible photographic image, the law

\[ I t^{p} = \mathrm{const}; \tag{5} \]

holds; here the exponent \(p\)—the so-called Schwarzschild coefficient—is a quantity characteristic of the given photographic material and is usually equal to \(0.7\text{–}0.9\).

Starting from this law, it is often thought that in sensitometry measuring exposure by changing the illuminance (the illumination scale) has advantages over changing the time (the time scale), since in the first case the variable exposure is proportional to the photographic effect, whereas in the second it is not. But this is a pure misunderstanding. Schwarzschild’s equation can be written, as the author himself indicates, in the form

\[ I^{q} t = \mathrm{const}, \tag{6} \]

where

\[ q = \frac{1}{p}, \tag{7} \]

and then the exposures will be proportional to the exposure time, but not proportional to the illuminance. In addition, it has subsequently been clarified that the Schwarzschild equation is in general highly conditional: the coefficient \(p\) is far from being a constant quantity, depending both on \(t\) and on \(I\), on the optical density, on the nature of the photographic material and, finally, on the wavelength. According to the latest investigations, in particular the work of Arens and Eggert^27, the properties of the photographic layer cannot be fully described by one or even several characteristic curves; this can be done only by constructing an entire characteristic surface with coordinates \(D, \lg I, \lg t\).

Sections of this surface parallel to the \(\lg t\) axis give a family of characteristic curves \(D - \lg t\) for different \(I=\mathrm{const}\); sections parallel to the \(\lg I\) axis give a family of characteristic curves for different \(t=\mathrm{const}\). It turned out that in both cases the individual curves of the family are not parallel to one another and have different form and slope. Thus, in reality, in the formation of the photographic po-

...blackening obeys some more complex law than that proposed by Schwarzschild. Without entering into a discussion of the series of equations proposed at various times \(^{28}\), let us point out that the most general form of the equation of photographic blackening is perhaps an equation close in form to Stark’s equation \(^{29}\), according to which the photographic density is

\[ D=\lg (kI^{m}t^{n}). \tag{8} \]

Such an equation, containing for \(I\) and \(t\) exponents different from unity and constant only within known exposure intervals, explains the variable slope of the characteristic curves \(D—\lg I\) and \(D—\lg t\), obtained by Arens and Eggert.

We thus arrive at the conclusion that there is no fundamental difference between the illumination scale and the time scale, and that the use of either of them in determining spectral sensitivity is permissible. But since in practical photographic work one deals with different brightnesses of the individual parts of the object being photographed over a known constant time, i.e. with the intensity scale, then, for the sake of the greatest correspondence of sensitometric data to practice, it is nevertheless preferable to use this latter scale. The interval of illumination of the test plate should be such that the exposure time in sensitometry approaches that practically used in photography; in most cases (in cinematography, in outdoor photography, etc.) the time will be from \(\frac{1}{100}\) to \(\frac{1}{10}\) second; in special cases, for example in astrophotography, minutes.

We thus arrive at the necessity of modifying the conditions of sensitometry depending on the purpose of the photographic material. As a first approximation this need not be done, but, of course, this is the only correct path. The testing of the material must correspond to the conditions of its use. True, in so doing the uniformity of the results is lost and their comparison becomes somewhat difficult, but the quality of the results obtained increases considerably.

This same question also appears clearly in another case—in the choice of development conditions in sensitometry. Jones and Sandvik \(^{15}\) acted successfully. The latter developed spectrograms up to a definite contrast, namely up to \(\gamma=1\), thereby largely excluding the influence of the developer. Practically, however, this is not a very convenient method. At the VII and VIII International Photographic Congresses (1928 and 1931) there was a tendency to establish a single sensitometric developer. A para-aminophenol developer of definite composition was chosen as such. At present, however, the inconsistency of such a kind of attempt has become almost obvious, and in a number of cases, for example in the industrial system of sensitometry according to DIN \(^{30}\) introduced in Germany only a few years ago, not a para-aminophenol but a practical metol-hydroquinone developer is used. In 1935 Jones and Russell \(^{31}\), in an article devoted specifically to standard sensitometry, brought this reverse tendency to its utmost expression: the authors propose that in sensitometry for each material one should use the developer recommended for it as optimal by the manufacturing organization. Development in this case is carried out until a \(\gamma\) lying between 0.8 and 1.1 is reached. It must also be taken into account that different developers will change somewhat the very form of the spectral-sensitivity curve. This is therefore possible because, in the transition from one developer to another, the form of the characteristic curves for different wavelengths will change unequally.

The next question is the choice of the photographic effect according to which the spectral sensitivity should be determined. In general sensitometry until the recent past sensitivity was determined either...

by the threshold, or by the inertia point, i.e., by the intersection of the continuation of the rectilinear portion of the characteristic curve with the abscissa axis (Hurter and Driffield). At present both of these methods, as obsolete, are gradually being abandoned. Usually the sensitivity is determined from certain characteristics of the underexposure region: from the energy that produces a blackening density of 0.1 above fog (DIN system), or from the energy corresponding to the minimum useful gradient, i.e., the point where

\[ \frac{dD}{d\lg E}=0.5\gamma \]

(Jones). The latter method is somewhat complicated and in spectral sensitometry has so far not been used. From the density 0.1 above fog, the spectral sensitivities were determined by Bilby and Stubbe. A number of authors (Jones and Sandvik, Leshchinskii, Wildt) determined spectral sensitivity from a density of 1.0 above fog. This method is not used in general sensitometry, but in spectral sensitometry it is very convenient; density 1.0 usually lies in the middle of the rectilinear portion of the characteristic curve, i.e., in the region of interest to us, and, moreover, is convenient for measurements, since it very significantly exceeds the fog value even for strongly fogging layers; taking into account the large number of measurements that must be made in constructing the spectral-sensitivity curve, this latter circumstance cannot be disregarded.

Fig. 14.

As regards the comparability of spectral sensitivities determined for different density values, here one must take into account the form of the characteristic curves at different wavelengths. If the characteristic curves \(D-\lg E\) with wavelength are displaced along the abscissa axis parallel to themselves, without changing their form and slope \((\gamma)\), then it is obvious that the spectral-sensitivity curves obtained from different densities will be completely similar to one another. This is illustrated schematically by Fig. 14, taken from the above-cited review article by Arens and Eggert.

In reality, invariance of the form of the characteristic curve at different wavelengths is by no means proven. In the literature there are many indications, very contradictory to be sure, according to which the contrast \(\gamma\) and the Schwarzschild coefficient \(p\) (more precisely, the form of the characteristic surface) depend on wavelength. This circumstance makes it necessary to approach with caution the comparison of spectral-sensitivity curves constructed for different density values (0.1; 1.0, etc.), and permits these curves to be considered parallel to one another only as a first approximation.

Final remark. Often, in order to evaluate the spectral properties of a photographic layer, one confines oneself to giving a spectrosensitogram. Such a procedure, even for purely practical purposes, can hardly be recommended. Owing to the sharp increase in the density of the light flux in the spectrum with wavelength (the maximum emission of the light source lies in the infrared part of the spectrum), the maximum sensitization is obtained very predominantly in comparison with the maximum of the “blue” sensitivity, creating a distorted notion of the character and quality of the sensitization. Moreover, this same circumstance produces an apparent displacement of the position of the maximum toward greater wavelengths—a phenomenon observed especially distinctly in the infrared part of the spectrum.

References

1. R. Davis and K. S. Gibson, Filters for the reproduction of sunlight and daylight and the determination of color temperature. Misc. Public. Bureau Stand. No. 114, 1931.

2. A. van Kreveld, Physica, 1, 60–77, 1933; Z. wiss. Phot., 32, 222–230, 1934.

3. J. H. Webb, J. Opt. Soc. Am., 26, 12–23, 1936.

4. M. Biltz and H. Brandes, Veröff. Agfa. 3, 85–92, 1933.

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8. H. Arens and J. Eggert, Veröff. Agfa, 1, 36–46, 1930; Z. wiss. Phot., 29, 239–261, 1930; M. Biltz, Veröff. Agfa, 4, 42–48, 1935.

9. A. Lagorio, Phot. Ind., 28, 629–631, 1930.

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12. H. Scheffers, Z. Physik, 20, 109–128, 1923.

13. P. S. Helmick, J. Opt. Soc. Am., 6, 998–1015, 1922; 9, 521–540, 1924.

14. G. R. Harrison, J. Opt. Soc. Am., 11, 113–123, 341–356, 1925.

15. L. A. Jones and Otto Sandvick, J. Opt. Soc. Am., 12, 401–416, 1926.

16. W. Leszinski, Z. wiss. Phot., 24, 261–275, 1927.

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19. R. Wildt, Phot. Korr., 69, 81–86, 1933.

20. J. Stobbe, Astron. Nachr., 251, 65–74, 1934.

21. M. Biltz, Physik. Z., 36, 559–563, 1935; Veröff. Agfa, 4, 26–34, 1935.

22. E. G. Valyashko and Yu. Gorokhovskii, Journ. techn. Phys. USSR; Photo-Cine-Chemical Industry, 1936 (in press).

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25. See, for example, Fig. 5 in the article by L. Kutzleb, Kinotechnik, 11, 328–331, 1929.

26. H. Arens and J. Eggert, Z. wiss. Phot., 29, 239–261, 1930; Veröff. Agfa, 1, 25–46, 1930. This article contains a very interesting and systematic exposition of the principles of spectral sensitometry.

27. H. Arens, Veröff. Agfa, 1, 11–24, 1930; 4, 15–25, 1935, and others.

28. This question is discussed in detail in the book by K. V. Chibisov, Theory of Photographic Processes, Vol. 1, Chap. 2, 1935.

29. J. Stark, Ann. Phys., (4) 33, 1456–1462, 1910; 35, 461–485, 1911.

30. E. Goldberg, Z. wiss. Phot., 31, 81–83, 1931.

31. L. A. Jones and M. E. Russel, Phot. Journ., 75, 657–675, 1935; J. Opt. Soc. Am., 25, 396–411, 1935.