Sensitometry
INTRODUCTION
The objective study of the response of imaging systems to light or other radiation is called sensitometry. It is concerned with the measurement of the exposure that a material has received and the amount of the resultant image. Sensitometry in silver-based photography which is the subject of this chapter is assessed by the amount of blackening, silver image formation, which takes place. In digital imaging sensors it is assessed by the output voltage, or the output pixel value and will be discussed in detail in Chapters 14 and 21. It is possible to produce photographs without any knowledge of sensitometry, but to obtain the best performance from photographic systems, under all conditions, an understanding of the principles governing the response of imaging systems is invaluable.
As sensitometry is concerned with the measurement of the performance of photographic materials and other light-sensitive systems, it is necessary to use precise terminology in defining the quantities that are measured. The impression that a photograph makes on us depends on physiological and psychological as well as physical factors, and for this reason the success of such an image cannot be determined from a simple series of measurements. This simply means that there are limitations to the help that sensitometry can give us.
THE SUBJECT
As far as the camera is concerned, a subject consists of a number of areas of varying luminance and colour. In the same way, a photographic print consists of areas of varying luminance and sometimes colour (luminance is measured in candelas per square metre). The variations of luminance in a subject are due to the reflection characteristics of different areas, and to the differing angles at which they are viewed. There may also be a significant variation in the illumination that the subject receives. The ratio of the maximum to the minimum luminance in a subject is defined as the subject luminance range.
It may surprise us at first to realize that a sunset, or the rippling of wind over water, can be reduced to areas of varying luminance. Yet it is so in the camera, and in the eye viewing a black-and-white print too, with the difference that the mind draws not only on the visual impression, but also on past experience. Thus, on viewing a picture of an apple, for example, we see more than just light and shade. Our past experience comes to the aid of the eyes in presenting to the mind a picture of an apple.
Our final goal in sensitometry is to relate the luminances of the print to the luminances of the subject. This involves the study, first, of the response of the negative material, then of the response of the positive material, and finally of the relation between the two. We shall consider each of these in turn. We refer to the light areas of a subject as the highlights and the dark areas as the shadows. To avoid confusion, the same terms should be applied to corresponding areas both in the negative and in the print, even though in the negative highlights are dense and shadows clear.
EXPOSURE
When a photograph is taken, light from the various areas of the subject falls on corresponding areas of the film. The photographic exposure, H (the effect produced on the emulsion), is, within limits, proportional to the product of the illuminance E and the exposure time t. We express this by the equation:
Before international standardization of symbols, the equation was written as E = It (E was exposure, I was illuminance) and this usage is still sometimes found.
The SI unit for illuminance is the lux (lx). Hence the exposure is measured in lux seconds (lx s). It should be noted that the lux is defined in terms of the human observer, who cannot see radiation in either ultraviolet or infrared regions of the spectrum. Inclusion of either of these bands in the imaging exposure may therefore yield erroneous results with some imaging systems.
As the subject luminance varies from area to area, it follows that the illuminance on the emulsion varies similarly, so that the film receives not one exposure over the entire surface but a varying amount of light energy, i.e. a range of exposures. As a general rule the exposure duration is constant for all areas of the film, variation in exposure over the film being due solely to variation in the illumination that it receives.
It should be noted that the use of the word ‘exposure’ as we use it here is quite different from such everyday use as: ‘I gave an exposure of 1/60 second at f/8.’ We can avoid confusion by designating the latter camera exposure.
DENSITY AND OTHER RELEVANT MEASURES
When a film has been processed, areas of the image that have received different values of illumination are seen to have differing degrees of darkening, corresponding to the amount of developed silver, or image dye, formed. The blackness of a negative, i.e. its light-stopping power, can be expressed numerically in several different ways. The following ways are of interest.
Transmittance
The transmittance, τ, of an area of a negative is defined as the ratio of the light transmitted It to the light incident upon the negative Ii. This can be expressed mathematically as:
Transmittance is always less than 1, unless expressed as a percentage. Thus, if 10 units of light fall on a negative and 5 are transmitted, the negative has a transmittance of 5/10 = 0.5, or 50%. Unfortunately transmittance is not the most useful concept in sensitometry because it decreases as blackness increases, and equal changes in transmittance do not appear as equal changes in blackness.
Opacity
Opacity, O, is defined as the ratio of the light incident on the negative, Ii, to the light transmitted, It. That is simply the reciprocal of transmission and can be expressed:
Opacity is always greater than 1 and increases with increasing blackness. From this point of view, it is a more logical unit to use in sensitometry than transmittance, but equal changes in opacity still do not represent equal changes in perceived blackness.
Density
Transmission density, DT, is defined as the logarithm to base 10 of the opacity. Hence:
Density is the unit of blackening employed almost exclusively in sensitometry. Like opacity it increases with increasing blackness, but has the following practical advantages:
1. The measured density is approximately linearly related to the amount of silver or image dye present; e.g. if the amount present in an image of density 1.0 is doubled, the density is increased to 2.0. The opacity, however, increases from 10 to 100, i.e. tenfold.
2. The final aim in sensitometry is to relate the tones of an image to those of the subject. Blackness in a reproduction depends on the way the eye assesses it, and is essentially physiological. The law relating the visual effect to stimulation is not simple, but over a wide range of viewing conditions the response of the eye is approximately logarithmic. If we view a number of patches in which density increases by equal steps, the eye accepts the steps as of equal increases in blackness. In this respect, therefore, a logarithmic unit is a satisfactory measure of blackening. Table 8.1 relates transmission density, opacity and transmittance. Densities of images on transparent and opaque bases are referred to as transmission and reflection densities respectively.
EFFECT OF LIGHT SCATTER IN A NEGATIVE
When light passes through a photographic image it is partially scattered. One result of this is that the numerical value of density depends on the spatial distribution of the incident light, and on the method adopted for the measurement of both this and the transmitted light. Three types of density have been defined according to the cone angles of illumination and light collection; these are illustrated in Figure 8.1 and described in Table 8.2.
1. Direct or specular density. This is determined by using parallel illumination, normal to the sample, and measuring only normal emergence, the straight-through rays, parallel to the axis.
2. Diffuse density. This may be determined in either of two ways:
a. By using parallel illumination, normal (i.e. at 90°) to the sample, and measuring total emergence (whether normal or scattered), or
b. By using diffuse illumination and measuring only normal emergence. The numerical value of diffuse density is the same with either method of measurement.
3. Doubly diffuse density (or double-diffuse density). This is determined by using diffuse illumination and measuring total emergence.
Practical measurements of any of these types of density are based on the ratio of a reading made by a photocell when the sample is not in place (taken as Ii) to the reading on the same photocell when the sample is in place (It). The difference between diffuse density and doubly diffuse density is usually quite small, but specular density is always greater than either.
Figure 8.1 The geometry of density measurement.
Callier coefficient
The ratio of specular density to diffuse density is termed the Callier coefficient, or Callier Q factor, and can be expressed as:
This ratio, which is never less than 1.0, varies with grain size, the form of the developed silver and the amount of the deposit. As far as the grain is concerned, the finer it is, the lower the resultant scattering and the nearer to unity is the Callier coefficient.
The factors above, which influence the value of Q, vary markedly with the degree and type of development used. Consequently the Callier coefficient varies with density and contrast in a complicated way. At low degrees of development, with one particular combination of film and developer, the value of Q was approximately constant at densities above about 0.3; for more complete development, however, there was no single value of Q that could be adopted.
One result of the variation of the Callier coefficient with density is that the tone distribution in a print produced with a condenser enlarger is likely to be different from that in a print produced using a diffuser enlarger. Colour photographic images, however, are essentially non-scattering, so that they possess Callier coefficients close to unity. Thus, in printing colour negatives there is seldom any measurable difference between the results from diffuser or condenser enlargers.
DENSITY IN PRACTICE
The types of density related to photographic practice are shown in Table 8.3.
Some kinds of illumination present an intermediate type of density, as, for example, when an opal bulb or a diffusing screen is used in a condenser enlarger. Apart from the true condenser enlarger and projectors, the effective density in all the examples quoted is either diffuse or doubly diffuse. Since the difference between the latter forms of density is slight, densities of negatives are expressed simply as diffuse densities.
If the image in a negative or print is not neutral in tone, its measured density will depend not only on the optics employed to measure it, but also on the colour of the light employed and the response to colour of the device employed to measure it. Considering these last two factors, we may consider density as being of four main kinds according to the spectral specifications involved:
1. Density at any specific wavelength, spectral density – determined by illuminating the specimen with monochromatic (of a narrow band of wavelengths – see Chapter 2) radiation.
2. Visual density – determined by measuring the illuminated specimen with a receiver having a spectral response similar to that of the normal photopic human eye, the eye functioning in bright lighting (see Chapters 4 and 5). This type of density is standardized as Status V and is used in the study of tone reproduction by both monochrome and colour materials.
3. Printing density – determined by illuminating the specimen with tungsten light and employing a receiver with a spectral response similar to that of photographic papers.
4. Arbitrary density – determined by illuminating the specimen with tungsten light and employing an unfiltered, or even filtered, commercial photo-sensor as the detector, the combination possessing an arbitrary and sometimes unspecified spectral sensitivity.
This classification applies equally to all three main types of density: specular, diffuse and doubly diffuse. For most monochrome photographic purposes diffuse visual density is employed.
Colour densities are also usually measured using diffuse densitometers. Colour images are composed of three dyes, each controlling one of the primary colours of light: red, green or blue. In practice, therefore, colour images are described in terms of their densities to red, green and blue light, the densitometer being equipped with filters to select each primary colour in turn.
The colour filters chosen for a densitometer usually select red, reen and blue spectral bands and measure the integrated effects of all three dye absorptions within those bands. Densities measured in this way are called arbitrary integral densities and are most commonly used in simple quality control measurements. For more useful results the densitometer filters and cell sensitivities are carefully chosen so that the densities measured represent the effect of the image either on the eye or on colour printing paper. Such measurements correspond to density categories (2) and (3) for black-and-white images, and are referred to as colorimetric and printing densities respectively. In practice, colorimetric densities are seldom measured because suitably specified (Status A) three-filter densities can usefully describe the response of the eye to visual neutral and near-neutral tones. This is all that is usually required. Printing (Status M) three-filter densities are, however, widely applied in the assessment of colour negatives for printing purposes, although measurements of this type can usually refer only to some defined ‘typical’ system. They are also generally specified for the control of colour negative processing and for the assessment of colour negatives for printing.
Table 8.3 Effective density in different photographic activities
APPLICATION |
EFFECTIVE DENSITY |
Contact printing |
|
(a) In a box, with diffuse source |
Doubly diffuse |
Enlarging |
|
(a) Condenser enlarger (point source, no diffuser) |
Specular |
Still or motion-picture projection |
|
All types |
THE CHARACTERISTIC (H AND D) CURVE
If density is plotted against exposure, a response curve for a film can be obtained. Although a curve of this type may occasionally be of value, a far more useful curve for most purposes is obtained by plotting density against the common logarithm (logarithm to base 10) of the exposure. This gives a curve of the shape shown in Figure 8.2 (together with a few important features), the type of response curve typical of ordinary photography. It is referred to as the characteristic curve or H and D curve, after F. Hurter and V.C. Driffield, who established curves of this type. The H and D curve is a diagram that shows the effect on an emulsion of every degree of exposure from gross underexposure to gross overexposure for any single development time and any particular developer. These variables have to be specified because the characteristic curve varies with processing conditions and even, to a smaller extent, with exposure intensity and duration. A similar form of characteristic curve may be obtained for a digital camera by plotting log output pixel value against log exposure (see Chapter 21).
The use of log10H instead of H as the unit for the horizontal axis of the response curve of a photographic material offers several advantages:
1. In practice, we consider changes in camera exposure in terms of the factor by which it is altered; the natural progression of exposure is geometric, not arithmetic. (When increasing an exposure time from 1/60 to 1/30 second, for example, we speak of doubling the exposure, not of increasing it by 1/60 second.) A logarithmic curve therefore gives the most reasonable representation of how density increases when exposure is changed. The series of camera exposure times 1/500, 1/250, 1/125, etc. is a logarithmic series, as is that of the printing exposure times 2, 4, 8, 16 s.
2. A D vs. log H curve shows, on a far larger scale than a density–exposure curve, the portion of the curve corresponding to just-perceptible blackening, i.e. with small values of exposure. The speed of a film is usually judged in terms of the exposure needed to produce quite small values of density.
3. The use of logarithmic units for both horizontal and vertical axes enables values of density in the photographic negative to be transferred readily to the log exposure axis of the characteristic curve of the print. This simplifies the task of relating the brightnesses of the original scene, the transmission densities of the negative and the reflection densities of the print.
Main regions of the negative characteristic curve
The characteristic curve of a negative material may be divided into four main regions: the toe or foot, an approximately linear portion, the shoulder and the region of solarization, as shown in Figure 8.2.
It is only on the linear portion that density differences in the negative are directly proportional to visual differences in the scene. For this reason the linear portion was at one time referred to as the region of correct exposure, the toe as the region of underexposure and the shoulder as the region of overexposure. As we shall see later in this chapter, however, such descriptions are misleading. The value of density reached at the top of the shoulder of the curve is referred to as Dmax, the maximum density obtainable under the given conditions of development.
Provided the horizontal and vertical axes are equally scaled, the numerical value of the tangent of the angle which the linear portion of the curve makes with the log H axis is termed gamma (γ). Thus, when that angle = 45°, γ = 1.
Gamma may be defined more rigorously in terms of the values of density and log exposure corresponding to any two points lying on the straight-line portion of the curve. In Figure 8.2:
This definition of γ does not depend on a characteristic curve at all, merely on the quantities: log exposure, which is known, and density, which is measured. The data required must, however, correspond to points on the linear part of the characteristic curve.
Gamma measures sensitometric contrast, i.e. the rate at which density increases as log exposure increases in the linear portion of the curve. It should be noted, however, that gamma gives information only about the linear portion; it tells us nothing about the other portions. Further, as will be seen later, the contrast of a negative is not determined by gamma alone: other factors play an important part, and with modern emulsions no portion of the curve may be strictly linear. In the case where there is no linear portion, the calculation of γ reduces to determining the maximum value of the gradient, technically at the point of inflection.
Figure 8.2 The conventional photographic characteristic curve of a negative material – the response curve obtained by plotting density against log exposure.
The term ‘γ’ is also used in the evaluation of transfer functions of digital systems and their components. The characteristics of digital imaging systems are described in detail in Chapter 21, which includes a consideration of the tone reproduction requirements of a variety of imaging systems. These are often characterized by ‘g’, a parameter derived from the opto-electronic conversion functions (OECFs) of the devices involved.
Sensitometric contrast is an important aspect of performance and, with experience, is readily appreciated from a superficial examination of the H and D curve (provided the abscissa and ordinate axes have been equally scaled). The region of solarization, or reversal, was of interest when first observed with rather simple emulsions. Modern emulsions require very large exposures to show this effect – commonly of the order of 1000 times greater than the maximum normal exposure. In general, the more efficient a material is at forming a latent image, the less likely is solarization to occur.
Below the toe, the curve becomes parallel to the log H axis, at a minimum density or Dmin. The value of density in this region is the sum of densities due to the film or paper base supporting the emulsion, the gelatin of the emulsion, any silver developed from unexposed emulsion grains, ‘fog’, and any residual chemical stain present after manufacture and processing of the film. This, usually small, density is sometimes misleadingly termed base density. The most generally used description is fog level, although Dmin is the more accurate. It is the minimum density obtainable with the process employed. Base density is strictly the density of the film or paper support while fog results from development of unexposed silver halide. The point corresponding to the first perceptible density above Dmin is called the threshold.
The intersection of the extrapolated straight-line portion of the curve with the Dmin is the inertia point, and the value of exposure at this point is the inertia. On published characteristic curves the log exposure axis may be marked ‘Relative log exposure’, often abbreviated to ‘Rel log H’ or, more properly, ‘Log relative exposure’, abbreviated to ‘Log rel H’. Use of a relative instead of an absolute log H scale does not affect the shape of the curve, but absolute values of emulsion speed cannot be determined directly from the curve.
Variation of the characteristic curve with the material
The characteristic curves of individual materials differ in their shapes and in their positions relative to the log H axis. The position of the curve against the log H axis depends upon the sensitivity or speed of the material. The faster the material, the further to the left the curve is situated. The threshold density occurs at the lowest exposures with fast emulsions. Film speed itself is dealt with in Chapter 20. The main variations in the shape of the characteristic curve are the length of the linear portion and its slope (gamma).
Photographic materials differ both in the maximum slope that can be achieved and in the rate at which the value of the slope increases. Modern negative materials are usually made to yield a gamma of 0.7 or so with normal development. The toe is long and the straight line may be short or even non-existent. Some fast materials have a bent-leg or dog-leg curve, which has in effect two straight-line portions of different slopes. The lower part of the curve is fairly steep, but at a higher density the slope becomes lower. This curve shape may have advantages when photographing subjects with intense highlights, e.g. night scenes.
Materials for copying are usually designed to have a short toe, which merges into the linear portion at a low density, and a long linear portion, the slope of which depends on the application for which the material is intended. Materials capable of yielding gammas from below 1 to 10, or more, are available.
In the duplication of negatives it is necessary to use a material possessing a long linear portion, the slope of which can readily be controlled in processing. The exposure should be confined to the linear portion, and it is advantageous to develop to a gamma of unity. Characteristic curves for specific materials are published by the film manufacturers.
Gamma–time curve
The characteristic curve is not a fixed function of an emulsion, but alters in shape with the conditions of exposure, e.g. the colour and intensity of the light source, and with the conditions of processing; in particular, the contrast is markedly affected by the development time. By plotting gamma as ordinate against development time as abscissa we obtain a curve, the general shape of which is illustrated in Figure 8.3.
Sensitometric contrast, gamma, increases very rapidly as development begins, and then at a more gradual rate until a point is reached where increased development produces no further increase in gamma. The value of gamma at this point is termed gamma infinity (γ∞). This varies from emulsion to emulsion and depends to some extent on the developing solution used. A material capable of yielding a high value of γ∞ is said to be a high-contrast material. It is rarely desirable to develop to gamma infinity, as prolonged development increases fog and graininess, either or both of which may become unacceptable before gamma infinity is achieved. Owing to chemical fog (development of unex-posed emulsion grains) gamma may decrease with development prolonged beyond gamma infinity, as the effect of fog density is greater on low densities than high.
Figure 8.3 Gamma–time curves for the same material in two different developers.
A gamma–time curve shows the value of gamma infinity obtainable with a given material and developer. It also shows the development time required to reach this or any lower value of gamma. We have seen that it is rarely desirable to employ the very top part of the gamma–time curve. It is also usually unwise to employ the very bottom part, where a small increase in development time gives a large increase in gamma, because in this region any slight inequalities in the degree of development across the film will be accentuated, with the likelihood of uneven density or mottle.
Figure 8.3 shows gamma–time curves for a film in two differing developers. Curve A was produced in an MQ–carbonate developer and curve B in an MQ–borax developer. Comparison of such curves assists in the choice of a suitable developer when the desired gamma is known. For example, if a gamma of 0.5 were desired the MQ–borax developer would be preferable to the other, since, with the latter, contrast changes rapidly with development time at the gamma required. But, to achieve a gamma of 1.1, the MQ–carbonate developer would be more suitable, the other requiring an excessively long development time to reach this value.
Gamma–time curves for individual materials under stated conditions of development are published by film manufacturers. Such curves can be of considerable assistance in the selection of a material and developer for a given task. Working conditions may, however, vary from those specified and in order to be of the greatest value, gamma–time curves for any given material should be determined by the user under the particular working conditions.
When plotting parameters such as Dmin, speed or contrast against development time, it is often useful to adopt a logarithmic scale for development time. This compresses the region of long development times and sometimes enables the more interesting results to approximate a straight-line graph. This is easier to draw and to use than a curve.
Variation of gamma with wavelength
Besides being dependent on development, gamma also depends to some extent on the colour of the exposing light. The variation within the visible spectrum is not great, but it becomes considerable in the ultraviolet region. The general tendency is for gamma to be lower as wavelength decreases. This variation of gamma can be largely ignored in ordinary photography, but must be taken into account when directly imaging by ultraviolet radiation (without assistance from visible fluorescence).
PLACING THE SUBJECT ON THE CHARACTERISTIC CURVE
A characteristic curve shows the response of a material under a wide range of exposures. Only part of this curve is used in any single negative. The extent of the portion used depends on the subject luminance ratio; its position depends on the actual luminances in the scene and on the camera exposure employed. Strictly, it is the illuminance ratio of the image on the film that concerns us here and, if flare is present, the illuminance ratio will be less than the subject luminance ratio. In the present context we shall assume that flare is absent.
We have observed (Figure 8.2) that the characteristic curves of negative materials possess a long toe. The part of the curve used by a ‘correctly exposed’ negative includes part of this toe and the lower part of the straight-line portion. This is illustrated in Figure 8.4.
Consider photographing the cube shown in Figure 8.5, in which S1 is the darkest area in the subject, S2 the next darkest, H1 the highest highlight and H2 the next highest. On a normally exposed, normally developed negative, the exposures and densities corresponding to these areas will be approximately as shown in Figure 8.4.
Figure 8.4 The portion of the characteristic curve employed by a ‘correctly exposed’ and ‘correctly developed’ negative, lies between S1 and H1.
Effect of variation of exposure of the negative
Figure 8.4 shows the positioning of tones, illustrated in Figure 8.5, on the characteristic curve of the correctly exposed and processed negative. If too little exposure is given, all tones will be recorded lower on the curve and S1and S2 will possess a much lower density separation on the negative, and in the print, shadow detail will have been lost. Highlight tones H1 and H2 will, however, lie on the near-linear part of the characteristic curve, and highlight tones will be well distinguished. Moderate underexposure of the negative may be compensated for by using a high grade of printing paper, but if S1 and S2 have identical densities in the negative, there can be no separation of shadow tones in the print. In a moderately overexposed negative, given normal development, the selected shadow and highlight tones will all record on the high-contrast part of the characteristic curve. The overall density of the negative is higher than normal and the density range is expanded. In particular, tone separation in the shadows is increased. In the rare case of gross overexposure, the shoulder of the characteristic curve may be reached, the density range of the negative will be reduced and highlight detail compressed or totally lost.
AVERAGE GRADIENT AND 
Since a negative usually occupies part of the toe of the curve as well as part of the straight line, gamma alone gives an incomplete picture of the contrast of an emulsion. A better measure is obtained by taking the slope of the line joining the two limiting points of the portion of the characteristic curve employed (Figure 8.6). This is referred to as the average gradient. It is always lower than gamma. Several limiting points on the curve are specified in standards concerning special photographic materials. For normal negative films the quantity 
(G-bar) was defined by Ilford Ltd as the slope of a line joining the point at a density of 0.1 above Dmin with a point on the characteristic curve 1.5 units log H in the direction of greater exposure.
CONTRAST INDEX
A measure of contrast devised by Kodak is the contrast index, which, like , takes into account the toe of the characteristic curve. The determination involves using a rather complicated transparent scale overlaid on the characteristic curve, although an approximate method is to draw an arc of 2.0 units cutting the characteristic curve and centred on a point 0.1 units above Dmin. This requires equally scaled log exposure and density axes. The slope of the straight line joining these two points is the contrast index. Characteristic curves of materials may differ in gamma but possess identical contrast index, or indeed . Negatives of identical contrast index or can be expected to produce acceptable prints using the same grade of printing paper.
EFFECT OF VARIATION IN DEVELOPMENT ON THE NEGATIVE
The negative represented by the curve in Figure 8.6 was given normal development. If we make two other identical exposures of the same subject, and give more development to one and less development to the other, we shall obtain two further curves such as those, together with the ‘normally developed’ curve (Figure 8.7). The camera exposure is the same in all three cases, so that the parts of the curves used, measured against the log H axis, are the same for all three.
Figure 8.7 Effect on negative of variations in development.
It will be seen that overdevelopment increases the density of the negative in the shadows to a small extent and in the highlights to a large extent. As a result, the over-developed negative as a whole is denser and, more important, its density range is increased. Underdevelopment has the reverse effect. It decreases density in both shadows and highlights, in the highlights to a greater extent than in the shadows, and the density range of the negative is reduced, as is its overall density. Thus, the major effect of variation in the degree of development is on the density range, often described as the contrast of the negative.
EXPOSURE LATITUDE
Exposure latitude is the factor by which the minimum camera exposure required to give a negative with adequate shadow detail may be multiplied, without loss of highlight detail.
We may call the distance along the log H axis between the lowest and highest usable points on the curve the useful exposure range. This depends principally upon the emulsion and the degree of development. These two factors also govern latitude, but this is also dependent upon the log luminance range of the subject. In practice, loss of highlight detail (setting the upper limit to exposure) often results from loss of resolution due to graininess and irradiation, before the shoulder is reached. As the required resolution usually depends upon the negative size and the consequent degree of enlargement in making the print, we may add ‘negative format’ to the practical factors governing useful exposure range and latitude. In general there is less exposure latitude with a small format than with a larger one.
The log luminance range of the average subject is less than the useful log exposure range of the film, and there is usually considerable latitude in exposure. If, however, we have a subject with a log luminance range equal to the useful log exposure range of the film, only one exposure level is permissible. With the exceptional subject having a luminance range greater than the useful exposure range of the film, no exposure level yields a perfect result; either shadow or highlight detail or both will be lost. This most commonly arises with high-contrast materials, such as colour reversal (slide) films, when shadow detail is usually sacrificed to preserve highlight information.
If the subject range is below average we have extra latitude. In practice, however, this is limited on the underexposure side by the fact that an exposure too near the minimum will be located entirely on the toe and may result in an unprintably soft negative. It is usually preferable to locate the subject on the characteristic curve such that at least part is on the linear portion. In this way better negative contrast and more satisfactory print quality are achieved.
THE RESPONSE CURVE OF A PHOTOGRAPHIC PAPER
The characteristic curve of a paper is obtained in the same way as that of a film, by plotting density against log exposure. Density in this case is reflection density and is defined by the equation:
where ρ (the Greek letter rho) represents the reflectance, which is the ratio of the light reflected by the image to the light reflected by the base or some specified ‘standard’ white. This definition is analogous to that of transmission density.
Figure 8.8 illustrates the general shape of the characteristic curve of a paper. This curve, like that of a negative material, can be divided into four main regions: toe, straight line (or linear region), shoulder and region of solarization, though the latter is seldom encountered in practice.
The main differences between the curve of a paper and that of a film are:
1. The shoulder is reached at a lower density and turns over sharply, the curve becoming parallel to the log H axis at a value of Dmax rarely exceeding a value of 2.1.
2. The toe extends to a fairly high density.
3. The straight-line portion is short and, in some papers, non-existent.
4. The slope of the linear portion is generally steeper than that of a camera film emulsion.
5. Fog (under normal development conditions with correct safe light) is almost absent, although the minimum density may slightly exceed that of the paper base material alone, owing to stain acquired in processing.
Figure 8.8 The ‘geography’ of the characteristic curve of a photographic printing paper.
Differences (2) and (4) arise from the fact that when a silver image on an opaque diffusing base is viewed by reflected (as opposed to transmitted) light its effective density is increased, because at moderate densities, light must pass through the image at least twice.
Maximum black
The practical consequence of (1) above is that the maximum density obtainable on any paper is limited, however long the exposure or the development. The highest value of density that can be obtained for a particular paper, with full exposure and development, is called the maximum black of the paper. The maximum density obtained on any given paper depends principally on the type of surface. Light incident on a print undergoes three types of reflection:
1. Part is reflected by the surface of the gelatin layer in which the silver grains are embedded.
2. Part is reflected by the silver grains themselves.
3. The remainder is reflected by the baryta or resin coating on the paper base.
The sum of these reflections determines the reflectance and hence the density of the print. By increasing the exposure received by a paper, and thus the amount of silver in the developed image, we can eliminate entirely the reflection from the paper base, but reflections from the gelatin surface of the emulsion and from the individual grains themselves cannot be reduced in this way. These reflections limit the maximum black obtainable.
Reflection from the emulsion surface depends upon the nature of this surface. A print will normally be viewed in such a way that direct, specular, reflection from its surface does not enter the eye. We are therefore concerned only with diffuse reflection. Now, the reflection from the surface of a glossy paper is almost entirely direct, so the amount of light reflected from the surface of such a paper, which enters the eye when viewing a print, is very small. In these circumstances, the limit to the maximum density is governed, principally, by the light reflected by the silver image itself. This is usually a little less than 1%, corresponding to a maximum density of just over 2.0. Reflection from the surface of a matt paper, however, is almost completely diffuse, so that an appreciable amount of light (say 4%) from the surface of the paper reaches the eye, in addition to light reflected from the silver image. (There may also be light reflected from particulate material, included in the emulsion of many matt papers.) The maximum black of matt papers is therefore relatively low. Semi-matt and ‘stipple’ papers have values of maximum black intermediate between those of matt and glossy papers. Table 8.4 shows typical values of maximum black obtainable on papers of three main types of surface.
Resin-coated printing papers are not glazed after processing but possess a high natural gloss and may achieve a Dmax of over 2.0 without glazing. Glossy colour prints possess little reflecting material other than the paper base, and values as high as 2.5 are not uncommon. The effect of variation in maximum black on the characteristic curve is confined largely to the shoulder of the curve, as shown in Figure 8.9.
Table 8.4 The maximum black of printing papers with different surfaces
SURFACE |
REFLECTION DENSITY (MAXIMUM) |
Glossy, glazed |
2.10 |
Glossy, unglazed |
1.85 |
Semi-matt |
1.65 |
Matt |
1.30 |
Figure 8.9 Characteristics of printing papers with different surfaces.
Exposure range of a paper
The ratio of exposures corresponding to the highest and lowest points on the curve employed in a normal print is termed the exposure range of the paper (Figure 8.10) and is expressed either in exposure units or log exposure units. It represents the usable exposure range of the paper and corresponds to the greatest negative density range, which can be fully accommodated.
Variation of the print characteristic curve with the type of emulsion
Photographic papers employ emulsions containing various proportions of silver chloride and silver bromide. Slow emulsions intended for contact printing have traditionally contained a high proportion of silver chloride, while enlarging papers contain a greater proportion of silver bromide. The names ‘chlorobromide’ and ‘bromide’ papers indicate different proportions of silver bromide present and the characteristic curves of these papers differ somewhat in shape. The practical effect of differing curve shapes is to alter the tonal relationships within the print, a matter of some subjective importance. Such subtle differences give additional control at printing.
Figure 8.10 Exposure range of a printing paper.
Variation of the print characteristic curve with development
With papers the characteristic curve varies with development, but rather differently from that of negative film. Figure 8.11 shows a family of curves for a bromide paper. The normally recommended development time for this paper (in the developer employed) is 2 minutes at 20°C. With more modern printing papers, development normally requires a minimum of about 1 minute. At longer development times the curve may be displaced to lower exposure levels but, unlike the curve of a chloride paper, the slope may increase slightly. In other words, both speed and contrast of a bromide paper may increase on prolonged development. The increase in contrast is usually not very great, but can be of practical value. The major effect of variation of development time on papers of all types is on the effective development speed of the paper.
Figure 8.11 Characteristic curves of a traditional bromide printing paper for different development times.
The situation may be complicated by the composition of ‘bromide’ paper, which may contain a significant proportion of silver chloride. This modifies the development behaviour so that there is no detectable contrast increase once maximum black has been reached.
With papers of all types, there is development latitude between the two extremes of under-and overdevelopment. With the paper shown in Figure 8.11, this extends from about 1.5 to 4 minutes. Between these times maximum black is achieved with no increase in fog. The ratio of exposure times required at the shortest and longest acceptable times of development is referred to as the printing exposure latitude. Development latitude and exposure latitude are interrelated – both cannot be used at the same time. Thus, once an exposure has been made there is only one development time that will give a print of the required density. In dish processing the development latitude may be reduced in modern printing papers by extended green sensitivity, which may make the emulsions liable to actinic exposure, exposure generating latent image, by yellow or orange safe lights. The effect may be visible, at low levels, as a reduction in tonal contrast of the prints made. There may be no increase in fog level, but a reduction of contrast may be observed.
REQUIREMENTS IN A PRINT
It is generally agreed that, in a print:
1. All the important negative tones should appear in the print.
2. The print should span the full range of tones, from black to white, that is capable of being produced on the paper used. (Even in high-key and low-key photographs it is usually desirable that the print should show some white and some black, however small these areas may be.)
In printing, the exposure of the paper in any area is governed by the negative density in the corresponding area: the greater the density of any negative area, the less the exposure, and vice versa. In order, then, to meet the requirements above, the exposure through the highlight (darkest) areas of the negative must correspond with the toe of the curve of the printing paper, and the exposure through the shadow (lightest) areas of the negative must correspond with the shoulder of this curve. Expressed sensitometrically, this means that the log exposure range of the paper must equal the density range of the negative.
Now, not all negatives have the same density range, which varies with the log luminance range of the subject, the emulsion used, the exposure and the degree of development. Therefore, no single paper will suit all negatives because, as we have seen, the log exposure range of a paper is a more or less fixed characteristic, affected only slightly (if at all) by development. A single paper with a sufficiently long log exposure range would enable requirement (1) to be met in all cases, but not requirement (2). Printing papers are therefore produced in a series of differing contrast grades or usable exposure ranges.
Paper contrast
In Figure 8.12 are shown the characteristic curves of a series of bromide papers. These papers all have the same surface and differ only in their contrasts, or usable exposure ranges, described as soft, normal and hard respectively. These are usually designated by grades ranging from 0 at very low contrast to 5 at very high contrast. All three papers have been developed for the same time. It will be noted that the three curves show the same maximum black, but that the steepness of the curve increases, and the exposure range decreases, as we progress from the ‘soft’ to the ‘hard’ paper. The soft paper with long log exposure range is intended for use with negatives of high density range. Conversely, the ‘hard’ paper, with short log exposure range, is intended for use with negatives of low density range.
Variable contrast papers comprise two emulsions of differing contrasts and possessing differing spectral sensitivities. The contrast is varied by suitably filtering the enlarger at exposure; typically, the highest grades are achieved using a grade 5 filter, which is magenta, and the lowest by using a grade 0 filter, which is yellow. Intermediate contrasts are achieved using either a set of appropriately designed colour filters, or by the use of a special enlarger head to vary the spectral distribution of the printing illuminant. The sensitometry of such papers will require similar filtration plus, usually, a correction filter to raise the colour temperature to that of a typical enlarger if a 2856 K source is used in the sensitometer. The characteristic curves corresponding to contrast grades will approximate those found for traditionally graded papers.
If negatives of the same subject, differing only in contrast, are each printed on papers of the appropriate exposure range, the prints will be practically identical. If, however, an attempt is made to print on a paper with too short a log exposure range, and exposure is adjusted to give correct density in, say, the highlights, then the shadows will be overexposed, shadow detail will be lost in areas of maximum black, and the result will appear too contrasty. If, on the other hand, a paper of too long a log exposure range is used (i.e. too soft a grade) and exposure is again adjusted for the highlights, the shadow areas of the print will be underexposed and the result will appear ‘flat’.
The softer the grade of paper, i.e. the longer its log exposure range, the greater is the exposure latitude (as defined earlier) in printing. It is, however, generally unwise to aim at producing negatives suited to the softest available paper because one then has nothing to fall back upon if, for some reason, a negative proves to be exceptionally contrasty. It is therefore generally best to aim at the production of negatives suitable for printing on a middle grade of paper.
A simple, if approximate, check on the exposure range of a paper can be made by giving to a strip of it a series of progressively increasing exposures. The exposure ratio is the ratio of the exposure time required to yield the deepest black that the paper will give, to that required to produce a just perceptible density. A typical set of exposure times, using an enlarger set up for normal use, can be achieved by a geometric series: 1, 2, 4, 8, 16, 32, 64, 128, 256 seconds. An opaque card may be advanced across the paper surface by one division after each exposure step – the exposures suggested will result in an overall series from 1 to 512 seconds. If necessary the lens aperture can be adjusted to ensure that all the exposed steps, from white to black, are obtained.
Some skilled monochrome printers use an interesting method for the control of tone reproduction. They use a brief uniform, non-image, pre-exposure or pre-flash to modify the characteristic curve shape of the printing paper. Generally speaking, the higher the intensity of the pre-flash, the lower is the contrast obtained. There may be some increase in the minimum density if a large reduction in contrast is attempted, but this may be acceptable.
RECIPROCITY LAW FAILURE
The reciprocity law, enunciated by Bunsen and Roscoe in 1862, states that for any given light-sensitive material, the photochemical effects are directly proportional to the incident light energy, i.e. the product of illuminance and exposure duration. For a photographic emulsion this means that the same density will be obtained if either illuminance or exposure duration is varied, provided that the other factor is also varied so as to keep constant the product H in Eqn 8.1.
Abney first drew attention to the fact that the photographic effect depends on the actual values of H and t, and not solely on their product. This so-called reciprocity failure arises because the effect of exposure on a photographic material depends on the rate at which the energy is supplied. All emulsions exhibit reciprocity failure to some extent, but it is usually serious only at very high or low levels of illumination, and for much general photography the reciprocity law can be considered to hold. In the sensitometric laboratory, however, the effects of reciprocity failure cannot and should not be ignored, or in certain practical applications of photography.
If sensitometry is to be a useful guide to the performance of photographic materials under their typical conditions of use, we have to approximate those conditions in the sensitometric laboratory. In practice it is very helpful to know and understand the behaviour of films within our own methods and conditions.
Practical effects of reciprocity failure
Reciprocity failure is encountered in practice as a loss of speed and increase in contrast at low levels of illumination, i.e at long exposure times. The degree of the fall-off in speed and the region at which maximum speed is obtained vary from material to material. The effects of reciprocity failure are illustrated in Figure 8.13, which illustrates the behaviour of a fast negative film at a range of exposure durations. With no reciprocity failure, all the curves would be identical and coincide with that for 0.02 and 0.2 s exposure time. A major effective speed loss, however, occurs at longer exposures, together with some contrast gain.
Figure 8.13 Characteristic curves of a fast negative film for different exposure durations.
As a result of reciprocity failure, a series of graded exposures made using a time scale yields a result different from a set made using an intensity scale. Consequently, in sensitometry, a scale appropriate to the conditions in use must be chosen if the resulting curves are to bear a true relation to practice. For the same reason, filter factors depend on whether the increase in exposure of the filtered negative is obtained by increasing the intensity or the exposure duration. Two types of filter factor are therefore sometimes quoted: ‘intensity-scale’ and ‘time-scale’ factors.
The variation of speed and contrast with differing exposure duration is usually different for each of the three emulsion layers present in colour materials. Consequently, departures from recommended exposing conditions may lead to unacceptable changes in colour balance for which no compensation may be possible. Fortunately, the manufacturers of colour films for professional use make films in two classes: one for short daylight, or electronic flash, exposures and the second for long, studio-lit exposures.
It should be noted that although the mechanisms underlying anomalous reciprocity effects are dependent on the illuminance on the emulsion and can be adequately explained on that basis, it is the duration of the exposure that is critical in determining the importance of reciprocity failure to the practical photographer.
Intermittency effect
An exposure given as a series of instalments does not usually lead to the same result as a continuous exposure of the same total duration. This variation is known as the intermittency effect. It is associated with reciprocity failure, and its magnitude varies with the material. In practical photography the intermittency effect is not usually important except, possibly, in the making of test strips on printing paper for determining correct printing exposures. If a series of separate exposures is used to make a test strip, the suggested time may not be appropriate for a single continuous printing exposure. In sensitometry, this effect cannot be ignored and a single, continuous, exposure is used.
SENSITOMETERS
A sensitometer is an instrument for exposing a photographic material in a graded series of steps, the values of which are accurately known. The essentials of a sensitometer are:
1. A light source of known standard intensity and colour quality. Many sources have been proposed and used at various times. The light source adopted as standard in recent years has been a gas-filled tungsten lamp operating at a colour temperature of 2856 K. The lamp is used with a selectively absorbing filter to yield a spectral distribution corresponding to daylight of 5500 K, modified by a typical camera lens. The filter used is made of a suitable glass. 5500 K corresponds to daylight with the sun at a height typical of temperate zones during the hours recommended for colour photography and is suitable for the exposure of colour and monochrome films designed for daylight use. Any sensitometric light source must be stabilized in terms of both luminous intensity and, particularly when used for colour materials, colour temperature. Fluctuations in mains voltage can alter both quantities, and are generally compensated by sophisticated voltage stabilizers. In most cases a DC supply to the lamp is used to avoid AC modulation of the exposure, which may be significant at short exposure times.
2. Modulation of the light intensity. To produce the graded series of exposures, it is possible to alter the illuminance to obtain sensitometric data, which will correctly reflect the behaviour of the material under the in-camera conditions of use. The exposure time and intensities should be comparable with those for which the material is designed.
A series of exposures in which the scale is obtained by varying the intensity – referred to as an intensity scale – can conveniently be achieved by use of a neutral ‘step wedge’. A sensitometer is designed so that the exposures increase logarithmically along the length of the strip. The log exposure increments are usually 0.30, 0.15 or 0.10. If, for any reason, it is desired to interrupt the exposure, this must be done in such a way that the intermittency effect does not affect the results.
DENSITOMETERS
The name densitometer is given to special forms of photometer designed to measure photographic densities. Instruments designed to measure the densities of films and plates are described as transmission densitometers, while those designed to measure papers are termed reflection densitometers. Some instruments are designed to enable both transmission and reflection densities to be measured, usually employing separate sensor heads for the two tasks. Densitometers are generally single-beam instruments as shown in Figure 8.14 and the use of solid-state detectors, such as photodiodes, is now almost universal.
Figure 8.14 A single-beam, direct-reading densitometer.
The commonest type of transmission densitometer uses a light-sensitive detector illuminated by a beam of light into which the sample to be measured is placed. The response of the detector is displayed as optical density. The typical features illustrated in Figure 8.14 constitute a single-beam, direct-reading densitometer. Such instruments are usually set up by adjusting the density reading to zero when no sample is present in the beam. This operation may be followed by a high-density setting, using some calibration standard, or even an opaque shutter for zero illumination. Once set up, the instrument is used for direct measurements of the density of samples placed in the beam.
Stability of light output, of any electronics used and of performance by the detector are required for accurate density determination. In practice, checks of the instrument zero may be required to eliminate drift. A further requirement of the direct-reading instrument is linearity of response to changes of illuminance.
Microdensitometers
These instruments are used to examine density changes over very small areas of the image. Such microstructural details are measured for the assessment of granularity, acutance and modulation transfer function – all important determinants of image quality (see Chapters 19, 20, 24). To measure the density of a very small area it is usual to adopt a typical microscope system, replacing the human eye by an electronic sensor. Microdensitometers are very precise instruments, with measuring intervals of a few micrometers – the output may be displayed using the monitor of a controlling computer and appropriate parameters may be directly determined by the same computer.
Colour densitometers
In addition to monochrome silver images, it is often necessary to make sensitometric measurements of colour images. These are generally composed of just three dyes absorbing red, green and blue light respectively. It is therefore possible to assess colour images by making density measurements in these three spectral regions. Colour densitometers are therefore similar to monochrome instruments but are equipped with three primary colour filters. These red, green and blue filters combine with the sensor characteristics to give three separate response bands, in red, green and blue spectral regions respectively (Figure 8.15).
The behaviour of a dye image can be assessed most effectively when the densitometer measures only within the spectral absorption band of the dye, so colour densitometers are usually equipped with narrow-band filters. In view of the spectral imperfections of image dyes it will be appreciated that a single colour density measurement (red, green or blue) represents the sum of contributions from all the dyes present. Such combined densities are described as integral densities. The measured densities depend on the spectral bands sampled, which are in turn dictated by the material to be examined.
Colour negatives are designed for printing on colour paper, and are assessed using an instrument possessing ISO Status M spectral responses appropriate to colour printing. The purpose of this exercise is to use a densitometer to assess colour negatives and hence to predict the printing conditions required to yield a good colour print. Instruments set up according to an ISO Standard for the measurement of masked negatives are said to give Status M densitometry. Images designed for viewing are measured using ISO Status A densities, which accurately assess neutral images as viewed by the human observer. Colorimetric densities, which would assess colour densities in terms of human colour vision, have only found application in research laboratories, and are not necessary for the quality control of either colour negative or positive materials.
Figure 8.15 Blue, green and red response bands for ISO Status A colour densitometry, used for the examination of colour reversal film and positive prints designed for the human observer.
The spectral responses of instruments for Status A and M densitometry are tightly specified. It may not, however, be necessary to establish a system meeting such specifications because arbitrary integral densities are often satisfactory for such purposes as quality control. As with black-and-white densitometers, the commonest type is the direct-reading single-beam instrument.
BIBLIOGRAPHY
Eggleston, J., 1984. Sensitometry for Photographers. Focal Press, London, UK.
James, T.H., 1977. The Theory of the Photographic Process, fourth ed. Macmillan, New York, USA.
Proudfoot, C.N. (Ed.), 1997. Handbook of Photographic Science and Engineering. IS&T Springfield, VA, USA.
SMPTE, 1963. Principles of Colour Sensitometry. Society of Motion Picture and Television Engineers, New York, USA.
Thomas, W. (Ed.), 1973. SPSE Handbook of Photographic Science and Engineering. Wiley, New York, USA.
Todd, H.N., Zakia, R.D., 1974. Photographic Sensitometry. Morgan & Morgan, Hastings-on-Hudson second ed., New York, NY, USA.