Monochromatic Photography

The most common material for photographic image recording is silver halide emulsion, depicted in Figure 11.3-1. In this material, silver halide grains are suspended in a transparent layer of gelatin that is deposited on a glass, acetate or paper backing. If the backing is transparent, a transparency can be produced, and if the backing is a white paper, a reflection print can be obtained. When light strikes a grain, an electrochemical conversion process occurs, and part of the grain is converted to metallic silver. A development center is then said to exist in the grain. In the development process, a chemical developing agent causes grains with partial silver content to be converted entirely to metallic silver. Next, the film is fixed by chemically removing unexposed grains.

The photographic process described above is called a nonreversal process. It produces a negative image in the sense that the silver density is inversely proportional to the exposing light. A positive reflection print of an image can be obtained in a two-stage process with nonreversal materials. First, a negative transparency is produced, and then the negative transparency is illuminated to expose negative reflection print paper. The resulting silver density on the developed paper is then proportional to the light intensity that exposed the negative transparency.

A positive transparency of an image can be obtained with a reversal type of film. This film is exposed and undergoes a first development similar to that of a nonreversal film. At this stage in the photographic process, all grains that have been exposed to light are converted completely to metallic silver. In the next step, the metallic silver grains are chemically removed. The film is then uniformly exposed to light, or alternatively, a chemical process is performed to expose the remaining silver halide grains. Then the exposed grains are developed and fixed to produce a positive transparency whose density is proportional to the original light exposure.

FIGURE 11.3-1. Cross section of silver halide emulsion.

The relationships between light intensity exposing a film and the density of silver grains in a transparency or print can be described quantitatively by sensitometric measurements. Through sensitometry, a model is sought that will predict the spectral light distribution passing through an illuminated transparency or reflected from a print as a function of the spectral light distribution of the exposing light and certain physical parameters of the photographic process. The first stage of the photographic process, that of exposing the silver halide grains, can be modeled to a first-order approximation by the integral equation

where X(C) is the integrated exposure, C(X) represents the spectral energy distribution of the exposing light, L(X) denotes the spectral sensitivity of the film or paper plus any spectral losses resulting from filters or optical elements and kx is an exposure constant that is controllable by an aperture or exposure time setting. Equation 11.3-1 assumes a fixed exposure time. Ideally, if the exposure time were to be increased by a certain factor, the exposure would be increased by the same factor. Unfortunately, this relationship does not hold exactly. The departure from linearity is called a reciprocity failure of the film. Another anomaly in exposure prediction is the intermittency effect, in which the exposures for a constant intensity light and for an intermittently flashed light differ even though the incident energy is the same for both sources. Thus, if Eq. 11.3-1 is to be utilized as an exposure model, it is necessary to observe its limitations: The equation is strictly valid only for a fixed exposure time and constant-intensity illumination.

The transmittance t(X) of a developed reversal or nonreversal transparency as a function of wavelength can be ideally related to the density of silver grains by the exponential law of absorption as given by t(X) = exp {-deD(X)} (11.3-2)

where D(X) represents the characteristic density as a function of wavelength for a reference exposure value and de is a variable proportional to the actual exposure. For monochrome transparencies, the characteristic density function D(X) is reasonably constant over the visible region. As Eq. 11.3-2 indicates, high silver densities result in low transmittances, and vice versa. It is common practice to change the proportionality constant of Eq. 11.3-2 so that measurements are made in exponent ten units. Thus, the transparency transmittance can be equivalently written as

where dx is the density variable, inversely proportional to exposure, for exponent 10 units. From Eq. 11.3-3, it is seen that the photographic density is logarithmically related to the transmittance. Thus, dxD(X) = -log t(X)

The reflectivity ro(X) of a photographic print as a function of wavelength is also inversely proportional to its silver density, and follows the exponential law of absorption of Eq. 11.3-2. Thus, from Eqs. 11.3-3 and 11.3-4, one obtains directly rCX) = 10-dxD(X) (11.3-5)

dxD(X) = -log10 ro(X) (11.3-6)

where dx is an appropriately evaluated variable proportional to the exposure of the photographic paper.

The relational model between photographic density and transmittance or reflectivity is straightforward and reasonably accurate. The major problem is the next step of modeling the relationship between the exposure X(C) and the density variable dx. Figure 11.3-2« shows a typical curve of the transmittance of a nonreversal transparency as a function of exposure. It is to be noted that the curve is highly nonlinear except for a relatively narrow region in the lower exposure range. In Figure 11.3-2b, the curve of Figure 11.3-2« has been replotted as transmittance versus the logarithm of exposure. An approximate linear relationship is found to exist between transmittance and the logarithm of exposure, but operation in this exposure region is usually of little use in imaging systems.

Continue reading here: Discrete Image Restoration Models

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