Resolving Power of a Photographic System

a photographic system’s ability to distinctly reproduce fine details of an object. Resolving power is determined by the minimum separation of lines of a regular one-dimensional grating (test pattern) that can be registered in a photographic image without a merging of the lines. Resolving power is measured by means of resolution testers and is usually expressed in mm^-1, that is, number of lines per mm. For photographic materials currently in use, the resolving power usually lies in the range 70–300 mm^-1, The resolving power of special materials used in holography may be 2,000 mm^-1 or more.

The physical nature of the resolving power is related both to the finite character of the resolving power of optical systems and the optical thickness of the emulsion layers of photographic materials. Photographic materials consist of highly dispersed microcrystals of silver halide, 0.1–3 microns in diameter, suspended in a gelatin in a concentration of 10⁸—10¹⁰ cm^-3. Since the difference between the refractive index of the gelatin and that of the silver halide is great, there is strong scattering of light in the photosensitive layer, by virtue of which optical radiation spreads beyond the limits of the optical image formed on the layer by the lens. Thus, the boundaries of the elements of the photographic image are blurred in comparison with the optical image. In addition, resolving power is affected by light absorption in the gelatin as the light travels between silver microcrystals and by the difference in the microcrystals’ light sensitivity.

Resolving power depends on exposure and is highest for the lower and central parts of the rectilinear segment of the characteristic curve of the photographic material. The dependence of resolving power on the photographic contrast of the grating image on the photosensitive layer may be expressed by the formula , where K = (E_max - E_min)/(E_max + E_min) and R_max is the resolving power for K = 1; here E_max and E_min are the brightnesses of the images of the light and dark lines. The resolving power has little dependence on the kind of developer and developing conditions but a strong dependence on the wavelength of the exposing light. It is appreciably higher for illumination with ultraviolet radiation—which usually is greatly absorbed by the emulsion layer—and its dependence on wavelength in the optical sensitization region varies for large- and small-grain emulsions.

Figure 1. Graph of modulation transfer function, in which the modulation transfer coefficient T(N) is represented as a function of the grating spatial frequency N (the reciprocal of the grating period). The curve C(N) of the eye’s contrast sensitivity characterizes visual acuity. The point of intersection of these two curves gives the value of the resolving power R_syst of the photographic system.

In a two-component photographic system consisting of a lens with a resolving power R_obj (in an aerial image) and a photosensitive layer with a resolving power R_layer, the resolving power R_syst can be determined only by approximate empirical formulas of the type 1/(R_obj)^α + 1/(R_layer)^α = m/(R_syst)^α, where 1 ≤ α ≤ 2 and 1 ≤ m ≤ 1.25. The resolving power of multicomponent systems, with allowance for image deterioration caused by a number of factors—such as the lens, the photosensitive layer, atmospheric turbulence between the object and lens, and movement of the image during exposure—is described by modulation transfer functions. These functions, also called frequency-contrast characteristics, characterize the quality of reproduction of grids of various spatial frequencies. Under certain conditions the modulation transfer function of a multicompo-nent system may be considered to be the product of the modulation transfer functions of the individual components. If the modulation transfer function of a system is defined, the resolving power of the system is the point of intersection of the curve of the modulation transfer function and the curve of the contrast sensitivity of the eye when viewing a photographic image of the grid in a microscope (Figure 1).