写真感光材料の粒状性

(I) Power Spectrumの測定

抄録

Of late, the power spectrum (spatial frequency spectrum) of grain pattern of photographic material is known to be valuable for evaluating its graininess and granularity. This paper presents the technique for measuring the power spectrum of grain pattern by scanning method and the experimental results obtained on uniformly exposed and developed black and white photographic materials. The experimental device consists of four distinct parts: the high speed scanning microphotometer, which scans a photographic material at the rate of one hundred millimeter a second with a small scanning aperture; the amplifier, which involves the high voltage source supplied to multiplier phototube; the frequency analyser, which analyses the wave form to its power spectrum with the narrow band pass filters; and the meter, which indicates the root mean square value of the current. The scanning aperture, on which the magnified image of grain pattern is projected by a microscope optical system, can be replaced with the use of a rotating aperture holder.
As the spectrum obtained by scanning method is one dimensional power spectrum, it is necessary to transform this spectrum to the two dimensional power spectrum (Wiener spectrum) which is convenient to treat the granularity transfer problem. The relation of these functions is given by the following equation:
ƒ(u)=∫^∞_-infin;F(u, v)|G(u, v)|²dv,
where u and v are the spatial frequency on the plane of grain pattern, ƒ(u) is the one dimensional spectrum obtained by scanning method, F(u, v) is the two dimensional spectrum, and G(u, v) is the response function (contrast transmission) of scanning aperture. It is not simple to solve this integral equation. However, if F(u, v) and G(u, v) are isotropic and decrease monotonously together with the increasing of spatial frequency, we can get F(u, v) by using the following equation. In this case, F(u, v)|G(u, v)|² can be expressed approximately by the sum of several error functions with different dispersions. The expressions is
F(u, v)|G(u, v)|²=_??_k_i/√2πpi exp(-u²+v²/2pi²).
Then ƒ (u) is given by
ƒ(u)=_??_k_iexp(-u²/2pi²).
The parameters (k_i, p_i) of error functions which are suitable for ƒ(u) obtained experimentarily, can be obtained by trial and error method. F(u, v) can be calculated by using these parameters and G(u, v). It is easy to give fairly good approximation by the sum of two or three error functions with proper parameters, for the level of ƒ(u) decreases quickly together with the increasing of spatial frequency u.
The normalized autocorrelation functions of grain pattern can be obtained by Kretzmer's optical autocorrelator, but the level of origin of this function can not be observed. On the other hand, measurement of level of power spectrum F(u, v) which is the Fourier transform of the autocorrelation function can be made with the device described in this paper.
The two dimensional power spectra, obtained on Fuji Neopan SSS Film and Fuji Medical X-ray Film by using a nominal aperture equivalent to a circle of 1μ in diameter in the plane of the grain pattern, are presented in figures.