Diffraction spectrometer, first devised by Lipson, has been constructed. A brief account of the principle of optical transform and details of design of the spectrometer are described. A note on the sign determination by optical transform methods is also given.
In the previous paper (part 1), a general study on the relation between wave optics and geometrical optics was made by applying the Fourier analysis. In the present paper, primary astigmatism, coma and spherical aberration are taken up as practical examples with the following results. In the case of astigmatism, if the magnitude |ω|λ of wave aberration is larger than 2λ, λ being the wave length, the geometric optical response function Rg(s) approximates the wave optical response function Rw(s) in the region of normalized frequency s, where |λs/2|<0.2. In the case of coma, if we consider the response function for the line image perpendicular to the sagittal direction, Rg(s) approximates Rw(s), when |ω|λ>1.2λ and |λs/2|<0.5; furthermore, the geometric optical response function Rg(t) for the line image perpendicular to the meridional direction, approaches Rw(t), when |ω|λ>1.6λ and |λt/2|<0.25. In the case of spherical aberration, if |ω|λ>1.3λ and |λs/2|<0.4, Rg(s) approximates Rw(s).
Method of measuring the response function of focusing screen is investigated. If the resultant response function of photographic lens, microscope and focusing screen is DR(w), and that of photographic lens and microscope is DLM(w), the response function of focusing, screen DF(w) is given by DF(w)=DR(w)/DL_??_(w). Hence, if DR(w) and DLM(w) are found experimentally DF(w) will be obtained. With this in view, an apparatus for measuring response function of focusing screen has been constructed and various focusing screens are examined concerning the relation of the response function to the performance of focusing screen.
Approximate relations between the tristimulus values (X, Y and Z) in the C. I. E. Trichromatic System and the concentration (C) of transparent colors are investigated. At low concentrations, it is found that the following equations are applicable. log 1/X=a0x+a1xC+a2xC2 log 1/Y=a0y+a1yC+a2yC2 log 1/Z=a0z+a1zC+a2zC2 For these emprical equations, some theoretical considerations are made. These empical equations can be adopted for the calaculation of tristimulus values at any concentration of transparent color.
The vacuum wavelengths of three radiations of Hg196 (0.579, 0.577, 0.546 μ) and three of Kr86 (0.646, 0.606, 0.565 μ) are measured in terms of the standard wavelength of red line of Michelson type cadmium lamp, the value of which is taken as 0.644 024 907P deduced from Edlén's formula. A Fabry-Perot etalon consisting of a pair of optical glass flats separated by 62.5 mm invar spacer is used in vacuum to obtain interference fringes. Observations of interference patterns are made photographically with the aid of a high dispersion spectrograph. The results (Table 1) are reported to Comite Consultatif pour la Définition du Métre and show good agreement with those of BIPM, PTB, NPL and NRC (see Table 2) Hg198: NBS electrodeless Hg'98 lamp containing 3mm Hg argon gas was excited by high frequency power source (200 MHz). The discharge column was viewed from the side through the surrounding water jacket and was kept at temperatures between 0° and 5°C by running water. Kr86: Engelhard type Kr66 hot cathode lamp cooled in liquid nitrogen was viewed from the end.
Method for determining the interference color of thin films using an automatic relay computer is studied. Numerical calculations involved in determining the interference color are performed more conveniently by taking the wavenumber as variable rather than the wavelength if the change of refractive index with wavelength is neglected. The C.I.E. colorimetric data on Eλxλ, Eλyλ, Eλzλ, are transformed into a table using the wavenumber as variable at 200cm-1 intervals. A table for wavenumbers extending from. 13, 000cm-1 to 27, 000cm-1 is given. Using this method, the interference color of stained lens surface coated with anti-reflecting film is determined. The results are shown plotted on the C.I.E. chromaticity diagram.
The value of response function (contrast transmission factor) of an optical system is obtained experimentally from the contrast of optical image of a sinusoidal grating, and as to the response function for the whole range of spatial frequencies, a number of gratings with different constants are required. To simplify the measurement, the “variable grating” with its constant varying stepwise from point to point is often employed. This alternative, however, introduces inaccuracy, for parts of different constants come within the circle of confusion of the optical system and the contrast of image no longer gives the true response function. The authors show analytically that, if instantaneous frequencies are taken as spatial frequencies, the contrast of image of variable grating approximately represents the response function. This is confirmed by numerical calculations in the case of sinusoidal variable grating, the pitch of which varied in geometrical and arithmetrical progressions and also according to a sinusoidal N. B. S. test chart, the frequency varying linearly with length of the chart. The error in the value of response function thus obtained is examined and its relation to the grating characteristics is made clear. Numerical calculations on square wave variable grating are also made and the error with this grating is compared with that with the sinusoidal variable grating.