Maggi ane Rubinowicz's formula of the diffraction by the Kirchhoff's screen is developed into more general cases. It is shown that, as far as the incident wave U(i) satisfies the wave equation, the integrand V of the Kirchhoff's integral Uk(P)=∫∫A1/4π[U(i)grad expiks/s-expiks/s gradU(i)]·ndS can be always expressed by the vector potential W in the following way, V=rot W Then by the Stokes' theorem, the diffracted wave Uk(P) is represented by Uk(P)=_??_Uj(s)(P)+_??_W·ldl, where Uj(s)(P) are contributions from the singular points of the vector potential which correspond to the points of the stationary phase in the Kirchhoff's integral, l being the unit vector along the line edge of the boundary Γ0 of the aperture A. For the incident wave which is slightly deformed from the ideal spherical wave, the approxi-mate vector potential is given by W(Q, P)=U(i)(Q)(expiks/s)(4π)-1(s×p)/(1+s·p), where s is the distance between the point Q on the aperture and the observing point P, _??_ being the unit vector of _??_/s and p being the unit vector of the geometrical optical ray, This gives us the same asymptotic formula of the contribution from the critical points of the first, second and third kind to the Kirchhof's integral. The accurate but not simple formula of the vector potential is also given for the general incident waves.
The Fourier analysis is an effective method for treating Fraunhofer diffraction phenomena, From this point of view, optical property of two dimensional phase filter having an axially sym-metric and periodic structure is analyzed by contrasting it with that of one dimensional. In particular, phase filters of rectangular, triangular and saw-tooth wave profile are treated. The results of the study show that these filters are characteristic either of a conical lens (a single- or multiple-power cone) or of a spherical lens (a single- or multiple-focus lens) according to their periodicity.
An interferometric photometer is applied to the measurement of intensity distributions of point images of low power microscope objectives having several amounts of primary spherical aberration, i.e., 0.0, 0.25, 0.5, 0.75, 1.0, 1.25 times the wavelength. Twyman lens interferometer being employed, light flux transmitted from the interferogram on the exit pupil of a lens is α+β|d(P)| cos (γ+δ) where d(P) is the amplitude on the image space. Modulation of the second term by alternating the phase of the reference wave by π at the rate of 300 cycles per second renders the output thro ugh the tuned amplifier to give the amplitude distribution. Experimental results show fairly good agreement with calcurated. This method has significant advantages photometrically over the direct scanning method, especially for high numerical aperture lenses with small residual aberrations.
Coefficients of aberration terms of the aberration function are useful quantities not only for lens designing, but also for calculating the intensity distribution of light in the neighborhood of Gaussian image point. There are three different expressions for the aberration function V: V=∑clnmσ2l+mrncosmφ ∑blnmσ2l+mrncosmφ ∑alnmσ2l+mRnm(r)cosmφ In this paper, relations among the coefficients a, b and c are investigated. When c's are obtained, b and a can be calculated successively from them.
Image-forming properties of transmitting and reflecting cone are studied. Expressions for the distribution of light intensity in the images of an ideal point source and an incoherently illuminated circular disk are derived. Results of both calculations and experiments show that, with the increase of distance from the cone, the image of the disk source changes gradually from diffraction image into geometric optical one. It is verified that Dyson's circular grating is equivalent to a composite of positive and negative transmitting cones.
In the author's previous papers, for assessing the performance of photographic lenses, the lens was considered to be a transmission line and the transmission distortion was introduced; the uniformity of the spatial frequency response over the image plane was discussed as non-linear distortion in the spatial frequency domain and the distortion factor of it was defined for the evaluation of the lens. The distortion factor is useful to evaluate the aberration which is concerned with the image angle; it gives the optimum correction of residual aberrations. In this point of view, the depth of focus is treated as a region where the linear and non-linear distortions are less than some definite values. The magnitudes of the distortions are normalized distances in the functional space in which the characters of a lens are represented. The linear distortion is measured by the distance between the spatial frequency response averaged in the image plane and the case in which ther esponse is 100%. The non-linear distortion is measured by the distance between the response and its averaged value. In the actual measurement or calculation, only the average of the response and of its square value are required, because the distances are computed from them easily.
A practical method of evaluating granularity of subtractive color film is reported. The gran-ularity of color film arises from local variations of color difference caused by the grain pattern of three dyes which constitute the image of color film. When spectral transmittance of these dyes can be regarded as that of block dyes, and the color variations caused by granularity is sufficiently small, the granularity E can be given by _??_ where _??_Y, _??_M, and _??_Y are the mean transmittance of yellow, magenta, and cyan layer respectively; y, m and c are the standard deviations of transmittance of each layer; v is the standard deviationn of visual transmittance variation; a1, a2, a3, b1, b2 and b3 are coefficients determined by the spectral stimulus values of Judd's uniform chromaticity system. By giving a reasonable value to the coefficient k, chromaticity and luminance difference can be evaluated by the same unit in the uniform chromaticity system. The standard deviations, y, m, c and v were measured by a high speed scanning microphotometer which was reported in the previous paper of this series. Then the granularity E was calculated by substituting the measured values into the equation. The numerical values of E corresponded fairly well to the value of graininess which was observed by the blending distance method. In this case, the correlation coefficient was 0.91. Therefore the equation which gives the granularity E can be regarded as a correct one. From the relative magnitude of coefficients of the equation, we find that the contribution of the transmittance varia-tion of magenta layer is dominant over the granularity of subtractive color film. The granularity of various commercial color films were measured by using this method and the data are presented in figures. The level of granularity increased monotonously with the increase of color density. There was a tendency of the granularity of color negative film being coarser than that of reversal color film.
Previously, one of the authors (H. K.) reported that the diffraction image formed by palarizing microscope is of four-leaf clover when the nicols are crossed. A similar image is obtained when a z-cut uniaxial crystal is observed. In the former, the case was limited because of the smallness of objective aparture, while in the latter, the aparture is widened to cover up the second dark ring of the conoscopic image and the diffraction image thus obtained is analyzed. Discussion is given as to the resolving power of polarizing microscope by giving heed to the very unusual form of the image.
Reflection characteristic of textile fabrics is that, when compared with that of metals, tiles, paper or the like, the diffusion of light is large and the specular reflection is extremely small, hence the degree of gloss does not vary much. For such materials, the gloss is best to be regarded as related to diffusivity and “diffused -gloss value Dn” is introduced which is defined by Dn=1/B(θs)_??_B(n-i·Δθ) where B(θ): brightness in the direction θ of reflected light, θs: angle of specular reflection, Δθ=θs/n i=0, 1, 2, ……n. Dn can be evaluated by assigning Dn=1 for mirror surface and Dn=1+n for perfect diffusive surface. In the evaluation, the shape of goniophotometric curve is taken into account. Dn×B(θs) approximates to the total amount of reflected light. For surfaces of large diffusivity, the difference in gloss values can be given magnified, while for surfaces of small diffusivity, it can be reduced within a narrow range. Grading of gloss by the proposed device is applied to actual goniophotometric curves, and discussion is given on the method of representing it in diagram.
Of late, the microspectrophotometry has been regarded as of necessity and is being eagerly taken up in the fields of biological, medical and physical studies as we see for example in the determination of spectral transmission of various objects such as blood corpuscles, nuclei of cells, cancer cells and many kinds of microcrystals. A single-beam microspectrophotometric apparatus, into which a PbS photoconductive infrared detector is incorporated, has been constructed enabling the intended work in near infrared region to be carried out. Its optical system consists of a double monochromator, objectives, eyepieces and other usual parts, and its photometric system, a PbS photoconductive detector, a main ampli-fier and other customary appliances. With ×30 and ×10 objectives, over 200 signal-to-noise ratios within the region of 0.8_??_1.5μ in wavelength were successfully obtained.
Time-lag τl of light emission relative to the initiation of electric current flow in various flash tubes is studied experimentally. The light emission is picked up by a vacuum photocell and is recorded by an oscilloscope. The influence of applied voltage on τl is similar, in general trend, to the voltage dependency on the formative time-lag of electric current which was already reported in the author's previous paper, namely, τl decreases with increasing voltage. Regarding the dependency of τl on the nature of gas in the flash tube, if all the other condi-tions such as discharge voltage, capacity and gas pressure are the same, τl in Xe is the largest (1_??_10μ sec), decreasing in sequence of Ar, Ne, He. The same relation holds for the dependency of intensity of emitted light on the nature of gas. The formative time-lags of discharge current and peak current, however, are affected by the nature of gas in reversed sequence. An attempt is made to explain the mechanism of the time-lag of light emission. The con-tinuous spectrum seen in a discharge of this kind in rare gases originates from the dissociation of diatomic molecular ions which comprise metastable atoms, and, for that reason, the observed time-lag can be explained as consisted of two stages: first, the time interval necessary for the electron temperature to rise and effect a sufficient number of metastable atoms to be formed: second, the time interval in which molecular ions are formed by collision between the metastable atoms and neutral atoms, the collision being caused by the subsequent rise of ion moleculer temperature.