By the use of an electronic computer, automatic correction concerning aberration of optical systems by the least square method is devised. Let the difference coefficients of aberrations φi (i=1, ····, m) by the variation of variables βf (j=1, ····, n) of a lens be denoted by aij. When the amount of change li of aberrations φi and the weighting factors wi of φi are given, the amounts Δβj of variation of βj are given by _??_(_??_wiaijaik)Δβj=(_??_wiliaik). The determinant D of the coefficient matrix is expressed by _??_ where the summation is carried out over all combinations of n integers γ1<γ2<····<γn chosen from 1, 2, ···· m. If the number n of variables happens to be larger than the number m of equations, D will be always zero, and the least square method will not hold. When m_??_n, D is expressed by the square sum of determinants of mCn matrixes. If the values of mCn is large (say more than 50) the chance of D=0 is very little. The program of automatic correction by the least square method is worked out and applied to a Tessar type lens and a Gauss type lens with satisfactory results.
The degree of coherence between three slits in a beam of quasi-monochromatic light from an incoherent slit source is investigated by the photo-electric method with Ebert optical system. Examples and discussions are given to illustrate the effects of the widths of primary source and the phase change of central fringe
This paper is an extension of the previous paper [Oyo Buturi 32, 677 (1963)] on coherent sources of light. Diffraction images of incoherent sources are quite different not only from those of coherent source but also from those of the Airy type pattern formed by an ordinary optical system. The diffraction images are calculated numerically by the Gaussian double quadrature method with an electronic computer and, shown in contour lines of intensity. Photographs of diffraction images taken with a high-pressure-mercury lamp are shown, and comparison is made between the diffraction images of coherent and incoherent sources, from which the case of partially coherent sources is speculated.
As a continuation of the previous work, four Nd3+ glass rods of square pillar type, 50×5×5mm, differing in doped Nd2O3 content from 0.1 to 1.0 weight percent, are prepared. For their optical examination, Twyman interferometer method is found better than the projection and the Schlieren methods. Of the four rods, one is optically homogeneous, the others are extremely': inhomogeneous with complicated striae. The homogeneous one has the threshold energy higher than homogeneous rods of circular section but lower than the inhomogeneous ones of square section. Results of a comparison made between near- and far-field patterns and interferograms of these rods tell that the state of laser emission inferable from the near-field patterns is closely related to the optical nature of rod material shown on the interferogram. With inhomogeneous rods, filaments of laser emission appear at specific places of the striae, they broaden gradually along the striae. An important point is that, it is not the extremum of optical path but the stria itself that orig-inates the laser emission. On far-field patterns of the homogeneous rod, there appear, in addition to the central square spot, line radiation patterns perpendicular to the sides of the rod and several intense spots along the line patterns. Interpretation of these patterns is made on the consideration of particular modes of rays that have closed paths in the rod. These modes are discussed. The far-field patterns of inhomogeneous rods are of circular type spots.