The contours of equal transmission of dielectric double layer and multilayer of alternate equal thickness are plotted on a diagram with δ1 and δ2 as ordinate and abscissa respectively, where δ1 and δ2 are the phase angles of constituent layers. Use of this diagram makes it possible to evaluate the spectral transmission of layers of any thickness. Analytical studies of maxima, minima, and saddle points of the contours of equal transmission are performed by the use of this diagram. Curves showing the relation between the thickness and refractive indices which gives R2=0 are also plotted on δ1-δ2 plane with refractive index as a parameter, where R2 is the amplitude reflectance of double layer. From these curves, the relations among the solutions of λ/4-λ/4 antireflection film, thin highindex and thick-low index double-layer film, and achromatic film are investigated. There is no perfect antireflection film except these three solutions. Numerical calculations of the contours of equal transmission of double-layer antireflection film, beam splitter of double-layer film and alternating three-layer film are given.
In the previous paper, optical properties of double-layer film were discussed by means of a diagram of contours of equal transmission. In the present paper, combinations of three layers which satisfy the antireflection condition R3(δ1, δ2, δ3)=u3(δ1, δ2, δ3)+iv3(δ1, δ2, δ3)=0 are studied, where R3 is the amplitude reflectance of the three-layer film, its real and imaginary parts being taken as u3 and v3, and δi(i=1, 2, 3) is the phase angle of each layer. The thickness of each layer can be determined from the coordinates of the intersection between a straight line passing through the origin and the intersecting line of the surfaces u3=0 and v3=0. With the use of Vasicek's virtual surfaces, the condition of antireflection is represented by r32=|R2(δ1, δ2)|2, δ3=tan-1_??_, where γ3 is Fresnel coefficient of the boundary surface between the third layer and the surrounding medium. Hence, the thicknesses that effect the antireflection are given from the coordinates of the intersection of curves on these diagrams in δ1-δ2 plane and from the value δ3. Conditions for achromatic and apochromatic solutions are investigated by plotting the value of |R3|2=0 in three dimensional space. Examples of the solution of antireflection film obtained from the diagram are as follows: BK-7(n0:1.52)+M(n1:1.70)+Sb2O3(n:2.02)+MgF2(n3:1.38)+Air(n4:1) BK-7(n0:1.52)+MgF2(n1:1.38)+ZnS(n2:2.30)+MgF2(n3:1.38)+Air(n4:1) The former combination is known as the solution of apochromatic coating and the latter is often used as a beam splitter.
Brightness of electroluminescent (EL) cell consisting of a thin layer film of dielectric material in which phosphor powder is dispersed is analyzed. The brightness depends on optical properties of the cell material and electric field in the phosphor particle. By macroscopical optical analysis on the layer, relations of brightness of the cell to the amount of light given out by each powder particle, transmittance and reflectance of the layer and reflectance of back surface of the layer are clarified. By electrical analysis, relation of electric field in the particle to mean field strength impressed on EL layer is first derived. Generally in a system composed of two components, mean field strength E1 in component 1 can be expressed as _??_ where ε1 and ε2 are the dielectric constants of the two components, ε the mean dielectric constant of the system, δ1 the volume ratio, and E0 the mean field strength in the system. By introducing Bruggeman's relation _??_ into the above, one obtains the expression for the inner field strength of the particle. This expression was proved valid for the practical EL cell. According to the above reasoning, the field strength, that is the brightness, of the cell becomes higher when a matrix of higher dielectric constant is used. Dielectric constant of a matrix can be increased by mixing powder of high dielectric constant with plastic. Use of a dielectric material of low optical absorption-barium titanate powder of reflectance 0.92-increased the mean dielectric constant, hence the brightness, of the cell as expected from the foregoing reasoning.
Institute of Industrial Science, University of Tokyo In this paper, preliminary studies are made on the Sparrow resolution criterion and its use in comparison with the use of the Rayleigh resolution criterion for slit and circular apertures. Application of this criterion in annular and double-slit apertures are treated. It is shown that, like the Rayleigh case, two point resolution is also increased in the Sparrow sense by using the annular and double-slit apertures. However, the central intensity is considerably reduced with the increase of a central obstruction. Discussions are conducted on the relation between the central obstruction ratio and the combined Fraunhofer diffraction patterns at the Sparrow critical point.
The intensity distribution of diffracted light by Echelette grating which is irradiated by natural light has been theoretically discussed by many workers. Their scaler theories can approximately explain the experimental values, but not so in the case of polarized light. Calling the polarized light P-polarized light when the electric vector of the incident light is perpendicular to the groove direction and S-polarized light when it is parallel to the groove, we know that the values of intensity distribution of P-polarized light measured and calculated from the scaler theory are nearly equal, but in the case of S-polarization they are fairly different which means that the scaler theory is no longer valid for S-polarized light, whereas the intensity distri bution formulae, derived on the assumption that the material of the groove surface is a perfect: conductor and that there is an apparent phase change in proportion to the depth of the groove, give the values which agree well with the experimental values. Originally, Echelette grating is provided with a fairly large blaze angle to separate the concerned diffracted light from the direction of zero order, and hence the grooves are made deep. If the width of the groove is much larger than the wavelength of incident light, the incident and reflected lights will interfere and produce the standing wave which will be localized only in the groove when the width of the groove becomes small. Since the antinode of the standing wave becomes the source of wavelets and positions of antinodes differ in the two polarizations, so in S-polarization a phase difference proportional to the depth of the groove is expected. When the substance of the groove surface is of dielectric, standing waves will not be produced on account of small amplitude of reflected waves therefore, the difference in intensity distribution between the two polarizations will not be found. This paper proves that the formulae derived from the above consideration explains well the experimental values reported hitherto, supplemented with remarks on the grating efficiency and the grating anomaly.
Solution is given to the Wiener apodization problem which is to find the pupil function (amplitude distribution over the exit pupil) which minimizes the second moment of the intensity diffraction pattern on the condition that the total energy passing through the aperture be constant. The problem is in the context of Fraunhofer diffraction pattern, and aberration-free systems with both circular and slit apertures are studied. The method used to solve this problem is the calculus of variation leading to Euler-Lagrange differential equation for the desired pupil functions. Diffraction patterns obtained with these pupil functions are also studied from the transfer function point of view.
For multilayer dielectric films of given refractive index illuminated by a beam of parallel ray, their optimum thickness is determined by a modified steepest ascent method. If a merit function, which represents the difference in spectral characteristics between the ideal case and the case of films of arbitrary thickness, is introduced by taking optical thickness as a variable, the problem of finding the optimum condition (synthesis) is reduced to that of finding the extreme value of the merit function. When optical thickness values approach to optimum ones, the secondary approximation theory becomes applicable by which the optimum values are uniquely determined as solution of simultaneous linear equations. These equations are obtained by differentiation of Taylor series expansion of the merit function in which the terms of higher than third order derivatives are neglected. A high pass filter of nine-layer film and a band pass filter of eleven-layer film with alternate high and low refractive indices are presented as designed samples. By introducing a weighting function given by the product of spectral distribution of light source multiplied by spectral sensitivity of a receptor, antireflection films of double layer were designed. Antireflection films of triple layer were also designed by the use of the secondary approximation theory.