New aberration coefficients are proposed in order to facilitate the application of traditional 5th order aberration theory to lens design. These coefficients can be combined into three terms which represent the fundamental defects in image formation, namely, the symmetric and asymmetric aberrations and distortion. Usefulness of the proposal is illustrated with two numerical examples.

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Third order aberration coefficients has a superiority to optical design process, because of their independency on each surface, and additionality of total optical system aberrations.
In this paper, we find the correspondence between the aberrations and the third order aberration coefficients, and then we are able to set our aimed value for Seidel's coefficients, which give us sufficient results for optical performance.
With this method, we design a Tessar Type lens of F=1: 2.8, f=50mm, and we show through the process, how we can use new method for ordinary optical design.
Modifying above, we expect the same method can be useful for new and unknown optical system designing.

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It is necessary for lens designer to calculate the estimated value of optical elements. In this case we made a trial of this calculation by use of the computer. This computer is called TOSBAC-3400 which have a main memory of sixteen thousand words and a disk memory of twenty four hundred thousand words. The program consist of fifty four sub programs which have about five thousand steps for all with FORTRAN base. It is possible to calculate the working hours for lens, prism and mirror.

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Lens performance should be evaluated with various aspects: image shapness, color reproduction, uniformity of illuminance, lens size, lens appearance, lens cost, and so on; because, a lens can be a good one for its user only when all of these aspects are well performed and balanced.
Especially, imaging performance should be presented to the lens user in a simple and plain way, but still complete enough for proper decision. Such a representation form will be proposed in this paper.

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If an object surface is a perfect diffuser, the contrast of the image produced by the optical system with a linear image shift due to the dispersion is obtained by the Fourier transform of the spectral response which is defined as the product of the relative spectral distribution of illumination and the relative spectral sensitivity of a detector.
Usually measured polychromatic OTFs depend on spectral responses of individual OTF measuring instruments. The author proposes that the spectral response of an OTF measuring instrument may be represented by a correlated color temperature. He also points out that a polychromatic OTF has the same characteristic as the metamerism of vision, as the result, there is an OTF corresponding to a metameric black.

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Assuming the viewing optical system such as spectacle glasses, binocular, telescope, as an afocal lens system, the performance evaluation methods of the system are discussed.
The first problem is the claculation of the White Light MTF which is solved by applying the Geometrical MTF calculation to the afocal system. The second problem is the evaluation method of the chromatic aberration. This problem is solved by the expression of the chromaticity distribution, which is appeared at the boundary of the polychromatic Edge Spread Function (E.S.F.) of the afocal image, on the Chromaticity Diagram.
As an instance of the calculation, the data of the binocular lens was used.

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The out-focused image of a lens with over-corrected spherical aberration is analyzed by means of wave theory of aberrations.

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The application of computer-generated holograms to the interferometric testing of aspheric surfaces is described.
When small F-number optical elements are tested, the required sample number of the hologram should be much increased. In order to reduce the sample number of the hologram, we propose the aberration balancing method. The optimum value of the defocus aberration is calculated. Errors due to the incorrect hologram size and due to misalignment of the optical system are estimated, and they are compared with errors in the case of conventionalmethods. Experimental results are shown for testing aspheric mirror of F/2.

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In many methods to measure MTF of an optical system, a pinhole or a slit is used as a test-target. A test lens is illuminated by the light flux emerging from a test-target. Non-uniformity of the illumination causes some errors on measured MTF values. In order to know this influence, a method has been developed. By this method, axial MTF of an optical system can be calculated simulating the actual MTF measuring process. A lens of high numerical aperature (F/0.75) is used as a test sample. The procedure of MTF calculation and the results are described in detail.

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MTF-based simplified test conditions and proposed criteria for the evaluation of the image quality of interchangeable lenses, including zoom lenses for 35mm cameras are described.
Measurements are to be made for white light, in the infinite conjugate plane, on axis and at two 0.35 d (d: diagonal length of the picture frame) Positions, at full aperture and f/8. The focus is to be set at full aperture for best focus at 30 lines/mm on axis.
The MTF responses at 10 lines/mm and 30 lines/mm are to be examined to evaluate the lenses.
Previously proposed conditions and criteria for fixed-focal length lenses are also described for reference.

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The working group on OTF standards of Japan Optical Engineering Research Association (JOERA) have made following works.
In interlaboratory comparisons of MTF measurements using two JOERA standard lenses and Sira 200mm doublet, the results of MTF measurements showed good coincidence in on-axis, but some variation in off-axis. We have examined the causes of the errors.
This year we intend to investigate white light OTF in both calculation and measurement.
In OTF standardization, we made up “definition and/or explanations of terms concerning OTF” and “standard graphical representations of MTF”, and we are preparing for the accuracy inspection of MTF measuring instrument by use of standard lenses and the like.

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