Hatsuzo Tashiro

Zone-plate inteferometer to measure the positioning error of a cutting tool

Abstract A simple type of zone-plate interferometer has been developed to measure precisely the positioning error of a cutting tool. Interference fringes obtained by the interferometer are little affected by air turbulence in the optical paths and by machine vibrations. The shape of the mirrors surface being tested is spherical and is manufactured with an ultraprecision lathe. A zone plate is set at the midposition between the vertex of the spherical mirror being tested and the center of curvature of the mirror. The error in the shape of the mirror and the positioning error of the tool can be determined by analyzing the interference fringes. Two spherical concave mirrors were measured. One mirror was manufactured with a tool that had same positioning error. The positioning error was observed as distortion of the interference fringes. The images obtained by the zone-plane interferometer agree well with the images obtained by a Fizeau interferometer and a computer simulation based on the experimental results. The other mirror was manufactured with the tool after the positioning error had been eliminated, based upon the results of the above experiments. The interference fringes of the mirror show no distortion, and the error in the shape of the mirror is small.

Method to obtain a clear fringe pattern with a zone-plate interferometer

When a zone-plate interferometer is used, a bright spot appears at the center of the image plane. The spot makes it difficult to analyze the interference fringes. A simple technique that is based on the principle of fringe-intensity reversal is proposed to analyze the fringes efficiently. A zone plate with a phase fraction of π/2 or 3π/2 is used in this technique to diminish the bright spot. Unlike the masking technique, no part of the data on the fringes is lost. The fringes can, therefore, be analyzed completely. The technique is described in detail, and the results of an experiment in which the shape error of a concave mirror was measured with the proposed zone plate is presented. The experimental results agree well with the results obtained with the Fizeau interferometer.

Localisation of fringes in moiré topography

Abstract The moire pattern produced by two separate gratings is characterised by a fringe localisation phenomenon. A theory based on the geometric shadow of light can account for the spatial location of moire fringes in topographical applications. The fringe location depends on the optical arrangement of the system and also on the surface slope of the specimen. Experimental results are introduced into practical usage.

Interpolation of contour intervals in Moire topography by phase modulation

Abstract A trial has been performed with respect to the interpolation of contour intervals in Moire topography by making use of phase modulation. A simple mechanical system can bring improved results for the precise measurements of shape of a specimen.

Localization of Fringes in Moiré Topography

A theory based on the geometric obstruction of light has been developed which accounts for the spatial localization of moire fringes in topographic application. The fringe location is proved to be dependent on the optical arrangement of the system, and the surface inclination of the specimen affects the phenomenon of spatial localization. The theory has been verified experimentally, and the results showed the validity of the expression given here.

A Study on Low-Pass Filter for Finite Length Data (2nd Report)

A low-pass filter is almost always applied to data of finite length. Therefore, unexpected vibration occurs at the data end of the low-pass filter output. To solve this problem, the previous report of this paper has proposed that two types of low-pass filters (i.e. spacial and frequency) can be used in a point symmetric extension method. To make the above proposal more specific, a point symmetric extension method was applied to reduce an abnormal value occurring in the filtered data at the data end where the center of the point symmetric method is applied. Before that, the data end was replaced by the generalized low-pass filtered output. Consequently this paper proposes a method to determine the center point of this point symmetric extension based on the sum of squared errors between the primary and the filtered output. This new method also uses a spatial low-pass filter and a frequency low-pass filter. The method is applicable not only to a low-pass filter that uses a point symmetric extension method but also to all other types of low-pass filters for minimizing the sum of squared errors between primary and filtered data.