Kazuhide Kamiya

Shape measurements of mirror surfaces with a lateral-shearing interferometer during machine running

Abstract A common path lateral-shearing interferometer with a minimum number of optical components has been developed. Because the interferometer is little affected by mechanical vibrations and air turbulence, it can be mounted on an ultraprecision lathe and can be used to measure the shapes of workpieces. A plane parallel glass plate is used to shear the wavefront under test in the interferometer. To analyze the interference fringes obtained by the interferometer precisely, a fringe-scanning method using a slight tilt of the glass plate is used. Zone plates that are computer-generated holograms are used to measure spherical and aspherical surfaces with the interferometer. A spherical and a parabolic concave mirror were measured with the interferometer. The spherical mirror was also measured by a Fizeau interferometer to compare the error with that measured by the lateral-shearing interferometer. The experimental results agreed well with those measured by the lateral-shearing interferometer.

High-precision analysis of a lateral shearing interferogram by use of the integration method and polynomials

Interferograms obtained with ordinary interferometers, such as the Fizeau interferometer or the Twyman-Green interferometer, show the contour maps of a wave front under test. On the other hand, lateral shearing interferograms show the difference between a wave front under test and a sheared wave front, that is, the inclination of the wave front. Therefore the shape of the wave front under test is reconstructed by means of analyzing the difference. To reconstruct the wave front, many methods have been proposed. An integration method is usually used to reconstruct the wave front under test rapidly. However, this method has two disadvantages: The analysis accuracy of the method is low, and part of the wave front cannot be measured. To overcome these two problems, a new, to our knowledge, integration method, improved by use of polynomials, is proposed. The validity of the proposed method is evaluated by computer simulations. In the simulations the analysis accuracy achieved by the proposed method is compared with the analysis accuracy of the ordinary integration method and that of the method proposed by Rimmer and Wyant. The results of the simulations show that the analysis accuracy of the newly proposed method is better than that of the integration method and that of the Rimmer-Wyant method.

Improved Saunders method for the analysis of lateral shearing interferograms

An interferogram obtained by use of ordinary interferometers, such as Fizeau and Twyman-Green interferometers, will show a contour map of the wave front under test. A lateral-shearing interferogram, however, will show a contour map of the difference between the wave front under test and a sheared wave front, that is, a contour map of the derivative of the wave front under test. Therefore one can reconstruct the shape of the wave front under test by analyzing that difference. Many methods for reconstructing a wave front have been proposed. The Saunders method reconstructs a wave front; rapidly however the wave-front data are reconstructed only at intervals of the amount of shear along the direction of the shear. Therefore the method has low spatial resolution. A method for reconstructing a wave front that is based on the Saunders method and has high spatial resolution is proposed. The method analyzes the differences that are produced by shearing of the wave front under test in many directions. This method requires a large number of interferograms for reconstructing the wave front. Here the method is described, and its validity is confirmed by simulation.

An instrument for manufacturing zone-plates by using a lathe

Abstract A laser writing system is developed in order to manufacture precise and inexpensive zone-plates. The zone-plates are a key component of an interferometer that measures shape error of spherical or aspherical mirrors on an ultrapecision lathe. The laser writer is mounted on the sliding table of the lathe. A glass plate coated with photoresist is attached to a chuck of the lathe and rotated. The zone-plate grating is written on the glass plate by a focused laser beam. Zone-plate writing is sped up by reducing the necessary number of computer instructions, causing no loss in the accuracy of the zone-plate. The accuracy of the zone-plate obtained by this inexpensive method is 0.1 μm and the same as that achieved by an electron beam writer.

Shape measurement of workpiece surface with zone-plate interferometer during machine running

Abstract A zone-plate interferometer is in the family of common-path interferometers that have the following feature: interference fringes are hardly influenced by air turbulence and machine vibrations. A new zone-plate interferometer with a three-dimensional optical system is developed in order to measure the shape error of spherical and aspherical mirrors manufactured with an ultra-precision cutting machine. Shape measurements of the mirrors are performed when they are turning at a speed of 900 rpm. The position of a zone-plate is arranged quickly and easily by using a Moire technique. The results obtained with the zone-plate interferometer agree well with those obtained with a Fizeau interferometer.

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.

Marked increase in photoluminescence from porous Si aged in ethanol solution

Photoluminescence properties of porous Si aged in ethanol solution and porous Si films aged in ambient air were studied. It was shown that the photoluminescence properties of porous Si strongly depend on aging time and environmental conditions. The photoluminescence intensity of porous Si dispersed in ethanol solution increases 50-fold with aging for 7 d. This increase is accompanied by increases in Si–O bond density and lifetime, indicating that the electron–hole pair is strongly confined by the formation of surface oxide thin films. The photoluminescence intensity of porous Si films decreases with aging in ambient air, suggesting that nonradiative recombination centers are formed by natural oxidation.

Shape error measurement using ray-tracing and fringe scanning methods: Projection of grating displayed on a liquid crystal panel

We present an improved Hartmann test, which has high spatial resolution with respect to the measuring points, for measuring projection mirrors. In the method, grid lines with a sinusoidal transmittance distribution are displayed on a liquid crystal panel and illuminated with a collimated laser beam. The beam transmitted through the liquid crystal panel reflects off the mirror surface being tested and reaches a screen. A charge-coupled device camera detects the projected images, which contain information about the inclination of the surface being tested. Any error in the shape of the mirror surface is identified by integrating the inclination. To increase the spatial resolution, the fringe scanning method is performed by shifting the grid lines on the liquid crystal panel. The grid lines are optimized for the shape of the mirror being tested. Because the grid lines are displayed by an electrical method, the shifting operation is easy and rapid, and furthermore, the displacement can be done precisely. The shape error of an off-axis parabolic mirror made of plastic is measured by the proposed method.

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.

Sharpening of CT images by cubic interpolation using B-spline

Computed tomography (CT) is a method by which an original image is reconstructed based on the data of projected images collected from various directions, and is widely used in the fields of medicine and industry. However, the edge of the image reconstructed by CT is unsharp, therefore, microflaws are often overlooked. We demonstrated that one of the causes of the decreased sharpness of the reconstructed image is associated with the linear interpolation during the back-projection process, and in our method, the linear interpolation is replaced by cubic interpolation using the B-spline. In addition, by calculating the control points of B-spline by Fourier transform, the process required for the calculation of the control points appears to be eliminated. In the experiment, the reduction of unsharpness to 1/2 that of the conventional method and the reduction of processing time to a level equivalent to that of the conventional method have been achieved.