Kazumi Murata

Bio: Kazumi Murata is an academic researcher from Hokkaido University. The author has contributed to research in topics: Holography & Laser. The author has an hindex of 11, co-authored 43 publications receiving 851 citations.

Reshaping collimated laser beams with Gaussian profile to uniform profiles.

Abstract: A set of holographic filters was developed to convert the Gaussian intensity distribution of a collimated laser beam into a uniform one. The design and the fabricating method of the holographic filters are presented and experimental results are shown.

Digital phase-measuring interferometry with a tunable laser diode.

Abstract: A digital phase-measuring interferometer with a laser-diode source has been developed that is based on a fringe-scanning technique with a stepwise wavelength change by variation of the laser injection current. The phase is changed to produce a relative phase difference between the beams in the two arms of the interferometer. Calibrated phase shifts used for a phase-extraction algorithm are derived from one-dimensional least-squares fits to cosine fringe functions to achieve accurate results. Experimental results are presented.

Talbot interferometry for measuring the focal length of a lens.

Abstract: A method for measuring the focal length of lenses using the Talbot effect and the moire technique is described. The test lens is placed in front of a set of two gratings. The first grating illuminated by the light passing through the test lens produces the magnified Talbot image. The moire fringe is generated by superimposing this Talbot image on the second grating. The tilt angle of the moire fringe is a measure of the focal length of the lens. In the experiments, the focal lengths of positive, negative, and power-distributed lenses are measured.

Measurements of phase objects using the Talbot effect and moire techniques.

Abstract: In this paper, we describe deflection mapping of phase objects using a Talbot interferometer. To examine the deflection of light by the phase objects, the moire fringes are generated by superimposing the Fourier image of the first grating on the second one in the interferometer. The phase object is placed in front of the first grating. The light passing through the objects and impinging on the first grating produces the shifted Fourier image, and the resultant moire fringes give the deflection mapping, which depends on the distribution of the refractive index of the phase object. The experiments show deflection mapping of a piece of plastic plate and a candle flame. This technique is used for measuring the focal length of a lens.

Heterodyne interferometry with a frequency-modulated laser diode

Abstract: A digital phase measuring interferometer with a frequency-modulated laser diode using the integrated-bucket technique is described. The injection current is continuously changed to introduce a time-varying phase difference between the two beams of an unbalanced Twyman-Green interferometer. The intensity of the interference patterns is integrated with a CCD array sensor for intervals of one-quarter period of the fringe. Using the intensity data a microcomputer calculates the phase to be detected. Some experimental results with the interferometer are presented; the rms repeatability obtained was λ/80.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Abstract: A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

I The Self-Imaging Phenomenon and its Applications

Abstract: Publisher Summary This chapter describes the self-imaging phenomenon and its applications. The self-imaging phenomenon requires a highly spatially coherent illumination. It disappears when the lateral dimensions of the light source are increased. When the source is made spatially periodic and is placed at the proper distance in front of the periodic structure, a fringe pattern is formed in the space behind the structure. The chapter discusses the theoretical and applicational aspects of the self-imaging phenomenon—that is, the property of the Fresnel diffraction field of some objects illuminated by a spatially coherent light beam. The applications of self-imaging are summarized in four main groups—namely, (1) image processing and synthesis, (2) technology of optical elements, (3) optical testing, and (4) optical metrology. The chapter describes the double diffraction systems using spatially incoherent illumination. The first periodic structure plays the role of a periodic source composed of a multiple of mutually incoherent slits. Depending on whether the periods of two periodic structures are equal, the Lau or the generalized Lau effect is discussed. Various applications of incoherent double-grating systems are described in the fields of optical testing, image processing, and optical metrology. After examining some cases of coherent and incoherent illumination, the general issue of spatial periodicities of optical fields and its relevance to the replication of partially coherent fields in space is discussed.

Finite series-expansion reconstruction methods

Abstract: Series-expansion reconstruction methods made their first appearance in the scientific literature and in the CT scanner industry around 1970. Great research efforts have gone into them since but many questions still wait to be answered. These methods, synonymously known as algebraic methods, iterative algorithms, or optimization theory techniques, are based on the discretization of the image domain prior to any mathematical analysis and thus are rooted in a completely different branch of mathematics than the transform methods which are discussed in this issue by Lewitt [51]. How is the model set up? What is the methodology of the approach? Where does mathematical optimization theory enter? What do these reconstruction algorithms look like? How are quadratic optimization, entropy optimization, and Bayesian analysis used in image reconstruction? Finally, why study series expansion methods if transform methods are so much faster? These are some of the questions that are answered in this paper.

Design and performance of a refractive optical system that converts a Gaussian to a flattop beam.

Abstract: A system of two aspheric lenses is described, which efficiently converts a collimated Gaussian beam to a flattop beam. Departing from earlier designs, both aspheric surfaces were convex, simplifying their fabrication; the output beam was designed with a continuous roll-off, allowing control of the far-field diffraction pattern; and diffraction from the entrance and exit apertures was held to a negligible level. The design principles are discussed in detail, and the performance of the as-built optics is compared quantitatively with the theoretical design. Approximately 78% of the incident power is enclosed in a region with 5% rms power variation. The 8-mm-diameter beam propagates approximately 0.5 m without significant change in the intensity profile; when the beam is expanded to 32 mm in diameter, this range increases to several meters.