There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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.

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

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.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Current medical imaging technologies allow visualization of tissue anatomy in the human body at resolutions ranging from 100 micrometers to 1 millimeter. These technologies are generally not sensitive enough to detect early-stage tissue abnormalities associated with diseases such as cancer and atherosclerosis, which require micrometer-scale resolution. Here, optical coherence tomography was adapted to allow high-speed visualization of tissue in a living animal with a catheter-endoscope 1 millimeter in diameter. This method, referred to as "optical biopsy," was used to obtain cross-sectional images of the rabbit gastrointestinal and respiratory tracts at 10-micrometer resolution.

In Vivo Endoscopic Optical Biopsy with Optical Coherence Tomography

The diffraction tomography theorem is adapted to one-dimensional length measurement. The resulting spectral interferometry technique is described and the first length measurements using this technique on a model eye and on a human eye in vivo are presented.

Measurement of intraocular distances by backscattering spectral interferometry

We propose a method for extending thespace bandwidth in parallel phase-shifting digital holography using a commercially available polarization-imaging camera. The effectiveness of the proposed method was numerically and quantitatively verified.

Method for extending the space bandwidth in parallel phase-shifting digital holography using a commercially available polarization-imaging camera

The authors review three-dimensional (3D) trajectory of minute object by parallel phase-shifting digital holography. Parallel phase-shifting digital holography is a technique capable of single-shot recording of a complex amplitude distribution of object wave from a dynamic object. The authors constructed an inverted microscope based on parallel phase-shifting digital holography. The microscope consisted of a continuous-wave laser, a Mach–Zehnder interferometer, a polarization imaging camera, and a magnification optical system. A high-speed polarization imaging camera was employed to record motion picture of holograms of the dynamic specimen. Motion picture of the holograms of a minute alum crystal sinking down in the solution of alum was recorded by the microscope at the rate of 60 frames per seconds (FPS). Refocused images of the crystal were successfully obtained for all of the sinking time. The 3D trajectory of the crystal was derived from the refocused images. Also, the authors constructed an inverted and vertical microscope based on parallel phase-shifting digital holography. A Volvox swimming in a water as a living microbe was recorded by the microscope at the rate of 1000 FPS. The 3D trajectory of the microbe curvedly moving in the area of 500 μm × 500 μm × 500 μm was successfully demonstrated from the reconstructed images of the microbe.

3D trajectory of minute object by parallel phase-shifting digital holographic microscope

We demonstrate a technique capable of obtaining spectral information and a three-dimensional (3D) profile of an object with a single-shot exposure. This technique is based on digital holography and the spectral estimation technique. In the demonstration of this technique, we simultaneously use three laser lines operating at 473, 532, and 633 nm to record the multiple complex amplitudes of the object corresponding to the wavelengths and obtain reconstructed monochrome images of each wavelength. A spectral estimation technique is applied to estimate the spectral reflectance of the object from the reconstructed monochrome images. We experimentally succeed in estimating the spectral reflectance of a lemon by using the technique.

Single-Shot Digital Holography Using a Spectral Estimation Technique

Fast measurement system of a moving three-dimensional phase object using digital holographic microscopy is presented. In the fabricated system, a three-dimensional phase object is put on a fast movable stage. Under the CW laser illumination, the holograms of the phase object are superimposed. We experimentally investigated the effect of the speed of the movable stage on the reconstructed data.

Phase measurement using high-speed movable stage by digital holography under CW laser illumination

PROBLEM TO BE SOLVED: To provide an imaging optical system using a holographic optical element by which a clear image is obtained using white light illumination, and not using illumination light with the same wavelength as the wavelength used when the holographic optical element is manufactured. SOLUTION: The imaging optical system 100 includes a wavelength selection reflection filter 4 disposed before the holographic optical element 1, and a wavelength selection transmission filter 5 disposed between the holographic optical element 1 and imaging means 3 as means to prevent background light under white light illumination from passing through the holographic optical element 1 and entering the imaging means 3. COPYRIGHT: (C)2010,JPO&INPIT

Osamu Matoba

Papers

Method for extending the space bandwidth in parallel phase-shifting digital holography using a commercially available polarization-imaging camera

3D trajectory of minute object by parallel phase-shifting digital holographic microscope

Single-Shot Digital Holography Using a Spectral Estimation Technique

Phase measurement using high-speed movable stage by digital holography under CW laser illumination

Imaging optical system