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

An optical identification system based a three-dimensional (3D) phase object is presented. The identification is implemented by the correlation between a speckle pattern of the 3D phase object and stored speckle patterns. To achieve a high level of recognition, we use two speckle patterns of the 3D object obtained by illuminating two wavelengths. Experimental and numerical results are presented to show the effectiveness of the proposed system.

Optical security based on three-dimensional phase object

As a high-speed three-dimensional (3D) imaging technique, parallel phase-shifting digital holography is presented. This technique records a single hologram of an object with an image sensor having a phase-shift array device and reconstructs the instantaneous 3D image of the object with a computer. In this technique, a single hologram in which the multiple holograms required for phase-shifting digital holography are multiplexed by using space-division multiplexing technique pixel by pixel. Also, we present a high-speed parallel phase-shifting digital holography system. The system consists of an interferometer, a continuous-wave laser, and a high-speed polarization imaging camera. Motion pictures of dynamic phenomena at the rate of up to 1,000,000 frames per second have been achieved by the high-speed system.

High-speed 3D imaging by parallel phase-shifting digital holography

A novel method for multiplier modulo using optical signal processing is presented. Multiplier modulo is an important process in a factorization algorithm. In the method, modulo operations are executed by phase modulation. We construct a prototype system of the presented method. The constructed system consists of a Michelson interferometer with a photo detector array. In the system, mirrors are put on both object and reference arms. A mirror in the object arm is slightly tilted and the angle depends on parameters for target multiplier modulo. An obtained interference fringe has information about desired results for modulo operations. The most feature of the presented system is that it achieves massive data processing for mulitiplier modulo in parallel with only simple implementation. We show experimental results to verify usefulness of the presented method. Moreover, we study on expansion to implement factorization.

An optical parallel processing for multiplier modulo using an optical interferometer

In a three-dimensional (3D) eye-gaze detection system with an integrated volume holographic imaging element (VHIE) and two image sensors, human eye gaze is detected by analyzing both the reflected images of two eyes of a human and the transmitted images that the human is watching. To make the detection of the reflected images of the eyes more effective, a noise filter for removing the background noise is fabricated and is then attached to the integrated VHIE. The results obtained by the noise reduction technique are presented.

Background Noise Reduction in an Integrated Volume Holographic Imaging Element for Eye-Gaze Detection

3D fluorescence imaging based on incoherent digital holography is very useful in the biological field. We have proposed a common-path and off-axis incoherent digital holography using a diffraction grating embedded with a lens to make the self-interference pattern. Based on the observation of the fluorescence image, active illumination of the holographic method is more efficient to avoid unwanted exposure to another area. We present the feasibility experiment to show the potential characteristics of our proposed system.

Osamu Matoba

Papers

Optical security based on three-dimensional phase object

High-speed 3D imaging by parallel phase-shifting digital holography

An optical parallel processing for multiplier modulo using an optical interferometer

Background Noise Reduction in an Integrated Volume Holographic Imaging Element for Eye-Gaze Detection

Active 3D fluorescence imaging based on holography