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 present an optoelectronic method to analyze three-dimensional (3D) scenes that is able to detect the presence, and also the position and orientation, of a reference 3D object. The data-acquisition procedure is based on digital holography. A phase-shifting interferometer records a single digital Fresnel hologram of the 3D scene with an intensity-recording device. Holographic information of the 3D reference object is also obtained with the same method. Correlation techniques are then applied to recognize the presence and position of the 3D reference object in the 3D scene. The technique also allows us to detect the 3D reference with a small out-of-plane rotation. Preliminary experimental results are presented that demonstrate the theory.

Shift-invariant three-dimensional object recognition by means of digital holography

We propose parallel three-step phase-shifting digital holography as a technique capable of noiseless instantaneous measurement of three-dimensional objects based on phase-shifting interferometry. The proposed digital holography carries out three-step phase shifting at the same time by using a phase-shifting array device located in the reference beam. The array device has a periodic three-step phase distribution, and its configuration is simplified compared with that required for conventional parallel phase-shifting digital holography. Therefore the optical system of the proposed parallel phase-shifting digital holography is more suitable for the realization of the proposed holography. We conduct both a numerical simulation and a preliminary experiment. The results of the simulation and experiment agree well with those of the conventional phase-shifting method and are superior to the results obtained by conventional digital holography by using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.

Parallel three-step phase-shifting digital holography

We propose a new imaging optics called the Transmissive Mirror Device (TMD). It consists of numerous micromirrors 
placed perpendicular to the surface of a flat, thin metal plate. The micro-mirror array is implemented 
by the inner walls of minute square holes, which are densely pitted on the device. The basic mode of operation 
is based on two reflections by a pair of adjacent mutually perpendicular mirrors, i.e., a dihedral corner reflector. 
Although the principal of operation is based on reflection by mirrors, the device is also transmissive and deflects 
light. Since this imaging system forms a real image at a plane symmetric point, the depth of the 3D image is 
inverted. Its optical defects are low optical transmittance and stray light caused by non-reflected light and that 
reflected once. We manufactured the device experimentally with nano-precision machining technology and also 
evaluated it.

Transmissive optical imaging device with micromirror array

A secure holographic memory system that uses fully phase encryption is presented. Two-dimensional arrays of data are phase encoded. Each array is then transformed into a stationary white-noise-like pattern by use of a random-phase mask located at the input plane and another at the Fourier plane. This encrypted information is then stored holographically in a photorefractive LiNbO3:Fe crystal. The original phase-encoded data can be recovered, by use of the two random-phase masks, with a phase-conjugate readout beam. This phase information can then be converted back to intensity information with an interferometer. Recording multiple images by use of angular multiplexing is demonstrated. The influence of a limited system bandwidth on the quality of reconstructed data is evaluated numerically. These computer simulation results show that a fully phase-based encryption system generally performs better than an amplitude-based encryption system when the system bandwidth is limited by a moderate amount.

Secure optical storage that uses fully phase encryption

A novel secure holographic memory system with polarization encoding is proposed. Two-dimensional original data are encoded as a two-dimensional polarization distribution. The polarization state at each pixel is scrambled by a mask that changes the polarization state into a random state. The mask can rotate the direction of the principal axes of the elliptically polarized light and can change the phase retardation at each pixel. The light with the random polarization state is stored as a hologram that can produce the vector phase-conjugate beam. In the decryption the vector phase-conjugation readout can recover the original polarization state by use of the same mask used in the encryption. Experimental results of encryption and decryption with a bacteriorhodopsin film are presented.

Osamu Matoba

Papers

Shift-invariant three-dimensional object recognition by means of digital holography

Parallel three-step phase-shifting digital holography

Transmissive optical imaging device with micromirror array

Secure optical storage that uses fully phase encryption

Secure optical memory system with polarization encryption