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

A novel security technique based on polarization encryption is proposed and is applied to a secure holographic memory system. Original binary data are described as two orthogonal linear polarization states. These input polarization states can be modulated by two polarization modulation masks located at the input and the Fourier planes. Each modulation mask can convert an input polarization state into an arbitrary elliptical polarization state. After the encryption of the polarization state, this encrypted polarization state is recorded as a hologram that can generate a vector phase conjugate beam. In the decryption process, the vector phase conjugate readout can cancel the polarization modulation at each mask and then the original polarization state can be recovered. The encryption and the decryption are demonstrated experimentally in a bacteriorhodopsin film.

Data Security in Holographic Memory using Double Random Polarization Encryption

Using parallel phase-shifting digital holography with a high-speed camera, the authors succeeded in phase-shifting interferometry at the rate of 180,000 fraames/s. Motion pictures of three-dimensional image of dynamically moving objects were demonstrated.

Parallel Phase-shifting Digital Holography for Recording 3-D Motion Pictures of Dynamic Phenomena

An electronic parallel processor for exponential modulo function based on digital optical computing is designed. As a result of implementation on a FPGA (Field Programmable Gate Array) device, a prototype system for the presented method can be demonstrated.

Design and prototyping of parallel exponential modulo function based on 2-D spatial coding and digital optical computing

Defect detection requires highly sensitive and robust inspection methods. This study shows that non-overlapping illumination patterns can improve the noise robustness of deep learning ghost imaging (DLGI) without modifying the convolutional neural network (CNN). Ghost imaging (GI) can be accelerated by combining GI and deep learning. However, the robustness of DLGI decreases in exchange for higher speed. Using non-overlapping patterns can decrease the noise effects in the input data to the CNN. This study evaluates the DLGI robustness by using non-overlapping patterns generated based on binary notation. The results show that non-overlapping patterns improve the position accuracy by up to 51%, enabling the detection of defect positions with higher accuracy in noisy environments.

Noise-robust deep learning ghost imaging using a non-overlapping pattern for defect position mapping.

We numerically evaluate the security capability of double random polarization encryption. Numerical results show that double polarization encryption has the same potential as double random phase encryption.

Osamu Matoba

Papers

Data Security in Holographic Memory using Double Random Polarization Encryption

Parallel Phase-shifting Digital Holography for Recording 3-D Motion Pictures of Dynamic Phenomena

Design and prototyping of parallel exponential modulo function based on 2-D spatial coding and digital optical computing

Noise-robust deep learning ghost imaging using a non-overlapping pattern for defect position mapping.

Double random polarization encryption for data security