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

It will be useful in biological applications if two or more physical parameters are simultaneously measured in a digital holographic microscope. In this paper, we present a hybrid digital holographic microscope that can measure simultaneously three-dimensional (3D) phase and 3D fluorescence distributions. This property has big advantage compared with conventional optical microscopes such as phase contrast microscope and fluorescence microscope. We present an optical setup for measuring both phase and fluorescence images. In the experiments, two objects that are fluorescence beads and egera densa are used. The separation method of phase and fluorescence images is presented.

A Hybrid Digital Holographic Microscopy for Biological Applications

1,000,000 FPS quantitative phase and 3D imaging of a high-speed and transparent object have been achieved by parallel phase-shifting digital holography Also, 3D imaging and tracking of a dynamic and micro object has been demonstrated

Parallel phase-shifting digital holography and its applications to high-speed 3D imaging and microscopy

Minimum optical energy required for parallel four-step phase-shifting digital holography is evaluated numerically by using photon-counting method. One of the attractive features of parallel phase-shifting digital holography is the instantaneous recording of fast 3D events where only the complex amplitude distribution of an object wave is obtained. The reconstruction is executed by numerical wave propagation such as angular spectrum propagation or Fresnel propagation. Numerical results indicate that required optical energy of an input image with 512 × 512 pixels is about 11 pJ. Under the criteria used in the evaluation, the required optical energy is independent of the image size.

Evaluation of parallel phase-shifting digital holography by photon-counting method

We demonstrate motion pictures of femtosecond light pulse propagation. We adopted digital light-in-flight recording by
holography as a technique for observation of femtosecond light pulse propagation. We recorded and reconstructed a
moving picture of femtosecond light pulse propagating on a diffuser plate on which a test chart pattern was printed. The
center wavelength and the duration of the light pulse were 800 nm and 96 fs, respectively. We successfully observed
femtosecond light pulse propagation for 530 fs by the technique.

Observation of femtosecond light pulse propagation by using digital light-in-flight recording by holography

We review an optical secure memory card using a three-dimensional (3D) scattering medium and 3D absorbers. The
information of 3D absorbers such as position, size, and number can be used as 3D data. The strong scattering effect can
make the data secure for measuring them by interferometer. To recover the absorption distribution, a computational
method is developed. We show the numerical results of the reconstructed absorption distribution and then show how
important to control the scattering coefficient in a volume medium. We also present preliminary experimental results to
make a scattering medium by using holes created by irradiation of femtosecond laser pulse.

Osamu Matoba

Papers

A Hybrid Digital Holographic Microscopy for Biological Applications

Parallel phase-shifting digital holography and its applications to high-speed 3D imaging and microscopy

Evaluation of parallel phase-shifting digital holography by photon-counting method

Observation of femtosecond light pulse propagation by using digital light-in-flight recording by holography

Optical fabrication of 3D scattering medium for secure optical memory card