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 encrypted optical memory system using double random phase codes in the Fresnel domain is proposed. In this system, two random phase codes and their positions form three-dimensional keys for encryption of images and are used as keys to recover the original data. The third dimension is the positions of the codes, which can have as many as three degrees of freedom. Original images encrypted by use of the two phase codes located in the Fresnel domain are stored holographically in a photorefractive material. We demonstrate in preliminary experiments encryption and decryption of optical memory in a LiNbO3:Fe photorefractive crystal by use of angular multiplexing.

Encrypted optical memory system using three-dimensional keys in the Fresnel domain.

This paper presents an overview of the potential of free space optical technology in information security, encryption, and authentication. Optical waveform posses many degrees of freedom such as amplitude, phase, polarization, spectral content, and multiplexing which can be combined in different ways to make the information encoding more secure. This paper reviews optical techniques for encryption and security of two-dimensional and three-dimensional data. Interferometric methods are used to record and retrieve data by either optical or digital holography for security applications. Digital holograms are widely used in recording and processing three dimensional data, and are attractive for securing three dimensional data. Also, we review optical authentication techniques applied to ID tags with visible and near infrared imaging. A variety of images and signatures, including biometrics, random codes, and primary images can be combined in an optical ID tag for security and authentication.

Optical Techniques for Information Security

A technique that combines the high speed and the high security of optical encryption with the advantages of electronic transmission, storage, and decryption is introduced. Digital phase-shifting interferometry is used for efficient recording of phase and amplitude information with an intensity recording device. The encryption is performed by use of two random phase codes, one in the object plane and another in the Fresnel domain, providing high security in the encrypted image and a key with many degrees of freedom. We describe how our technique can be adapted to encrypt either the Fraunhofer or the Fresnel diffraction pattern of the input. Electronic decryption can be performed with a one-step fast Fourier transform reconstruction procedure. Experimental results for both systems including a lensless setup are shown.

Optoelectronic information encryption with phase-shifting interferometry

A three-dimensional (3D) object reconstruction technique that uses only phase information of a phase-shifting digital hologram and a phase-only spatial-light modulator is proposed. It is well known that a digital hologram can store both amplitude and phase information of an optical electric field and can reconstruct the original 3D object in a computer. We demonstrate that it is possible to reconstruct optically 3D objects using only phase information of the optical field calculated from phase-shifting digital holograms. The use of phase-only information enables us to reduce the amount of data in the digital hologram and reconstruct optically the 3D objects using a liquid-crystal spatial light modulator without optical power loss. Numerical evaluation of the reconstructed 3D object is presented.

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Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram.

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

Osamu Matoba

Papers

Encrypted optical memory system using three-dimensional keys in the Fresnel domain.

Optical Techniques for Information Security

Optoelectronic information encryption with phase-shifting interferometry

Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram.

Parallel two-step phase-shifting digital holography