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

We report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a
number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field, high-resolution
complex sample image. By adopting a wavefront correction strategy, the FPM method can also correct for aberrations and
digitally extend a microscope’s depth of focus beyond the physical limitations of its optics. As a demonstration, we built a
microscope prototype with a resolution of 0.78 µm, a field of view of ∼120 mm^2 and a resolution-invariant depth of focus
of 0.3 mm (characterized at 632 nm). Gigapixel colour images of histology slides verify successful FPM operation. The
reported imaging procedure transforms the general challenge of high-throughput, high-resolution microscopy from one
that is coupled to the physical limitations of the system’s optics to one that is solvable through computation.

Wide-field, high-resolution Fourier ptychographic microscopy

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

Have you ever felt that the very title, Progress in Optics, conjured an image in your mind? Don’t you see a row of handsomely printed books, bearing the editorial stamp of one of the most brilliant members of the optics community, and chronicling the field of optics since the invention of the laser? If so, you are certain to move the bookend to make room for Volume 16, the latest of this series. It contains seven chapters on widely diverging topics, written by well-known authorities in their fields. These are: 1) Laser Selective Photophysics and Photochemistry by V. S. Letokhov, 2) Recent Advances in Phase Profiles (sic) Generation by J. J. Clair and C. I. Abitbol, 3 ) Computer-Generated Holograms: Techniques and Applications by W.-H. Lee, 4) Speckle Interferometry by A. E. Ennos, 5 ) Deformation  Invariant, Space-Variant Optical  Pattern Recognition by D. Casasent and D. Psaltis, 6) Light Emission from High-Current Surface-Spark Discharges by R. E. Beverly, and 7) Semiclassical Radiation  Theory within a  QuantumMechanical Framework by I. R. Senitzkt. The  breadth of topic  matter  spanned  by  these  chapters makes it impossible, for this reviewer at least, to pass judgement on the comprehensiveness, relevance, and completeness of every chapter. With an editorial board as prominent as that of Progress in Optics, however, it seems hardly likely that such comments should be necessary. It should certainly be possible to take the authority of each author as credible. The only remaining judgment to be  made on these chapters is their readability. In short, what are they like to read? The first sentence of the first chapter greets the eye with an obvious typographical error: “The creation of coherent laser light source, that have tunable radiation, opened the . . . .” Two pages later we find: “When two types of atoms or molecules of different isotopic composition ( A and B ) have even one spectral line that does not overlap with others, it is pos-

Progress in optics

Quantitative phase imaging (QPI) has emerged as a valuable method for investigating cells and tissues. QPI operates on unlabelled specimens and, as such, is complementary to established fluorescence microscopy, exhibiting lower phototoxicity and no photobleaching. As the images represent quantitative maps of optical path length delays introduced by the specimen, QPI provides an objective measure of morphology and dynamics, free of variability due to contrast agents. Owing to the tremendous progress witnessed especially in the past 10–15 years, a number of technologies have become sufficiently reliable and translated to biomedical laboratories. Commercialization efforts are under way and, as a result, the QPI field is now transitioning from a technology-development-driven to an application-focused field. In this Review, we aim to provide a critical and objective overview of this dynamic research field by presenting the scientific context, main principles of operation and current biomedical applications. Over the past 10–15 years, quantitative phase imaging has moved from a research-driven to an application-focused field. This Review presents the main principles of operation and representative basic and clinical science applications.

Quantitative phase imaging in biomedicine

We use the coherence of a light beam to encode spatial information. We apply this principle to obtain spatial superresolution in a limited aperture system. The method is based on shaping the mutual intensity function of the illumination beam in a set of orthogonal distributions, each one carrying the information for a different frequency bandpass or spatial region of the input object. The coherence coding is analogous to time multiplexing but with multiplexing time slots that are given by the coherence time of the illumination beam. Most images are static during times much longer than this coherence time, and thus the increase of resolution in our system is obtained without any noticeable cost.

/pdf/spatial-information-transmission-using-orthogonal-mutual-1l2i4lnsny.pdf

Spatial information transmission using orthogonal mutual coherence coding.

A new criterion for determining the expansion center for circular-harmonic filters

A morphological optoelectronic image processor based on the threshold decomposition concept is described and demonstrated. Binary slices of a gray-scale input image are optically convolved with a binary structuring element of arbitrary size and shape in a noncoherent convolver. The slices are displayed on a liquid-crystal spatial light modulator of 320 × 264 pixels. The kernels are implemented as modifications of the system impulse response. The processor’s convolution patterns are recorded with a CCD camera and fed into a PC by a frame grabber. Subsequent elementary morphological operations are looped. Examples of processing an input image of 256 × 256 pixels and 16 gray levels with kernels of arbitrary size are presented.

Optoelectronic morphological image processor.

Pattern recognition with high discrimination can be achieved with a morphological correlator. A modification of this correlator is carried out by use of a binary slicing process instead of linear thresholding. Although the obtained correlation result is not identical to the conventional morphological correlation, it requires fewer calculations and provides even higher discrimination. Two optical experimental implementations of this modified morphological correlator as well as some experimental results are shown.

/pdf/modified-morphological-correlation-based-on-bit-map-1zk303tok2.pdf

Javier Garcia

Papers

Spatial information transmission using orthogonal mutual coherence coding.

A new criterion for determining the expansion center for circular-harmonic filters

Optoelectronic morphological image processor.

Modified morphological correlation based on bit-map representations

Pattern recognition using sequential matched filtering of wavelet coefficients