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

A convenient relation between fractional Fourier transform patterns and diffraction patterns is obtained by applying the Gauss equa- tion of geometrical optics. Thus, Fresnel and fractional domains cannot be considered as independent domains, since one is just a geometrical image of the other, providing a physical and direct connection. © 2000 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(00)02006-7)

/pdf/from-fresnel-patterns-to-fractional-fourier-transform-1m58ulpmen.pdf

From Fresnel patterns to fractional Fourier transform through geometrical optics

A shift-and-scale-invariant elliptic coordinate-transformed phase-only filter in proposed The filter is built in three steps: the complex conjugate of a basic-size target spectrum is calculated, its phase-only part is taken, and then the elliptic coordinate transformation is made In the extreme case the scale ratio of recognizable objects equals 1:15, permitting good recognition of object sizes S within the range 083 ≤ S ≤ 125 Discrimination abilities and relative Horner efficiencies of a few versions of the filter are calculated

Shift-and-scale-invariant pattern recognition using an elliptic coordinate-transformed phase-only filter.

Rotation-invariant pattern recognition can be achieved with circular-harmonic decomposition. A common problem with such a filter is that, because it is only a single term out of the circular decomposition, it does not contain much of the reference object's energy. Thus, the obtained correlation selectivity is low. This problem is solved by use of wavelength multiplexing. First, different harmonic terms are encoded by different wavelengths, and then they all are added incoherently in the output correlation plane. This process leads to rotation-invariant pattern recognition with a higher discrimination ability.

/pdf/invariant-pattern-recognition-by-use-of-wavelength-3bj7052srq.pdf

Invariant pattern recognition by use of wavelength multiplexing.

http://rua.ua.es/dspace/bitstream/10045/46239/1/2015_Mas_etal_OpticsComm_proof.pdf

Novel image processing approach to detect malaria

In this paper we present a novel approach of realizing a safe, simple, and inexpensive sensor applicable to bone fractures
and pigmented lesions detection. The approach is based on temporal tracking of back-reflected secondary speckle pattern
generated while illuminating the affected area with a laser and applying periodic pressure to the surface via a controlled
vibration. The use of such a concept was already demonstrated for non-contact monitoring of various bio-medical
parameters such as heart rate, blood pulse pressure, concentration of alcohol and glucose in the blood stream and intraocular
pressure. The presented technique is a safe and effective method of detecting bone fractures in populations at risk.
When applied to pigmented lesions, the technique is superior to visual examination in avoiding many false positives and
resultant unnecessary biopsies. Applying a series of different vibration frequencies at the examined tissue and analyzing
the 2-D speckle pattern trajectory in response to the applied periodic pressure creates a unique signature for each and
different pigmented lesion. Analyzing these signatures is the first step toward detection of malignant melanoma. In this
paper we present preliminary experiments that show the validity of the developed sensor for both applications: the
detection of damaged bones as well as the classification of pigmented lesions.

Javier Garcia

Papers

From Fresnel patterns to fractional Fourier transform through geometrical optics

Shift-and-scale-invariant pattern recognition using an elliptic coordinate-transformed phase-only filter.

Invariant pattern recognition by use of wavelength multiplexing.

Novel image processing approach to detect malaria

Remote optical configuration of pigmented lesion detection and diagnosis of bone fractures