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 method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT’s in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from −1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT are discussed.

/pdf/fractional-fourier-transform-calculation-through-the-fast-19gin8k5g2.pdf

Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm

A technique based on superresolution by digital holographic microscopic imaging is presented. We used a two dimensional (2-D) vertical-cavity self-emitting laser (VCSEL) array as spherical-wave illumination sources. The method is defined in terms of an incoherent superposition of tilted wavefronts. The tilted spherical wave originating from the 2-D VCSEL elements illuminates the target in transmission mode to obtain a hologram in a Mach-Zehnder interferometer configuration. Superresolved images of the input object above the common lens diffraction limit are generated by sequential recording of the individual holograms and numerical reconstruction of the image with the extended spatial frequency range. We have experimentally tested the approach for a microscope objective with an exact 2-D reconstruction image of the input object. The proposed approach has implementation advantages for applications in biological imaging or the microelectronic industry in which structured targets are being inspected.

/pdf/superresolved-imaging-in-digital-holography-by-superposition-tibn6ktzys.pdf

Superresolved imaging in digital holography by superposition of tilted wavefronts.

We propose a method for increasing the resolution of an aperture limited optical system by illuminating the input with a speckle pattern. The high resolution of the projected speckle pattern demodulates the high frequencies of the sample and permits its passage through the system aperture. A decoding provides the superresolved image. The speckle pattern can be generated in a simple manner in contrast with other structured light superresolution methods. The method is demonstrated in microscopy test images.

/pdf/synthetic-aperture-superresolution-by-speckle-pattern-45z159p10q.pdf

Synthetic aperture superresolution by speckle pattern projection

The resolving power of an imaging system in digital lensless Fourier holographic configuration is mainly limited by the numerical aperture of the experimental setup that is defined by both the restricted CCD size and the presence of a beam splitter cube in front of the CCD. We present a method capable of improving the resolution in such a system configuration based on synthetic aperture (SA) generation by using time-multiplexing tilted illumination onto the input object. Moreover, a priori knowledge about the imaged object allows customized SA shaping by the addition of elementary apertures only in the directions of interest. Experimental results are provided, showing agreement with theoretical predictions and demonstrating a resolution limit corresponding with a synthetic numerical aperture value of 0.45.

https://www.uv.es/~gpoei/articulos/(2010)%20AO%2049%20845%20Synthetic%20aperture%20superresolved%20microscopy%20in%20digital%20lensless%20Fourier%20holography%20by%20time%20and%20angular%20multiplexing%20of%20the%20object%20information.pdf

Synthetic aperture superresolved microscopy in digital lensless Fourier holography by time and angular multiplexing of the object information

We present a new approach to obtain superresolved images in digital holography by means of synthetic aperture generation using common-path interferometry and off-axis illumination in optical imaging systems. The paper includes two parts. First, we present a simple approach to double the resolution of an optical system using tilted illumination onto the object and an optical element in the image plane to produce the holographic recording. Then we present a novel approach consisting of attaching a diffraction grating in parallel together with the object in the input plane and using off-axis illumination provided by a Vertical Cavity Surface Emitting Lasers (VCSEL) array to allow us achieving a major improvement in the optical resolution limit with an extremely low penalty in the complexity of the resulting system. Experimental investigation based on commercial microscope objectives is presented.

/pdf/superresolution-optical-system-by-common-path-interferometry-29ugaqn6jb.pdf

Javier Garcia

Papers

Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm

Superresolved imaging in digital holography by superposition of tilted wavefronts.

Synthetic aperture superresolution by speckle pattern projection

Synthetic aperture superresolved microscopy in digital lensless Fourier holography by time and angular multiplexing of the object information

Superresolution optical system by common-path interferometry.