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

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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

Two-photon excitation provides a means of activating chemical or physical processes with high spatial resolution in three dimensions and has made possible the development of three-dimensional fluorescence imaging, optical data storage, and lithographic microfabrication. These applications take advantage of the fact that the two-photon absorption probability depends quadratically on intensity, so under tight-focusing conditions, the absorption is confined at the focus to a volume of order λ3 (where λ is the laser wavelength). Any subsequent process, such as fluorescence or a photoinduced chemical reaction, is also localized in this small volume. Although three-dimensional data storage and microfabrication have been illustrated using two-photon-initiated polymerization of resins incorporating conventional ultraviolet-absorbing initiators, such photopolymer systems exhibit low photosensitivity as the initiators have small two-photon absorption cross-sections (δ). Consequently, this approach requires high laser power, and its widespread use remains impractical. Here we report on a class of π;-conjugated compounds that exhibit large δ (as high as 1, 250 × 10−50 cm4 s per photon) and enhanced two-photon sensitivity relative to ultraviolet initiators. Two-photon excitable resins based on these new initiators have been developed and used to demonstrate a scheme for three-dimensional data storage which permits fluorescent and refractive read-out, and the fabrication of three-dimensional micro-optical and micromechanical structures, including photonic-bandgap-type structures.

Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication

We first provide an overview of 3-D shape measurement us- ing various optical methods. Then we focus on structured light tech- niques where various optical configurations, image acquisition tech- niques, data postprocessing and analysis methods and advantages and limitations are presented. Several industrial application examples are presented. Important areas requiring further R&D are discussed. Finally, a comprehensive bibliography on 3-D shape measurement is included, although it is not intended to be exhaustive. © 2000 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(00)00101-X)

Overview of three-dimensional shape measurement using optical methods

Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

Advantages of the lensless Fourier holography setup for the reconstruction of digitally recorded holograms in holographic interferometry are presented. This very simple setup helps to achieve a maximum lateral resolution of the object under investigation. Also, the numerical-reconstruction algorithm is very simple and fast to compute. A mathematical model based on Fourier optics is used to describe discretization effects and to determine the lateral resolution. The recording and the reconstruction processes are regarded as an optical imaging system, and the point-spread function is calculated. Results are verified by an experimental setup for a combined shape and deformation measurement.

Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology

Direct shape measurement by digital wavefront reconstruction and multi-wavelength contouring

We present a method by which the phase and the amplitude of a wave front are obtained by processing a sequence of intensity patterns recorded at different planes. We do not use any reference wave, as one does for holography. Simulations and experimental results are presented.

Wave-front reconstruction from a sequence of interferograms recorded at different planes.

A system based on digital holographic interferometry for the measurement of vibrations is presented. A high-power continuous laser (10 W) and a high-speed CCD camera are used. Hundreds of holograms of an object that has been subjected to dynamic deformation are recorded. The acquisition speed and the time of exposure of the detector are determined by the vibration frequency. Two methods are presented for triggering the camera in order to acquire at a given phase of the vibration. The phase of the wavefront is calculated from the recorded holograms by use of a two-dimensional digital Fourier-transform method. The deformation of the object is obtained from the phase. By combination of the deformations recorded at different times it is possible to reconstruct the vibration of the object.

High-speed digital holographic interferometry for vibration measurement

Most of the neural networks proposed so far for computational imaging (CI) in optics employ a supervised training strategy, and thus need a large training set to optimize their weights and biases. Setting aside the requirements of environmental and system stability during many hours of data acquisition, in many practical applications, it is unlikely to be possible to obtain sufficient numbers of ground-truth images for training. Here, we propose to overcome this limitation by incorporating into a conventional deep neural network a complete physical model that represents the process of image formation. The most significant advantage of the resulting physics-enhanced deep neural network (PhysenNet) is that it can be used without training beforehand, thus eliminating the need for tens of thousands of labeled data. We take single-beam phase imaging as an example for demonstration. We experimentally show that one needs only to feed PhysenNet a single diffraction pattern of a phase object, and it can automatically optimize the network and eventually produce the object phase through the interplay between the neural network and the physical model. This opens up a new paradigm of neural network design, in which the concept of incorporating a physical model into a neural network can be generalized to solve many other CI problems.

/pdf/phase-imaging-with-an-untrained-neural-network-225tm5sdo3.pdf

Wolfgang Osten

Papers

Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology

Direct shape measurement by digital wavefront reconstruction and multi-wavelength contouring

Wave-front reconstruction from a sequence of interferograms recorded at different planes.

High-speed digital holographic interferometry for vibration measurement

Phase imaging with an untrained neural network.