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

Abstract With the advances in scientific foundations and technological implementations, optical metrology has become versatile problem-solving backbones in manufacturing, fundamental research, and engineering applications, such as quality control, nondestructive testing, experimental mechanics, and biomedicine. In recent years, deep learning, a subfield of machine learning, is emerging as a powerful tool to address problems by learning from data, largely driven by the availability of massive datasets, enhanced computational power, fast data storage, and novel training algorithms for the deep neural network. It is currently promoting increased interests and gaining extensive attention for its utilization in the field of optical metrology. Unlike the traditional “physics-based” approach, deep-learning-enabled optical metrology is a kind of “data-driven” approach, which has already provided numerous alternative solutions to many challenging problems in this field with better performances. In this review, we present an overview of the current status and the latest progress of deep-learning technologies in the field of optical metrology. We first briefly introduce both traditional image-processing algorithms in optical metrology and the basic concepts of deep learning, followed by a comprehensive review of its applications in various optical metrology tasks, such as fringe denoising, phase retrieval, phase unwrapping, subset correlation, and error compensation. The open challenges faced by the current deep-learning approach in optical metrology are then discussed. Finally, the directions for future research are outlined. 

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Deep learning in optical metrology: a review

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In 3D optical metrology, single-shot structured light profilometry techniques have inherent advantages over their multi-shot counterparts in terms of measurement speed, optical setup simplicity, and robustness to motion artifacts. In this paper, we present a new approach to extract height information from single deformed fringe patterns, based entirely on deep learning. By training a fully convolutional neural network on a large set of simulated height maps with corresponding deformed fringe patterns, we demonstrate the ability of the network to obtain full-field height information from previously unseen fringe patterns with high accuracy. As an added benefit, intermediate data processing steps such as background masking, noise reduction and phase unwrapping that are otherwise required in classic demodulation strategies, can be learned directly by the network as part of its mapping function.

Deep neural networks for single shot structured light profilometry

A new method of phase unwrapping is proposed for the absolute phase estimation based on the first-order polynomial phase approximation within a symmetric window generated around each pixel. The accurate estimation of polynomial coefficients is performed by formulating them as the elements of a state vector in a state space model. The extended Kalman filter offers a robust approach for the state estimation with the capability of handling high noise power. The polynomial coefficients estimates obtained at a given pixel are used as the initial conditions of the Kalman filter for its neighboring pixel, which results in the unwrapped phase estimation. The simulation and experimental results validate the performance of the proposed phase unwrapping method along with its ability of handling the masked phase fringe patterns with the help of a predefined binary mask and a pixel selection strategy.

Local-polynomial-approximation-based phase unwrapping using state space analysis

Simultaneous unwrapping and low pass filtering of continuous phase maps based on autoregressive phase model and wrapped Kalman filtering

A novel technique is proposed for the simultaneous measurement of all three components of displacement from a single recording of the interference field in digital holographic interferometry. The interference field is divided into a number of rectangular segments, and in each of these segments, the interference field is represented as a multicomponent low-order two-dimensional (2D) polynomial phase signal. 2D-product high-order ambiguity function based analysis is applied to obtain an accurate estimation of the 2D polynomial coefficients. These coefficients are further used to compute the interference phases. The simulation and experimental results show the robustness of the proposed method to noise and its effectiveness in multiple phase estimation.

Rishikesh Kulkarni

Papers

Local-polynomial-approximation-based phase unwrapping using state space analysis

Simultaneous unwrapping and low pass filtering of continuous phase maps based on autoregressive phase model and wrapped Kalman filtering

Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry.

Automated surface feature detection using fringe projection: An autoregressive modeling-based approach

Simultaneous estimation of unwrapped phase and phase derivative from a closed fringe pattern