Physics-informed deep learning for fringe pattern analysis

Recently,deep learning has yielded transformative success across optics and photonics,especially in optical metrology.Deep neural networks (DNNs) with a fully convolutional architecture (e.g.,U-Net and its derivatives) have been widely implemented in an end-to-end manner to accomplish various optical metrology tasks,such as fringe denoising,phase unwrapping,and fringe analysis.However,the task of training a DNN to accurately identify an image-to-image transform from massive input and output data pairs seems at best naive,as the physical laws governing the image formation or other domain expertise pertaining to the measurement have not yet been fully exploited in current deep learning practice.To this end,we introduce a physics-informed deep learning method for fringe pattern analysis (PI-FPA) to overcome this limit by integrating a lightweight DNN with a learning-enhanced Fourier transform profilometry (Le FTP) module.By parameterizing conventional phase retrieval methods,the Le FTP module embeds the prior knowledge in the network structure and the loss function to directly provide reliable phase results for new types of samples,while circumventing the requirement of collecting a large amount of high-quality data in supervised learning methods.Guided by the initial phase from Le FTP,the phase recovery ability of the lightweight DNN is enhanced to further improve the phase accuracy at a low computational cost compared with existing end-to-end networks.Experimental results demonstrate that PI-FPA enables more accurate and computationally efficient single-shot phase retrieval,exhibiting its excellent generalization to various unseen objects during training.The proposed PI-FPA presents that challenging issues in optical metrology can be potentially overcome through the synergy of physics-priors-based traditional tools and data-driven learning approaches,opening new avenues to achieve fast and accurate single-shot 3D imaging.

Advances in optical engineering for future telescopes

Significant optical engineering advances at the University of Arizona are being made for design, fabrication, and construction of next generation astronomical telescopes. This summary review paper focuses on the technological advances in three key areas. First is the optical fabrication technique used for constructing next-generation telescope mirrors. Advances in ground-based telescope control and instrumentation comprise the second area of development. This includes active alignment of the laser truss-based Large Binocular Telescope(LBT) prime focus camera, the new MOBIUS modular cross-dispersion spectroscopy unit used at the prime focal plane of the LBT, and topological pupil segment optimization. Lastly, future space telescope concepts and enabling technologies are discussed. Among these, the Nautilus space observatory requires challenging alignment of segmented multi-order diffractive elements. The OASIS terahertz space telescope presents unique challenges for characterizing the inflatable primary mirror, and the Hyperion space telescope pushes the limits of high spectral resolution, far-UV spectroscopy. The Coronagraphic Debris and Exoplanet Exploring Pioneer(CDEEP) is a Small Satellite(Small Sat) mission concept for high-contrast imaging of circumstellar disks and exoplanets using vector vortex coronagraph. These advances in optical engineering technologies will help mankind to probe, explore, and understand the scientific beauty of our universe.

Ion Beam Figuring System for Synchrotron X-Ray Mirrors Achieving Sub-0.2-µrad and Sub-0.5-nm Root Mean Square

Optics with high-precision height and slope are increasingly desired in numerous industrial fields.For instance,Kirkpatrick-Baez(KB)mirrors play an important role in synchrotron X-ray applications.A KB system is composed of two aspherical,grazing-incidence mirrors used to focus an X-ray beam.The fabrication of KB mirrors is challenging due to the aspherical departure of the mirror surfaces from base geometries and the high-quality requirements for slope and height residuals.In this paper,we present the process of manufacturing an elliptical cylinder KB mirror using our in-house-developed ion beam figuring(IBF)and metrology technologies.First,the key aspects of figuring and finishing processes with IBF are illustrated in detail.The effect of positioning error on the convergence of the residual slope error is highlighted and compensated.Finally,inspection and cross-validation using different metrology instruments are performed and used as the final validation of the mirror.Results confirm that relative to the requested off-axis ellipse,the mirror has achieved 0.15-μrad root mean square(RMS)and 0.36-nm RMS residual slope and height errors,respectively,while maintaining the initial 0.3-nm RMS microroughness.

Advantages of white LED lamps and new detector technology in photometry

Light emitting diode(LED)lighting is becoming more and more popular,as incandescent lamps are being phased out globally.LEDs have several advantages over incandescent lamps,including energy efficiency,robustness,long lifetime,and good temporal stability.The three latter features make LEDs attractive candidates as new photometric standards.Because the spectra of white LEDs are limited to the visible wavelength range,a novel method for the realization of photometric units based on the predictable quantum efficient detector(PQED)can be utilized.The method eliminates the need of photometric filters that are traditionally used in photometry,and instead relies on carrying out the photometric weighting numerically based on the measured relative spectrum of the source.The PQED-based realization simplifies the traceability chain of photometric measurements significantly as compared with the traditional filter-based method.The measured illuminance values of a white LED deviate by only 0.03%when determined by the new and the traditional methods.The new PQED method has significantly lower expanded uncertainty of 0.26%(k=52)as compared with that of the traditional filter-based method of 0.42%(k=52).Furthermore,when filtered photometers that measure LED lighting are calibrated using LED lamps as calibration sources instead of incandescent lamps,a significant decrease in the uncertainty related to the spectral mismatch correction can be obtained.The maximum spectral mismatch errors of LED measurements decreased on average by a factor of 3 when switching from an incandescent lamp to an LED calibration source.

Reflections about the holographic and nonholographic acquisition of surface topography: where are the limits?

Recording and(computational)processing of complex wave fields offer a vast realm of new methods for optical 3D metrology.We discuss fundamental similarities and differences between holographic surface topography measurement and non-holographic principles,such as triangulation,classical interferometry,rough surface interferometry and slope measuring methods.Key features are the physical origin of the ultimate uncertainty limit and how the topographic information is encoded and decoded.Besides the theoretical insight,the discussion will help optical metrologists to determine if their measurement results could be improved or have already hit the ultimate limit of what physics allows.

Solving the inverse grating problem by white light interference Fourier scatterometry

Scatterometry is a well-established,fast and precise optical metrology method used for the characterization of sub-lambda periodic features.The Fourier scatterometry method,by analyzing the Fourier plane,makes it possible to collect the angle-resolved diffraction spectrum without any mechanical scanning.To improve the depth sensitivity of this method,we combine it with white light interferometry.We show the exemplary application of the method on a silicon line grating.To characterize the sub-lambda features of the grating structures,we apply a model-based reconstruction approach by comparing simulated and measured spectra.All simulations are based on the rigorous coupled-wave analysis method.