On-axis deflectometric system for freeform surface measurement.

We propose an on-axis deflectometric system for the accurate measurement of freeform surfaces with large slope ranges. A miniature plane mirror is attached on the illumination screen to fold the optical path and achieve the on-axis deflectometric testing. Due to the existence of the miniature folding mirror, the deep-learning method is applied to recover the missing surface data in a single measurement. Low sensitivity to the calibration error of system geometry and high testing accuracy can be achieved with the proposed system. The feasibility and accuracy of the proposed system have been validated. The system is low in cost and simple in configuration, and it provides a feasible way for the flexible and general testing of freeform surfaces, with a significant potential of the application in on-machine testing.

Deep-learning-based deflectometry for freeform surface measurement.

We propose a deep-learning based deflectometric method for freeform surface measurement, in which a deep neural network is devised for freeform surface reconstruction. Full-scale skip connections are adopted in the network architecture to extract and incorporate multi-scale feature maps from different layers, enabling the accuracy and robustness of the testing system to be greatly enhanced. The feasibility of the proposed method is numerically and experimentally validated, and its excellent performance in terms of accuracy and robustness is also demonstrated. The proposed method provides a feasible way to achieve the general measurement of freeform surfaces while minimizing the measurement errors due to noise and system geometry calibration.

Design and error calibration of an on-axis deflectometric microscope system.

An on-axis deflectometric microscope system (ODMS) is proposed for the microscopic surface measurement with high accuracy and a large slope dynamic range. To reduce the geometry sensitivity, a beam splitter is employed to build the coaxial configuration among the illumination screen, camera, and tested sample, which facilitates the calibration of system geometrical parameters. Due to the small working distance, the system model miscalibration in the model-ray-tracing-based "null" testing could cause obvious geometrical aberrations. In this paper, the geometrical aberrations due to the system model miscalibration are analyzed, and the corresponding calibration method based on computer-aided reverse optimization is applied to achieve accurate measurement. In addition, the systematic error introduced by the system components in the ODMS are also discussed. Both the simulation and experiment have been carried out to demonstrate the feasibility and high accuracy of the proposed measurement method. The proposed system is compact in structure, large in measurable slope range, and high in spatial resolution, providing a viable metrological tool for the microscopic testing of various freeform surfaces, microstructural elements, and micro-devices.

High-accuracy deflectometric microscope system with a large slope range.

We propose an off-axis deflectometric microscope system for microscopic surface testing with both high measurement accuracy and a large slope dynamic range. A high-luminance liquid crystal display directly illuminates the tested sample with coded fringes, and then the reflected fringes passing through a microscope objective are captured by a pinhole camera, from which the deflectometric microscopic testing with a large slope range can be achieved. The accuracy of the proposed system is validated numerically and experimentally, and a large measurable slope dynamic range is also demonstrated. The proposed system provides a feasible way with the slope range in the order of sub-radians and sag resolution better than 0.05 nm.

Calibration of geometrical aberration in transmitted wavefront testing of refractive optics with deflectometry.

Deflectometry, with its noticeable advantages such as simple structure, large dynamic range, and high accuracy comparable to interferometry, has been one of the powerful metrological techniques for optical surfaces in recent years. In the "null" deflectometric transmitted wavefront testing of refractive optics, ray tracing of the test system model is required, in which both the miscalibration of system geometrical parameters and optical tolerances on tested optics could introduce significant geometrical aberrations in the testing results. In this paper, the geometrical aberration introduced by a system modeling error in the transmitted wavefront testing is discussed. Besides, a calibration method based on polynomial optimization of geometrical aberration is presented for the geometrical aberration calibration. Both simulation and experiment have been performed to validate the feasibility of the proposed calibration method. The proposed method can calibrate the optical tolerances on tested optics effectively, and it is feasible even with a large geometric error, providing a viable way to address the uncertainty in system modeling in transmitted wavefront testing of freeform refractive optics with large dynamic range.

Frequency modulation nonlinear correction and range-extension method based on laser frequency scanning interference.

A phase spread frequency sampling method is proposed. This method can be used to correct the nonlinearity in the beat frequency of a measurement signal. The proposed method expands the phase of the auxiliary interference beat signal, thereby satisfying the Nyquist sampling theorem, correcting the nonlinearity in the beat frequency of the measured signal, and solving the problem of limited range. The conditions over which the frequency sampling method can be applied are expanded. The measurement range is flexibly expanded by performing multiple phase expansions.

Error Analysis of the Combined-Scan High-Speed Atomic Force Microscopy.

A combined tip-sample scanning architecture can improve the imaging speed of atomic force microscopy (AFM). However, the nonorthogonality between the three scanners and the nonideal response of each scanner cause measurement errors. In this article, the authors systematically analyze the influence of the installation and response errors of the combined scanning architecture. The experimental results show that when the probe in the homemade high-speed AFM moves with the Z-scanner, the spot position on the four-quadrant detector changes, thus introducing measurement error. Comparing the experimental results with the numerical and theoretical results shows that the undesired motion of the Z-scanner introduces a large error. The authors believe that this significant error occurs because the piezoelectric actuator not only stretches along the polarization direction but also swings under nonuniform multifield coupling. This article proposes a direction for further optimizing the instrument and provides design ideas for similar high-speed atomic force microscopes.

Sub-Nyquist computational ghost imaging with deep learning.

We propose a deep learning computational ghost imaging (CGI) scheme to achieve sub-Nyquist and high-quality image reconstruction. Unlike the second-order-correlation CGI and compressive-sensing CGI, which use lots of illumination patterns and a one-dimensional (1-D) light intensity sequence (LIS) for image reconstruction, a deep neural network (DAttNet) is proposed to restore the target image only using the 1-D LIS. The DAttNet is trained with simulation data and retrieves the target image from experimental data. The experimental results indicate that the proposed scheme can provide high-quality images with a sub-Nyquist sampling ratio and performs better than the conventional and compressive-sensing CGI methods in sub-Nyquist sampling ratio conditions (e.g., 5.45%). The proposed scheme has potential practical applications in underwater, real-time and dynamic CGI.

Compact snapshot dual-mode interferometric system for on-machine measurement.

To meet the need of on-machine metrology in optical manufacturing, a compact and snapshot dual-mode interferometric system is proposed for surface shape and roughness measurement. To simplify the measurement process between surface shape and roughness, a novel concept of using optical filters to separate the beam paths in the reference arm is introduced. A pixelated camera with a micro-polarizer array acquires four pi/2 phase-shifted interferograms simultaneously to minimize the environmental disturbance. Besides, the configuration-optimization-based subaperture stitching technique is introduced to extend the measurable aperture range. Both numerical analysis and experiments have been carried out to demonstrate the feasibility of the proposed compact snapshot dual-mode interferometer. The proposed system provides a powerful and portable tool to achieve on-machine surface characterization of various optical elements over a wide range of spatial frequencies and aperture sizes.

Probe misalignment calibration in fiber point-diffraction interferometer.

The measuring probe integrated with multiple fiber point-diffraction sources can be applied to measure both the three-dimensional coordinates and highly accurate point-diffraction wavefront. The probe determines the achievable measurement accuracy of fiber point-diffraction interferometer (PDI), in which the fiber exit end plane is required to be parallel with the detector plane. The probe misalignment due to fabrication error could introduce significant measurement error. A high-precision method is proposed to calibrate the probe misalignment in fiber PDI, including the central positioning based on phase difference and tilt adjustment based on Zernike polynomials fitting. Both numerical simulation and experiments have been carried out to demonstrate the feasibility and accuracy of the proposed probe misalignment calibration method. The proposed method provides a feasible way to address the processing uncertainty on measuring probe in fiber PDI, and enables high-precision geometry alignment and misalignment calibration in the interferometric testing systems with case of no imaging lens.

Compact snapshot multiwavelength interferometer.

We propose a snapshot and compact multiwavelength interferometer for real-time testing of optical surfaces with large slopes. A color camera with a micropolarizer array simultaneously captures the phase-shifted interferograms of multiple wavelengths, from which four interferograms with π/2 phase shift at each wavelength are extracted for multiwavelength phase-shifting interferometric measurement. The accuracy of the proposed system is validated experimentally, and the testing of freeform surface with large slopes is also demonstrated. The proposed system provides a feasible way to obtain the instantaneous online measurement of freeform surfaces while minimizing environmental disturbance.

Reconfigurable snapshot polarimetric imaging technique through spectral-polarization filtering.

In this Letter, we propose a simple, low-cost, reconfigurable snapshot polarimetric imaging technique for a color camera to measure polarization properties with spectral-polarization filters. Experimental results demonstrate the unique capabilities, such as obtaining circular or elliptical polarized information in a snapshot, that are not available from commercial polarization cameras and other polarization imaging techniques.

Accurate calibration of geometrical error in reflective surface testing based on reverse Hartmann test.

The deflectometry provides a powerful metrological technique enabling the high-precision testing of reflective surfaces with high dynamic range, such as aspheric and freeform surfaces. In the fringe-illumination deflectometry based on reverse-Hartmann-test configuration, the calibration of system geometry is required to achieve "null" testing. However, the system miscalibration can introduce a significant systematic error in the testing results. A general double-step calibration method, which is based on the low-order Zernike aberration optimization and high-order aberration separation, is proposed to separate and eliminate the geometrical error due to system miscalibration. Both the numerical simulation and experiments have been performed to validate the feasibility of the proposed calibration method. The proposed method provides a general way for the accurate calibration of system geometrical error, avoids the over-correction and is feasible for the testing of various complex freeform surfaces.

Computer-aided high-accuracy testing of reflective surface with reverse Hartmann test.

The deflectometry provides a feasible way for surface testing with a high dynamic range, and the calibration is a key issue in the testing. A computer-aided testing method based on reverse Hartmann test, a fringe-illumination deflectometry, is proposed for high-accuracy testing of reflective surfaces. The virtual "null" testing of surface error is achieved based on ray tracing of the modeled test system. Due to the off-axis configuration in the test system, it places ultra-high requirement on the calibration of system geometry. The system modeling error can introduce significant residual systematic error in the testing results, especially in the cases of convex surface and small working distance. A calibration method based on the computer-aided reverse optimization with iterative ray tracing is proposed for the high-accuracy testing of reflective surface. Both the computer simulation and experiments have been carried out to demonstrate the feasibility of the proposed measurement method, and good measurement accuracy has been achieved. The proposed method can achieve the measurement accuracy comparable to the interferometric method, even with the large system geometry calibration error, providing a feasible way to address the uncertainty on the calibration of system geometry.

High-precision method for submicron-aperture fiber point-diffraction wavefront measurement.

It is a key issue to measure the point-diffraction wavefront error, which determines the achievable accuracy of point-diffraction interferometer (PDI). A high-precision method based on shearing interferometry is proposed to measure submicron-aperture fiber point-diffraction wavefront with high numerical aperture (NA). To obtain the true shearing point-diffraction wavefront, a double-step calibration method based on three-dimensional coordinate reconstruction and symmetric lateral displacement compensation is proposed to calibrate the geometric aberration in the case of high NA and large lateral wavefront displacement. The calibration can be carried out without any prior knowledge about the system configuration parameters. With the true shearing wavefront, the differential Zernike polynomials fitting method is applied to reconstruct the point-diffraction wavefront. Numerical simulation and experiments have been carried out to demonstrate the accuracy and feasibility of the proposed measurement method, and a good measurement accuracy is achieved.

Simultaneous polarization Mirau interferometer based on pixelated polarization camera.

We propose a polarization Mirau interferometer using the pixelated polarization camera to acquire the four phase-shifted interferograms simultaneously by which motionless phase shift can be realized. A wire-grid polarizer is employed as the polarization beam splitter to realize the adjustable fringe contrast. Due to the limited contrast ratio of split orthogonally polarized beams with a wire grid polarizer, the corresponding calibration method by superposition of exchanged transmitted and reflected beams is proposed to obtain the uniform fringe contrast in four phase-shifted interferograms. The accuracy of the proposed system is demonstrated experimentally, and a precision better than 1/500 wavelength is achieved. The proposed system provides a feasible way to obtain the instantaneous measurement with minimizing environmental disturbance.

High-NA fiber point-diffraction interferometer for three-dimensional coordinate measurement.

The numerical aperture (NA) and power of diffraction wave in point-diffraction interferometer (PDI) could significantly limit the measurement range of the system. A fiber point-diffraction interferometer with high NA is proposed for the measurement of absolute three-dimensional coordinates. Based on the single-mode fiber with submicron aperture, the diffraction wave with both high NA and high power is obtained, by which the achievable measurement range of the PDI can be extended. A double-iterative method based on Levenbery-Marquardt algorithm is proposed to determine the three-dimensional coordinates under measurement. Numerical simulation and comparison experiments have been carried out to demonstrate the accuracy and feasibility of the proposed PDI system, with both high measurement precision and nice repeatability achieved.

Analysis of diffraction wavefront in visible-light point-diffraction interferometer.

As a key element in point-diffraction interferometer (PDI), the diffraction pinhole determines the sphericity of the reference wavefront and achievable precision of the testing system. The point-diffraction wavefront error, aperture angle, and light transmittance in the PDI operating at visible light, which are determined by pinhole dimension, are analyzed based on finite difference time domain (FDTD) method. The study shows that an aperture angle about 75° can be obtained with a 1 µm pinhole diameter, and the corresponding testing precision is better than root mean square λ/1000 within 0.35 NA. Both the numerical simulation and experiments have been carried out to demonstrate the feasibility of the proposed analysis approach, and a good agreement is obtained between calculated and measured parameters in visible-light PDI. The proposed simulation approach with the FDTD method provides a feasible way to analyze the diffraction wavefront in visible-light PDI, as well as a powerful tool for the design and optimization of PDI system.

Experimental Studies on Fabricating Lenslet Array with Slow Tool Servo.

On the demand of low-cost, lightweight, miniaturized, and integrated optical systems, precision lenslet arrays are widely used. Diamond turning is often used to fabricate lenslet arrays directly or molds that are used to mold lenslet arrays. In this paper, mainly by real-time monitoring position following error for slow tool servo, different fabrication parameters are quantitatively studied and optimized for actual fabrication, then by actual fabrication validation, uniform and high-fidelity surface topography across the actual whole lenslet array is achieved. The evaluated fabrication parameters include sampling strategy, inverse time feed, arc-length, etc. The study provides a quick, effective, and detailed reference for both convex and concave lenslet array cutting parameter selection. At the end, a smooth zonal machining strategy toolpath is demonstrated for fabricating concave lenslet arrays.

Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces.

A point diffraction interferometer (PDI) with adjustable fringe contrast is presented for the high-precision testing of spherical surfaces. The polarizing components are employed in the PDI to transform the polarization states of the test and reference beams, and a good fringe contrast can be realized by adjusting the relative intensities of interfering waves. The proposed system is compact and simple in structure, and it provides a feasible way for high-precision testing of spherical surfaces with low reflectivity. The theory of the interferometer is introduced in detail, along with the properties of optical components employed in the system, numerical analysis of systematic error, and the corresponding calibration procedure. Compared with the testing results of the ZYGO interferometer, a high accuracy with RMS value about 0.0025λ is achieved with the proposed interferometer. Finally, the error consideration in the experiment is discussed.