Single-shot deflectometry for dynamic 3D surface profile measurement by modified spatial-carrier frequency phase-shifting method

Specular Surface Shape Measurement with Orthogonal Dual-Frequency Fourier Transform Deflectometry

Three-dimensional (3D) shape measurement for specular surfaces is becoming increasingly important in various applications. A novel orthogonal dual-frequency fringe is proposed in the specular surface shape measurement to overcome the phase jumping and discontinuities in spatial phase unwrapping. The fringe recalibrated high-accuracy phase information from its high-frequency fringe component with low-ambiguity phase information from its low-frequency fringe component. An improved Fourier transform deflectometry method based on the orthogonal dual-frequency fringe is proposed to measure 3D specular surface shapes. Simulation results showed that the orthogonal dual-frequency Fourier transform deflectometry (ODD) method could precisely reconstruct flat surfaces with an error of 2.16 nm rms, and concave surfaces with an error of 1.86 μm rms. Experimental results showed that the reconstructed shapes of both the flat mirror and the concave mirror measured by the ODD measurement system were highly comparable to those obtained by the phase-measuring deflectometry (PMD) method. This new fringe provides a distinctive approach to structured pattern construction and reduces the phase unwrapping ambiguities in specular surface shape measurement. The ODD method can achieve accurate 3D shape measurement for specular surfaces by sampling only one fringe, providing a possible basis for future real-time measurement of specular surfaces.

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.

Surface Shape Distortion Online Measurement Method for Compact Laser Cavities Based on Phase Measuring Deflectometry

Conventional phase measuring deflectometry (PMD) takes up a large measurement space and is not suitable for compact online measurement, as the liquid crystal display (LCD) has to be placed in parallel with the mirror under test. In this paper, a compact online phase measuring deflectometry (COPMD) with the LCD screen set perpendicular to the mirror under test is presented for surface shape distortion real-time measurement. The configuration of the COPMD in an enclosed laser cavity is proposed, and the principle of the method is theoretically derived by using the vector-form reflection law. Based on the analysis model, the fringe modulation regulation of the LCD is revealed, and the measurement errors caused by misalignments of the components are illustrated. The validity and flexibility of the COPMD method are verified in the experiment by using a single-actuator deformable mirror as the mirror under test and the PMD method as the comparison. The proposed COPMD method remarkably expands the application range of the conventional PMD method, as it could make efficient use of compact space and is applicable for real-time measurement in enclosed laser facilities and assembled laser systems.

Surface Measurement of a Large Inflatable Reflector in Cryogenic Vacuum

The metrology of membrane structures, especially inflatable, curved, optical surfaces, remains challenging. Internal pressure, mechanical membrane properties, and circumferential boundary conditions imbue highly dynamic slopes to the final optic surface. Here, we present our method and experimental results for measuring a 1 m inflatable reflector’s shape response to dynamic perturbations in a thermal vacuum chamber. Our method uses phase-measuring deflectometry to track shape change in response to pressure change, thermal gradient, and controlled puncture. We use an initial measurement as a virtual null reference, allowing us to compare 500 mm of measurable aperture of the concave f/2, 1-meter diameter inflatable optic. We built a custom deflectometer that attaches to the TVAC window to make full use of its clear aperture, with kinematic references behind the test article for calibration. Our method produces 500 × 500 pixel resolution 3D surface maps with a repeatability of 150 nm RMS within a cryogenic vacuum environment (T = 140 K, P = 0.11 Pa).

Single-shot 4-step phase-shifting multispectral fringe projection profilometry

Phase-shifting profilometry (PSP) is considered to be the most accurate technique for phase retrieval with fringe projection profilometry (FPP) systems. However, PSP requires that multiple phase-shifted fringe patterns be acquired, usually sequentially, which has limited PSP to static or quasi-static imaging. In this paper, we introduce multispectral 4-step phase-shifting FPP that provides 3D imaging using a single acquisition. The method enables real-time profilometry applications. A single frame provides all four phase-shifted fringe patterns needed for the PSP phase retrieval algorithm. The multispectral nature of the system ensures that light does not leak between the spectral bands, which is a common problem in simultaneous phase-shifting with color cameras. With the use of this new concept, custom composite patterns containing multiple patterns can be acquired with a single acquisition.

Single-shot detection of 8 unique monochrome fringe patterns representing 4 distinct directions via multispectral fringe projection profilometry

Spatial resolution in three-dimensional fringe projection profilometry is determined in large part by the number and spacing of fringes projected onto an object. Due to the intensity-based nature of fringe projection profilometry, fringe patterns must be generated in succession, which is time-consuming. As a result, the surface features of highly dynamic objects are difficult to measure. Here, we introduce multispectral fringe projection profilometry, a novel method that utilizes multispectral illumination to project a multispectral fringe pattern onto an object combined with a multispectral camera to detect the deformation of the fringe patterns due to the object. The multispectral camera enables the detection of 8 unique monochrome fringe patterns representing 4 distinct directions in a single snapshot. Furthermore, for each direction, the camera detects two π-phase shifted fringe patterns. Each pair of fringe patterns can be differenced to generate a differential fringe pattern that corrects for illumination offsets and mitigates the effects of glare from highly reflective surfaces. The new multispectral method solves many practical problems related to conventional fringe projection profilometry and doubles the effective spatial resolution. The method is suitable for high-quality fast 3D profilometry at video frame rates.

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.

Lock-in vibration retrieval based on high-speed full-field coherent imaging

The use of high-speed cameras permits to visualize, analyze or study physical phenomena at both their time and spatial scales. Mixing high-speed imaging with coherent imaging allows recording and retrieving the optical path difference and this opens the way for investigating a broad variety of scientific challenges in biology, medicine, material science, physics and mechanics. At high frame rate, simultaneously obtaining suitable performance and level of accuracy is not straightforward. In the field of mechanics, this prevents high-speed imaging to be applied to full-field vibrometry. In this paper, we demonstrate a coherent imaging approach that can yield full-field structural vibration measurements with state-of-the-art performances in case of high spatial and temporal density measurements points of holographic measurement. The method is based on high-speed on-line digital holography and recording a short time sequence. Validation of the proposed approach is carried out by comparison with a scanning laser Doppler vibrometer and by realistic simulations. Several error criteria demonstrate measurement capability of yielding amplitude and phase of structural deformations.

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.

Radial polarizing phase-shifting interferometry with applications to single-shot n interferogram measurements and potential usage for white light interferogram analysis

In this research, we present an interferometric system to analyze transparent samples using interferograms generated by a phase-shifting radial shear grating interferometer for two cases: the first obtaining n simultaneous phase-shifting interferograms using a coherent light source and the second one using sequential phase steps with a white light source. For the first case, the simultaneous interferograms are generated using two optical systems: the first one generates the polarized pattern while the second one consists of a 4f system creating replicas of the output interferograms. By using a 2D sinusoidal phase grating, we have the advantage of obtaining up to nine replicated interferograms, all of them with comparable intensities and having amplitudes modulated by the 2D sinusoidal phase grating diffraction orders as zero-order Bessel's functions. To obtain the optical phase map, several phase shifts are generated by placing a polarizing filter covering each replicated interferogram. We highlight the advantage of using n simultaneous interferograms by comparing resulting optical phases processed by a conventional four-step algorithm against those obtained by an implemented n=N+1 method, reducing errors with noisy interferograms. Results for n=7 and n=9 cases are presented. In addition, we have tested the setup with white light interference techniques by employing the polarizer radial shearing interferometer; for this case, the optical phase is calculated with the four-step and the three-step algorithms. Results of testing the developed system to examine static and dynamic phase objects are also included.

Hand-guided qualitative deflectometry with a mobile device

We introduce a system that exploits the screen and front-facing camera of a mobile device to perform three-dimensional deflectometry-based surface measurements. In contrast to current mobile deflectometry systems, our method can capture surfaces with large normal variation and wide field of view (FoV). We achieve this by applying automated multi-view panoramic stitching algorithms to produce a large FoV normal map from a hand-guided capture process without the need for external tracking systems, like robot arms or fiducials. The presented work enables 3D surface measurements of specular objects 'in the wild' with a system accessible to users with little to no technical imaging experience. We demonstrate high-quality 3D surface measurements without the need for a calibration procedure. We provide experimental results with our prototype Deflectometry system and discuss applications for computer vision tasks such as object detection and recognition.

Phase-modulation combined deflectometry for small defect detection

Deflectometry has been widely used to detect defects on specular surfaces. However, it is still very challenging to detect defects on semispecular or diffuse surfaces because of the low contrast and low signal-to-noise ratio. To address this challenge, we proposed a phase-modulation combined method for accurate defect detection. Based on the phase and modulation of captured fringes, a dual-branch convolutional neural network is employed to simultaneously extract geometric and photometric features from the phase-shifting pattern sequence and modulation, which improves the defect detection performance significantly. Compared to state-of-the-art methods, we believe the results demonstrated the proposed method's effectiveness and capability to reduce false positives.

Single-shot freeform surface profiler

We propose a novel and simple method of single-shot freeform surface profiler based on spatially phase-shifted lateral shearing interferometry. By the adoption of birefringent materials, the laterally shearing waves are simply generated without any bulky and complicated optical components. Moreover, the phase maps that lead to the 3D profile of the freeform surface can be instantly obtained by the spatial phase-shifting technique using a pixelated polarizing camera. The proposed method was theoretically described and verified by measuring several samples in comparison to the measurement results with a well-established stylus probe.

Optical 3-D Profilometry for Measuring Semiconductor Wafer Surfaces with Extremely Variant Reflectivities

A new surface profilometry technique is proposed for profiling a wafer surface with both diffuse and specular reflective properties. Most moiré projection scanning techniques using triangulation principle work effectively on diffuse reflective surfaces, on which the reflected light beams are assumed to be well captured by optical sensors. In reality, this assumption is no longer valid when measuring a semiconductor wafer surface having both diffuse and specular reflectivities. To resolve the above problem, the proposed technique uses a dual optical sensing configuration by engaging two optical sensors at two different viewing angles, with one acquiring diffuse reflective light and the other detecting at the same time specular surface light for achieving simultaneous full-field surface profilometry. The deformed fringes measured by both sensors could be further transformed into a 3-D profile and merged seamlessly for full-field surface reconstruction. Several calibration targets and industrial parts were measured to evaluate the feasibility and accuracy of the developed technique. Experimental results showed that the technique can effectively detect diffuse and specular light with repeatability of one standard deviation below 0.3 µm on a specular surface and 2.0 µm on a diffuse wafer surface when the vertical measuring range reaches 1.0 mm. The present findings indicate that the proposed technique is effective for 3-D microscale surface profilometry in in-situ semiconductor automated optical inspection (AOI).