Infinite deflectometry enabling 2π-steradian measurement range

Modeling, fabrication, and metrology of 3D printed Alvarez lenses prototypes

In this work, we present the fabrication of two 3D printed plano-freeform prototypes, designed in such a way that, when assembled, an Alvarez lens is formed. The freeform surface of each element was mathematically described using Zernike polynomials and verified by implementing an off-axis null-screen test. Additionally, a characterization by refraction of the assembled lens was performed. Experimental images show the suitability of additive manufacturing engineering for prototyping freeform optics by providing a practical demonstration of the Alvarez lens concept.

Multi-view stitching phase measuring deflectometry for freeform specular surface metrology

Phase measuring deflectometry (PMD) offers notable advantages for precision inspection of specular elements. Nevertheless, if confronts challenges when measuring freeform specular surfaces due to the dispersion of reflection rays from surfaces with high local slopes. Here, we propose a multi-view stitching PMD. It utilizes distinct sensors combining with a screen to capture the appearance of each region. After precisely calibrating the entire system to correct the absolute depth of each region, the appearances of all regions are precisely stitched together, reconstructing the comprehensive appearance of the surface. Through experimental setup, we measured the 3D morphology of a spherical lens with a curvature radius of 155.04 mm and a peak-to-valley (PV) value of 2.9 mm, which yielded a measurement accuracy of 5.3 µm (relative error: 0.18 %). Furthermore, we successfully measured the appearance of a curved mobile phone screen with local slopes ranging from -46.1° to 51.3°, and freeform acrylic sheet with local slopes ranging from -6.7° to 7.7° and a PV value of 5.3 mm.

Three-dimensional stitching of stereo-deflectometry based on marker points

As a non-contact and three-dimensional (3D) mirror surface measurement method, stereo-deflectometry has been developing rapidly in recent years. For solving the problem of the measurement of large surface inclination with traditional stereo-deflectometry, 3D stitching of stereo-deflectometry based on marker points is proposed. In this method, the 3D points in the subregions under different perspectives were measured. Meanwhile, the 3D coordinates of the marker points on the sample table, which were calculated by binocular stereo vision, were used for coarse stitching, and the ICP algorithm was used for fine stitching. In order to verify the 3D stitching algorithm, we built a measurement system for the freeform surface of an ultra-short lens with a diameter of about 100 mm and a steepness of 52.6°. The spherical fitting error of the reflective bowl after stitching is within 60 mm. The experimental results verify the feasibility of the method, leading to potential mass application of stereo-deflectometry in 3D measurement of complex optical surfaces with a large aperture and high steepness.

Non-planar illumination deflectometry for axicon metrology

We introduce an on-axis deflectometry test configuration for axicon metrology. Axicons are challenging to measure due to their characteristically steep, convex geometry. However, if an axicon is coaxially aligned with a camera and a surrounding cylindrical illumination source, high-resolution surface measurements can be obtained via the principle of deflectometry. Emitted from the temporally modulated source, light deflects at the conical surface and into the entrance pupil of a camera, illuminating the full axicon aperture except the ø 0.5-mm rounded tip. Deflectometry measurements of a 100° and 140° axicon show holistic cone angle agreement within 0.035° against touch probe data and up to 7.93 root μm mean square difference from a best-fit cone. We discuss the non-planar illumination architecture, sensitivity, and experimental results of arbitrary apex angle axicons.

Telephoto-lens-based Optical Differentiation Wavefront Sensor for freeform metrology

We report an Optical Differentiation Wavefront Sensor based on a telephoto lens system and binary pixelated filters. It provides a five-fold reduction in the system length compared to a 4f system with identical effective focal length. Measurements of phase plates with this system are compared to measurements performed with a commercial low-coherence interferometer. The telephoto-lens-based system can measure wavefronts with accuracy better than λ/10 Root Mean Squared (RMS) at λ=633 nm. Experimental investigation shows that the system has a high tolerance to components alignment errors.

Null-screen testing of the complementary freeform surfaces of an adjustable focus lens

A novel null-screen technique to test freeform optical surfaces for ophthalmic use is presented. We present an off-axis experimental setup to evaluate the surface shape of a two-element commercial adaptable focus lens based on the Alvarez principle. The advantages of the method are that it is fast, easy to implement, and reduces costs. This metrology technique is validated by testing both the convex and the concave complementary freeform elements of the spectacle under test. We also apply two methods to recover the surface shape of both elements: numerical integration and a custom probabilistic algorithm. Results are compared with a reference surface finding that for method 1, the RMS value in sagitta differences is 32.6 microns for the convex surface and 26.5 microns for the concave surface. Meanwhile, for method 2, the RMS value in sagitta differences found is 19.8 microns for the convex surface and 16.9 microns for the concave surface. Results show agreement in RMS in sagitta differences for both surfaces in each of the reconstruction methods employed.

Advances in reconfigurable optical design, metrology, characterization, and data analysis

Reconfigurable freeform optical systems greatly enhance imaging performance within non-symmetric, compact, and ergonomic form factors. In this paper, several advances improve design, testing, and monitoring of these systems. Specific enhancements include definition of polynomials for fast and efficient parameterizations of vector distributions in non-circular apertures and merit based function optimization. Deflectometry system improvements enable metrology for almost any conceivable optic shape and guide deterministic optical figuring process during the coarse grinding phase by including modulated infrared sources. As a demonstration of these improvements, parametric optimization is tested with the tomographic ionized-carbon mapping experiment, a reconfigurable optical system. Other case studies and demonstrations include metrology of a fast, f/1.26 convex optic, an Alvarez lens, and real-time monitoring of an array of independently-steerable hexagonal mirror segments as well as an induction formed surface and inflatable Mylar mirror.

Flexible one-shot geometric calibration for off-axis deflectometry

Off-axis deflectometry is widely applied in the measurement of specular surfaces. However, the measuring accuracy depends on the reliability of geometrical calibration. Existing methods are inconvenient to be utilized due to their disadvantages of low efficiency and operational complexity. A simple geometrical calibration method is proposed by applying a flat mirror with markers, and only one image needs to be captured. A compensation process is introduced to correct the form error of the mirror. Experimental results show that the re-projection errors decrease from 0.319 pixels down to 0.12 pixels; thus the measuring efficiency and accuracy of optical surfaces can be greatly improved.

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.

High-performance optical differentiation wavefront sensing towards freeform metrology

We report the demonstration of freeform optics metrology with an optical differentiation wavefront sensor that relies on spatially dithered distributions of binary pixels to synthesize a far-field amplitude filter. Analysis of experimental results and comparison with a commercial low-coherence-length interferometer shows that freeform phase plates with different magnitude of wavefront slopes can be accurately characterized. RMS accuracy of ∼ λ/10 and precision of ∼ λ/70 at 633 nm were achieved with pixelated filters having 2.5-µm pixels. Simulations that describe the characterization of a freeform optical component in the presence of photodetection noise and filter nonlinearity demonstrate the robustness of this wavefront-sensing approach for freeform optics characterization.

High contrast thermal deflectometry using long-wave infrared time modulated integrating cavity source

We introduce a scalable temporally modulated long-wave infrared source design. The design makes use of an array of resistive blackbody heating elements which radiate into a custom aluminum integrating cavity. The output of the box is a rectangular slit, built to match the traditional tungsten ribbon profile for an infrared deflectometry source. Temporal modulation allows for signal isolation and improved resilience to background fluctuations in an infrared deflectometry source. Infrared deflectometry measurements using the new source design and a traditional tungsten ribbon, both with similar radiant flux, were compared for a ground glass surface, an aluminum blank, and an aluminum blank under thermal load (150 °C). Signal-to-noise ratio was ∼4 times higher for the new design and demonstrated improved source temporal stability and geometry. Further, the new design successfully measured the previously untestable hot aluminum flat. The new design improves infrared deflectometry and allows for high contrast thermal deflectometry measurements of optics under thermal load.