Phase measuring deflectometry is a powerful measuring method for complex optical surfaces, which captures the reflected fringe images encoded on the screen under the premise of focusing the measured specular surface. Due to the limited depth of field of the camera, the captured images and the measured surface cannot be focused at the same time. To solve the position-angle uncertainty issue, in this Letter, the wavefront coding technology is used to modulate the imaging wavefront of the deflectometry, thereby making the measuring system insensitive to the defocus and other low-order aberration including astigmatism, field curvature, and so on. To obtain the accurate phase, the captured fringe images are deconvoluted using the modulated point spread function to reduce the phase error. Demonstrated with a highly curved spherical surface, the measurement accuracy can be improved by four times. Experiments demonstrate that the proposed method can successfully reconstruct the complex surfaces defocusing the captured images, which can greatly release the focusing requirement and improve measurement accuracy. (C) 2022 Optica Publishing Group

The phase measuring deflectometry is a powerful measuring method for complex optical surfaces, which captures the reflected fringe images associated with a displaying screen and calculates the normal vectors of the surface under test (SUT) accordingly. The captured images are usually set conjugate to the SUT, which in turn makes the screen defocused. As a result, the blurring effect caused by the point spread function (PSF) of the off-axis catadioptric imaging system can bias the solved phases. In order to correct the phase errors, a light field is constructed based on the Fourier compressive sensing method to describe the light transmission between the screen and camera pixels. Fringe modulation is conducted to enhance the robustness against noise, and then, space-variant PSFs can be extracted from the light field. The true phases are obtained by solving a Wiener deconvolution problem, with the merit function adaptively regularized by adjusting the damping parameter. The proposed method can correct adaptively the phase errors induced by the complex aberrations. Compared to the reference measurements, the form accuracy can be improved by four times.

Traditional hyperspectral imaging (HI) systems are constrained by a limited depth of field (DoF), necessitating refocusing for any out-of-focus objects. This requirement not only slows down the imaging speed but also complicates the system architecture. It is challenging to trade off among speed, resolution, and DoF within an ultra-simple system. While some studies have reported advancements in extending DoF, the improvements remain insufficient. To address this challenge, we propose a novel, to our knowledge, differentiable framework that integrates an extended DoF (E-DoF) wave propagation model and an achromatic hyperspectral reconstructor powered by deep learning. Through rigorous experimental validation, we have demonstrated that the compact HI system is capable of snapshot capturing of high-fidelity images with an exceptional DoF reaching approximately 5 m, marking a significant improvement of over three orders of magnitude. Additionally, the system achieves over 90% spectral accuracy without aberration, nearly doubling the accuracy performance of existing methods. An asymmetric freeform surface design is introduced for diffractive optical elements, enabling dual functionality with design freedom and E-DoF. The sparse prior conditions for spatial texture and spectral features of hyperspectral cubic data are integrated into the reconstruction network, effectively mitigating texture blurring and chromatic aberration. It foresees that the optimal strategy for achromatic E-DoF can be adopted into other optical systems such as polarization imaging and depth measurement.

Deterministic optics fabrication using sub-aperture tools has been vital for manufacturing precision optical surfaces, industrial robotic polishing, which is a more economical and intelligent method is required in modern fabrication process. However, the challenge of robotic polishing lies in the widely used spiral and raster paths, which may leave excess waviness from the tool path, and the unavoidable constant removal layer is added to obtain positive dwell time which cause low polishing accuracy. The waviness can be removed by either using smoothing tools sequentially or randomizing the tool path. However, process efficiency and accuracy are not well considered in the existing tool-path planning. A density adaptive path based on a stacked rotation convolution model to ensure polishing accuracy and efficiency while avoiding waviness generation is proposed in this study, and then the dwell time is calculated by anti-aliasing space-variant deconvolution. The robotic polisher experimental results confirm that the root mean square (RMS) of the final surface figure has been successfully reduced and stabilized at 7.355 nm, and the convergence effect at unit wavelength has been significantly augmented with an improvement of 367%, reducing the measurement from 28% to 131%; in addition, no obvious mid-spatial frequency (MSF) peak was generated in the PSD analysis of density adaptive path polishing results. Henceforth, the polishing accuracy, efficiency, and MSF error of robotic polishing can be greatly enhanced.

Freeform optics, offering high degrees of design freeform to control light propagation, have already been widely applied in various photoelectric equipment. The form quality of those optics is crucial to their opto-electronics functionalities, which requires to be measured accurately. The deflectometry is a promising technology to test the complex freeform surfaces. In general, there is a designed surface model for the monoscopic deflectometry to estimate the positions of whole measured points to solve the issue of height-slope ambiguity. However, the unknown or inaccurate surface model can induce errors into the measured normal, thereby decreasing the measurement precision. In this paper, without relying on the known surface model, the proposed method iteratively optimizes a sphere model to describe the measured surface by changing the spherical radius. In order to reduce the global error, the space-variant spheres are optimized, respectively, to estimate the whole-aperture surface coordinate. With the help of the iteration surface reconstruction process, the optimal number of the space-variant spheres is achieved to meantime obtain the final reconstructed surface. Compared to the measurements by using the plane model, the form accuracy can be improved by three times. Experiments demonstrate that the proposed method can successfully reconstruct the complex surfaces without the need of a known surface model, which can greatly improve the measuring flexibility and measurement accuracy.

The industrial robot-based polisher has wide applications in the field of optical manufacturing due to the advantages of low cost, high degrees of freedom, and high dynamic performance. However, the large positioning error of the industrial robot can lead to surface ripple and seriously restrict the system performance, but this error can only be inefficiently compensated for by measurement before each processing at present. To address this problem, we discovered the period-phase evolution law of the positioning error and established a double sine function compensation model. In the self-developed robotic polishing platform, the results show that the Z-axis error in the whole workspace after compensation can be reduced to ±0.06mm, which reaches the robot repetitive positioning error level; the Spearman correlation coefficients between the measurement and modeling errors are all above 0.88. In the practical polishing experiments, for both figuring and uniform polishing, the ripple error introduced by the positioning error is significantly suppressed by the proposed model under different conditions. Besides, the power spectral density (PSD) analysis has shown a significant suppression in the corresponding frequency error. This model gives an efficient plug-and-play compensation model for the robotic polisher, which provides possibilities for further improving robotic processing accuracy and efficiency.