Endoscopic imaging is an indispensable tool for visual inspection of surfaces in hard-to-access places. The conventional optical endoscope only enables imaging the regions that lie close to the focal plane, and therefore improving the depth of field (DOF) of an endoscopic system has recently attracted much attention. Here, we propose and demonstrate a simple, cost-effective, and easily available industrial endoscopic system, which is composed of a rigid tube and group of optical lenses. The outer diameter of the designed endoscopic modality presented in this article is 3 mm. By employing the wavefront coding technique, the DOF of newly-designed endoscope was extended to 2.7 mm in the proof-of-concept experiment, which is an increase of almost 10 times compared to the initial counterpart.

Photonic time-stretch (PTS) technology enables revolutionary technical breakthroughs in ultrafast electronic and optical systems. By means of employing large chromatic dispersion to map the spectrum of an ultrashort optical pulse into a stretched time-domain waveform (namely, using the dispersive Fourier transformation), PTS overcomes the fundamental speed limitations of conventional techniques. The chromatic dispersion utilized in PTS can be implemented using multiple optical prism arrays, which have the particular advantages of low loss in the extended spectrum outside of the specific telecommunication band, flexibility, and cost-effectiveness. In this article, we propose and demonstrate the PTS technology established for a pair of prisms, which works as a data acquisition approach in ultrafast digitizing, imaging, and measurement regimes.

Multi-channel optical systems can provide more feature information compared to single-channel systems, making them valuable for optical remote sensing, target identification, and other applications. The division of aperture polarization imaging modality allows for the simultaneous imaging of targets in the same field of view with a single detector. To overcome the limitations of conventional refractive aperture-divided systems for miniaturization, this work proposes an off-axis catadioptric aperture-divided technique for polarization imaging. First, the design method of the off-axis reflective telescope structure is discussed. The relationship between optical parameters such as magnification, surface coefficient, and primary aberration is studied. Second, by establishing the division of the aperture optical model, the method of maximizing the field of view and aperture is determined. Finally, an off-axis catadioptric cooled aperture-divided infrared optical system with a single aperture focal length of 60 mm is shown as a specific design example. Each channel can achieve 100% cold shield efficiency, and the overall length of the telescope module can be decreased significantly. The image quality of each imaging channel is close to the diffraction limit, verifying the effectiveness and feasibility of the method. The proposed off-axis catadioptric aperture-divided design method holds potential applications in simultaneous infrared polarization imaging.

In freeform optical metrology, wavefront fitting over non-circular apertures is hindered by the loss of Zernike polynomial orthogonality and severe sampling grid distortion inherent in standard conformal mappings. To address the resulting numerical instability and fitting bias, we propose a unified framework curve-shortening flow (CSF)-guided progressive quasi-conformal mapping (CSF-QCM), which integrates geometric boundary evolution with topology-aware parameterization. CSF-QCM first smooths complex boundaries via curve-shortening flow, then solves a sparse Laplacian system for harmonic interior coordinates, thereby establishing a stable diffeomorphism between physical and canonical domains. For doubly connected apertures, it preserves topology by computing the conformal modulus via Dirichlet energy minimization and simultaneously mapping both boundaries. Benchmarked against state-of-the-art methods (e.g., Fornberg, Schwarz–Christoffel, and Ricci flow) on representative irregular apertures, CSF-QCM suppresses area distortion and restores discrete orthogonality of the Zernike basis, reducing the Gram matrix condition number from >900 to <8. This enables high-precision reconstruction with RMS residuals as low as $3\times {10}^{-3}\lambda$ and up to 92% lower fitting errors than baselines. The framework provides a unified, computationally efficient, and numerically stable solution for wavefront reconstruction in complex off-axis and freeform optical systems.

Interferometric measurement of large aperture freeform surfaces often requires sub-aperture stitching to achieve full aperture measurement. We propose layout preselection based on the Hessian response of the design surface to two planar translations and rotation about the optical axis. After removing the best-fit sphere, first-order Hessian responses form a scaled matrix that quantifies the weakest constraint on these variables. The resulting sensitivity field guides overlap placement toward regions with stronger constraints while weakly sensitive regions are covered within individual subapertures. Responses from adjacent overlaps are then assembled to rank feasible layouts by their weakest collective registration constraint. Global orientation selection and subaperture center adjustment refine the retained layouts. The method was evaluated on 180 design surfaces from the Zernike, XY polynomial, and Q-type families. After registration with three degrees of freedom, adjusted layouts yielded median translation and rotation errors of 5.42 $\mathsf{\mu }\mathrm{m}$ and 0.228 mrad, respectively, with a median stitching error root mean square (RMS) of 23.95 nm. All three interquartile ranges were narrower than for regular layouts. Using the recovered planar estimates to initialize registration with six degrees of freedom (DoF) reduced median subsequent iteration counts. These results support Hessian-based overlap planning for improved planar registration and initialization of full aperture reconstruction.

In freeform optical metrology, wavefront fitting over non-circular apertures is hindered by the loss of Zernike polynomial orthogonality and severe sampling grid distortion inherent in standard conformal mappings. To address the resulting numerical instability and fitting bias, we propose a unified framework curve shortening flow (CSF)-guided progressive quasi-conformal mapping (CSF-QCM), which integrates geometric boundary evolution with topology-aware parameterization. CSF-QCM first smooths complex boundaries via curve-shortening flow, then solves a sparse Laplacian system for harmonic interior coordinates, thereby establishing a stable diffeomorphism between physical and canonical domains. For doubly connected apertures, it preserves topology by computing the conformal modulus via Dirichlet energy minimization and simultaneously mapping both boundaries. Benchmarked against state-of-the-art methods (e.g., Fornberg, Schwarz-Christoffel and Ricci flow) on representative irregular apertures, CSF-QCM suppresses area distortion and restores discrete orthogonality of the Zernike basis, reducing the Gram matrix condition number from >900 to < 8. This enables high-precision reconstruction with RMS residuals as low as $3\times10^{-3}\lambda$ and up to 92\% lower fitting errors than baselines. The framework provides a unified, computationally efficient, and numerically stable solution for wavefront reconstruction in complex off-axis and freeform optical systems.