A panoramic annular lens can provide abundant spatial information in real time with its compact and scalable structure. To deal with extreme temperature environments and to improve the utilization of an image plane, we propose a high-performance compact athermal panoramic annular lens with separated radial optical power. By introducing multiple free-form surfaces, the system achieves a field of view of (40∘∼100∘)×360∘, an f-number of 2.2, and a total length of 40 mm. The modulation transfer function of the system's full fields of view is greater than 0.5 at 200 lp/mm, and the distortion is less than 2.5%. It can work stably in the range of -30∘C to 70°C. The proposed system is compact, athermal, and high-performing and has broad application prospects in the fields of visual positioning and biomedicine.

The numerical method based on the fast Fourier transform (FFT) is generally applied to calculate the Fresnel diffraction field, which would suffer from sampling constraints. To break this limit, in this Letter, the semi-analytic Fresnel diffraction calculation method is proposed based on polynomial decomposition. The diffraction field is computed by using properly analytic Fresnel diffraction basis functions (FDBFs) according to the application requirements. Analytic FDBF is calculated based on Legendre or Chebyshev polynomials by using the object-domain frequency division multiplexing method. The proposed method offers arbitrary sampling, high-flexibility, and high-accuracy diffraction calculation in the full Fresnel region. The computational efficiency and accuracy of the proposed method are compared with FFT-based methods. It has potential application in light field analysis, wavefront sensing, and image processing.

Freeform surfaces play an important role in modern optical systems with compactness and better performance. The fabrication tools tend to impart a structured signature on optical surfaces, called ripple errors, during the freeform surface manufacturing process. The description and extraction of ripple errors for freeform surface fabrication and testing have attracted extensive attention. In this paper, we develop a fast and accurate method to describe ripple errors for the large aperture based on Fourier model coupling. The polynomial expression is transformed into Fourier series form and surface errors are reconstructed by frequency feature extraction combining with the least square method. The high accuracy and efficiency of the proposed method for representing and filtering ripple errors consuming little computer memory are demonstrated using real experimental data. The proposed method offers a robust and powerful tool not only suitable for surface error characterization but also for image filtering and analysis.

Parameters mismatching between the real optical system and phase retrieval model undermines wavefront reconstruction accuracy. The three-dimensional intensity position is corrected in phase retrieval, which is traditionally separated from lateral position correction and axial position correction. In this paper, we propose a three-dimensional intensity position correction method for phase diverse phase retrieval with the cross-iteration nonlinear optimization strategy. The intensity position is optimized via the coarse optimization method at first, then the intensity position is cross-optimized in the iterative wavefront reconstruction process with the exact optimization method. The analytic gradients about the three-dimensional intensity position are derived. The cross-iteration optimization strategy avoids the interference between the incomplete position correction and wavefront reconstruction during the iterative process. The accuracy and robustness of the proposed method are verified both numerically and experimentally. The proposed method achieves robust and accurate intensity position correction and wavefront reconstruction, which is available for wavefront measurement and phase imaging.

The specification and characterization of mid-spatial-frequency (MSF) ripples for the large-square-aperture optical elements, typically used in high-power laser systems, have received considerable critical attention. It is necessary to resort to a simple and robust way to characterize error surfaces for facilitating prediction of performance degradation and guiding the fabrication and tolerance settings. In this paper, we characterize residual periodic surface undulations called ripple errors for the large square aperture generated from modern subapertures and deterministic optical fabrication techniques through two methods, taking a step from qualitative judgment to quantitative analysis. The cross artifact reduction technology, instead of traditional windowed preprocessing, is introduced into power spectral density to suppress spectrum leakage while retaining the information about the part. An efficient algorithm to generate Legendre moments for two-dimensional Legendre polynomials is proposed to quantify ripple errors. This work contributes to understanding the optical degradation caused by MSF errors and associating the design and performance index with surface parametric description.