Step/stare imaging with focal plane arrays (FPAs) has become the main approach to achieve wide area coverage and high resolution imaging for long range targets. A fast steering mirror (FSM) is usually utilized to provide back-scanned motion to compensate for the image motion. However, the traditional optical design can just hold one field point relatively stable, typically the central or on-axis field point, on the FPA during back-scanning; all other field points may wander during the exposure due to imaging distortion characteristics of the optical system, which reduces the signal to noise ratio (SNR) of the target. Aiming toward this problem, this paper proposes a non-rotationally symmetric field mapping method for the back-scanned step/stare imaging system, which can make all field points stable on the FPA during back-scanning. First of all, the mathematical model of non-rotationally symmetric field mapping between object space and image space is established. Then, a back-scanned step/stare imaging system based on the model is designed, in which this non-rotationally symmetric mapping can be implemented with an afocal telescope including freeform lenses. Freeform lenses can produce an anamorphic aberration to adjust distortion characteristics of the optical system to control image wander on an FPA. Furthermore, the simulations verify the effectiveness of the method.

Optical zoom systems have found widespread applications in fields such as security and mobile phone lenses. The theory of zoom lens design has also developed from the first order to the third order. To address the demands for large aperture, wide field, and aspheric surfaces, a zoom system design method based on high-order structural aberration coefficients is introduced. Initially, the structural aberration forms, encompassing intrinsic aberrations, extrinsic aberrations, and aspheric aberrations, were derived using existing high-order aberration theory. The fifth-order aberration contributions of the system can be directly determined with only a first-order layout and predetermined materials. Based on the above derivation, a zoom system design method is proposed, which utilizes the lens model surfaces and aspheric surfaces with zero optical power to formulate a merit function and optimize the initial structure to meet first-order, third-order, and fifth-order performance simultaneously. This method was validated through the implementation of both refractive and reflective lenses.

The deformation of the image plane due to gravity, clamping forces, and surface shape errors can significantly impact the exposure accuracy and imaging quality of the doubly telecentric projection optical system. To address the issues of resolution and image quality degradation resulting from non-conjugate image planes, this paper proposes a high-precision method for compensating image plane deformation using a dual-prism approach, establishes an analytical compensation model, and the theoretical derivation and quantification of the effects of compensation devices on image plane defocus, tilt, and aberration are provided. Compared to traditional simulation methods, the proposed approach offers a more predictable and precise compensation framework. The optimized design of the dual-prism compensation device has been validated through simulations, demonstrating the ability to control image plane deformation within 3.011 µm, which is smaller than the system’s depth of focus. The results indicate that this method significantly enhances the imaging accuracy of doubly telecentric projection optical systems and presents a novel theoretical tool for optimizing the design of optical compensation devices, thereby advancing the development of high-precision optical compensation technologies.

A full-field astigmatism characterization and optimization method based on Legendre polynomial expansion is proposed to address the difficulty of directly constraining linear astigmatism in off-axis reflective optical systems. In this method, the full-field astigmatism distribution is treated as a function of field coordinates and decomposed using orthogonal Legendre polynomials. The first-order expansion coefficients are used to characterize the linear astigmatism component, thereby establishing a quantitative metric for linear astigmatism evaluation. By integrating the ZOS-API with a user-defined operand (UDOC) in ZEMAX, direct constraint and optimization of linear astigmatism are achieved. An off-axis three-mirror system is used as a design example to validate the proposed method. The results show that the linear astigmatism coefficient is reduced from 0.024967 to 0.008183, a reduction of 67.22%, while both the spot diagrams and the modulation transfer function (MTF) are significantly improved. The proposed method effectively suppresses linear astigmatism in off-axis reflective optical systems and provides what we believe to be a new approach for their optimization design.