Piston errors between isolated regions remain a major obstacle in segmented phase unwrapping. We propose a robust phase unwrapping method based on phase gradient-domain reconstruction and the least-squares algorithm. The approach reconstructs and bridges segmented phase islands in the gradient domain, providing a continuous gradient field for subsequent unwrapping. To ensure robustness under varying noise conditions, an adaptive dual-domain filtering strategy is introduced. A Noise Index (NI) is defined to quantify the density of gradient outliers, enabling dynamic switching between gradient-domain filtering and a cascaded complex-domain and gradient-domain filtering scheme. In addition, a residual iterative process is employed to correct local phase errors. Numerical simulations and experimental validations confirm that the proposed method successfully eliminates piston errors among phase islands, maintains accurate global phase reconstruction under various obscuration and noise conditions, and achieves high computational efficiency, thereby providing a reliable and practical solution for optical interferometric applications.

A multi-aberration evaluation function is proposed based on the confocal conic mirrors, aiming to search for the optimal starting-point of unobscured four-mirror reflective imagers. Typical aberrations in the off-axis confocal conic system are quantitatively calculated, and the multi-aberration evaluation function is subsequently established to determine the optimal initial structure. Off-axis aberrations such as astigmatism, coma, and field curvature in the initial structure are simultaneously constrained through the proposed evaluation function. An off-axis four-mirror scanning-type space camera is presented as example, where a multi-aberration evaluation function is formulated based on design specifications. Particle swarm optimization algorithm is applied to find the optimal solution, resulting in a confocal conic configuration with excellent on- and off-axis imaging performance. Then, freeform surfaces are further introduced to optimize and expand field of view (FOV). An off-axis four-mirror space camera is realized with an entrance pupil diameter (EPD) of 200 mm, an F-number of 4, a FOV of 4° × 24°, and working band covering the visible and near-infrared (NIR) wavelengths, which also achieves high-quality imaging.

In this paper, we propose a design method for an extreme ultraviolet lithography (EUVL) objective system based on off-axis conic surfaces and a visualized full-field aberration correction derived from nodal aberration theory. We divide the entire system into three groups with different combinations of off-axis conic surfaces. A starting point with no ray obstruction and zero image telecentricity is established by ideal object-image transformation with off-axis conic surfaces for each group. By analyzing the relationships between specific freeform terms and primary aberrations, targeted terms are utilized to efficiently correct aberrations. Then, an EUVL objective system with a NA of 0.33 is designed. The maximum RMS wavefront error is 0.015 λ, and the average RMS wavefront error is smaller than 0.01 λ. The EUVL objective system can maintain performance with relaxed tolerance requirements, with 97% of the cases exhibiting RMS wavefront error below 0.03 λ. This study provides an EUVL objective system that achieves both high optical performance and good manufacturability, providing a valuable reference for the design and optimization of multi-mirror optical systems.

The aberration of the telescope system itself can easily lead to the change of its optical ellipticity, which interferes with the detection of dark matter. To ensure the accuracy of dark matter detection,the ellipticity of the telescope system must be precisely controlled. In this paper,an optical design method for telescope with freeform surfaces incorporating optical ellipticity criterion is proposed. It addresses the challenge of traditional optical design methods in which optical design software is unable to directly take the ellipticity in the merit function. Implementing the numerical interaction between optical design software Zemax and numerical calculation software Matlab through MZDDE. Extract point spread function data from Zemax,calculate the ellipticity value using Matlab algorithm, and then import it into the merit function editor of Zemax to assign weights for optimization. In this way,the astronomical ellipticity is included throughout the optical design procedure. A complete evaluation function system integrating wavefront aberration and ellipticity has been constructed. Based on the relationship between ellipticity and non-rotationally symmetric aberrations such as coma and astigmatism,we put forward the principle of preferentially correcting the aberration components which exhibit stronger correlation with ellipticity. With the help of the full-field aberration map in the optical design software,we analyze the correlation between the aberration nodal distributions and ellipticity node distributions. And the specific freeform surface items to be modified and the surfaces of the freeform items to be added in each step are determined based on the aberration theory. The aberration components with strong ellipticity correlation are taken as the priority correction parameters for iteration,which contributes the design idea of incorporating the ellipticity criterion into the main off-axis aberration correction. Based on the evolution law of aberration nodes and ellipticity nodes in the optimization process of the off-axis three-mirror system, an optimization strategy for the Zernike term of the freeform surface type is established. Accordingly,an off-axis three-mirror freeform surface astronomical telescope is designed,with an effective focal length of 600 mm, an aperture of 200 mm,and a field of view of 4 degrees x4 degrees. Through the joint optimization of wave aberration and ellipticity, the imaging quality and optical ellipticity are synchronously and effectively controlled. The wave aberration is close to the diffraction limit,with the maximum ellipticity value of 0.030 3,and the average value of 0.015 6. It meets the requirements of the dark matter detection with the maximum ellipticity value of less than 0.15 and the average value of less than 0.05. The traditional optimization design method adopts a gradual upgrade of surface shape,gradually adding freeform terms in order from low order to high order, and continuously maintaining the variability of system structural variables during the addition process. This method lacks optimization targeting for the current aberration of the system,and blindly using freeform terms on multiple surfaces will lead to aberration correction degradation and unnecessary freeform surface deviation. Compared with the traditional aberration correction optimization method from low-order terms to high-order terms, the application of the proposed method adopts relatively small freeform surface deviation. By adjusting the aberration nodes,the imaging quality and ellipticity performance of the designed freeform surface telescope are controlled synchronously. The maximum value of ellipticity is further compressed,and the ellipticity distribution is more evenly distributed. The design freedom of the freeform surface is fully leveraged.

The projection model regulates the mapping relationship between the object and image for the imaging system, where they are related by the focal length. The distortion is defined as the departure from the similarity between the object and image, or the departure from the targeted projection model. Thus, the focal length and distortion represent the actual relationship of the optical system. The focal length is the most important and basic parameter of an optical system, which is theoretically defined utilizing the" minor aperture method". According to the regulation of" minor aperture method", the ray close and parallel to the optical axis is traced, and then its angle of convergence after passing through the optical system is recorded for focal length calculation. This regulation is easy to execute during the optical design process but hard to execute for the measurement of the built performance of the optical system. The" minor image height method"is the frequently adopted regulation for focal length measurement, in which ray with minor field of view is traced, and the corresponding image height is recorded for focal length calculation. The" minor image height method" is easy to execute for both design and measurement, and aligns well with the definition of projection. Therefore, if the definition of the focal length is developed from the on axis field of view to the off-axis field of views, then the local focal length which is a field dependent parameter is involuntary generated. And the" minor image height method"is adopted for local focal length definition, in which the image height increment for a minor angle increment is regulated for each field of view. Moreover, the distortion is represented by the variable local focal length for different field of views. And then, the local focal length can be adopted in the process of optical system design for distortion control, for its calculation in the design coincides well with the measurement in the experiment, which is the outstanding priority according to its regulation. A fisheye lens with field of view of 160 degrees, F-number of 4.2, on focal length of 1.61 mm is firstly designed utilizing the local focal lengths for 11 sampled field of views as the target. It is composed of 6 pieces of lenses,in which one aspherical surface is set at a plastic lens,and the equidistant projection is fulfilled. Inspired by the foveated fisheye, the theory of high resolution with rectilinear projection in the central field of view is proposed,and the aforementioned fisheye lens is successfully transformed to the configuration with equidistant projection for the 50% central field of views,adopting the local focal length as the optimization target. Other than objects in the infinity,there are some cases in which the objects is imaged from finite distance,and the object is sometimes even curved. The wide angle lenses with field of view of 120 degrees,F-number of 2.8,on focal length of 1mm are then designed still utilizing the local focal length as the optimization target. The curved objects are 1 000 mm away from the lenses,with the radius of curvature of 800,1 000,1 200,- 20 000 mm and infinity,corresponding to convex spherical objects,concave spherical object and plane object respectively. The target local focal length is derived according to the imaging purpose for equal resolution on the curved objects. Diffraction limited imaging quality is achieved,and local focal length relative error is constrained to less than 0.6% with 11 sampled field of views,and the distortion is then less than 0.21%. The generation of local focal length provide a novel parameter for optical system design with complex projections,leveraging its priority of design and measurement coincidence.

Large-aperture elements would induce unnegligible systematic errors due to material inhomogeneity, manufacturing or gravity, that are difficult to correct in an extreme large aperture flat interferometer and result in reference wavefront distortion. We propose an active-compensation method for systematic errors by employing a deformable mirror into the interferometer to modulate reference wavefront. A mapping relationship between sag of the deformable mirror and reference wavefront error is derived by theory of matrix optics, and two interferometer optical paths are designed for whether the deformable mirror is located at the pupil or not. The algorithm for calculating and controlling the sag of a deformable mirror can eliminate the need for the deformable mirror to be positioned at the pupil in order to achieve controllable modulation of the wavefront. This algorithm has been validated through the intentional introduction of systematic errors into the 1000 mm aperture flat interferometer for effective compensation. Moreover, the optimization algorithm in Ansys Zemax is utilized to calculate the optimal solution for surface shape of the deformable mirror, treating it as a nominal value. The algorithm error is on the order of 10-6 - 6 mm, falling within the acceptable tolerance range for the deformable mirror's surface shape. (c) 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

提出了一种基于表面双向反射分布函数(BRDF)离散测量值直接追迹散射光线的方法,以各向同性表面为例,先对随散射角离散变化的表面BRDF离散测量数据组做空间坐标转换,由散射角半球空间转换到方向余弦空间;再通过等间距赋值插等值方式得到方向余弦空间内分布的BRDF数据;然后,利用舍选抽样法不受限于累积分布函数(CDF)求解过程的优点,设计新的散射概率模型,以方向余弦空间内BRDF数值比表示离散光线的概率分布,设定检验条件筛选出散射光线的空间坐标,实现散射光线追迹.为验证本文方法的准确性与适用性,设置相同的入射角、追迹光线数量等仿真参数,编制了本文光线追迹方法的仿真程序,对不同光机元器件建模仿真,对比商用LightTools软件的仿真结果,计算二者的通用质量指数UQI作为比对评价指标.结果表明,基于舍选抽样BRDF离散数值的散射光线追迹方法,运算结果数据准确,与商用LightTools软件的仿真结果相比,UQI值均在0.998以上,且波动范围小,本方法具有良好地适用性.

针对长焦镜头小型化、轻量化的设计需求,基于离轴三反结构探索紧凑型长焦光学系统设计方案.利用圆锥曲面焦点共轭的光学特性,通过相邻反射面焦点重合的方式构造可对轴上点完善成像的初始结构,并在此基础上,通过追迹特征光线建立针对离轴三反结构的光线无遮拦判定条件,从小视场出发制定视场扩展与自由曲面面形的优化设计策略.以长焦手机镜头为例,设计了一款F数为 5、等效焦距达 196 mm、视场范围±3.8°的离轴三反式紧凑型长焦镜头.其尺寸为 26 mm×24 mm×10 mm,仅由 3 个反射面构成,MTF优于 0.2@114 lp/mm,畸变低于 0.5%,相对照度高于 95%,像面无暗角.该系统无遮拦,无色差,且相较于常规潜望式长焦镜头,在小型化、轻量化方面具备明显优势,为紧凑型长焦镜头设计提供了新的解决思路.

The effect of stray light on system signals in space platform optical machine systems cannot be ignored. The components of an optical machine system are essential sources of stray light,and their surface light scattering characteristics directly affect the distribution of stray light in the system. Ray tracing and stray light analysis based on the surface scattering characteristics of system components is an important research content in optical design and simulation. The Bidirectional Reflectance Distribution Function (BRDF) is commonly used to accurately characterize the scattering property of surface about optical machine structures in stray light analysis. The Monte Carlo method (MCM) is the primary method of scattered ray tracing in optical machine systems. It is commonly used in scientific research experiments and stray light analysis software. The core of Monte Carlo scattered ray tracing lies in the reasonable selection of the bidirectional scattering distribution function model and the correct construction of the probability model. In practical applications,due to the particularity of the micro- morphology and texture distribution of the surface of the system components,the surface scattering characteristics show complex and diversified features,which are accompanied by the innovation of machining technology and the appearance of new material surfaces. The number of BRDF models in the commercial software is small,and the application scenarios are limited,so the real-time measured discrete data of BRDF on the optical surface are needed. In some instances,the reconstruction of the BRDF function model and the numerical analysis process is complicated. Moreover, there are some problems,such as fitting errors and limitations of application conditions of the model. The inverse transformation method is often used to solve the probability model of ray tracing. Although the inverse transformation method can efficiently generate random samples that obey the specified distribution,the BRDF of most scattering models is modulated by ray coordinate variables. In the design process of complex probabilistic models based on the reconstructed BRDF model for complex PDF,there are problems such as Cumulative Distribution Functions (CDF) without analytical solutions. To simplify the modeling process of surface scattering and enhance the applicability of the scattered ray tracing method,this paper proposes a way to directly trace the scattered rays based on the surface discrete BRDF measurements. Under the condition that the surface is isotropic, the procedures are shown as follows:Firstly,the spatial coordinate transformation of the discrete measurement data of surface BRDF, which discontinuously varies versus the scattering angle,is converted from the scattering angle hemisphere space to the direction cosine space;Then,the BRDF data distributed in the direction cosine space is obtained by equal interval assignment interpolation equivalent method. Then,a new scattering probability model is designed using the advantage of the rejection sampling method unlimited to the CDF-solving process. The BRDF numerical ratio in the cosine space direction represents the probability distribution of discrete rays. The space coordinates of scattered rays are screened out by setting the test conditions to realize the scattering ray tracing. To verify the accuracy and applicability of the proposed method,the same incident angle,the number of tracing rays,and other parameters in the simulation were set. The simulation program is prepared in Matlab according to the proposed method,and the simulation results in Matlab are compared with those in LightTools. Wherein the BRDF model and parameters of Harvey,ABg,and multiple scattering surfaces characterizing the surface scattering characteristics of various optical and mechanical components were set in LightTools. Different visual and mechanical parts are modeled and simulated. BRDF data in the section where incident light and mirror-reflected light are located were obtained using the analytical formula of the BRDF model and its parameters. The above data were taken as the discrete measured data of BRDF in the simulation program of the proposed method in this paper. The general quality index UQI is the comparison evaluation index of the simulation results between commercial LightTools software and the proposed method. The results show that the scattering energy distribution obtained by the proposed ray tracing method is highly consistent with the LightTools simulation. The different optical and mechanical components are modeled and simulated,the UQI values are all above 0.998,and the fluctuation range is small. The calculation results of the ray tracing method in this paper are accurate and have good applicability.

Objective The bidirectional reflectance distribution function（BRDF） is commonly used to accurately characterize the scattering property of the surface of opto-mechanical structures in stray light analysis. Software for stray light analysis based on the Monte Carlo method（MCM） can construct probability models for scattered ray tracing on the basis of BRDF models. However, the types of BRDF models allowing surface property setting in the software are limited. Although the inverse transform technique can be used to construct probability models, the BRDF of most scattering models is modulated by multiple variables with complex forms, and the analytical solution of the cumulative distribution function is absent.Consequently, this method becomes invalid, and it also limits the application of BRDF models to some extent. As scattered ray tracing is limited by the difficulty in obtaining an analytical solution, a probability model for scattered ray tracing is constructed by the rejection sampling method. The proposed method circumvents the integral solution process by setting test conditions and then screens out the effective samples to achieve scattered ray tracing, whereby it gains the advantage of wide applicability.Methods The rejection sampling method is applied to construct the probability model for MCM-based scattered ray tracing in the present study. Specifically, the BRDF describing the scattering model is converted into a probability density function, and random sampling based on uniform distribution is performed. Then, a reasonable squeezing function is used,and the effective samples are screened out under the test conditions. Finally, the effective samples are taken as the direction of the scattered ray, and scattered ray tracing based on the BRDF model is thus achieved. For the shift-invariant BRDF model, a symmetric sampling scheme is further proposed to sample the half-space after determining the sampling interval. The angular coordinates are converted into direction cosines, and the effective samples are selected by the rejection sampling method. The effective samples in the half-space are then used to obtain those in the full-space by applying mirror symmetry about the axis of symmetry. Simulation programs are prepared in Matlab according to the proposed method, and the simulation results in Matlab are compared with those in LightTools from the aspects of repeatability and accuracy. The same simulation parameters of surface property, incidence angle, and number of traced rays are set to simulate the BRDF models commonly used in engineering for scattered ray tracing. Since scattered energy distribution is the direct reflection of the simulated tracing results, the universal quality index（UQI） is used to quantify the different energy distributions on the analyzed surface at different times of simulation. The repeatability and accuracy of the simulation are described by the UQI.Results and Discussions The ABg model of the oxidatively blackened mechanical component for scattered ray tracing is simulated, and the obtained UQI values of the simulation results based on the proposed method and those of the results in LightTools are all higher than 0. 9985（Fig. 5）. The simulation results based on the rejection sampling method are comparable to those in LightTools in terms of repeatability and accuracy. The ABg model is used to model the two scattering surfaces of shiny aluminum alloy and standard lens glass for scattered ray tracing, and the Harvey model is used to model an optical surface for the same purpose. The UQI values of the simulation results based on the proposed method and those of the results in LightTools are all higher than 0. 9994（Fig. 6）. The scattered energy distribution based on the simulation programs is highly consistent with the result delivered by LightTools, which verifies the rationality and validity of the proposed method. The Phong model and the K-correlation model that are not included in LightTools are also simulated for scattered ray tracing, the UQI values obtained which are used to describe the repeatability of the simulation are all higher than 0. 9970（Fig. 7）. This result further verifies the universality of the proposed method.Conclusions To address the limited applicability of the existing scattered ray tracing methods based on probability models, this study proposes the probability model by the rejection sampling method. Specifically, the BRDF is converted into the probability density function, and the probability model is thereby constructed for random sampling. Then, the effective samples that meet test conditions are used as the direction of the scattered ray. Finally, the spatially continuous distribution of scattered energy is converted into the probability distribution of a discrete ray, and scattered ray tracing is thus achieved. For the shift-invariant BRDF model, a symmetric sampling method is further proposed to enhance the sampling rate by halving the sampling area and then mirroring it. In the case of BRDF models with different materials, ray tracing programs are constructed to achieve scattered ray tracing in Matlab. To verify the simulation results based on the proposed method and those delivered by LightTools in terms of repeatability and accuracy, this study sets the same simulation parameters in Matlab and LightTools. The simulation results based on the rejection sampling method in the present study are almost the same as those in LightTools, and scattered ray tracing based on BRDF models that are not included in LightTools is also achieved.

自由曲面设计自由度多、面型表征能力强等优势使成像光学系统突破了传统面型表征和系统结构的限制,在进一步提高成像质量的同时可以实现大视场、大孔径、小型化、轻量化等设计目标.良好的初始结构可以充分发挥自由曲面对像差的校正能力,提高系统设计效率.与共轴光学系统相比,自由曲面成像光学系统设计存在可参考样例少、像差理论尚不完善等问题,其初始结构的构造与求解仍然是先进光学设计领域的前沿热点问题之一.结合课题组多年的研究心得,探讨了现有的自由曲面成像光学系统初始结构设计方法,依据自由曲面构造原理将其分为同轴系统离轴化法、直接设计法、视场孔径扩展法和分段拼接融合设计方法,并分别介绍其设计原理和思路.最后对自由曲面成像光学系统初始结构设计中亟待解决的问题进行了分析总结.

Objective Given the increased prevalence of digestive diseases in recent years, the endoscope has been widely used for abdominal diagnoses, including those related to the stomach and intestines. Researchers are working to develop more effective and less invasive techniques for patients to benefit from endoscopy. A large field-of-view (FOV) and high resolution will reduce examination time and improve evaluation accuracy. Moreover, a compact endoscope structure is critical for minimising patient discomfort. In conventional wide-field camera lenses, a large panoramic scene needs to be focused onto an image sensor plane, to reduce the field curvature caused by the strong mismatch between the focal planes. The concentric lens consists of four refractive surfaces, and the centres of curvature of each refractive surface coincide at one point. Therefore, off-axis aberration does not exist. Only spherical and axial chromatic aberrations need to be corrected. Therefore, this structure can be applied to optical systems with miniaturisation, high image quality, and a large FOV; however, the image surface formed by the concentric system is curved. In this study, we correct the curvature of the field in the concentric sphere system by designing an annularly stitched aspheric surface to achieve flat-field imaging with a large FOV. Methods In this study, an optical system with full FOV is regarded as a combination of multiple single- or small-FOV sub-system units, then the sub-field units are solved separately, and the formation of a complete complex surface is optimised to realize the construction of a complete optical system. First, the initial concentric structure is solved with well-corrected spherical and chromatic aberration. Then, based on the FOV, an annularly stitched surface is constructed by dividing the surface into rings and calculating the initial structure parameters of each zone based on the flat-field conditions. The Q-type aspheric surface characterises different annuli to ensure imaging quality while obtaining good splicing results. Simultaneously, the continuity constraint condition of the annularly stitched aspheric surface is derived. Finally, a complete surface is optimized to realize the construction of a complete electronic endoscope. Results and Discussions The deviation of normal and sag between adjacent rings has been reduced to less than one-tenth of the test wavelength (typically test wavelength 632. 8 nm) through optimisation. These rings are then fused after the optimisation. The system diagram is shown in Fig. 10. Compared with the modulation transfer function (MTF) curve of the initial structure in Fig. 3, the MTF of the system after optimisation is more than 0.3 at the spatial frequency of 72 lp/mm (Fig. 11). Thus, the curvature of the full FOV is reduced from 0. 5 mm in the initial structure to within 0. 1 mm [Fig. 12 (a)] , the imaging requirements of electronic endoscope objectives are met. To validate the design results' manufacturability, a Monte Carlo simulation analysis was performed 200 times within the tolerance range (Fig. 14) . Consequently, in the full FOV, considering mass production and assembly, a probability that an optical system with an average diffraction MTF greater than 0. 3 at 72 lp/mm frequency can be obtained is more than 90%. Conclusions Based on the concentric structure, multiple rings are superimposed on the last surface to obtain different optical powers to generate the initial surface shape of the splicing surface of the rings. The surface shapes of the multiple rings are fused to generate a complete continuous surface after the continuous conditions are optimized. In the design, the Q-type aspheric surface is used to characterise different ring zones to ensure imaging quality. An electronic endoscope objective lens operating in the visible band is designed using this method. The objective comprises only four refractive surfaces, with a total system length of 2. 81 mm and FOV of 90 degrees. The field curvature of the system is less than 0.1 mm, the distortion is within 20%, the MTF reaches 0.3 at 72 lp/mm, and the relative illuminance of the full FOV is greater than 0. 5, which meets the imaging requirements of electronic endoscope objectives. The system uses the imaging advantages of the concentric objective lens with a large FOV and small volume. The annularly stitched aspheric surface is used to correct the curvature of the field caused by the spherical lens. Compared with the traditional structure, our electronic endoscope objective lens is more compact and readily manufacturable.

Y We present a compact dual-view endoscope imaging system with a field of view (FOV) of +/- 80 degrees and F/# of 3.4. The endoscope consists of two optical configurations for increasing FOV within the volume constraint. The front view configuration is a fisheye lens with a FOV of +/- 55 degrees, and the side view configuration is a panoramic annular lens that covers the remaining FOV. The two configurations are combined by a hybrid lens that consists of center refractive portion and side catadioptric portion. Both the front and rear surfaces of the hybrid lens are aspherized with the use of annularly stitched Q-type aspheres. Thus, a compact endoscope is successfully implemented with fewer lenses, with a total length of 11.5 mm and a maximum diameter of 5.5 mm. The modulation transfer function at 167 lp/mm is above 0.4 over the entire FOV. The relative illumination is more than 0.65 and the optical distortion is within 10%. Moreover, the near telecentric condition is fulfilled and supports constant magnification focusing.

In this paper, a direct design method for an off-axis two-mirror telecentric scanning system with a linear field of view (FOV) is proposed. A single freeform mirror structure is firstly considered, in which the aberration free geometry of the off-axis parabolic (OAP) surface is leveraged to provide the focusing function and build surface contour of the sub-region on the mirror for each FOV. Multiple OAP surfaces for construction of the freeform mirror are located at an OAP base to satisfy the telecentric condition. The imaging distortion of this single freeform mirror structure is analyzed and found unavoidable due to the unsymmetrical geometry of the OAP base. A freeform reflective corrector is supplemented, and it is constructed from multiple plane surfaces located at a curved base to fulfill the f-theta scanning geometry. Thus, a two-mirror structure composed of one freeform primary mirror and one freeform reflective corrector is established. Each plane-OAP surfaces pair corresponds to a specific FOV. These multiple OAP surfaces and multiple plane surfaces are then expanded and mixed respectively, to construct the freeform primary mirror and freeform reflective corrector. An f-theta two-mirror freeform scanning system with ±10.4° linear FOV is designed using the proposed construction method. The design result is diffraction-limited, and a scanning error less than 5 μm and telecentricity angle less than 0.2° are achieved.

We substitute a freeform surface consisting of the off-axis parabolic (OAP) surfaces for the collimating mirror and each sub-region of the focusing mirror, to achieve an aberration free spectrometer.

The classic Czerny-Turner spectrometer consists of a plane grating and two spherical mirrors. The optical path geometry adopted for incident and grating dispersed light is off-axis reflection, so the spherical collimating and focusing mirrors introduce coma and astigmatism. The conventional configuration is asymmetrical for coma automatic compensation, but suffers from astigmatism. We substitute the off-axis parabolic (OAP) surfaces for spherical surfaces of the collimating mirror and each sub-region of the focusing mirror, to achieve an aberration free configuration. The multiple OAP surfaces are then expanded and mixed, to construct a freeform surface integrating the collimating and focusing mirrors into a single element. Results show that a 0.1 nm spectral resolution is achieved over a bandwidth of 400 nm centered at 800 nm, in the designed spectrometer comprised of a plane grating and one freeform mirror. The construction method is advantageous to integrated optic design, and the resulting freeform mirror spectrometer is compact, and simplifies manufacture and alignment.

We present a compact dual-view endoscope objective lens with a field of view (FOV) of +/- 80 degrees and F/# of 3.4. The endoscope consists of two optical configurations for increasing FOV within the volume constraint. The front view configuration is a fisheye lens with a FOV of +/- 55 degrees, and the side view configuration is a panoramic annular lens that covers the remaining FOV. The two configurations are combined by a hybrid lens that consists of center refractive portion and side catadioptric portion. Both the front and rear surfaces of the hybrid lens are aspherized with the use of annularly stitched Q-type aspheres. Thus, a compact endoscope is successfully implemented with fewer lenses, with a total length of 11.5 mm and a maximum diameter of 5.5 mm. The modulation transfer function at 167 lp/mm is above 0.4 over the entire FOV. The relative illumination is more than 0.65 and the optical distortion is within 10%. Moreover, the near telecentric condition is fulfilled and supports constant magnification focusing.