Freeform Optical Systems Research Articles

Design of off-axis reflective dual-channel zoom freeform optical systems

In this work, two off-axis reflective dual-channel zoom optical systems are conceived and designed. These two systems achieve good imaging quality and compact system volume by introducing freeform surfaces. Firstly, the system models of the off-axis reflective dual-channel zoom optical systems are introduced, and the first-order analysis is carried out. Then, a design method of an off-axis reflective dual-channel zoom freeform optical system is introduced, and two examples are designed using this method. In one example, the two channels have a separate primary mirror and share a secondary mirror and a third mirror. The system achieves a zoom ratio of 2 times. The two different channels of the other system have separate third mirror and share the primary mirror and the secondary mirror. The system achieves a zoom ratio of 4 times. The two systems have good imaging performance close to the diffraction limit in the visible light band. Finally, the proposed off-axis reflective dual-channel zoom freeform optical system is analyzed and discussed.

Design method of off-axis reflective freeform zoom optical systems

This paper presents a design method for off-axis reflective zoom optical systems. The method can be used to design off-axis zoom optical systems that include multiple mirrors. First, off-axis spherical systems for different zoom positions are solved to approximately meet the requirements for the optical power at different zoom positions, ensuring the convergence of subsequent calculations. Then, the system's optical power and aberrations are corrected by iterating the freeform surfaces point-by-point, thereby obtaining good starting points for further optimization. To illustrate the effectiveness of the method, three design examples are provided, including two off-axis three-mirror zoom optical systems and one off-axis four-mirror zoom optical system. Using the proposed method, good starting points for these systems are obtained. After optimization, the imaging quality of these three systems is close to diffraction limited.

Design Method of Freeform Surface Optical Systems with Low Coupling Position Error Sensitivity.

Freeform off-axis reflective systems are significantly more difficult to align and assemble owing to their asymmetric surface shapes and system structures. In this study, a freeform surface system design method with low coupling position error sensitivity (FCPESM) was proposed. First, we established a mathematical model of a reflective system when it was perturbed by coupling position errors and used the clustering-microelement method to establish the coupling error sensitivity evaluation function. The evaluation function was then applied to the design process of a freeform surface off-axis three-mirror optical system. The results showed that the FCPESM optical design method can significantly relax the assembly tolerance requirements of optical systems on the basis of ensuring image performance. In this study, the reflective system was perturbed by tilt and decenter simultaneously, and the disturbance mechanism of position errors on optical systems was further improved. Through this research, freeform surface systems with both image performance and error sensitivity can be obtained, which makes freeform off-axis reflective systems with better engineering realizability.

Automatic generation method for long-focal-length unobscured freeform optical systems with small volume

The existing design methods for long-focal-length unobscured freeform systems rarely consider the imaging quality requirements and volume constraints simultaneously, causing most of the final designs to not fulfill the requirement of light weight. This study proposes a method to automatically design a long-focal-length unobscured reflective system that satisfies volume constraints while maintaining high imaging quality. First, a method to adaptively set the structural parameter range is proposed, and multiple parameters for different systemic specifications can be effectively calculated within it. Subsequently, the systemic volume and area functions are constructed using the ray tracing method, where the tilt angles, distances between mirrors, and radii of curvature of the mirrors are chosen as the optimization parameters. Third, a comprehensive objective function is jointly established combining ray obscuration and convergence as performance evaluation factors. Then, the structural parameters of a long-focal-length unobscured system with small volume are easily obtained via the simulated annealing method. Finally, the improved W-W method is used to further enhance the imaging quality of the system, and an unobscured freeform reflective optical system with three mirrors is automatically generated. Experimental results demonstrate that our method can automatically calculate the parameter ranges to facilitate the search for structural parameters, and effectively design the long-focal-length unobscured freeform systems with small volume and high imaging quality.

Initial design with confocal conic mirrors for freeform optical imaging systems

Freeform surfaces that can offer high degrees of freedom for aberration correction have been widely used in various imaging applications. Initial design is particularly critical in the optical design of freeform imaging systems due to the significantly expanded solution space. Here, we present a method to find an initial point for the optical design of four-mirror freeform imaging systems. The method is computationally simple, easily accessible, and theoretically supported. The effectiveness of the method is demonstrated by designing a four-mirror confocal system without field-constant aberration and linear astigmatism. We also generalize the proposed method to four-mirror confocal systems with “double-pass surface.” The proposed method can yield a promising starting point for the design of freeform off-axis imaging systems.

Design Method for Freeform Off-Axis Three-Mirror Anastigmat Optical Systems with a Large Field of View and Low Error Sensitivity

A freeform off-axis three-mirror anastigmat (TMA) optical system with a large field of view (FOV) can obtain target image information with a larger spatial range and more spatial details, which is a development trend within the realm of space optics. The optical aberration increases exponentially with the FOV, resulting in a significant increase in error sensitivity for large-FOV optical systems. To address this issue, a method for designing optical systems with a large FOV and low error sensitivity is proposed. The FOV is gradually expanded from a small initial value in equal-length increments until it reaches the full FOV. At each step, the error sensitivity is recalculated and controlled to a lesser extent than in the previous step. In this design process, the freeform surface is used to correct the aberration and obtain low error sensitivity. An optical system with a focal length of 1000 mm and an F-number of 10 is used as an example, and the FOV is enlarged from 5° × 1° to 20° × 4°. The design results show that the modulation transfer function (MTF) of the optical system can reach 0.45@50 lp/mm, and the average wavefront aberration is 0.029λ. After four rounds of FOV expansion and error sensitivity optimization, the error sensitivity is reduced by 37.27% compared to the initial system, which verifies the correctness and practicality of the method.

Using deep learning to automatically generate design starting points for free-form imaging optical systems: retraction.

The referenced article [Appl. Opt.61, 6241 (2022)APOPAI0003-693510.1364/AO.460977] has been retracted by the authors.

Design of a Large Field of View and Low-Distortion Off-Axis Optical System Based on a Free-Form Surface

Free-form surfaces have good aberration correction capability and balance capability for nonrotationally symmetric imaging systems. In this study, we analyzed the quantitative relationship between X–Y polynomial combination and aberration for the efficient design of X–Y free-form optical systems. The purpose of this study was to provide an exhaustive design method for off-axis triple inverse optical systems with X–Y free-form surfaces. Finally, we designed a free-form off-axis optical system with a large field of view (FOV) and low distortion based on the off-axis triple inverse optical system without an intermediate image plane. The primary mirror (PM) of the system adopted an X–Y polynomial free-form surface to correct the aberration of different FOVs of the system and improve the image width and quality. The optical system had a focal length of 1000 mm, an F-value of 9.5, an FOV angle of 23° × 1°, a maximum distortion grid in the FOV less than or equal to −0.05%, and a full-field average wave aberration better than 0.055 λ (λ/18.2, λ = 632.8 nm). The analysis of the design results showed that the system had high-quality imaging and a compact structure. This design method can provide a technical reference for the study of such free-form off-axis systems.

Desensitization design method of a freeform optical system based on local curve control.

In this Letter, an error sensitivity evaluation function of freeform optical systems is proposed, and a desensitization design method is established. This method adopts the idea of micro-elements and, based on geometric optics theory, studies the relationship between the local curve of the freeform surface and the change of the wavefront error (ΔWE) when the optical system is disturbed by the position error, and realizes the desensitization design of the optical system. By simply changing the evaluation function, the method can be applied to the desensitization design of any optical system with any surface (spherical, aspheric, and freeform surface).

Desensitization Design Method for Freeform TMA Optical Systems Based on Initial Structure Screening

Achieving aberration correction can improve the imaging quality of an optical system, and reducing the error sensitivity of system can improve the realizability of the system. In order to obtain an off-axis three-mirror optical system with high image quality and low error sensitivity, a design method is proposed which obtains the initial structure of the three-mirror anastigmatic (TMA) optical system with low error sensitivity through a nondominated sorting genetic algorithm II (NSGA-II). Combining the comprehensive evaluation function of image quality and error sensitivity, this method iteratively selects multiple freeform surface types to determine the combination with the lowest error sensitivity and obtains the freeform TMA optical system with optimal overall performance. A freeform TMA optical system is designed by the method proposed in this paper, and the error sensitivity of the optical system is analyzed. The results show that the image quality of the freeform optical system is effectively improved and the error sensitivity is effectively reduced with the same error applied, which verifies the correctness and practicality of the method.

Design Method of Freeform Off-Axis Multi-Mirror Optical Systems

A data point calculation method that does not require the use of Fermat′s principle and a simple and general design method of starting points of freeform off-axis multi-mirror optical systems are proposed in this paper, which aim to promote the realization of high-performance reflective systems containing freeform surfaces. Taking a planar system and the required parameters as the input, a good starting point for a freeform off-axis multi-mirror system can be automatically obtained using the proposed method. The design of a freeform off-axis five-mirror system with a low F-number is taken as an example to show the effectiveness of the proposed method. The method can also be used for the design of freeform reflective systems with other numbers of mirrors.

Using deep learning to automatically generate design starting points for free-form imaging optical systems.

In this paper, we propose a method to automatically generate design starting points for free-form three-mirror imaging systems with different folding configurations using deep neural networks. For a given range of system parameters, a large number of datasets are automatically generated using the double seed extended curve algorithm and coded optimization. Deep neural networks are then trained using a supervised learning approach and can be used to generate good design starting points directly. The feasibility of the method is verified by designing a free-form three-mirror system with three different folding configurations. This method can significantly reduce the design time and effort for free-form imaging systems, and can be extended to complex optical systems with more optical surfaces.

Analysis of polarization characteristics of freeform surface optical system

Freeform surfaces are widely used in off-axis optical systems with large aperture, large field of view, and long focal length. The polarization effect caused by the non-rotationally symmetrical shape has an impact on the system’s polarization imaging quality and measurement accuracy. Based on Jones’ notation, this paper proposes a polarization aberration analysis method for fringed Zernike polynomial freeform optical systems and constructs a full-field polarisation aberration analysis model of non-rotationally symmetric freeform reflective optical systems. The light propagation vector k is added on the basis of the two-dimensional ray tracing algorithm. By tracing the full-field polarized light of the off-axis optical system in the field of view, the Jones pupil diagram is obtained. The phase aberration, diattenuation and retardance are separated by Pauli decomposition and SVD decomposition. The off-axis freeform surface optical system is designed. The analysis results show that the phase aberration of the off-axis freeform surface optical system is directly related to the surface shape of the freeform surface. The changes of the freeform surface to the diattenuation and retardance are both 56% of the diattenuation and retardance of the sistem. For deep-space telescopes and lithography systems, it is of great significance for improving system accuracy to master this change.

Unified mathematical framework for a class of fundamental freeform optical systems.

We present a unified mathematical framework for sixteen fundamental optical systems. The systems have a parallel or point source and a parallel, point, near-field or far-field target. These choices give eight configurations if we use reflectors only and take the minimum number of freeform surfaces required. Similarly, we get eight lens systems if we only use lens surfaces. The mathematical model for each system is based on Hamilton's characteristic functions and conservation of luminous flux. Some configurations lead to standard or generalized Monge-Ampère equations. The remaining systems are described by so-called generated Jacobian equations.

Generating starting points for designing freeform imaging optical systems based on deep learning.

Deep learning is an important aspect of artificial intelligence and has been applied successfully in many optics-related fields. This paper proposes a generalized framework for generation of starting points for freeform imaging optical design based on deep learning. Compared with our previous work, this framework can be used for highly nonrotationally symmetric freeform refractive, reflective, and catadioptric systems. The system parameters can be advanced and the ranges of these system parameters can be wide. Using a special system evolution method and a K-nearest neighbor method, a full dataset consisting of the primary and secondary parts can be generated automatically. The deep neural network can then be trained in a supervised manner and can be used to generate good starting points directly. The convenience and feasibility of the proposed framework are demonstrated by designing a freeform off-axis three-mirror imaging system, a freeform off-axis four-mirror afocal telescope, and a freeform prism for an augmented reality near-eye display. The design framework reduces the designer's time and effort significantly and their dependence on advanced design skills. The framework can also be integrated into optical design software and cloud servers for the convenience of more designers.

Design of freeform surface off-axis reflective optical systems based on quantum genetic algorithm

Design of freeform surface off-axis reflective optical systems based on quantum genetic algorithm

"First time right" - calculating imaging systems from scratch -INVITED

Freeform optics can be used to greatly extend the functionalities, improve performance, and reduce the volume and weight of optical systems. Today, the design of imaging systems largely relies on efficient ray tracing and optimization algorithms. Such a "step-and-repeat" approach to optical design typically requires considerable experience, intuition, and eventually "trial-and-error" guesswork. This time-consuming process applies especially to freeform optical systems. In this work, we present a deterministic direct optical design method for freeform imaging systems based on differential equations derived from Fermat’s principle and solved using power series. The method allows calculating all optical surface coefficients that ensure minimal image blurring for each individual order of aberrations. We demonstrate the systematic, deterministic, scalable, and holistic character of our method with several catoptric and catadioptric design examples.

Kinematic mirror mount design for ultra-precision manufacturing, metrology, and system level integration for high performance visible spectrum imaging systems

High-performance freeform optical systems, designed for broad spectral imaging from the visible to the far infrared, place new demands on optical design, precision manufacturing, and precision metrology. To meet the tolerances on figure, roughness, and relative positioning in such systems requires the ability to perform metrology and manufacturing corrections on freeform optics in a continuous feedback loop. This feedback loop requires a common interface for machining and manufacturing platforms. This paper describes the design, analysis, and testing of such an interface suitable for use with single point diamond turning and deterministic micro-grinding. The interface utilizes a torsionally preloaded, robust, kinematic mount capable of supporting manufacturing process loads while maintaining the position repeatability in five degrees of freedom required for the measurement and correction of optical figure. Results from a prototype system demonstrate absolute in-plane position uncertainty less than 200nm and 50nm, respectively, and axial position uncertainty is 40nm absolute and 10nm relative. The absolute and relative angular positioning uncertainties less than 1µrad and 0.25µrad respectively. The results exceed the requirements for many optical systems. The mount is also suitable for use in opto-mechanical assembly, so that the same platform can be used for manufacturing, metrology, final assembly, testing, and service.

Design method for assembly-insensitive freeform reflective optical systems.

The sensitivity of an optical system to assembly errors can greatly affect the actual image quality. The system design must be changed if its tolerance for assembly errors is too tight. In this paper, we present an automated design method for initial systems of freeform reflective optical systems that are insensitive to assembly errors. By this method, an assembly-insensitive initial system comprised of surfaces with different types (sphere, aspheric, freeform) can be obtained directly without human interaction. To illustrate the design process, an assembly-insensitive off-axis optical system that has two freeform surfaces and one spherical surface is designed, which shows the effectiveness of the proposed method.

Design method for freeform optical systems containing diffraction gratings.

A design method for freeform optical systems containing diffraction gratings is developed based on Fermat's principle and Ludwig's grating ray-tracing equation. The proposed method can calculate fine starting-points for diffraction-grating-based imaging spectrometers with high performance and novel geometries. It can also be extended to design optical systems that contain other dispersive elements, such as prisms and diffractive optics. Two freeform imaging spectrometers are designed by this method to meet the diffraction-limited specifications.