Off-axis Three-mirror Imaging System Research Articles

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.

Freeform optical surface design in an off-axis reflective imaging system by a double seed curve extension algorithm.

A double seed curve extension (DSCE) method is proposed to design a freeform surface directly in an off-axis reflective imaging system. Compared with the basic seed curve extension (SCE) method, the DSCE can effectively reduce the error of freeform surface construction and improve the imaging quality of the off-axis reflective imaging system. In addition, the method can be employed to design an off-axis reflective imaging system consisting of multiple freeform surfaces with several virtual image points set in advance. In order to verify the DSCE method, three examples are given. One is the off-axis freeform one-mirror system, one is a compact off-axis three-mirror imaging system with two freeform surfaces, and the other is an off-axis reflective system with three freeform surfaces. The modulation transfer function (MTF) of the one-mirror system is greater than 0.9 at 20 lp/mm, which is close to the diffraction limit. The average of the sagittal and tangential MTFs of the second system designed by the SCE and DSCE methods are 0.26 and 0.74 at spatial frequency of 20 lp/mm, respectively. And the MTF of the last system designed by the DSCE method is greater than 0.9 at 20 lp/mm, which is better than that of the SCE method.

Direct generation of starting points for freeform off-axis three-mirror imaging system design using neural network based deep-learning.

In this paper, we propose a framework of starting points generation for freeform reflective triplet using back-propagation neural network based deep-learning. The network is trained using various system specifications and the corresponding surface data obtained by system evolution as the data set. Good starting points of specific system specifications for further optimization can be generated immediately using the obtained network in general. The feasibility of this design process is validated by designing the Wetherell-configuration freeform off-axis reflective triplet. The amount of time and human effort as well as the dependence on advanced design skills are significantly reduced. These results highlight the powerful ability of deep learning in the field of freeform imaging optical design.

Design of off-axis three-mirror systems with ultrawide field of view based on an expansion process of surface freeform and field of view.

Unobscured reflective optical systems with a wide field of view (FOV) have significant application values. However, the aberration increases with the increase of the system FOV, so a wide FOV system is difficult to design. In this paper, a design method that is effective in achieving off-axis three-mirror systems with ultrawide FOV is proposed. In this method, the system FOV is expanded stepwise in the design process, and the surface optical freeform polynomial terms are extended based on the judgment of image quality and some constraint conditions, and to obtain a prospective ultrawide FOV system. A freeform off-axis three-mirror imaging system with a focal length of 1000mm, an F-number of 10, and an ultrawide FOV of 80°×4° is designed as an example. This design result shows that the system has a high imaging quality of RMS wavefront error value of 0.040λ(λ=0.633 μm), and it demonstrates that the method is effective in achieving off-axis three-mirror systems with an ultrawide FOV.

Design method for freeform reflective-imaging systems with low surface-figure-error sensitivity

Freeform surfaces are difficult to manufacture due to their lack of rotational symmetry. To reduce the requirements for manufacturing precision, a design method is proposed for freeform reflective-imaging systems with low surface-figure-error sensitivity. The method considers both the surface-figure-error sensitivity and optical specifications, which can design initial systems insensitive to surface figure errors. Design starts with an initial planar system; the surface-figure-error sensitivity of the system is reduced during construction. The proposed method and another that is irrelevant to figure-error sensitivity are used to design a freeform off-axis three-mirror imaging system. Comparison of the sensitivities of the two systems indicates the superiority of our proposed method.

Manufacturing-constrained optical design methodology for cylindrical freeform reflective imaging system.

Off-axis reflective imaging systems are widely used, but manufacturing issues are seldom considered in their design. This paper proposes a direct design method for cylindrical freeform imaging systems considering manufacturing constraints to facilitate ultraprecise raster milling. The initial freeform shapes of a well-restricted system configuration are constructed using feature data points and calculated based on the constant optical path length condition. An iterative process with coefficient adjustment of the surface expression is employed to optimize the freeform mirrors for both image quality and the degree of deviation from a reference surface. The method's feasibility is validated by designing an off-axis three-mirror imaging system that operates at F/2.0 with a 100 mm entrance pupil diameter and a 4° × 4° field of view. The freeform surfaces are guaranteed to be distributed along a cylinder 150 mm in radius for ultraprecise raster milling.

Multiple surface expansion method for design of freeform imaging systems.

The relative aperture size and the field-of-view (FOV) are two significant parameters for optical imaging systems. However, it is difficult to improve relative aperture size and FOV simultaneously. In this paper, a freeform design method is proposed that is particularly effective for high performance systems. In this step-by-step method, the FOV is enlarged from a small initial value in equal-length steps until it reaches the full FOV; in each step, part of the area of one system surface is constructed. A freeform off-axis three-mirror imaging system with large relative aperture size and a wide FOV is designed as an example. The system operates at F/2.5 with 150 mm effective focal length and a 60° × 1° FOV. The average root-mean-square wavefront error of the system is 0.089λ (working wavelength λ = 530.5 nm).

Corrective polishing of freeform optical surfaces in an off-axis three-mirror imaging system

The application of freeform surface in the off-axis three-mirror imaging system can greatly improve its optical performance. However, it is difficult for fabrication of freeform optical surface to high precision by traditional machining technology. This paper focuses on the corrective polishing of the primary mirror and tertiary mirror, which are fabricated on one monolithic substrate and described by NURBS-based freeform surfaces, in an off-axis three-mirror imaging system. The integrated polishing process system is proposed for polishing the two mirrors on the 4-axis CNC polishing machine by use of spherical polishing tool. The tool influence function (TIF) module, polishing path generation and dwell time calculation module included in the integrated polishing process system are described respectively. The material removal on the measurement line of part surface is predicted to validate the dwell time calculation algorithm. The polishing experiments of the primary mirror and tertiary mirror are performed to verify the proposed integrated polishing process system.

Starting configuration design method of freeform imaging and afocal systems with a real exit pupil.

Optical system configurations with a real exit pupil have important applications. However, there are few effective design methods of these systems for choice, especially for the systems using freeform surfaces. In this paper, we propose a novel starting configuration design method of freeform optical systems with a real exit pupil before the image plane. This method works for both the cases of imaging systems with optical power and afocal systems. Each single freeform surface in the starting configuration is generated directly using the light rays of multiple fields and different pupil coordinates. With a proposed multi-step design strategy, not only the given system specifications and the desired object-image relationships (or magnification for the afocal system) are achieved, the generation of a real, small-distorted exit pupil with a given size and shape (which means the imaging relationships of the pupils) can be also considered. The system generated by this method can be taken as a good starting configuration for further optimization. The benefits and feasibility of this design method are demonstrated by two design examples. One example is a freeform off-axis three-mirror imaging system. The other example is a freeform off-axis three-mirror afocal telescope. Both of the systems have a modulation transfer function (MTF) that is closed to the diffraction limit.

Design of a freeform, dual fields-of-view, dual focal lengths, off-axis three-mirror imaging system with a point-by-point construction-iteration process

In this Letter, we propose a novel configuration and design method of freeform, dual fields-of-view (FOVs), dual focal lengths, off-axis three-mirror zoom imaging systems. The switch of the two zooms is achieved by rotating a single mirror element. The design of a freeform, dual focal lengths zoom system is realized by a point-by-point design approach for the first time to our knowledge. This method enables the direct design of freeform surfaces from initial planes using given system specifications and configuration, and the designed system can be taken as a good starting point for further optimization. A freeform, dual FOVs, dual focal lengths, off-axis three-mirror zoom system is demonstrated. The F-numbers of the two zooms are 2 and 2.4. The dual FOVs are 3°×3° and 2.5°×2.5°. After final optimization, both of the zooms achieve high performances.

Compact freeform off-axis three-mirror imaging system based on the integration of primary and tertiary mirrors on one single surface

In this Letter, a novel and compact freeform off-axis three-mirror imaging system and its detailed design method are proposed. The primary mirror and tertiary mirror of the system have the same surface analytical expression and they are integrated on one single freeform surface. In this way, the alignment process is made much easier due to the much fewer degrees of freedom. In addition, the difficulty and cost for the data handling, fabrication, and testing of the freeform surfaces and system can also be significantly reduced in some cases, especially compared with the configuration having multiple surfaces of different expressions integrated on one monolithic substrate. The final system has a 100 mm effective focal length and a 4°×3° field of view. The modulation transfer function of the system is close to the diffraction-limit.

Tool path generation for ultra-precision polishing of freeform optical surfaces in an off-axis three-mirror imaging system

The optical performance of the off-axis three-mirror imaging system can be greatly improved using freeform surfaces. This article focuses on the polishing of the primary mirror and tertiary mirror in an off-axis three-mirror imaging system. The primary mirror and tertiary mirror are fabricated on one monolithic substrate and described by non-uniform rational B-spline–based freeform surfaces. The separated and integrated polishing strategies are presented for polishing the two mirrors on the four-axis computer numerical control polishing platform. A tool path generation approach is proposed for polishing of the non-uniform rational B-spline–based freeform surface. Three kinds of the tool paths are given for ultra-precision polishing of the primary mirror and tertiary mirror with the freeform surfaces. The concentric circle path and the approximately concentric circle path are generated for polishing two mirrors separately, while the spiral path is calculated for integrated polishing of two mirrors simultaneously. The polishing tool posture along the planned tool paths is also analyzed. The ultra-precision polishing experiments of the primary mirror and tertiary mirror on the four-axis computer numerical control polishing platform are performed to verify the proposed approach for tool path generation.

Design method of freeform off-axis reflective imaging systems with a direct construction process.

In this paper, a novel method is proposed to design the freeform off-axis reflective imaging systems. A special algorithm is demonstrated to calculate the data points on the unknown freeform surface using the rays from multiple fields and different pupil coordinates. These points are used to construct the multiple three-dimensional freeform surfaces in an imaging system which works for a certain object size and a certain width of light beam. An unobscured design with freeform surfaces can be obtained directly with this method, and it can be taken as a good starting point for further optimization. The benefit of this design method is demonstrated by designing a freeform off-axis three-mirror imaging system with high performance and system specifications. The final system operates at F/1.49 with a 64mm entrance pupil diameter and an 8° × 9° field-of-view (FOV). The performance of the system is diffraction limited at LWIR (long-wavelength-infrared).