Three-mirror Anastigmat Optical System Research Articles

Desensitization design method of an off-axis three-mirror anastigmatic optical system based on the nodal aberration theory

A design method for an off-axis three-mirror anastigmatic optical system with low misalignment sensitivity is proposed. Based on the transformed pupil coordinate and nodal aberration theory, the analytical expressions between the optical parameters and misalignments are derived and an as-built performance evaluation model is established. The effects of mirror spacings and the off-axis magnitude value on the misalignment sensitivity are analyzed. With the desensitization design method proposed in this paper, a low-sensitivity off-axis TMA optical system can be designed. The simulation experiments show that, the misalignment sensitivity of the off-axis TMA optical system obtained by our method is approximately 60% that of the system obtained by nominal performance optimization method, and the as-built performance is about 1.49∼1.54 times that of the nominal performance optimization method.

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.

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.

Misalignment algorithm of a wide-field survey telescope based on third-order quadratic nodal aberration theory

Off-axis three-mirror anastigmatic (TMA) telescopes with designed decenters and tilts, have many misalignment degrees of freedom and strong coupling between each misalignment degree of freedom. Therefore, it is difficult to establish misalignment equations only using A222 and A131 in nodal aberration theory (NAT). In addition, for off-axis TMA optical systems with designed decenters and tilts, the robustness of the existing fifth-order NAT misalignment calculation algorithm based on high-order Zernike coefficients and boresight errors decreases, so it is difficult to realize its engineering application. To solve the issue of insufficient practicality of the existing misalignment algorithm based on fifth-order NAT, a third-order NAT calculation algorithm based on quadratic aberration field decenter vectors is derived and established. Two concepts of inherent aberration field decenter vector and misalignment aberration field decenter vector are proposed. Taking an off-axis TMA optical system with 6-m focal length as the research object, simulations, and alignment verification experiments were carried out. Compared with the existing fifth-order NAT misalignment algorithm, the results show that when measurement noise is not considered, the two methods can both obtain convergent calculation results, and the average RMS wavefront errors (WFE) of the optical system are both corrected to be below 0.0574 waves. When different levels of measurement noise are introduced, the robustness of the fifth-order NAT misalignment algorithm decreases, and there are even cases where the optical system completely fails to be corrected. However, the algorithm based on quadratic aberration field decenter vectors shows better robustness. Under different levels of measurement noise, this algorithm could correct the average RMS WFE of the optical system to around 0.0574 waves.

Desensitization design method of unobscured three-mirror anastigmatic optical systems with an adjustment-optimization-evaluation process.

An off-axis three-mirror anastigmatic optical system with the offset apertures configuration as a typical unobscured optical system is frequently used in various optical instruments. The practical applications show that this type of system has a higher sensitivity in alignment. To reduce the alignment sensitivity of the unobscured optical systems, a desensitization design method with an adjustment-optimization-evaluation process is proposed. By ray path difference analysis based on the optical system mathematical models, the mirror off-axis magnitude value is determined as a significant factor influencing system alignment sensitivity. Accordingly, in the desensitization design process, the mirror off-axis magnitude value is set as an adjustment, and the image quality and system sensitivity are set as the criteria. By a design example, it proves that the desensitization design method is effective and practical, and the design result sensitivity analysis not only verifies that the off-axis magnitude is a significant factor that influences the system alignment sensitivity, but also finds that there is a positive correlation relation between system sensitivity and off-axis magnitude value. The desensitization method can design the unobscured optical systems with less alignment sensitivity and robust tolerance.

Initial On-Orbit Modulation Transfer Function Performance Analysis for Geostationary Ocean Color Imager

The world`s first geostationary ocean color imager (GOCI) is a three-mirror anastigmat optical system 140 mm in diameter. Designed for 500 m ground sampling distance, this paper deals with on-orbit modulation transfer function (MTF)measurement and analysis for GOCI. First, the knife-edge and point source methods were applied to the 8th band (865 nm) image measured April 5th, 2011. The target details used are the coastlines of the Korean peninsula and of Japan, and an island 400 meters in diameter. The resulting MTFs are 0.35 and 0.34 for the Korean East Coastline and Japanese West Coastline edge targets, respectively, and 0.38 for the island target. The daily and seasonal MTF variations at the Nyquist frequency were also checked, and the result is on average. From these results, we confirm that the GOCI on-orbit MTF performance satisfies the design requirements of 0.32 for 865 nm wavelength.

双向大视场消畸变低温红外目标模拟光学系统设计

To overcome the shortcomings of off-axis Three Mirror Anastigmatic(TMA) optical systems in larger sagittally FOVs and smaller meridionally FOVs,this paper designs a bidirectional TMA optical system for cryogenic infrared target simulation system based on the symmetric rule of optical system.Both the sagittally and meridionally FOVs are 5°,the larger FOV optical system at 3-5 μm has a focal length of 400 mm and a F number of 8.By using the structural parameters of the optical system and the non-spherical coefficients of the mirrors to adjust and correct the eccentric and tilt of the three-mirror and to eliminate distortion and other aberrations,the system shows that the MTF is better than 0.71 at 6.5 lp/mm,the aberration of the whole FOV is λ/250(RMS) and the maximum radius of diffuse point is less than 7.0 μm(RMS),which achieves diffraction limit.Moreover,the maximum distortion in the whole FOV is less than 0.04%.Finally,it proves that the optical system has good imaging quality both in the visible and infrared spectral regions.

改进的离轴三反光学系统的设计

The key design of off-axial Three-mirror Anastigmat(TMA) systems was summarized,and an improved design of the off-axial TMA optical systems was proposed with a new optical structure.By taking two designed systems for examples,the optical elements of the TMA system were reasonably arranged,the secondary mirror was designed as a spherical surface,and the primary and the third mirrors were optimized with high-order aspheric coefficients.Obtained results show that the Modulation Transform Function(MTF) curve of the designed system approaches to the optical diffraction limit with an improved value of 0.6 at the spatial frequency of 50 pl/mm.Compared with the common off-axial TMA optical system,the Strehl ratio can be increased from 0.91 to 0.93.The surface tolerance is relaxed from λ/50 to λ/40,and the assembling tolerances of the primary mirror,second mirror and the third mirror can be relaxed by a factor of 4.The improved design makes the manufacture and assembly of the off-axial TMA optical system much easier,and helps the system to achieve excellent performance in the level of optical diffraction limit.These are beneficial to the popularization of off-axial TMA optical systems.

Design of an off-axis three-mirror anastigmatic optical system with wavefront coding technology

Wavefront coding (WFC) technology can extend the depth of focus of an optical system, which makes the application of this technology to space cameras extremely attractive. This paper introduces the application of wavefront coding to three-mirror anastigmatic optical systems. A transition model is established, in which the secondary mirror is regarded as the wavefront coding element and redesigned according to mathematical calculation. A comparison of modulation transfer function (MTF) behavior between the traditional system and the innovative system with wavefront coding technology is provided. The MTF behavior of both on-axis and off-axis field-of-view points remains the same in spite of the extended depth of focus. It is also observed that the system becomes very insensitive to aberration related to defocus through WFC technology. Errors in optical design and its improvement are discussed. The linear transition model is proven to be an acceptable one. Finally, an extension factor for the depth of focus is defined, and its effect is presented graphically.

Image restoration of an off-axis three-mirror anastigmatic optical system with wavefront coding technology

Wavefront coding technology can extend the depth of focus of a well-corrected three-mirror anastigmatic optical system by about ten times, but the image obtained directly by charge-coupled devices blurs at the same time. An effective image restoration must be applied to these blurred images. This paper describes an innovative method that restores the blurred image, which combines the optical design software and mathematical software. The point spread function of system with wavefront coding technology is quite different from the usual and difficult to simulate by a disk function or other simple function in most cases. The commercial optical design software is applied to obtain the point spread function. If a 1×1-pixel image with brightness 255 is set as the point source of a optical system, the result of calculation software using a ray tracing algorithm will itself be the digital point spread function. This is proven to be a simple and effective way to acquire the complicated point spread functions of unusual optical systems such as those using wavefront coding technology. A regularization factor and contrast-adjusting factors are introduced into the classical Wiener filter, which achieves good restored images: the root-mean-square error is less than 0.0193, while the peak signal-noise ratio is higher than 23.7. Some parameters of the filter can be adjusted so that the restored image is more suitable for evaluation by eye. It is also shown that a single filter can restore all the images within the extended depth of focus.