Alignment off-axis optical system using Nodal Aberration Theory

Jiang, Bo; Zhou, Shifeng; Jiang, Keyong; Fu, Huai-yang; Mei, Chao

doi:10.1117/12.2032379

SPIE Proceedings

2013

DOI: 10.1117/12.2032379

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Alignment off-axis optical system using Nodal Aberration Theory

Bo Jiang

Shifeng Zhou

Keyong Jiang

et al.

Abstract: We present the Fringe Zernike coefficients of the parent system pupil can be converted into coefficients of off-axis system, it is show that the coefficients of the Fringe Zernike polynomials in the off-axis pupil only contain orders equal to or lower than the Fringe Zernike polynomials originally placed on the parent pupil, and for the 3 rd aberration the pupil transformation matrix has been finding. Using nodal aberration, we get the misaligned matrix of rotational symmetry parent optical system. Then with t… Show more

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Cited by 3 publications

References 13 publications

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Active compensation for optimal RMS wavefront error in perturbed off-axis optical telescopes using nodal aberration theory

Wen

Han

2021

Appl. Opt.

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This paper presents an active compensation strategy for RMS wavefront error of perturbed off-axis telescopes in the framework of nodal aberration theory. First, the orthogonalized expression of the wave aberration function in the vector form for perturbed off-axis telescopes is derived by using RMS normalization. The orthogonalized aberration function is applied to analytically describe the RMS wavefront error in perturbed off-axis telescopes with circular apertures. Then, the system compensation model for perturbed off-axis telescopes is established. The compensation model takes the weighted square sum of the RMS wavefront errors at representative field points as the objective function, which is minimized to obtain the optimal compensation solution of off-axis systems with perturbation constraints. The compensation model is solved by using a particle swarm optimization algorithm. Then, the off-axis three-mirror anastigmatic telescope is taken as an example, and the system compensations for the misaligned tertiary mirror and deformed primary mirror are discussed. After compensation, the average RMS wavefront errors in the perturbed off-axis systems are greatly reduced, which can well meet the system requirements. Finally, Monte Carlo simulations of the optimal compensation method and sensitivity table method are carried out to demonstrate the correctness and accuracy of the proposed method.

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Active compensation for optimal RMS wavefront error in perturbed off-axis optical telescopes using nodal aberration theory

Wen

Han

2021

Appl. Opt.

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Nodal aberration properties of coaxial imaging systems using Zernike polynomial surfaces

2015

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As a combination of the nodal aberration theory (NAT) and the freeform surface optical design, the nodal aberration properties of Zernike polynomial surfaces in a coaxial imaging system are analyzed in detail in this paper. The aberrations induced by the Zernike polynomial terms on either the reflective or the refractive surfaces in the system can be quantitatively calculated, which can be used to predict the surface figure or mount-induced errors, or as guidance for aberration correction and optimization during the freeform optical design. Specially, some new kinds of aberrations with complex field dependence can be generated by the Zernike polynomial terms, which further lead to the discovery of linear or multilinear nodes (cruciate nodes) in the aberration field. This linear nodal property will benefit the design of some kinds of freeform optical systems with a linear field of view. Furthermore, an iterative method based on the NAT is proposed to correct the field-constant aberrations.

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Optical compensation for the perturbed three mirror anastigmatic telescope based on nodal aberration theory

Zhang¹,

Xu²,

Ma³

et al. 2017

Opt. Express

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In this paper, the Zernike coefficient is analytically expressed as the product of the dependence of aberration field decenter vectors (related with perturbations) and the dependence of fields of view (FOVs), on the frame work of nodal aberration theory (NAT). By expanding and analyzing this expression, an alignment strategy by optical compensation for the perturbed on-axis or off-axis telescope is presented. Specifically, two cases, corresponding to the misalignment of tertiary mirror (TM) and the deformation of primary mirror (PM), respectively, are discussed for the same three mirror anastigmatic (TMA) telescope. Here the misaligned TM and the deformed PM are compensated only by aligning secondary mirror (SM). By analyzing the aberration field after compensation with the nominal, it is found that either PM or TM can be compensated by SM. It is also found TM is more easily compensated than PM. In the end, the NAT method developed here used for optical compensation is compared to merit function regression (MFR) method and sensitivity table method (STM). By comparing NAT method with MFR method, it is shown that the calculated correction values of SM based on NAT method is very close to the referred values obtained from MFR method. It proves the correctness of NAT method developed here. By comparing NAT method with STM, it demonstrates that the computation accuracy of NAT method is much higher in poor conditions and NAT method is less sensitive to measurement errors. It is further illustrated that the theory of optical compensation by SM developed here is correct and applicable.

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Alignment off-axis optical system using Nodal Aberration Theory

Cited by 3 publications

References 13 publications

Active compensation for optimal RMS wavefront error in perturbed off-axis optical telescopes using nodal aberration theory

Active compensation for optimal RMS wavefront error in perturbed off-axis optical telescopes using nodal aberration theory

Nodal aberration properties of coaxial imaging systems using Zernike polynomial surfaces

Optical compensation for the perturbed three mirror anastigmatic telescope based on nodal aberration theory

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