• Korean Journal of Optics and Photonics
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• v.16 no.5
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• pp.423-427
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• 2005

In this paper, we propose easily tooling method for Seidel third order aberration, which are not well utilized in actual design process due to the complication of mathematical operation and the difficulty of understanding Seidel third order aberration theory, even though most insightful and systematic means in pre-designing for the initial data of optimization. First, using paraxial ray tracing and Seidel third order aberration theory, spherical aberration coefficient is derived for a two-mirror system with a finite object distance. The coefficient, which is expressed as a higher-order nonlinear equation, consists of design parameters(object distance, two curvatures, and inter-mirror distance) and effective focal length(EFL). Then, the expressed analytical equation is solved by using a computer with numerical analysis method. From the obtained numerical solutions satisfying the nearly zero coefficient condition($<10^{-6}$), linear fitting process offers a linear relationship called the curvature linear equation between two mirrors. Consequently, this linear equation has two worthy meanings: the equation gives a possibility to obtain initial design data for optimization easily. And the equation shows linear relationship to a two-mirror system with a finite object distance under the condition of corrected third order spherical aberration.

• Journal of the Optical Society of Korea
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• v.19 no.2
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• pp.136-143
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• 2015

Image deblurring by a deconvolution method requires accurate knowledge of the blur kernel. Existing point spread function (PSF) models in the literature corresponding to lens aberrations and defocus are either parameterized and spatially invariant or spatially varying but discretely defined. In this paper, a parameterized model is developed and presented for a PSF which is spatially varying due to lens aberrations and defocus in an imaging system. The model is established from the Seidel third-order aberration coefficient and the Hu moment. A skew normal Gauss model is selected for parameterized PSF geometry structure. The accuracy of the model is demonstrated with simulations and measurements for a defocused infrared camera and a single spherical lens digital camera. Compared with optical software Code V, the visual results of two optical systems validate our analysis and proposed method in size, shape and direction. Quantitative evaluation results reveal the excellent accuracy of the blur kernel model.

• Korean Journal of Optics and Photonics
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• v.18 no.1
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• pp.19-23
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• 2007

We derived analytically the generalized curvature linear equation useful in the initial optical design of a two-mirror system with finite object distance, including an infinite object distance from paraxial ray tracing and Seidel third order aberration theory for coma coefficient. These aberration coefficients for finite object distance were described by the curvature, the inter-mirror distance, and the effective focal length. The analytical equations were solved by using a computer with a numerical analysis method. Two useful linear relationships, determined by the generalized curvature linear equations relating the curvatures of the two mirrors, for the cancellation of each aberration were shown in the numerical solutions satisfying the nearly zero condition ($<10^{-10}$) for each aberration coefficient. These equations can be utilized easily and efficiently at the step of initial optical design of a two-mirror system with finite object distance.