On the Theory of Aplanatic Aspheric Systems

Wassermann, Günter; Wolf, Ervin

doi:10.1088/0370-1301/62/1/302

Cited by 145 publications

(36 citation statements)

References 8 publications

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“…A non-isotropic point source is positioned at the origin of a Cartesian coordinate system O in R³ and emits rays in a set of directions defined by the aperture Ω given as a closed set on a unit sphere S centered at O. I(m) is Figure 1 Layout of a typical system [10].…”

Section: Tailoring Methodsmentioning

confidence: 99%

“…The Wassermann-Wolf differential equation was derived by Wasserman and Wolf in 1949 and used to design two aspheric surfaces for centered system, as shown in Figure 1, basing on the Abbe sine condition to solve a firstorder differential equation, and the system could correct axial stigmatism and sine condition [10]. In 1957, Vaskas provided a method to extend the Wassermann-Wolf method to a more general situation, in which the two surfaces can be separated by a number of known surfaces [11].…”

Section: Wassermann-wolf Differential Equationmentioning

confidence: 99%

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Design of freeform optics

Cheng

Zhang

2013

Advanced Optical Technologies

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Freeform optics has certain characteristics such as complex surfaces and more degrees to be controlled, so that it is capable of achieving optical mapping relationship, which cannot be achieved by the conventional optical surfaces. There is no applicable method for designing all freeform optics in the optical field until now. The selection of design methods should be based on specific applications. The paper introduces the main optical freeform design methods and their typical applications.

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Section: Tailoring Methodsmentioning

confidence: 99%

Section: Wassermann-wolf Differential Equationmentioning

confidence: 99%

Design of freeform optics

Cheng

Zhang

2013

Advanced Optical Technologies

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“…they were free from spherical aberration and circular coma of all orders [2]. Later, Wassermann and Wolf [3] generalized Schwarzschild approach presenting a method for the design of two aspherical surfaces as a solution of two simultaneous first-order ordinary differential equations. Standard integrating methods have been applied to obtain the numerical solution to get the aspherical profiles, although Willstrop and Lynden-Bell gave analytical solutions of the Schwarzschild design [4,5].…”

Section: Introductionmentioning

confidence: 99%

Single freeform surface imaging design with unconstrained object to image mapping

Liu¹,

Benı́tez²,

Miñano³

2014

Opt. Express

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An imaging design approach which is free of third-order astigmatism for one freeform optical surface and the image is presented in this paper. A set of differential equations is derived from generalized ray tracing. The solution of the above derived equations provides the anastigmatic freeform optical surface, the image surface and the object to image mapping. The obtained design can be used as a good starting point for optimization. As an example, a reflective freeform surface is designed for a single reflective Head Mounted Display (HMD). This example has a 3 mm pupil, 15mm eye clearance, 24-degree diagonal full field of view, and the final design yields an average MTF of 62.6% across 17 field points.

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“…Aplanatic designs have long been known through the work of Schwarzschild [11], Wassermann and Wolf [12], Welford [13], Mertz [14,15] and others. Recently Lynden-Bell and Willstrop derived an analytic expression of more general aplanats [16,17].…”

Section: Introductionmentioning

confidence: 99%