Exact analytical astigmatic function of aspherical surfaces

B. A. Hristov

doi:10.1117/12.826811

21 August 2009 Exact analytical astigmatic function of aspherical surfaces

B. A. Hristov

Proceedings Volume 7428, Current Developments in Lens Design and Optical Engineering X; 74280S (2009) https://doi.org/10.1117/12.826811
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

Abstract

We derive an exact analytical image astigmatic function for aspherical and hyper-aspherical surfaces of arbitrary shape that describes correctly (without any approximations) image astigmatism for the whole object space and investigate this function for two general cases: in the presence and in the absence of object astigmatism. So we discover the boundary astigmatism correction ability of aspherical surfaces. We prove that in general there are two anastigmatic points on each chief ray in every aspherical surface. We find as well analytical expressions for anastigmatic and extreme points of the function and its vertical and horizontal asymptotes. As a result we prove that in the object and image space of every refracting aspherical surface at each stop position there are two pairs of anastigmatic surfaces one of them coincides with the refracting surface itself. In the object and image space of every reflecting aspherical surface at each stop position there is in general one anastigmatic surface which coincides with the reflecting surface itself. There are special cases when the whole space of the reflecting aspherical surface is anastigmatic.

Citation Download Citation

B. A. Hristov "Exact analytical astigmatic function of aspherical surfaces", Proc. SPIE 7428, Current Developments in Lens Design and Optical Engineering X, 74280S (21 August 2009); https://doi.org/10.1117/12.826811

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available