Nonlinear model of the optimal tolerance design for a lens system

Songlin Zhuang; Zhijin Qu

doi:10.1117/12.47938

1 January 1991 Nonlinear model of the optimal tolerance design for a lens system

Songlin Zhuang, Zhijin Qu

Proceedings Volume 1354, 1990 Intl Lens Design Conf; (1991) https://doi.org/10.1117/12.47938
Event: 1990 International Lens Design Conference, 1990, Monterey, CA, United States

Abstract

In this paper we propose a nonlinear model which can be considered as a mathematical programming problem with linear and quadratic constraints to design the optimal tolerance of a lens system. Owing to the negligence of the nonlinear property of a optimized lens system the existing studies on the tolerance design are unable to solve the optimal tolerance design problem. For realizing this purpose i. e. maximizing the tolerance of the lens system we propose a nonlinear model which can be considered as a mathematical programming problem with linear and quadratic constraints to design the optimal tolerance of a lens system. Assuming X (x1 . . . x 2'' EJ and ''F(X) are parameters of a lens system manufacturing error for each parameter and merit function of the image quality respectively. The following statements are supposed adequately. (A1) The probability density of k N(o that is Ek is normal distribution with zero mean and variance a. (A2) The difference of the merit function between the real system and the design system can be approximately expressed by quadratic expression. 4(X+cr)(X) c3a: E1 (1) where V () and H () (A3) The purpose of the optimal tolerance design is to determine the variances (a . . . a) of (E1 . . . E and satisfy the following conditions: (i) D(M) (ii) M(L4) m (2) (iii) E po as great as possible

Citation Download Citation

Songlin Zhuang and Zhijin Qu "Nonlinear model of the optimal tolerance design for a lens system", Proc. SPIE 1354, 1990 Intl Lens Design Conf, (1 January 1991); https://doi.org/10.1117/12.47938

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