Nonlinear model of the optimal tolerance design for a lens system

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