Zernike Polynomiales· for Opticl Ssytew. With Borizantal Recta_nguJar Aperture

Abstract

For  small   aberrations,  the  Â·suehl'  ratio of  an . im i'ng syStem

• depends on trne aberration v·ariance. Its· aberration fu.nct1on ·is e:qJanded in terms 9f-l nike polynomials. which are_ oirrh6goilal over a circular apeltitte. Their advane Uejn the    f;:l t tbat they call be icl.eritified. witl·c1a:s.sh::aj. abe,ttati{)ns 'balanced to jield  minimum varia,.o_q,and

thuS maximum St:rehl  t"a;tio. [n r«enr pap-er, we derived Cl<lse4 .fonn or

Zmike   polyhotnials  that  ate  orthonormal  over "- horizontal rect'angul'ar pupil'. (p.anil.lel to· the >Htxi.es) with ar'€a equal 1t.  Ustng the circle pO:lynomials as the · basis functions. f(;)r  th:ehl- onb.ogonalization

p_ver  such   pupil,    we: ;derive   closed-foim  polyr.wmials   that   are ortbonormaJ  over   rectangular  pupil  by us ng,  Gram-sl1m.it  method These· polynomials,  we unique in that they  rue_ not  <:>nly  orthogonal

acrossuch- pupils,. but aJ:so -re.present balanced -classicl aberrations,

just as tbe Zemike ·circlpolyiiornials are unique in- these respects but

also repr sent balanced dasskal  aberration$.