For small aberrations, the ·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$.
