TY - JOUR ID - TI - Orthonormal Vector Polynomials in a Unit Annular Pupil AU - Sundus Y. Hasan* and Thill A. Kadhum ** PY - 2014 VL - 2 IS - 1 SP - 42 EP - 71 JO - Muthanna Journal of Pure Science (MJPS) مجلة المثنى للعلوم الصرفة SN - 22263284 25725181 AB - A set of orthonormal polynomials, which represent scalarfunctions, are given in this paper that represent balanced basisover an area of annular pupil. These functions are used torepresent the aberration of imaging systems with annularpupils. Another orthonormal set of polynomials related to those,which represent vector quantities, can be generated from thegradients of annular Zernike polynomials (ZP), and theorthogonality is made by MATLAB code for Gram Schmidtorthogonalization method (GSOM). A relation of thesepolynomials to the circular ZP and circular ZP gradients arerepresented also in this work.

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