R et al Kingslake's Applied optics and optical engineering,Vol.III PDF

By R et al Kingslake

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Extra resources for Applied optics and optical engineering,Vol.III

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4 Orthonormalization of Zernike Circle Polynomials over Noncircular Pupils ................................................................................................. 6 Summary................................................................................................................. 1 INTRODUCTION In optical design, we trace rays from a point object through a system to determine the aberrations of the wavefront at its exit pupil. In optical testing, we determine the aberrations of a system or an element interferometrically.

The object radiates a spherical wave. For perfect imaging, the diverging spherical wave incident on the system is converted by it into a spherical wave converging to the Gaussian image point P ¢ . Generally, the wave exiting from real systems is only approximately spherical. The optical path length of a ray in a medium of refractive index n is equal to n times its geometrical path length. Consider rays from a point object traced through the system up to the exit pupil such that each one travels exactly the same optical path length.

Z j Fk = 1 Ú Z ( x , y ) Fk ( x , y ) dx dy . A pupil j (3-21) Equation (3-19) can be written in a matrix form as MC ZF = 1 , (3-22) where C ZF is a J ¥ J matrix of the inner products between the Zernike polynomials Z j and the orthonormal polynomials Fk . The elements of this matrix are given by J Z k Fi T [ = Â M ij Z j Z k j =1 ] T J [ ] = Â Z k Z j M ij j =1 , (3-23) T [ ] where, for example, M ij is the transpose of the matrix with elements M ij (obtained by interchanging the rows and columns of the matrix M ).

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Applied optics and optical engineering,Vol.III by R et al Kingslake


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