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| In optical interferometric measurement, Zernike polynomials are the well-known method for the wavefront reconstruction, which are usually used in the single field point. The corresponding Zernike terms are not true wavefront aberration functions because of lack of field parameters. The Bi-Zernike polynomials are proposed to express the wavefront aberration function. The field and pupil parameters are separated and described respectively by orthonormal Zernike polynomials. Meanwhile, the orthogonality of Bi-Zernike polynomial function is proved and the numerical simulation for Bi-Zernike aberration term characterized by pupil dependence is shown for visualization. Further, the coefficients of the Bi-Zernike functions are the linear combination of W-coefficients of the power series expansion of wavefront aberration function, which can be used to balance aberration. Besides, the modified wavefront aberration function expressed as the combination of Bi-Zernike polynomial functions can be equivalently transformed to the Robert Gray's analytic expression form. |
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| Keywords:Geometric optics, Wavefront aberration function, Bi-Zernike polynomials, orthogonality, |
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