Wavefront analysis of concentric pupil zones

In optical design verification and interferometric lens testing, wavefront aberrations are expanded in orthogonal Zernike circle polynomials. Due to the continuity of these polynomials, they are less suitable for expanding discontinuous wavefronts. Examples of lenses that contain phase discontinuities are DVD objective lenses that are CD compatible. One of such compatibility solutions is a lens comprising a central pupil zone with one or more concentric annular pupil zones, separated by phase or intensity discontinuities. We have derived an expression that relates the Strehl intensity of the diffraction focus of such discontinuous pupil to the coefficients of the Zernike circle polynomial expansion in the central pupil zone and the Zernike annular polynomial expansion in the concentric annular pupil zones. Furthermore, we have developed a formalism to optimize the Strehl intensity by subtracting piston, tilt and defocus from the wavefront by correcting the coefficients of the Zernike circle and annular polynomials. Numerical calculations have shown that the approximation for the Strehl intensity of discontinuous wavefronts results in deviations from the actual intensity at the diffraction focus, that are comparable to the classical approximation for continuous wavefronts.