We used the explicit expression of Zernike polynomials in Cartesian coordinates to fit and describe the freeform surface of progressive addition lens (PAL). The derivatives of Zernike polynomials can easily be calculated from the explicit expression and used to calculate the principal curvatures of freeform surface based on differential geometry. The surface spherical power and surface astigmatism of the freeform surface were successfully derived from the principal curvatures. By comparing with the traditional analytical method, Zernike polynomials with order of 20 is sufficient to represent the freeform surface with nanometer accuracy if dense sampling of the original surface is achieved. Therefore, the data files which contain the massive sampling points of the freeform surface for the generation of the trajectory of diamond tool tip required by diamond machine for PAL manufacture can be simplified by using a few Zernike coefficients.
The back surface of progressive addition lens (PAL) is a non-rotationally symmetric freeform surface. The local radius varies progressively from the far zone to the near zone along the intermediate zone to give the addition power. Numerical simulation method is performed to calculate the discrete points on the freeform surface in polar coordinate and generate the data files containing the trajectory of diamond tool tip for surface machining. The fabrication of PAL is accomplished by using self-developed single-point diamond turning machine with voice coil fast tool servo. The polished freeform surface profile measured by a 3-axes coordinate measuring machine shows little deviation to the simulation result. Surface power and cylinder of the fabricated PAL is also measured for comparison with theoretical design.
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