4. Numerical analysis of point-diffraction wavefront

As one of the most important elements in the PDI, the point source for the diffracted reference wavefront determines the achievable accuracy in the measurement. Purely empirical design of point source parameters is both time consuming and costly. The numerical method based on diffraction theory is a feasible way for the analyzing point-diffraction wavefront. The scalar diffraction theory is valid only when the pinhole size is several times larger than the operating wavelength. For the high-NA spherical wavefront emerging from a tiny aperture with the size comparable with or less than operating wavelength, the vector diffraction theory (that is a nonapproximate method) is required to realize the accurate estimation of diffracted wavefront error. In this section, numerical analysis based on finite difference time domain (FDTD) method (that is a vector diffraction theory) [27] is presented. Figure 10 shows the flow diagram for the simulation of point-diffraction wavefront based on FDTD method. Due to limitations of computer memory capacity and runtime, FDTD cannot be directly applied to calculate the farfield distribution of pinhole diffraction. In the first step, the near-field distribution of point diffraction is analyzed with the FDTD method, and then the near-to-far field transition based on Huygens' principle is performed to obtain the far-field distribution of point-diffraction wavefront at the position under study. Finally, the sphericity evaluation is carried out to get the departure of point-diffraction wavefront from an ideal sphere.
