Analysis of three-dimensional diffraction wavefront error for point diffraction interferometer

Point diffraction interferometry is a promising method for spherical or aspherical measurement with nanometer or even sub-nanometer accuracy. As the accuracy of a PDI is mainly depends on its diffraction reference wavefront, an accurate estimation of the diffraction wavefront error plays a critical role for system's design and optimization. Although, various error factors may affect the quality of this diffraction wavefront, alignment error of the focusing spot to the pinhole is the decisive one. The common analyses for the diffraction wavefront error mainly based on plane wave approximation of the incidence beam can't be used to analyze the influence of the misalignment error. Meanwhile, most of these analyses are limited to two-dimensional analysis and therefore is not enough to show the complete error distribution. In this paper, a three-dimensional (3-D) analysis based on Gaussian incidence is developed, and the influences of lateral shift, defocus and tilt alignment errors of focusing spot to the pinhole are analyzed. Here, a 3-D analysis model of diffraction wavefront was established based on Rayleigh-Sommerfeld diffraction theory of a Gaussian incidence for error analysis of various alignment errors. After that, 3-D diffraction wavefront error distribution and the peak-valley (PV) comprehensive evaluation result in different lateral shift, defocuses, and tilt alignment errors were acquired through numerical simulation. The achieved results will be benefit for choosing the pinhole parameters and theoretically accuracy evaluation of diffraction wavefront for nano profilometry.