Vector simulation of pinhole diffraction behavior for high numerical aperture converging incident beam at deep ultraviolet wavelength

Abstract

For in situ calibration of high numerical aperture wavefront sensor, a small pinhole, whose diameter should be less than the diffraction limit of incident beam, is used to generate reference spherical wavefront. In this way, the calibration accuracy is determined by the quality of pinhole diffracted quasi-spherical wavefront. Combining scalar and vector diffraction theory, a pinhole diffraction model is established to determine the pinhole parameters which could generate high quality quasi-spherical wavefront. The model includes three steps. Firstly, scalar diffraction theory is utilized to propagate light from exit pupil of test optics to the pinhole’s incident near-field. Secondly, vector diffraction theory is used to propagate light from pinhole’s incident near-field to the pinhole’s emergent near-field. Finally, scalar diffraction theory is utilized again to propagate light from pinhole’s emergent near-field to the detection plane of wavefront sensor. The most important feature of this model is that the influence of test optics’ exit pupil aberrations on the quality of reference spherical wavefront can be taken into account quantitively. Based on the modeling approach above, we conduct a simulation on the pinhole diffraction behavior of light with wavelength of 193.3 nm, X-polarized, numerical aperture of 0.75. The results show that, in order to achieve reference spherical wavefront error of 2 mλ rms, pinhole mask made up of Chromium membrane with pinhole diameter of 170 nm and membrane thickness of 200 nm should be chosen. At the same time, the pinhole lateral alignment, pinhole sidewall and pinhole eclipse should be controlled in ±20 nm, ±30 nm and ±10 nm, respectively. Also the requirement on the exit pupil aberrations of test optics is given based on wavefront error and intensity uniformity on detection plane.