45.5X Infinity Corrected Schwarzschild Microscope Objective Lens Design

Abstract

In this article, the design of a 45.5X (numerical aperture (NA) =0.5) infinity corrected, or infinite conjugate, Schwarzschild reflective microscope objective lens is discussed. Fast Fourier transform modulation transfer function (FFT MTF= 568.4 lines/mm at 50% contrast for the on-axis field-of-view), root-mean-square wavefront error (RMS WFE= 0.024 waves at 700 nm), point spread function (PSF, Strehl ratio= 0.972), encircled energy (0.88 µm spot radius at 80% fraction of enclosed energy), optical path difference (OPD=-0.644 waves) and Seidel coefficients calculated with Zemax® are provided to show that the design is diffraction-limited and aberration-free. Furthermore, formulas expressing the relationship between the parameters of the two spherical mirrors and the Schwarzschild objective lens focal length are given. In addition, tolerance and sensitivity analysis for the Schwarzschild objective lens, two spherical mirrors indicate that tilting the concave mirror (or secondary mirror) has a higher impact on the modulation transfer function values than tilts introduced by the convex mirror (or primary mirror). Finally, the performed tolerance and sensitivity analysis on the lens design suggests that decentering any of the mirrors by the same distance has the same effect on the modulation transfer function values.