45.5X Infinity Corrected Schwarzschild Microscope Objective Lens Design: Optical Performance Evaluation and Tolerance Analysis Using Zemax®

45.5X Infinity Corrected Schwarzschild Microscope Objective Lens Design: Optical Performance Evaluation and Tolerance Analysis Using Zemax®

Sami D. Alaruri (Independent Scholar, Washington, USA)
DOI: 10.4018/IJMTIE.2018010102

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.
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2. Theoretical Background (Bentley & Olson, 2012; Edmund Optics, N.D.)

As shown in Figure 1, in the Schwarzschild objective lens arrangement the negative (convex-primary mirror) and positive (concave-secondary mirror) spherical mirrors are placed concentric to each other and the two mirrors are separated by twice the lens focal length. Such an arrangement allows for the elimination of the third-order aberrations, namely, spherical aberrations, coma and astigmatism. Also, the concentric spherical mirrors arrangement allows for the generation of a distortion-free and flat field image.

Mathematical formulas expressing the relationship between the Schwarzschild objective lens negative (or convex mirror) and positive (or concave mirror) spherical mirrors curvature, R1 and R2, and the separation between the two spherical mirrors, d, in terms of the Schwarzschild objective lens focal length, f, are given by

IJMTIE.2018010102.m01
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IJMTIE.2018010102.m02
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IJMTIE.2018010102.m03
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