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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 17 — Jun. 10, 2011
  • pp: 2759–2772

Calculation of the modulation transfer function for object brightness distribution function oriented along any direction in axis-symmetrical optical systems

Psang Dain Lin and Wei Wu  »View Author Affiliations

Applied Optics, Vol. 50, Issue 17, pp. 2759-2772 (2011)

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The literature deals with the modulation transfer function (MTF) only for object brightness distribution functions (OBDFs) oriented along the meridional and sagittal directions. This paper addresses computation of the geometrical MTF for an off-axis source point when the OBDF is oriented along any arbitrarily defined direction. This study finds that the MTF is not a monotonic increasing or decreasing function when the direction of the OBDF is changing. Consequently, the extreme MTF values may occur when the OBDF is aligned at any direction between the meridional and sagittal directions. Four theorems are provided for the MTF and the phase shift variations that take place when the OBDF is translated or rotated. It is found that the MTF and the phase shift are symmetrical or antisymmetrical about certain directions. Thus, to observe all possible changes in the MTF and the phase shift, it is sufficient to rotate the OBDF through a range of just 90 ° . The presented method is based on a recent irradiance method for MTF computation that does not rely on counting the number of ray hits on a mesh, making the method immune to effects of grid size and thus improving traditional accuracy.

© 2011 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design
(080.3620) Geometric optics : Lens system design
(080.1753) Geometric optics : Computation methods
(080.2468) Geometric optics : First-order optics

Original Manuscript: December 14, 2010
Revised Manuscript: March 24, 2011
Manuscript Accepted: March 24, 2011
Published: June 9, 2011

Psang Dain Lin and Wei Wu, "Calculation of the modulation transfer function for object brightness distribution function oriented along any direction in axis-symmetrical optical systems," Appl. Opt. 50, 2759-2772 (2011)

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