Abstract
The Modulation Transfer Function (MTF) is a measure of an optical system’s ability to transfer contrast from the specimen to the image plane at a specific resolution. It can be computed either numerically by geometrical optics or measured experimentally by imaging a knife edge or a bar-target pattern of varying spatial frequency. Previously, MTF accuracy was generally affected by the size of the mesh on the image plane. This paper presents a new MTF computation method based on the irradiance model, without counting the number of rays hitting each grid. To verify the method, the MTF in the sagittal and meridional directions of an axis-symmetrical optical system is computed by both the ray-counting and the proposed methods. It is found that the grid size meshed on the image plane significantly affects the MTF of the ray-counting method, sometimes with significantly negative results. The proposed irradiance method is immune to issues of grid size. The CPU computation time for the two methods is approximately the same.
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Abbreviations
- (xyz)0 :
-
The world coordinate frame
- (xyz) n :
-
The coordinate frame imbedded in image plane
- 0 P i :
-
The ith incident point defined with respect to (xyz)0
- 0 ℓ i :
-
The ith unit directional vector defined with respect to (xyz)0
- \({[}{}^{0}\mathbf{P}_{i}\ {}^{0}\boldsymbol{\ell}_{i}{]}_{}^{T}\) :
-
The refracted ray at ith boundary surface.
- [0 P 0 0 ℓ 0]T :
-
The source ray originating from source point 0 P 0 with its unit directional vector 0 ℓ 0.
- (α 0,β 0):
-
Spherical coordinates defining 0 ℓ 0=[Cβ 0 Cα 0 Cβ 0 Sα 0 Sβ 0 0]T
- ∂(x n ,z n )/∂(α 0,β 0):
-
Jacobian matrix between (x n ,z n ) of the image plane and (α 0,β 0)
- B(x n ,z n ):
-
Point spread function on the image plane
- L(x n ):
-
Line spread function on the image plane
- F n :
-
Energy flux (in watts) on the image plane
- I(x n ):
-
Image energy distribution at x n on the image plane
- ν:
-
Frequency of the brightness variation in cycles per unit length
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Lin, PD., Liu, CS. Geometrical MTF computation method based on the irradiance model. Appl. Phys. B 102, 243–249 (2011). https://doi.org/10.1007/s00340-010-4349-3
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DOI: https://doi.org/10.1007/s00340-010-4349-3