- Home
- Sequential Ray Tracing
- Ray Tracing Theory
- Understanding the MTF Operands
- Home
- Optimization
- Understanding the MTF Operands
Understanding the MTF Operands
- By Mark Nicholson
- Published 7 May 2007
- Ray Tracing Theory , Optimization
-
Rating:
Diffraction MTF optimization
The MTF algorithm used by the Analysis feature, which produces a graph of MTF for all spatial frequencies that the lens can support, is based upon Fraunhofer diffraction theory. The method involves a fast Fourier transform of a grid of rays traced to the pupil (hence the name FFT MTF). The resulting MTF is the modulation as a function of spatial frequency for a sine wave object, although optionally the real, imaginary, phase, and square wave response is available.
When it comes to optimization, usually only specific spatial frequencies are required, and it is unnecessary to compute the MTF at all supported frequencies. Therefore, The MTF* operands which compute MTF at a specific spatial frequency (see the User's Guide for full documentation) support a GRID parameter that can switch between the grid method used by the graphics window and a fast, sparse-sampling method that is the default and strongly recommended for most (almost all) optimization cases.
In a manner similar to Gaussian Quadrature, the sparse sampling computation converges very, very quickly, and computes the MTF to arbitrary precision with vastly fewer rays than the grid method. And, most importantly, it is fully accurate in all cases where Fraunhofer theory is applicable.
This table demonstrates the convergence of the two methods, and the time taken to converge, as the sampling is increased for a calculation of the polychromatic MTF at 50 lp/mm, on-axis in the double Gauss sample file provided with ZEMAX:
Here is the same data, this time for the edge of the field of view:
Note that generally speaking, 1% convergence is adequate for the purposes of optimization and tolerancing. Experimental methods of measuring MTF are generally not repeatable below 0.1% in any case. Extreme precision is not required for good optimization results; three significant figures is usually adequate. However, both algorithms will converge to arbitrary precision with adequate sampling, and the fast algorithm will do so many orders of magnitude faster when extreme precision is needed.
The grid algorithm will converge faster in only one known case: where aberrations are very large and the resulting MTF very low: less than about 5%. Note that MTF is not normally used to specify performance, much less be used as an optimization or tolerancing target, in this regime. ZEMAX automatically traps this condition and switches to the grid method in this case. Note also that the geometric MTF calculation is a better choice in this regime.
When it comes to optimization, usually only specific spatial frequencies are required, and it is unnecessary to compute the MTF at all supported frequencies. Therefore, The MTF* operands which compute MTF at a specific spatial frequency (see the User's Guide for full documentation) support a GRID parameter that can switch between the grid method used by the graphics window and a fast, sparse-sampling method that is the default and strongly recommended for most (almost all) optimization cases.
In a manner similar to Gaussian Quadrature, the sparse sampling computation converges very, very quickly, and computes the MTF to arbitrary precision with vastly fewer rays than the grid method. And, most importantly, it is fully accurate in all cases where Fraunhofer theory is applicable.
This table demonstrates the convergence of the two methods, and the time taken to converge, as the sampling is increased for a calculation of the polychromatic MTF at 50 lp/mm, on-axis in the double Gauss sample file provided with ZEMAX:
Here is the same data, this time for the edge of the field of view:
Note that generally speaking, 1% convergence is adequate for the purposes of optimization and tolerancing. Experimental methods of measuring MTF are generally not repeatable below 0.1% in any case. Extreme precision is not required for good optimization results; three significant figures is usually adequate. However, both algorithms will converge to arbitrary precision with adequate sampling, and the fast algorithm will do so many orders of magnitude faster when extreme precision is needed.
The grid algorithm will converge faster in only one known case: where aberrations are very large and the resulting MTF very low: less than about 5%. Note that MTF is not normally used to specify performance, much less be used as an optimization or tolerancing target, in this regime. ZEMAX automatically traps this condition and switches to the grid method in this case. Note also that the geometric MTF calculation is a better choice in this regime.