FFT-based methods of computing the Point Spread Function and MTF are well known, and are based on Fraunhofer diffraction theory. The primary assumptions made are:

• The f/# is large enough so that scalar diffraction theory applies
• The region over which the diffraction PSF has significant energy is small compared to the distance from the exit pupil of the optical system to the image surface
• The exit pupil is not significantly distorted with respect to the entrance pupil. This means a uniform distribution of rays on the entrance pupil remains reasonably uniform on the exit pupil
• The sampling is set high enough to accurately model the PSF

Many, but not all, optical imaging systems meet the simplifying assumptions necessary for the Fraunhofer diffraction theory used by the FFT MTF algorithm.

The Huygens MTF is not based upon the FFT. The only assumptions are that the the f/# is large enough so that scalar diffraction theory applies and that the sampling is set high enough to accurately model the PSF 

You can read more about the Huygens calculation in the article What is a Point Spread Function.

Virtually all imaging systems meet the simplyifying assumptions necessary for computing the Huygens PSF. The Huygens MTF is generally slower than the FFT (Fraunhofer) MTF, but more accurate for those cases where the FFT MTF assumptions do not apply.

There is another case where only the Huygen's calculation can be used: if the chief ray cannot be traced through the system, then a chief-ray centered reference sphere cannot be created. The reference sphere is essential for many wavefront calculations. In this case, the Huygens PSF and MTF calculations can be used. One such case is this multiple mirror telescope, in which the chief ray has no path the the image surface.



Because the chief ray cannot trace to the image surface, OPD cannot be calculated, and any parameter derived from OPD cannot be calculated:



The Huygens' PSF and MTF calculations work perfectly, as they are not dependent on any one ray used as a reference:





This file is part of the standard ZEMAX distribution, and can be found at {ZEMAXroot}\Samples\Non-sequential\Miscellaneous\Multiple mirror telescope.ZMX.

A final benefit of the Huygen's method is that the MTFs over multiple configurations can be summed. This is also of use in multiple mirror telescopes, but particularly in the case of very long baseline instruments, where the primary mirrors are separated by large distances. In this case it is not desired to use a common entrance pupil, because too few rays hit the primary mirrors to be efficient. In this specific case the Huygens' MTF calculation is uniquely capable.

To optimize or tolerance using Huygens' MTF, use the MTH* operands.