>Psychtoolbox>PsychOptics

Convert a 2D point spread function to a 2D optical transfer fucntion.
[xSfGridCyclesDeg,ySfGridCyclesDeg,otf] = PsfToOtf([xGridMinutes,yGridMinutes],psf,varargin)

Converts a point spread function specified over two-dimensional
positions in minutes to a optical transfer function specified over
spatial frequency in cycles per degree. For human vision, these are
each natural units.

The input positions should be specified in matlab’s grid matrix format
and x and y should be specified over the same spatial extent and with
the same number of evenly spaced samples. Position (0,0) should be at
location floor(n/2)+1 in each dimension. The OTF is returned with
spatial frequency (0,0) at location floor(n/2)+1 in each dimension.

Spatial frequencies are returned using the same conventions.

If you want the spatial frequency representation to have frequency
(0,0) in the upper left, as seems to be the more standard Matlab
convention, apply ifftshift to the returned value. That is
otfUpperLeft = ifftshift(otf);
And then if you want to put it back in the form for passing to our
OtfToPsf routine, apply fftshift:
otf = fftshift(otfUpperLeft);
The isetbio code (isetbio.org) thinks about OTFs in the upper left
format, at least for its optics structure, which is one place where
you’d want to know this convention.

No normalization is performed. If the phase of the OTF are very small
(less than 1e-10) the routine assumes that the input psf was spatially
symmetric around the origin and takes the absolute value of the
computed otf so that the returned otf is real.

We wrote this rather than simply relying on Matlab’s potf2psf/psf2otf
because we don’t understand quite how that shifts position of the
passed psf and because we want a routine that deals with the
conversion of spatial support to spatial frequency support.

If you pass the both position args as empty, both sf grids are
returned as empty and just the conversion on the OTF is performed.

PsychOpticsTest shows that this works very well when we go back and
forth for diffraction limited OTF/PSF. But not exactly exactly
perfectly. A signal processing maven might be able to track down
whether this is just a numerical thing or whether some is some small
error, for example in how position is converted to sf or back again in
the OtfToPsf.

See also OtfToPsf, PsychOpticsTest.