Pixel oversampling when nxy is even produces asymmetric PSF

[ptbrown1729]

• psfmodels version: '0.3.2'
• Python version: 3.9
• Operating System: Windows 10 Enterpise

Description

I have a use case where it is helpful to work with even-sized PSF arrays. The documentation in PSFmodels says not to do this, but I thought it might be useful to look into what the problem is. I am expecting the output PSF's to always be symmetric about the center, which is at pixel (nxy-1)//2. I find that this is the case except when nxy is an even number.

It looks like part of the issue is in this code

  R = new double[npx_];
  int idx = 0;
  double xi, yi;
  for (int y = -xymax_; y <= xymax_; ++y)
  {
    for (int x = -xymax_; x <= xymax_; ++x)
    {
      xi = (double)x - xp_;
      yi = (double)y - yp_;
      R[idx] = sqrt(xi * xi + yi * yi);
      ++idx;
    }
  }
}

where xymax_ = ((nx_)*p.sf - 1) / 2;

If, for example nx_ = 4 and p.sf = 3 then the coordinates would get grouped (-5, -4, -3); (-2, -1, 0); (1, 2, 3); (4, 5, ?), and the asymmetry between the 0th and 2nd grouping is clear

It seems like this should work for the even case also if the loop went from

xymin_  = -((nx_ - 1) // 2) * p.sf - (p.sf//2) ;
xymax_ = ((nx_ + 2) // 2) * p.sf - (p.sf + 1)//2;

for the even case there should be p.sf more coordinate points which are greater than zero versus less than zero.

nx_=4 and p.sf = 3 would then get grouped (-4, -3, -2); (-1, 0, 1); (2, 3, 4); (5, 6, 7)

What I Did

import psfmodels
import matplotlib.pyplot as plt

dxy = 0.065
wvl = 0.488
na = 1.3
neven = 4
nodd = 3

# without oversampling
sf = 1
psf_even1 = psfmodels.vectorial_psf(0, neven, dxy, wvl=wvl, params={"NA": na, "sf": sf}, normalize=False)
psf_odd1 = psfmodels.vectorial_psf(0, nodd, dxy, wvl=wvl, params={"NA": na, "sf": sf}, normalize=False)

# with oversampling
sf = 3
psf_even3 = psfmodels.vectorial_psf(0, neven, dxy, wvl=wvl, params={"NA": na, "sf": sf}, normalize=False)
psf_odd3 = psfmodels.vectorial_psf(0, nodd, dxy, wvl=wvl, params={"NA": na, "sf": sf}, normalize=False)

figh = plt.figure()
ax = figh.add_subplot(2, 2, 1)
ax.imshow(psf_even1[0])
ax.set_title("PSF, even sf = 1")

ax = figh.add_subplot(2, 2, 2)
ax.imshow(psf_odd1[0])
ax.set_title("PSF, odd sf = 1")

ax = figh.add_subplot(2, 2, 3)
ax.imshow(psf_even3[0])
ax.set_title("PSF, even sf = 3")

ax = figh.add_subplot(2, 2, 4)
ax.imshow(psf_odd3[0])
ax.set_title("PSF, odd sf = 3")

[tlambert03]

hey @ptbrown1729, I'm so sorry this one slipped through the cracks.

I suspect you've long moved on to something that works for you. You're absolutely correct that using even sized arrays wouldn't be a difficult change. that "warning" was largely inherited from some legacy code and I hadn't looked into recently.

was this issue essentially just a suggestion for modification? If so, thanks very much, I appreciate you looking into it and I can incorporate these changes

[ptbrown1729]

@tlambert03 - no worries, and yes just a suggestion for modification/improvement. This is an issue that took me a long time to track down, and still seems like unexpected behavior.

Where I use these functions, I wrap them with code to throw an error if oversampling is requested with an even sized grid.

I guess there is a bigger issue with supporting even-sized PSF's at all, which is there is not a natural choice of center location. So the PSF starts to depend on what routine you use for convolving an image with it.