Hi all,
I am wondering if someone can help me with a science question. I would also like to know if something similar is implemented in wide surveys like LSST, DES, HSC, etc.
Setup:
I have an image (say a coadd), its corresponding variance map, and a PSF. For simplicity, assume the pixel noise is uncorrelated.
Goal:
I want to generate a series of images with different PSFs (wider than the original). I can get the kernels, say k.
Im_conv = fftconvolve(im_ori, k, mode='same')
var_new = fftconvolve(var_ori, k**2, mode='same')
So far so good.
Q1. After convolution the noise is no longer uncorrelated, but for my purposes I do not calculate the covariance matrix. Is this acceptable in practice?
Q2. The main issue is that after convolution the noise decreases (especially in the faint outskirts). This leads to different depths for different kernels (or PSFs). I want to keep the depth consistent across the series. I understand there may not be a perfectly correct way of doing this, but is there a practical way surveys handle it?
Q3. Ideally, one could separate the readout/background component from the Poisson component in var_ori, then add back noise from
var_residual = var_readout - var_new
But this is not possible since the readout variance is not always constant across the image; it can be patchy (rectangular features).
So I was thinking of the following:
var_residual = np.clip(var_ori - var_new, 0, None)
im_final = Im_conv + np.random.normal(0, np.sqrt(var_residual))
I know this is not perfect ; it adds uncorrelated noise on top of correlated noise, and it slightly distorts the Poisson part. But is this acceptable for practical purposes? Compared to var_new, the residual will be small in bright, Poisson-dominated pixels, and significant only in the outskirts where background/readout dominates.
Q4. To be safer, how about adding one more layer of noise:
im_final2 = im_final + np.random.normal(0, np.sqrt(var_new + var_residual))
so that the time series includes both the Poisson and the added components?
Thanks in advance! I’ve been scratching my head on this and was not sure where best to ask.