`zernike.opd_expand_nonorthonormal` and `zernike.opd_expand_segments` give different results for the same inputs

[kjbrooks]

In trying to reconstruct a JWST OPD, I found that using the new zernike.opd_expand_segments, I was getting strange results for segments C3 and C4 (behind the diagonal struts) that did not match the reconstruction that I was getting when I used zernike.opd_expand_nonorthonormal previously. My understanding is that zernike.opd_expand_segments should not give different results, just be more efficient. If this understanding is incorrect, please let me know.

I have two functions that only differ in using opd_expand_nonorthonormal or opd_expand_segments:

def fit_terms_to_surface(self, aperture, nterms, ap_centroid, ap_radius, iterations=15):
        '''
        Fit WSS Hexikes to a defined surface
        '''
        def get_basis(*args, **kwargs):
            return basis

        rho, theta = self.define_rho_theta(ap_centroid, ap_radius)
        basis = poppy.zernike.hexike_basis_wss(nterms=nterms, npix=self.npix, rho=rho,
                                               theta=theta, aperture=aperture > 0.)
        self.new_coeffs = poppy.zernike.opd_expand_nonorthonormal(self.opd, 
                                                         aperture=aperture > 0., 
                                                         nterms=nterms, 
                                                         basis=get_basis,
                                                         iterations=iterations)

        self.reconstructed = poppy.zernike.opd_from_zernikes(self.new_coeffs, 
                                                             basis=get_basis, 
                                                             aperture=aperture > 0.)
        self.reconstructed[~np.isfinite(self.reconstructed)] = 0.0

and

def fit_terms_to_segments(self, aperture, nterms, ap_centroid, ap_radius, iterations=15):
        '''
        Fit WSS Hexikes to a segment
        '''
        def get_basis(*args, **kwargs):
            return basis

        rho, theta = self.define_rho_theta(ap_centroid, ap_radius)
        basis = poppy.zernike.hexike_basis_wss(nterms=nterms, npix=self.npix, rho=rho,
                                               theta=theta, aperture=aperture > 0.)
        self.new_coeffs = poppy.zernike.opd_expand_segments(self.opd,
                                                   aperture=aperture > 0., 
                                                   nterms=nterms, 
                                                   basis=get_basis, iterations=iterations)

        self.reconstructed = poppy.zernike.opd_from_zernikes(self.new_coeffs, 
                                                             basis=get_basis, 
                                                             aperture=aperture > 0.)
        self.reconstructed[~np.isfinite(self.reconstructed)] = 0.0

These functions give different results. In the below figures, the same stretch is used in both cases. Using poppy.zernike.opd_expand_nonorthonormal in the function fit_terms_to_surface above:

Using poppy.zernike.opd_expand_segments in the function fit_terms_to_segments above:

[mperrin]

@kjbrooks, could you send me or post here a bit more of the notebook setting up your problem case? In particular the above code samples appear to be using a get_basis function defined elsewhere. I’d like to see if I can find time today or tomorrow to start digging into what’s going on here...

[kjbrooks]

In the case above that you mention, get_basis is defined in the functions I copied above. I have noticed if that function exists outside of these functions, there is some hysteresis. I am working on a simplified notebook now and will attach it when I am done.

[mperrin]

Aha, I didn’t read the above code closely enough. But I think there may be a problem in having the basis variable defined after the get_basis function! Try flipping the order of those.

[kjbrooks]

I think I have identified at least part of the issue. In creating a simplified notebook I discovered that my results (while still different between opd_expand_nonorthonormal and opd_expand_segments) were different than when I posted the above result plots. Part of this is notebook issues (read: human error) since I thought I had re-run the cells, but either I forgot, or something else happened. What I have discovered is that the remaining strength in C3 and C4 in the second set of plots above, is due to an iterations problem. I had been keeping the default iterations for opd_expand_segments which is 2, and when creating the above plots, I had changed it to 15 to match what I use for opd_expand_nonorthonormal but that change didn't get propagated so it looked to me that that had not made a difference. It looks to me like the best solution now is to use iterations=15 for opd_expand_segments in order to get get a better solution, however, I do want to reiterate that the results between opd_expand_nonorthonormal and opd_expand_segments are still different. Here is my simplified notebook where I have set the default iterations to the poppy default and have shown a couple of example of different iterations for the decomposition of the same OPD, using both methods.

I have also moved the get_basis function, though that hasn't seemed to make much of a difference.

[mperrin]

The default iterations stuff bothers me; I don't know why it needs to be so high. Need to figure out a way to make this a more automatic process, where for instance you give it a desired tolerance and it automatically iterates until it achieves that tolerance. I'll take a look at the notebook, thanks.

[kjbrooks]

And here is grab_opd_info.py since that is necessary to run the notebook.