Project: Building a faster and lighter model

[tobias-liaudat]

This needs #4 .

• [x] For a reconstructed non-parametric WFE, check out the energy as a distribution of Zernikes up to index k. Then see the energy that is left when the WFE was decomposed over the k Zernikes (the energy of the non-parametric part).

This is useful to quantify how much energy is coming from a Zernike k contribution and how much from the rest (non-Zernike contribution) for one of the WFE we recover with WaveDiff.

• [x] Plot the PSF (super resolved) generated by the parametric contributions of the WFE alongside with the predicted (parametric and non-parametric) and the ground truth.

To discuss... Building a Delta WFE to approximate the PSF generated by HR WFE by a LR WFE.

• [x] Repeat experiment subtracting the zeroth-order zernike.

[CentofantiEze]

For the model (type poly) trained with as many Zernikes as the used for the dataset generation (n_gt_zernikes = 45) the predicted WFE is decomposed on its parametric and non-parametric contributions. The figure shows, for each training dataset, this contributions as well as their energy proportion in the WFE. The number of data-driven features is 6, as the degree of the non-parametric polynomial is set to d_max_nonparam = 2. More details about the parameters used for the model can be found in the bash file used to submit the training job.

[CentofantiEze]

Super-resolved PSFs from parametric WFE contributions for both models. As the non-parametric WFE doesn't contains a lot of information in this particular training set (n_zernikes = n_gt_zernikes) the non-param PSF doesn't contribute much to the final predicted PSF, one can see that the predicted PSF is pretty similar to the generated by the parametric WFE contribution.

In fact the relative RMS of the PSF non parametric residual against the predicted PSF is: 1.02%

[CentofantiEze]

We can see the parametric and non-parametric WFE contributions for each trained model. In this case both models have the following parameters: n_zernikes = 15, d_nonparam = 5. The reconstructed parametric WFE is not sufficient to represent the ground truth WFE and we can clearly see that the non-parametric contribution plays an important role now. In both cases the energy proportion of the non-param WFE increased a lot (since the parametric model is too simple). Some questions rise looking to this plot :

• Why parametric WFEs have different signs?
• Does the zero-order zernike, i.e. average value, plays a role on the forming of the PSF?

[tobias-liaudat]

• Why parametric WFEs have different signs? Mmm not sure, I should think a bit on that..

• Does the zero-order zernike, i.e. average value, plays a role on the forming of the PSF? Nope, the first three Zernike's don't play a role in the morphology of the PSF. The zeroth order doesn't affect at all the PSF. The first and second orders just represent an x-coordinate shift or an y-coordinate shift.

[CentofantiEze]

Here we can see the energy distribution of the WFE. The full WFE was predicted, then projected to the first n_zernikes = 15 polynomials and each coefficient was squared to get each zernike energy contribution. A n_zernikes WFE is reconstructed and subtracted to the predicted one to get the residual non-parametric WFE. The energy of this residual contribution was computed as the sum of the pixels squared over the number of pixels inside the circular aperture (internal product between zernikes). Te residual energy was split into the last 30 bins (gt_n_zernikes - n_zernikes) for a beter visualization.

Questions:

• Should I get the energy of each zernike from the learnt coefficients or should I re-project the WFE (param+nonparam) onto the corresponding coefficient as done here?
• Why the zero-order coefficient is so far from ground truth? Do we care?

[tobias-liaudat]

I think it is worth repeating the experiment but subtracting or the mean of the WFE or the zeroth-order. It should be approximately the same using the mean of the zeroth-order. However, it may change due to the fact that we have the obscurations...

For the moment, we could be coherent from what I did in the OPD metrics and subtract the mean of the WFE before projecting. For example, what is done here in the OPD metrics (for the WFE reconstruction) where I'm subtracting the mean here.

[CentofantiEze]

Only parametric vs full WFE to PSF. The parametric contribution of the predicted WFE was propagated to get the given PSF, which is compared with the predicted PSF. We can see that in general the only-parametric PSFs are much simpler and with round basic shape. This is expected because the number of zernikes used for the parametric part is fairly poor.

Questions/observations:

• The model that learnt with the full resolution dataset (4096x4096) produces more primitive/simple PSF shapes. This was seen for other stars too.
• The residual non-parametric contributes up to the 15% of the predicted PSF.

[tobias-liaudat]

• Should I get the energy of each Zernike from the learnt coefficients or should I re-project the WFE (param+nonparam) onto the corresponding coefficient as done here?

Mmm what would be the most interesting is to be able to see both. I mean, it would be nice to see the contribution of the "only parametric" part, and then also the total contribution of parametric+non-parametric. Then, it would be nice to see the predicted non-parametric energy for n_zerinke>15 on the different Zernikes for 15<n_zerinke<45. Because we can see the comparison with the ground truth. Then, it would be nice to see the rest in only one bin (for example put in the bin=46 all the energy left for n_zerinke>45.

I would have three labels for the bar plot, Ground truth energy (as before), Predicted param energy (the parametric estimation), Predicted full WFE energy (projecting the full WFE to all the different coefficients until n_zernike<45 and adding all the energy for the n_zernike>45 in the bin number 46.

• Why the zero-order coefficient is so far from the ground truth? Do we care?

As the zeroth-order does not affect the observations (they are normalized) the data is not constraining at all its value. This means that it can change kind of freely.

[tobias-liaudat]

Mm I'm rethinking this comment.

What would be the correct way of removing the zeroth-order?

I think that the correct way should be to extract the zeroth-order where the Zernikes are actually orthogonal. This is the case when we only consider the circular aperture (neglecting the other obscurations). So the best way would be to subtract the mean computed on the circular aperture. This is not exactly what I am currently doing in the OPD metrics :/ (I might need to update them...)

N.B. When we apply Euclid obscurations with the spider arms and the central obscurations, the Zernikes are not orthogonal no more.

[tobias-liaudat]

Experience done and is documented in the section 1 of the overleaf.