Format wavefront aberration distribution

[tcassanelli]

We now know that the wavefront aberration distribution, $W(x, y)$ is a function with dimensions, there could be many conventions but what I think we should adopt is the following: $$W(x, y) = \sum K_{n\ell} U^\elln \quad \Rightarrow \varphi = \frac{2\pi}{\lambda} W(x, y)$$ then the fill phase of the aperture distribution (a.k.a., the pupil function) is given by the factor $\frac{2\pi}{\lambda}$, hence for the phase to be in radians, the aberration must have units of length, not important what value are since that information will be absorbed by. $K{n\ell}$ set.

[tcassanelli]

Then I suggest to do the following:

phi = (W / wavel.to_value(apu.m) + delta / wavel) * 2 * np.pi * apu.rad

instead of

https://github.com/astronomy-laboratory/pyoof/blob/0c42031452327384d656ba0c3ff8ca55b46def5e/pyoof/aperture/aperture.py#L431

so we expose the constant wavel.

[tcassanelli]

You should also include the key parameter wavel in the phase function

https://github.com/astronomy-laboratory/pyoof/blob/0c42031452327384d656ba0c3ff8ca55b46def5e/pyoof/aperture/aperture.py#L256

or equivalently, you could force the system to return $W(x,y)$ with units of length, i.e.

https://github.com/astronomy-laboratory/pyoof/blob/0c42031452327384d656ba0c3ff8ca55b46def5e/pyoof/aperture/aperture.py#L247-L252

hence,

return W * apu.m

whatever you think is more elegant, requires less modifications, and solves the problem. I agree that there's no clear solution path here ... in the future we should come up with a better way of defining the coefficients.

[VicentePenaLet]

I made fits taking different amount of wavelengths from 250, 350 and 450 um. And compared the resulting Zernike Coefficients with the Real Zernike Coefficients of the simulation. In this graph I'm plotting the error in each of the K for the different test. it seems like the best fit is taking a single frequency of 450. Taking different frequencies seems to average to performance of the single frequency fits. below are the mean square errors for each of the wavelength combinations

• mse at wavel (250,): 2.8924365404896213e-11
• mse at wavel (350,): 1.602792976104331e-11
• mse at wavel (450,): 1.6930642357025475e-11
• mse at wavel (250, 350): 2.1127937234330985e-11
• mse at wavel (250, 450): 2.0603551318572783e-11
• mse at wavel (350, 450): 1.7808212820166247e-11
• mse at wavel (250, 350, 450): 1.8814149956317777e-11

[tcassanelli]

What do you mean with:

I'm plotting the error in each of the K for the different test.

Are taking the covariance matrix diagonal to obtain this value or is this something else?

Not sure if this is the best way to evaluate this. I would have done the following:

• Take those same simulations and results
• Compute the perpendicular displacement (i.e., the phase equivalent in perpendicular displacement units) for each case
• Compute the RMS for each displacement map (which should be given a tolerance since the edges get ugly; i.e., evaluating in a radius r < pr * .8)
• Then make this same plot but with the RMS results

That way you are comparing the overall fit and not only a few parameters isolated. Remember that even if this is a simulation the aperture is not super orthonormal and correlation among parameters will exist.

[tcassanelli]

Maybe there's a relationship between the pr and the observing frequency?