Plot SNR vs d_z

[tcassanelli]

We'd like to plot the output SNR against the radial offset $d_z$. The plot should tell us the level at which the SNR stabilizes with a threshold of SNR_threshold = 100. Notice that there are many parameters that could be vary here, but let's try to keep it consistent. Potential things to vary:

• Noise level
• d_z range
• Observing frequency
• Dish diameter (primary mirror) After this exercise we should know, roughly, what are the best combinations between $d_z$ and observing frequency.

[tcassanelli]

Notice that we should also check the SNR function, is it ok the one that we are currently using? this result will be super dependent on that

https://github.com/astronomy-laboratory/pyoof/blob/94d1e324837ededf2b1886ed1ebdfcebd2fa7474/pyoof/math_functions.py#L160-L216

[VicentePenaLet]

I plotted the SNR vs d_z for 3 different levels of noise. the d_z is increased from 0 to 10 with a 0.5 increment. note that the y axis is logarithmic. from this is easy to see how the snr falls-off as the telescope gets more and more defocused. we also can see how different frequencies are affected differentely.

here is another one where I increase the d_z from -5 to 5 with a 0.2 increment.

[tcassanelli]

Could you plot only the portion positive for $d_z$? adding the $-d_z$ I do not think includes more information since it should be the same. What surprises me is the fact that different frequencies do not differ that much? or I am thinking this wrong? Perhaps we should think about how to properly compute the SNR as well ...

[tcassanelli]

Also, since we know this from optics, what is the expected size of the out-of-focus beam given a certain frequency and $d_z$? With this information we could perhaps select the area (in squared degrees) for the SNR?

[VicentePenaLet]

Here is the graph showing only the positive d_z.

Could you plot only the portion positive for dz? adding the −dz I do not think includes more information since it should be the same. What surprises me is the fact that different frequencies do not differ that much? or I am thinking this wrong? Perhaps we should think about how to properly compute the SNR as well ...

My interpretation is that for very high values of d_z the results shouldn't change much because we are getting the whole beam regardless, and for very high values, we are getting mostly noise, so we should only care for what happens in the middle. In this case for example we can see there is a significant difference in the d_z in which the SNR goes lower than 100 which I think is interesting.

Regarding the calculation of SNR, in the case of the simulation we can exactly what's signal and what noise so we can calculate the exact SNR and use that as a baseline. Im not sure how to estimate it from real data though, in some applications you can estimate by dividing the mean by the variance of the data, but im not sure that is valid for our purposes.