Astig naming

[atsju]

I'm currently trying to learn more about the underlying algorithms to better understand some parts of DFTFringe.

George, your video is amazing: https://youtu.be/T5DNzVPwrzc?t=845

Wyant	Name
0	Piston
1	Tilt X
2	Tilt Y
3	Defocus
4	Astigmatism 0°
5	Astigmatism 45°
6	Coma X
7	Coma Y
8	Primary Spherical
9	Trefoil X
10	Trefoil Y oblique
11	Secondary Astigmatism 0°
12	Secondary Astigmatism 45°
13	Quadrafoil X
14	Quadrafoil Y oblique
15	Secondary Coma X
16	Secondary Coma Y
17	Secondary Spherical

I propose that we rename the astig terms 0° 45° instead X Y. All other terms are correct.
I think this is was just a small copy paste error in the beginning as all other terms are X/Y and now everybody got used to it.

Perhaps there is a historical reason for the current naming that I'm unaware of, but if not, it might make the terminology a little clearer for new users.

[githubdoe]

Yes it is historical and x/y is the correct term but confusing to most all. However that is it's name.

[atsju]

I found a paper from Mr. Wyant
https://wp.optics.arizona.edu/jcwyant/wp-content/uploads/sites/13/2016/08/Zernike_Polynomials_For_The_Web.pdf

Also other papers use "oblique" for trefoil, quadrafoil and non orthogonal terms. Which is less confusing.

Many naming conventions are probably coexisting.

[gr5]

Mostly I've seen it called "oblique" or "Y". I'm probably the only one who ever called it "45".

[gr5]

Here's a sample Zygo report. In the teal area at the top right they have total astig magnitude and angle. To me that's the most useful way to present that particular zernike data but seems like too much work.

[atsju]

I have found "oblique" (most occurence) and "at 45°" but no "Y" ouside of DFTFringe

We already have polar astig (angle and magnitude) in astig stats dialog :)

[gr5]

What do they call "x astig"?

[atsju]

From the 2 sources I cited, these are the namings. But there are probably other.

[githubdoe]

Y was the term used in the era that DFTFringe was first written. It was not; invented by me. It was not a typo.

[atsju]

Thanks for the clarification. I agree that X/Y astigmatism is a valid convention and that my earlier assumption that it was incorrect was too strong.

My intention was not to argue correctness, but to suggest that terminology such as vertical/oblique (or 0°/45°) may be more familiar to many optics users, as it is common in the literature.

That said, I understand the desire to keep consistency with the existing codebase and nomenclature.

[githubdoe]

They are called x and y because in polar form they use cos and sin terms respectively.

Many find the X term confusing thinking it only defines how much the astig is along the x axis. But instead it defines the major axis which is X and the sign defines if that edge goes up or down compared to the middle. When the sign is - the edge along the vertical axis curves up instead of along the horizontal axis.

[githubdoe]

The polar form of astig is much more intuitive. Since astig has a magnitude and a angle. That is why I added the show astig as polar function. It is much more intuitive I think. Find it under the View menu.

[githubdoe]

You see astig is a combination of both the X and y. Neither each alone can tell you enough about the asig. All the asymmetric terms need more than one term to describe them but they are actually just a magnitude and an angle. In reality as a quality metric it is usually enough to just look at their magnitude checking that they are near zero. If you need more info in order to figure them directly (Usually a bad idea) then you use the contour or 3D plot or specifically for astig use the view polar astig command.

[atsju]

Thank you Dale. It's clear.

Total astig is a combination of X (also named horizontal or vertical or 0°) astig on the right and of Y (also named oblique or 45°) astig on the left

[githubdoe]

The important part of Zernike values to DFTFringe is that it needs to use only a few of them and the user needs to understand just a few as well.

DFTFringe needs to subtract piston, tilt, and defocus from the wave front. They are attributes of the setup and not of the mirror. It may need to also subtract a portion of SA that too is an attribute of the test and not the mirror.

The user should be concerned with astig and primary SA when doing figuring. All other terms usually will be (should be ) next to 0. If they are not zero the errors will show up in all the plots and so one does not need to concern themselves with their zernike values at all. Even the values of astig and SA show up in the plots so that one does not really have to look at the zernike values either. It sometimes helps to look at them but you don't really have to.

[gr5]

So Dale, since most software out there seems to use "45" or "oblique", is it okay to change it or do you really want it to be X and Y astig?