Zernike Noll indexing different from what Anand expects?

[mperrin]

Issue by josePhoenix Monday Aug 31, 2015 at 18:29 GMT Originally opened as https://github.com/mperrin/poppy/issues/112

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Anand says tip and tilt are swapped, and maybe entries on lower rows of the Zernike pyramid as well. Note to self to check this and see if I can reproduce.

[mperrin]

Comment by josePhoenix Thursday Sep 03, 2015 at 19:17 GMT

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Can confirm that at least tip/tilt are swapped: zernike.noll_indices(2) returns (1, 1) when it should be (1, -1) for the first entry on the second row of the triangle. Everything else looks fine up to Z_15

[mperrin]

Comment by mperrin Thursday Sep 03, 2015 at 19:27 GMT

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I am confused.

Both wikipedia (https://en.wikipedia.org/wiki/Zernike_polynomials#Noll.27s_sequential_indices) and the Online Encyclopedia of Integer Sequences (https://oeis.org/A176988) indicate a mapping of j=2 --> (n,m) = (1,1). I.e. those agree with what is currently coded in poppy.

What reference are you using for j=2 --> (1, -1) ?

[mperrin]

Comment by mperrin Thursday Sep 03, 2015 at 19:31 GMT

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See also:

In [7]: poppy.zernike.noll_indices(2)
Out[7]: (1, 1)

In [8]: poppy.zernike.str_zernike(1,1)
Out[8]: '\\sqrt{4}* ( 1 r^1  ) * \\cos(1 \\theta)'

This agrees with the definition for $Z_2 = 2 r \cos \theta$ given in Table 1 of Noll 1976. See the following horrible URL:

https://www.osapublishing.org/view_article.cfm?gotourl=https%3A%2F%2Fwww%2Eosapublishing%2Eorg%2FDirectPDFAccess%2FCEE5519A%2DB678%2D4BF5%2D371C8DC6335E764C%5F56041%2Fjosa%2D66%2D3%2D207%2Epdf%3Fda%3D1%26id%3D56041%26seq%3D0%26mobile%3Dno&org=

[mperrin]

Comment by josePhoenix Thursday Sep 03, 2015 at 19:33 GMT

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Ah, Wikipedia is not in agreement with itself. I was going off what Anand said and this figure: https://upload.wikimedia.org/wikipedia/commons/9/9f/ZernikePolynome6.svg

[mperrin]

Comment by mperrin Thursday Sep 03, 2015 at 19:39 GMT

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Argh. Perhaps the appropriate bug fix here is replacing that figure on wikipedia?

Wait, ha, if you click through to the figure page, the caption has an erratum that the Noll indices for tip and tilt are interchanged. See https://en.wikipedia.org/wiki/Zernike_polynomials#/media/File:ZernikePolynome6.svg

Yeah that should just flat out be fixed on wikipedia. Do you want to edit the svg or shall I?

[mperrin]

Comment by josePhoenix Thursday Sep 03, 2015 at 19:44 GMT

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I can do it. Took me a minute to find my login info.

[mperrin]

Comment by josePhoenix Thursday Sep 03, 2015 at 19:55 GMT

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Ugh, uploading proves more complicated than anticipated.

[mperrin]

Comment by josePhoenix Thursday Sep 03, 2015 at 19:58 GMT

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https://commons.wikimedia.org/wiki/Commons:FAQ#How_can_I_upload_a_new_version_of_a_file.3F

Guess I'll check back next week!

[mperrin]

Comment by josePhoenix Monday Sep 21, 2015 at 21:57 GMT

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Fixed the picture on Wikipedia (and the copy I pinned to my wall)