Look here:

http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-7-6-262

Seidel coefficients are essentially just like Zernike coefficients.

http://www.telescope-optics.net/Seidel_aberrations.htm

http://www.wiley-vch.de/books/sample/3527403795_c01.pdf

http://fp.optics.arizona.edu/Sasian/2012opti517/2012/L4_2012_OPTI_517_Aberration_Coefficients.pdf

http://fp.optics.arizona.edu/OPTI471b/Reading/Lab6/Chapter3_BasicAberrationsandOpticalTesting.pdf

http://homepage.tudelft.nl/q1d90/FBweb/josa94.pdf

http://books.google.de/books?id=Jg1JW4kWD1UC&pg=PA287&lpg=PA287&dq=%22seidel+coefficients%22&source=bl&ots=inX7R-kBlc&sig=bS43cViW0FsdBh10mUq0UQ7fVa4&hl=de&sa=X&ei=r3lhUqH0OMTQtAabjIGQBw&ved=0CEsQ6AEwAw#v=onepage&q=%22seidel%20coefficients%22&f=false

http://books.google.de/books?id=aCC-IciqKkYC&pg=PA132&lpg=PA132&dq=%22seidel+coefficients%22&source=bl&ots=5sSBwNAJdQ&sig=mKP5pHND30adqOZ8KNwS30xijY4&hl=de&sa=X&ei=r3lhUqH0OMTQtAabjIGQBw&ved=0CHIQ6AEwCA#v=onepage&q=%22seidel%20coefficients%22&f=false

http://books.google.de/books?id=PuN7l2A2uzQC&pg=PA65&lpg=PA65&dq=%22seidel+coefficients%22&source=bl&ots=jIrA5cqpFp&sig=cjdY2XjqrvbHXWGG5YcBV7SWP9U&hl=de&sa=X&ei=r3lhUqH0OMTQtAabjIGQBw&ved=0CHYQ6AEwCQ#v=onepage&q=%22seidel%20coefficients%22&f=false

Samuel, the question/discussion was not concerning how Seidel coefficients are defined.

Well, then there is no (hi)story...

From the moment seidel aberrations were described (by seidel), were the seidel coefficients defined...

Do they have any physical meaning? No, are only weight factors as zernike coeffs are, and so describe just the magnitude/relative importance of the aberrations.

Can you redefine the coefficients, yes, but this will not add anything to the meaning of your coefficients.

As I understand your paragraph posted on Oct 17, you are interested interested in a description of the refracted and/or reflected wavefront from a symmetrical optical system. In some work co-authored by myself and colleague (JA Hoffnagle) published in 2008 and 2011, we construct an exact solution to the eikonal equation for a plane wave reflected or refracted from an arbitrary surface. The two JOSA-A papers are:

1. JA Hoffnagle and DL Shealy, "Refracting the k-function: Stavroudis's solution to the eikonal equation for multielement optical systems," JOSA-A, vol. 28.6, 1312-1321 (2011).

2. DL Shealy and JA Hoffnagle, "Wavefront and caustics of a plane wave refracted by an arbitrary surface," JOSA-A, vol. 25.9, 2370-2382 (2008).

Good luck....and there are a number of authors in optics literature who have used these results since 2008.

Samuel, yes, there is a solution to question which Kaccie has originally raised and which was also raised by Schwarzschild in 1905 as cited in DLS and JAH JOSA-A, 28.6, 1312-1321, 2011. See two JOSA-A for details....David

Samuel, I didn't see your last response until now. You still misunderstand me. The coefficients for Seidel aberration were taught (at least to me) as "wavefront coefficients". And yes, they do have physical meaning, and that is the peak-to-valley at the edge. Zernike coefficients also have physical meaning, and that is the rms of the corresponding mode. This is why you didn't answer the question. Suppose you defined a new set of coefficients and called them "Mosquera coefficients" and defined them to be Zernike coefficients divided by 3, then it would also confuse me.

David, I'm talking about Seidel coefficients.

Again, the situation is much more confuse then...

There are no single set of Zernike coefficients either...

You have the normalized ones (eg OSA, ISO, ANSI), and the non-normalized ones (eg Malacara, Born&Wolf) (following your example of Mosquera=Zernike/3) --> 2 sets

the ones following mathematical axis (eg OSA, ISO, ANSI), and the ones following the geographical axis (eg Malacara, Born&Wolf) --> 2 sets

the ones describing WFE and the ones describing OPD --> 2 sets

just in few lines you have 8 different sets of Zernike coeffs all describing EXACTLY the SAME wavefront...

Again, Seidel coefficients are essentially just like Zernike coefficients.

From the moment seidel aberrations were described (by seidel), were the seidel coefficients defined...

Both Seidel and Zernike are only weight factors of their corresponding polynomial base and so describe just the magnitude/relative importance of the aberrations (similar to Fourier series).

Can you redefine the coefficients, yes, but this will not add anything to the meaning of your coefficients.

I apologize Samuel, but I disagree with your reasoning. Thank you for trying to explain this from your point of view.

Thanks Kaccie,

no need to appologize.

But what do you think of the fact that there are at least 8 different (all valid) sets of Zernike coeffs all describing EXACTLY the SAME wavefront...?

In visual sciences this has changed in the last times after OSA//ISO//ANSI standards hold.

Hi Samuel,

Zernikes, at least at the level I'm familiar with, do not bother me a bit. If somebody gives me a list of Zernike coefficients and tells me that they're ordered according to OSA and are in microns, it would be clear to me which coefficient corresponds to which mode and what the rms error of that specific mode is.

OK, and does not happen the same if someone gives you a list of Seidel coefficients?

http://www.telescope-optics.net/Seidel_aberrations.htm

although:

http://www.sinopt.com/learning1/desnotes/seizern.htm

Maybe I have not got your point yet, but for me whether talking about Zernike or Seidel (or even Taylor or Fourier) coefficients is equivalent.

even there is a conversion scheme between Seidel and Zernike:

http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-7-6-262

http://www.opticsinfobase.org/ol/abstract.cfm?uri=ol-8-7-407

as well as:

http://www.univie.ac.at/nuhag-php/janssen/data/p210.pdf

I didn't realize there were a few more posts until now - All these resources Sam are great but I would like to ask you to please stop posting things that don't have anything to do with the topic of discussion. It just adds confusion... I did not ask how to convert from Seidel to Zernike.

If someone gives me a list of Seidel coefficients, I can of course convert them into something that's meaningful. My question was regarding Seidel coefficients themselves - specifically why they themselves don't seem to have any physical meaning.

I found the following material very interesting

http://www.wiley-vch.de/books/sample/3527403795_c01.pdf

So,please tell me the Author name and Book details (like ISBN No,etc)