Seidel vs. Zernike

[musicvirtuoso]

So, I'm doing some research into monochromatic aberrations and want to pose a topic for discussion. I'm sure I'm only touching the tip of the iceberg with this, so hopefully someone (Darryl, maybe) can comment.

When we all initially learn about aberrations (especially those who are "self-taught"), we are given the names of the five Seidel aberrations and usually it's left at that. I can appreciate the optical profundity of Zernike's polynomials, but are these actually used in practical application for ophthalmic devices? As far as I've gathered when looking at portions of the unit disc (ie: when using limited data points), orthogonality of Zernike polynomials is not maintained as it is otherwise, which would be counter-intuitive to the concept or draw of the polynomials(?). Whereas apparently, they are useful when addressing aspheric surfaces because you can determine higher-order terms without the need for the lower-order terms, unlike the Seidel polynomial (is this correct?)

Apparently, beyond third-order aberrations, even the loose relationship between Seidel and Zernike falls aparts. So are there people, firstly, accounting for or compensating for these aberrations, and what do you use?

[Barry Santini]

It's easy (I think):

Newton needed calculus to facilitate mathematical handling of data for his equations of motion and thermodynamics.

Total lightpath analysis for the eye needs to handle the total wavefront aberration through Zernike polynomials.

Barry

[HarryChiling]

So, I'm doing some research into monochromatic aberrations and want to pose a topic for discussion. I'm sure I'm only touching the tip of the iceberg with this, so hopefully someone (Darryl, maybe) can comment.

When we all initially learn about aberrations (especially those who are "self-taught"), we are given the names of the five Seidel aberrations and usually it's left at that. I can appreciate the optical profundity of Zernike's polynomials, but are these actually used in practical application for ophthalmic devices? As far as I've gathered when looking at portions of the unit disc (ie: when using limited data points), orthogonality of Zernike polynomials is not maintained as it is otherwise, which would be counter-intuitive to the concept or draw of the polynomials(?). Whereas apparently, they are useful when addressing aspheric surfaces because you can determine higher-order terms without the need for the lower-order terms, unlike the Seidel polynomial (is this correct?)

Apparently, beyond third-order aberrations, even the loose relationship between Seidel and Zernike falls aparts. So are there people, firstly, accounting for or compensating for these aberrations, and what do you use?

They are different ways of describing the same thing.

[musicvirtuoso]

It's easy (I think):

Newton needed calculus to facilitate mathematical handling of data for his equations of motion and thermodynamics.

Total lightpath analysis for the eye needs to handle the total wavefront aberration through Zernike polynomials.

Barry

So this is to say that mathematically (for ophthalmic purposes), we use Zernike polynomials more often than Seidel's... ?

[musicvirtuoso]

They are different ways of describing the same thing.

Maybe I'm just approaching this incorrectly. Are you saying that they use both methods equally for describing aberrations?

[Barry Santini]

So this is to say that mathematically (for ophthalmic purposes), we use Zernike polynomials more often than Seidel's... ?

If I understand Zernickes correctly, they can be handled ("added", tec.?) easily to get to the sum or subtraction of the total wavefront.

Sorta like tint percentages vs. Densities. Densities can be added/subtracted. percentages cannot.

B

[HarryChiling]

So this is to say that mathematically (for ophthalmic purposes), we use Zernike polynomials more often than Seidel's... ?

Maybe I'm just approaching this incorrectly. Are you saying that they use both methods equally for describing aberrations?

My understanding is that zernike surfaces can be added together to produce more complex surfaces. Since the defraction focus of the human eye can be better described by a deformed wavefront than a conic wavefront the zernikes lend themselve well in application to describing a surface with a balanced amount of aberrations for best focus. The convetional expansion series do better at describing conic surfaces so they would be more difficult to use.

I hope that makes some sense.

[Uncle Fester]

(Pardon my ignorance showing)

Pronounced Seidel rhymes with bridal? Zernike rhymes with her nike (sneakers)?

[jherman]

off axis vertex?

[Darryl Meister]

I actually provide a fairly detailed discussion about Zernike and Seidel aberrations in part 2 of my two-part article, Wavefront Aberrations and Spectacle Lenses.

There are a couple of notable differences, including the fact that Seidel aberration equations generally apply only to a rotationally symmetrical optical system, like spherical lenses, and Seidel equations have "field-dependent" terms for off-axis viewing angles. Zernike aberration equations, on the other hand, also apply to asymmetrical optical systems and Zernike equations do not have field-dependent terms.

Because Zernike equations do not have field-dependent terms, Zernike aberrations are calculated at a specific angle of view, while many Seidel aberration equations include a term that varies with the angle of view, often increasing as the angle of view increases. Consequently, Zernike Astigmatism does not distinguish between on-axis astigmatism produced by surfaced cylinder power and oblique astigmatism produced at off-axis angles of view. Similarly, Zernike Defocus does not distinguish between on-axis defocus produced by surfaced sphere power and curvature of the field produced at off-axis angles of view.

Taylor polynomials are often associated with Seidel aberrations as well, and can be used in lieu of Zernike polynomials, although Zernike polynomials are more common in vision science for describing wavefront aberrations.

Best regards,
Darryl

[drk]

Great question, great answers. Good thread.

[Barry Santini]

Clarity as always, Darryl!

Thanks!

Barry

[musicvirtuoso]

That's awesome. Thanks, Darryl.

[rolandclaur]

thanks for the info and read.. I found it very informative.. a little over my head!! Anybody know any online resources that I can take advantage of to read further technical material without having to pay a steep fee like the one for abdo.org.uk? Thanks again

[musicvirtuoso]

(Pardon my ignorance showing)

Pronounced Seidel rhymes with bridal? Zernike rhymes with her nike (sneakers)?

Yes, Seidel -> like bridal ("z-eye-dle")
Zernike -> like "her lick" ("tserneekeh" - the best American transcription I could do)

[Darryl Meister]

Anybody know any online resources that I can take advantage of to read further technical material without having to pay a steep fee like the one for abdo.org.uk?

The article I wrote was for the ABDO, so be sure that you're not paying to read the very same article that I have already posted for free. Unless, of your course, you need CE credits for the ABDO.

You are probably not going to find anything more comprehensive on the wavefront aberrations of spectacle lenses, although there is a ton of stuff available on the Internet regarding ocular wavefront aberrations.

Best regards,
Darryl

[rolandclaur]

The article I wrote was for the ABDO, so be sure that you're not paying to read the very same article that I have already posted for free. Unless, of your course, you need CE credits for the ABDO.

You are probably not going to find anything more comprehensive on the wavefront aberrations of spectacle lenses, although there is a ton of stuff available on the Internet regarding ocular wavefront aberrations.

Best regards,
Darryl

Believe me I don't think I need to find anything more "comprehensive" then what you had written.. I'm still going over it and trying to understand it. I was just curious if any of you guys knew of any other websites connected to professional journals where I can have access to the articles written.. That abdo website is pretty pricey.. Thanks again Darryl