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Doing a research on aberrations in order to

by Septim
Tags: aberrations, order, research
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Septim
#1
Mar12-12, 08:34 AM
P: 121
Hello everyone,

I am doing a research on aberrations in order to prepare a presentation. I looked at Optics, Hecht and Introduction to Optics, Pedrotti; however, I think they use different conventions for aberrations. Is there an established standard for aberrations(I heard the name Seidel)? I also wonder what the third order aberration means; is it sine expanded to include angle cubed or the aberrations are written up to 3rd order of the aperture diameter for example. I am pretty confused about this topic and in need of a good resource which will guide me and possibly derive some of the aberration formulas explaining each one in detail. Any suggestion is appreciated.

Thanks
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ProTerran
#2
Mar13-12, 10:31 AM
P: 29
It is very complex topic. There is so many good books like for example Rudolf Kingslake Lens Design Fundamentals - in that book you will find detail derivation of all kinds of aberrations.
Septim
#3
Mar13-12, 12:50 PM
P: 121
Thanks for your reply; I looked at that book but found it kind of confusing. If you have any other suggestions I would appreciate it.

Andy Resnick
#4
Mar13-12, 05:51 PM
Sci Advisor
P: 5,523
Doing a research on aberrations in order to

Quote Quote by Septim View Post
Hello everyone,

I am doing a research on aberrations in order to prepare a presentation. I looked at Optics, Hecht and Introduction to Optics, Pedrotti; however, I think they use different conventions for aberrations. Is there an established standard for aberrations(I heard the name Seidel)? I also wonder what the third order aberration means; is it sine expanded to include angle cubed or the aberrations are written up to 3rd order of the aperture diameter for example. I am pretty confused about this topic and in need of a good resource which will guide me and possibly derive some of the aberration formulas explaining each one in detail. Any suggestion is appreciated.

Thanks
The Seidel aberrations are referred to as 'third order' because the expansion sin(q) = q + q^3/3! + q^5/5!+... has a third-order polynomial after the paraxial sin(q) ~ q approximation. There are 7 third order aberrations (piston, tilt, spherical, coma, petvzal, distortion, astigmatism), a bunch of 5th order, 7th order, etc.

Alternatively, the wavefront aberration is written in terms of Zernike polynomials- mapping a Zernike coefficient with a Seidel aberration is not possible, but there are ways to convert one to the other.

A good resource (free, etc.) is the MIL-HDBK 141 (Optical Design)

http://www.optics.arizona.edu/ot/opt..._HDBK_141.html

3rd order aberrations are in Chapter 8.
Septim
#5
Mar14-12, 03:32 PM
P: 121
Thanks you I will take a look at that.
Septim
#6
Mar15-12, 08:43 PM
P: 121
I need to derive the third order spherical aberration formula for a thin lens which consists of two refracting surfaces how can I do so? I am attaching an image file containing the formula at the bottom of the page. Thanks for your help.

Attached Thumbnails
ss.jpg  


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