What are 1st, 2nd and 3rd order lens aberrations?

[OPTIDONN]

I was doing some reading on lens aberrations and saw some referance to 1st and 3rd order aberrations. What are they and what is the differance? Are there and 2nd order aberrations?

 

[Claude Bile]

One can derive an equation that gives the error in an image on the image plane as a function of the incident (imperfect) wavefront. 1st order aberrations vary as h (where h is the distance from the centre of the lens), 3rd order aberrations vary as h^3 and so on. The reason there is no 2nd, 4th, 6th.. order aberrations (i.e. no h^2, h^4, h^6...dependances) is because of the cylindrical symmetry of the lens.

There is only 1 first order aberration and it is called defocus.

There are 5 third order aberrations;
Spherical Aberration
Coma
Astigmatism
Distortion
Curvature of Field

The origin of these aberrations (i.e. why they appear) can be found here;

http://wps.aw.com/wps/media/objects/877/898586/topics/topic12.pdf

Claude.

 

[OPTIDONN]

Much of this is still new to me what does ^ mean? Thanks for the answer though. It has cleared a few things up!

 

[Claude Bile]

It means 'to the power of', sorry I was a bit lazy.

h^3 = $$h^3$$

and so forth.

Claude.