Lens Aberrations: 1st, 3rd & 2nd Orders Explained

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SUMMARY

This discussion clarifies the distinctions between first, second, and third order lens aberrations. First order aberrations, specifically defocus, vary linearly with the distance from the lens center (h). In contrast, third order aberrations, which include Spherical Aberration, Coma, Astigmatism, Distortion, and Curvature of Field, vary as h^3. The absence of second, fourth, and sixth order aberrations is attributed to the cylindrical symmetry of the lens. For further details, refer to the provided resource on the origins of these aberrations.

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  • Basic knowledge of wavefront theory in optics
  • Awareness of cylindrical symmetry in optical systems
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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?
 
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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.
 
Much of this is still new to me what does ^ mean? Thanks for the answer though. It has cleared a few things up!
 
It means 'to the power of', sorry I was a bit lazy.

h^3 = h^3

and so forth.

Claude.
 

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