Can somebody explain in the simple words what are the physical reasons for the formation of the Distortion aberration? Why in some cases created Barrel distortion, in other cases created Pincushion distortion and in third case there is Mustache distortion? I want understand this phenomenon to improve optical setup restrictions. Thank you in advance!
when you place a straw in a glass of water, you will notice by looking at the glass sideways that the straw is broken in your view. It does not follow the straight line. This is due to different mediums that the straw is which is air and water (also the glass and curvature of the glass that you are holding). The light bends when travels from one medium to another.
Maybe one way to think of it is this way. First, aberrations appear in non-paraxial.
Let's say we are imaging a flat object onto a flat screen. As we move off axis in the object plan, lens-object distance increases. Therefore magnification must change as well - it depends on radial distance in the object plane.
This is different from a spherical aberration, when magnification depends on position of the ray in the entrance pupil (at the lens, basically).
Sorry about the potato explanation. It's been a while since my physical optics classes :D.
Thank you Adam, you gave a good explanation of the general aberration formation, but I interested in the specific aberration known as Distortion:
http://en.wikipedia.org/wiki/Distortion_(optics)
From the Wikipedia, I could not understand the reason for the distortion.
Vladimir,
Aberrations theory can be introduced on an abstract level. I was taught in this way many years ago. If you are a 'theoretician type' of a person, this might be for you.
The difference of actual position of a beam and ideal position as a function of parameters, describing the input beam, is presented as a Tailor series. It's easy to see that second (all even!) order terms are zero for an axially symmetric system. First order terms are just linear translation of coordinates (re-focusing). Usually only third order terms are considered. The space of these third order terms can be described via a set of orthogonal functions as a basis of the space. The usual terms distortion, comma etc. are the names of the functions of the most commonly used basis. Different bases are possible. Aberrations of 5th order are also considered sometimes, mostly for aspheric optics.
'Pincushion' and 'barrel' correspond to different signs of a third order term coefficient.
Hope this helps on a general (or is in meta?) level.
I want to add some lines to Vladimir's answer; perhaps more linked to the practical issues. From Feynman's lectures on physics I remember that the second order surfaces are not enough to describe Fermat's principle, while technologically it is hard to control the higher order corrections which must be taken into account. Also internal stresses in the optical material which are residual or due to nonzero weight of a lens will give another type of distortions.
Continuing a bit...
On the practical level, it's relatively easy to calculate new values of each of the aberration coefficients when you add an element to a system. Analytically, just by neglecting higher order terms. Obtaining the full analytical function is not scalable so easily in hand derivation. That's why aberration calculations for spherical elements were very popular throughout centuries.
I was doing this kind of calculations for a month or two when I was a 3rd year student, for a particular system. Then my supervisor made them all within 10 minutes, continuously asking "Do you have the same formula?", and accepted my work when all mine were the same as his.
I guess, it could be possible to obtain the full analytical function for much bigger systems with the help of computer symbolic algebra. I never seen or looked for this kind of results though.
Vladimir, I was taught there is no distortion in the lens system without spherical aberration and iris. So, let me take an example of an iris in front of a thin lens with spherical aberration. Because of the spherical aberration, the image of the iris is formed closer to the lens in its back than in case for without spherical aberration. Given a square grid object, the ray starting from each point on the object grid, passing through the iris, should crosses with the optical axis closer to the lens than ideal case, forming negatively distorted grid image. (barrel) Reversely thinking, if you set the square grid object in the image plane, an iris after the lens with spherical aberration will cause positively distorted grid image. (pincushion)
Shigeo, in your example you say spherical aberration, but your description corresponds better to field curvature...
Well, it is hard to explain without drawing. But, I am discussing about the longitudinal spherical aberration in imaging the iris, which determines the height of the principal ray on the conjugate plane of the object plane, therefore distortion.
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