Optics - why chromatic aberrations

[Cspeed]

I understand that chromatic aberrations occur because the different wavelengths of light are separated, but I don't exactly understand what conditions control it. I understand the photography aspect better than the physics of this subject now.

I know that CAs are most common at the edges of photos, especially when the lens has been stopped down all the way (the aperture is completely open). Can any explain/point me to the reasoning behind this? Why should aperture affect this? Are there any equations which exist to explain it? And why at the edges only? Thank you.

 

[mgb_phys]

Chromatic aberation is simply different colours being bent by a different amount and so coming to a different point on the focal plane.
Rays at the edge of a lens have to be bent more and so the difference in bending between red and blue is larger in absolute terms and the separation is physically larger at the focal plane.

 

[Cspeed]

Thank you! That was so obvious and I don't know why I missed it. But what about aperture?

 

[mgb_phys]

At large apertures (ie small numbers, = big hole) the whole lens width is used, the rays at the edge of the glass bend more so more aberration.
With a small aperture (large number = small hole) only the centre of the lens is used, the rays are almost on axis so not bent much so less aberration.

 

[dlgoff]

Don't know if you need this wikipedia page since mgb_phys has given you the answer, but they do have some info that might be of interest.
http://en.wikipedia.org/wiki/Aberration_in_optical_systems"

 

[Cspeed]

Do you have any idea how much the CAs decrease as you decrease the size of the 'hole?' Does making the opening a little bit smaller reduce it mostly, or is it more of a linear relationship, so that half the diameter of opening means half as much CA? My guess is the latter.

 

[turbo]

It's more complex than that. CA can be combated in a lot of ways, one of the most popular recently seems to be making up lens-sets of materials of various refractive indexes to come up with a compromise in which longer and shorter wave-lengths can be coaxed to focus onto approximately the same points.

 

[Andy Resnick]

Chromatic aberration is casued by dispersion- the index of refraction varies with wavelength. In order to make 'achromats', 'apochromats', 'superachromats', etc.. requires use of different glasses that have different dispersions.

There's also two kinds of CA- longitudinal and transverse, and I think they are independent. Some optical designers further distinguish between transverse axial, longitudinal axial, transverse, and longitudinal. 'halos' are transverse, while longitudinal means different colors have different focal planes.

As for the severity of CA and numerical aperture (f/#), the aberration function depends on the height of the exit pupil-increasing the numerical aperture increases the exit pupil diameter, increasing the aberration.

 

[Savant13]

Reflecting telescopes (as opposed to reflecting) have no chromatic aberration. I find it surprising that there are no reflecting cameras

 

[turbo]

Reflecting telescopes (as opposed to reflecting) have no chromatic aberration. I find it surprising that there are no reflecting cameras

There have been quite a number of catadioptric lenses produced for SLRs over the years. They have a problem with the optical effects of central obstruction that can be more serious than the CA of well-corrected lenses.

 

[Cspeed]

As for the severity of CA and numerical aperture (f/#), the aberration function depends on the height of the exit pupil-increasing the numerical aperture increases the exit pupil diameter, increasing the aberration.

I don't fully understand the 'exit pupil,' but can you confirm that increasing the aperture from f/3.5 to f/22 increases the exit pupil diameter and causes more aberrations?

 

[turbo]

f:# is quite important in refractors. It is easier to figure longer focal lengths with less chromatic aberration because the curvatures of of the lens elements are shallower. It is much more difficult to figure fast refractors, and it becomes necessary to select lens materials with wider ranges of dispersions in order to pull this off. Takahashi and Astro-physics have both been able to produce some nice fast apochromatic refractors. Takahashi has a lot of astrophotographers on board. Their OTA's are pricey, but really high-quality.

 

[Andy Resnick]

I don't fully understand the 'exit pupil,' but can you confirm that increasing the aperture from f/3.5 to f/22 increases the exit pupil diameter and causes more aberrations?

Going from f/3.5 to f/22 *decreases* the numerical aperture and *decreases* the diameter of the exit pupil. The stopping down a lens by that much corresponds to a decrease in exit pupil diameter of 85% and a decreased throughput of 97% (if I did my math correctly).

 

[Andy Resnick]

Reflecting telescopes (as opposed to reflecting) have no chromatic aberration. I find it surprising that there are no reflecting cameras

Reflecting systems have their own set of problems- off-axis coma, for example:

http://en.wikipedia.org/wiki/Reflecting_telescope#Reflecting_telescope_designs

 

[Cspeed]

Wait - I just remembered something. I thought I heard that it's good to stop up a f/1.8 max aperture lens, for example, to 2.5 or so to reduce CA. And you would stoop up a f/2.5 max aperture lens to 3.2 or whatever to keep the CA from being too severe.

Can anyone say if it matters what the MAX aperture is?

 

[Andy Resnick]

Stopping down (increasing the f/# is stopping down, right?) a lens will, in general, decrease all aberrations, chromatic and otherwise. High NA lenses are more difficult to correct, and are more complex systems than low NA lenses.