Chromatic aberration (II)
This aberration concerns only lenses. It is known as the secundary spectrum. Under polychromatic illumination, Abbe number, which expresses the relationship between the dispersion and the refracting power of the glass, defines the dispersion of wavelengths. When the different wavelengths of the visible spectrum do not focus exactly at the same focal plane, chromatic aberration occur. Their intensities depend on the dispersion of the glass. They occur because the refractive index is a function of the wavelength of the light, like in a prism. The blue light is more refracted that the red light producing fringes of false colors around bright objects (bright stars, Moon limb, venus, etc), mainly a purple or yellow secondary image. This chromatic aberration can be removed by using appropriate combination of glasses of different indexes of refraction, so that all colors focus at the same focal point.
Achromat or semi-apochromatic doublets can reduce this problem but cannot eliminate it, especially if you look far way from the axis where chromatic aberrations subsists. Only aprochromat triplets remove the residual colors, hence their expensive price.
When you look at a ray beam passing through a lens, it is easy to understand that its focal plan depends on the distance from the optical axis. Usually a optical surface is a section of sphere since it is the easiest shape to make. But with a spherical surface, lens or mirror, incoming rays from differents heigths from the axis do not bend at the same position and focus at slightly different distance along the axis. So if the center of the image stay in focus an bright, the edges of the field appear blurry and dimmer. This effect is called the spherical aberration. The factor to take in account is refered as the "lens bending".
Spherical aberration is dependent upon focal length, aperture, shape and how far the object is from the axis. Typically, a simple positive lens is undercorrected for the spherical aberration. The result is obvious : off-axis rays focus closer to the lens than the paraxial rays (rays entering the lens on or near the optical axis).
This aberration is quite easy to recognize when analyzing the diffraction image of a star by moving rapidly the focuser in and out. If you can stops the focuser at accurate positions, you will discover that the Airy discs are maybe not symmetric along the focus plane. This asymmetry around the paraxial focal point describes visually the spherical aberration.
The most famous case of spherical aberrations occured on the Hubble Space Telescope. Its optical defect was corrected by making the mirror a slightly non-spherical conic section and using new imaging algorithms like the well-known deconvolution function to correct its myopia. For some times Aries Instruments provides an optical accessory called SAFIX that removes this aberration. One uses it like a Barlow.
Coma aberration which means "comet" in latin, is similar to spherical aberration; it applies to rays entering the lens at an angle. You probably created this aberration being kid by tilting a lens under the sunlight. At the beginning the projected image of the sun is circular but as you tilt the lens with respect to the sun direction the resulting image takes an elongated shape, like a comet.
This coma aberration is dependent upon lens shape. Rays incoming from the periphery of the lens focus closer to the axis and produce a larger blurry spot than the paraxial rays. As coma is proportional to the distance to the central axis, more the rays are away from the center, more the focal point changes of position and get blurry images, mainly off-axis.
For a newtonian the length of the coma is expressed as L = (3/16)(D/F)2a, where D is the primary mirror diameter, F the focal length and a the distance to the axis. For the Palomar telescope of 5.08 m used in newtonian configuration, the focal length is 16.3 m. The relation tell us that L = a/55. That means that at 55" for the axis the coma is already 1" long ! To stay below that resolution, the useful field is only 9 mm wide...
This effect is the most obvious on fast scopes like dobsonians or poor quality astrographs. SCT will all their spherical mirrors display also an important coma larger than an optimized design with one or two aspherical or aplanetic mirrors (Ritchey-Chrétien, etc). Commercial designs could perform significantly better scopes but this is not often the case for financial reasons.
Coma can be corrected by using corrective lenses placed symmetrically around the axis. Ross or Wynne corrector using two to four lenses are built to correct this aberration as well as the others. For visual observations, this effect can be suppressed using for example the Tele Vue Paracorr suited to newtonian scopes