But it remains a problem in several lens types, most notably ultrawide lenses, long telephoto lenses, and extreme zooms. It is accomplished by combining glass elements with different dispersion properties. Minimizing chromatic aberration is one of the traditional goals of lens design. It is sometimes confused with another effect, which we call pixel shift- a color channel offset that is typically uniform over the sensor and can be caused by physical misalignment of multi-chip sensors or demosaicing errors. It appears as color fringing, most visibly on tangential edges near the boundaries of the image. (Others include coma, astigmatism, spherical aberration, and curvature of field.) It occurs because the index of refraction of glass varies with the wavelength of light, i.e., glass bends different colors by different amounts. Note that if f 1 = f 2 the separation is just equal to the focal length of each of the lenses, and this condition is used for the Ramsden eypiece as mentioned above.Chromatic aberration (CA) is one of several aberrations that degrade lens performance. Multiplying by (n-1) allows us to express this in terms of the lens powers and yieldsĪnd using P=1/f this can be expressed in terms of the focal lengths This is the condition for no change in lens power with respect to the index n, i.e., zero chromatic aberration. The derivative of the power with respect to n is Here, K will be used to represent the dependence upon the radii of the lens surfaces. Where the individual lens powers for a thin lens can be expressedd asįrom the lens-makers formula. The power of a pair of thin lenses is given by The caveat is that these expressions presume thin lenses and paraxial rays (close to optical axis), so it is not a perfect solution. If the power does not depend on the index of refraction n, you have eliminated chromatic aberration. The variation of index of refraction with light wavelength or color is called dispersion, and the zero derivative implies that the dispersion is zero. If you take the derivative of the power expression with respect to n and set it equal to zero, you can solve for the required separation of the lenses which makes that derivative equal to zero. This approach to minimizing chromatic aberration uses two lenses of the same type of glass so that there is just one index of refraction n, and the expression for the combined power of the lens combination depends upon that index of refraction. Two equal positive lenses are used in eyepieces like the Ramsden eyepiece for correction. Spaced Doublet Approach to Chromatic AberrationĪnother approach to chromatic aberration reduction is to use two positive lenses separated by one half the sum of their wavelengths. In practice, so-called apochromatic lenses have been produced in the 4 to 16 mm focal length range for microscope objectives (Pedroti & Pedroti) with the use of fluorite elements. One could use three lenses to achieve the same focal length for three wavelengths. Lens Aberrationsīetter correction of chromatic aberration has been achieved than that afforded by the achromat doublets. If the powers of the lenses of the doublet give a focus point in front of the doublet as shown above, it is said to be a positive achromat.Ĭhromatic aberration for three colors can be eliminated with and apochromat triplet. Cemented doublets of this type are a mainstay of lens design. The idea is to use a lens pair with the strongest lens of low dispersion coupled with a weaker one of high dispersion calculated to match the focal lengths for two chosen wavelengths. Lens AberrationsĪn achromat doublet does not completely eliminate chromatic aberration, but can eliminate it for two colors, say red and blue. Such doublets are often cemented together (called achromat doublets)and may be used in compound lensessuch as the orthoscopic doublet. The use of a strong positive lens made from a low dispersion glasslike crown glass coupled with a weaker high dispersion glass like flint glass can correct the chromaticaberration for two colors, e.g., redand blue. One way to minimize thisaberration is to use glassesof different dispersion in a doublet or other combination. Chromatic Aberration Chromatic AberrationĪ lens will not focus different colors in exactly the same place because the focal length depends on refraction and the index of refraction for blue light (short wavelengths) is larger than that of red light (long wavelengths).The amount of chromaticaberration depends on the dispersion of the glass.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |