Chromatic Aberration

Index Lens concepts Thick lens concepts  

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Doublet for Chromatic AberrationThe use of a strong positive lens made from a low dispersion glass like crown glass coupled with a weaker high dispersion glass like flint glass can correct the chromatic aberration for two colors, e.g., red and blue. Such doublets are often cemented together (called achromat doublets) and may be used in compound lenses such as the orthoscopic doublet.

Index Lens concepts "Reference Jenkins & White p 156 ff  

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Achromat DoubletsAn achromat doublet does not completely eliminate chromatic aberration, but can eliminate it for two colors, say red and blue. 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. Cemented doublets of this type are a mainstay of lens design. 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. Chromatic aberration for three colors can be eliminated with and apochromat triplet.

Index Lens concepts "Reference MeyerArendt Ch 1.6  

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Apochromatic TripletsBetter correction of chromatic aberration has been achieved than that afforded by the achromat doublets. One could use three lenses to achieve the same focal length for three wavelengths. In practice, socalled 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.

Index Lens concepts Reference Pedrotti & Pedrotti  

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Spaced Doublet Approach to Chromatic Aberration
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. 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. 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 the power does not depend on the index of refraction n, you have eliminated chromatic aberration. The caveat is that these expressions presume thin lenses and paraxial rays (close to optical axis), so it is not a perfect solution. The power of a pair of thin lenses is given by where the individual lens powers for a thin lens can be expressedd as from the lensmakers formula. Here, K will be used to represent the dependence upon the radii of the lens surfaces. The power for the lens pair is then The derivative of the power with respect to n is This is the condition for no change in lens power with respect to the index n, i.e., zero chromatic aberration. Multiplying by (n1) allows us to express this in terms of the lens powers and yields And using P=1/f this can be expressed in terms of the focal lengths 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.

Index Lens concepts Reference MeyerArendt, Ch 5,4th Ed.  

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