Chromatic aberration
From Freepedia
Chromatic aberration is caused by the dispersion of the lens material, the variation of its refractive index n with the wavelength of light. The term purple fringing is also commonly used.
Since the focal length f of a lens is dependent on n, different wavelengths of light will be focused on different positions. Chromatic aberrations can be both longitudinal, in that different wavelengths are focused at a different distance from the lens; and transverse or lateral, in that different wavelengths are focussed at different postions in the focal plane (because the magnification of the lens also varies with wavelength).
Lateral chromatic abberation of a lens is seen as "fringes" of color around the image, because each color in the optical spectrum cannot be focused at a single common point on the optical axis. However, there exists a point called the circle of least confusion, where this effect can be minimized.
Chromatic aberration can be further minimized by using an achromatic doublet or achromat in which two materials with differing dispersion (usually crown and flint glass) are bonded together to form a single lens. This reduces the amount of chromatic aberration over a certain range of wavelengths, though it does not produce perfect correction. By combining more than two lenses of different chemical composition, the degree of correction can be further increased, as seen in an apochromatic lens or apochromat.
Many types of glass have been developed to reduce chromatic aberration, most notably, glasses containing fluorite. These hybridized glasses have a very low level of optical dispersion; only two compiled lenses made of these substances can yield a high level of correction.
Image:Lens6a.png Image:Lens6b.png
For a doublet consisting of two thin lenses in contact, the Abbe number of the lens materials is used to calculate the correct focal length of the lenses to ensure correction of chromatic abberation. If the focal lengths of the two lenses for light at the yellow Fraunhofer D-line (589.2 nm) are f1 and f2, then best correction occurs for the condition:
- <math>f_1 \cdot V_1 + f_2 \cdot V_2 = 0</math>
where V1 and V2 are the Abbe numbers of the materials of the first and second lenses, respectively. Since Abbe numbers are positive, one of the focal lengths must be negative, i.e. a diverging lens, for the condition to be met.
The overall focal length of the doublet f is given by the standard formula for thin lenses in contact:
- <math>\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2}</math>
and the above condition ensures this will be the focal length of the doublet for light at the blue and red Fraunhofer F and C lines (486.1 nm and 656.3 nm respectively). The focal length for light at other visible wavelengths will be similar but not exactly equal to this.
A disadvantage of over-correcting for chromatic aberration in photographic lenses is the production of unpleasant bokeh.
The use of achromats was an important step in the development of the optical microscope.
