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8.1 Introduction
A single element that is corrected for spherical aberration for two chosen wavelengths can be advantageous for alignment purposes in the visible spectrum when the application is in the infrared region. We design such an element for the helium-neon and the carbon dioxide lines. The wavelength for a HeNe laser is 0.6328μm, and is 10.6 μm for a CO 2 laser. The design principle is to determine the shape of the lens for the longer wavelength first and then place a diffractive structure on one side of the lens to add the required power for the shorter wavelength to maintain focus position. Since the wavelength ratio is large, 10.6â0.6328â17, the step height of the diffractive structure for the short wavelength is d=λ nâ1 =0.6328 2.5907â1 â
0.4μm.
This is in the domain of surface roughness for the infrared region.
First, we have to pick a material that is fitting for both wavelengths. We choose ZnSe with an index of refraction of n 0.6328 =2.5907andn 10.6 =2.4027. We elect for our design example 100 mm as a focal length and a relative aperture of fâ#=2, and begin with a thin-lens pre-design.
8.2 Basic Lens Shape for the Long Wavelength
Considering that it is much easier to place a diffractive structure on a flat surface when the number of zones is high, which will be the case here; we opt for an aspheric plano-convex shape and aspherize the first surface to eliminate spherical aberration.
The front radius is R 1 =(n 10.6 â1)f CO 2 =(2.4027â1)Ã100=140.27mm. This shape leads to a focal length for the shorter wavelength of f HeNe =R 1 n 0.6328 â1 =140.27 2.59207â1 =88.1054mm.
To maintain a common focal length for both wavelengths, a negative diffractive power has to be added to the flat surface. That diffractive power is determined with Ï D =Ï CO 2 âÏ HeNe .
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