5 June 2018 Alternative approach to find start points for polychromatic correction
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Abstract
The use of Abbe-numbers to choose lens materials is well established in the optical design community. Also the color correction impact of rotationally symmetric diffractive structures (DOE) has a simple expression as Abbe-number. Tables of relative partial dispersions facilitate the way of finding tri- or polychromatic corrections as well. But these tables are only available for important wavebands like VIS, MWIR and LWIR. Apart from these bands, Abbe-numbers and partial dispersions must be generated or, in case of DOE, given relations have limited evidence. An alternative approach is taken from the power-relation of the thin lens model. Its geometrical part is collected as curvature difference. The glass selecting part is the equation term containing the refractive index. The DOE-power depends on the first term of phase shift expansion and the wavelength. This first term fixes the geometry of the DOE. Relations to the step height of DOE in different wavebands will be provided. The sum of all optical powers (refractive and diffractive) has to be equal to the reciprocal of the focal length of the entire lens system. An arbitrary number of wavelengths might be taken into consideration, and a system of linear equations is generated. Doing so, the minimum number of power elements (refractive and diffractive) for a polychromatic correction can be determined. The number of respected wavelengths defines the kind of chromatic correction. Calculated single lens powers and DOE-geometry serve as reasonable starting points for the lens design procedure. In the dichromatic case (often called achromatic), the focal length is equal for two wavelengths. The proposed approach provides a system of two linear equations. The result in the VIS is the well-known crown/flint-combination without diffractive. An alternative solution – one-lens-design with DOE - is very common in the LWIR-band. Lenses with extreme long focal lengths need a trichromatic correction (sometimes also called apochromatic). The proposed approach generates a system of three linear equations: an equal power sum at three wavelengths. The result can be a three-lens-design without DOE having stronger curved surfaces and a less fast aperture. The alternative solution is a two-lens-design with DOE having a faster aperture. SWIR-examples will be provided. Using the proposed approach, the design of dual band systems starts with the request of four equal optical powers at boundaries of each waveband. It generates a system of four linear equations. The solution with the minimal expense is a three-lens-design using one DOE. A MWIR and LWIR-example with only three lenses will be provided. The proposed approach refers only to refractive index values of each lens material at interesting wavelengths. These values are available in electronic glass catalogues. The knowledge of Abbe-numbers is helpful to choose glasses, but the calculation of reasonable power distribution bases on refractive indexes. The proposed approach does not limit the number of respected wavelengths, since innovative multiband solutions can be simulated as well. This approach is a helpful tool for finding starting points for the lens design solutions with a minimal count of optical elements.
© (2018) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Norbert Schuster, Norbert Schuster, } "Alternative approach to find start points for polychromatic correction ", Proc. SPIE 10690, Optical Design and Engineering VII, 1069008 (5 June 2018); doi: 10.1117/12.2305710; https://doi.org/10.1117/12.2305710
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