### Thermal Power changes

 To predict how a lens will change power (inverse focal length) with temperature, the therm optic coefficient,β, is used. This applies to a refractive or diffractive lens. The prime ' is used to denote that power has been thermally cycled. The DΦ/DT is a derivative. The equation simplified by changing the derivative to a linear shift (Δ) or  DΦ/DT ≅ ΔΦ/ΔT. If the therm optic coefficient, β, is inverted it becomes the thermal abbe number Vt. This concept is introduced because making a passively athermal lens has identical equations for color correcting. Said another way: if you understand the equations behind constructing an achromatic doublet, then making a passively athermal lens is identical! Refractive therm optics coefficients (reference 1 to 4) The full equation for the therm optic coefficient is For infrared materials, the index of air is 1.0 and Dnair/dT=0 Schott literature in the 1970s used another form of the therm optic coefficient. This is used for inhomogeneous temperature effects Diffractive therm optic coefficients If you are using a diffractive optical element (DOE) or a holographic optical element (HOE), then the therm optic coefficient is different. So if you have plate window with a pure diffractive on it, the therm optic coefficient, β, is simple a function of the coefficient of thermal expansion, α, of the diffractive substrate. If you are doing a detailed model in a ray trace program and you want to see how a specific optical prescription parameter is thermally cycled, see here. References: Introduction to opto-mechanical design, D. Vukobratovich, SPIE press 1993"Introduction to Optomechanical Design", Course Notes Opti 690 University of Arizona, D. Vukobratovich, Spring 1995Private Communications with Dan Vukobratovich.Handbook of thermo-optic coefficients of optical materials with applications By Gorachand Ghosh"The influence of temperature on diffractive lens performance",  G. P. Behrmann, J. P. Bowen, Applied Optics, Vol. 32, Issue 14
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Scott Sparrold,
Oct 9, 2011, 7:22 AM
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Scott Sparrold,
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Scott Sparrold,
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Scott Sparrold,
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Scott Sparrold,
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