Two Ramp Filters
As an interesting design exercise, we decided to create two ramp filters. The goal is to create filters in which the transmittance increases (or decreases) linearly over some wavelength range. Too make it slightly more difficult, we also require the transmittance to be 0% and 100% on either side of the ramp.Here are the specific requirements for the normal-incidence increasing-transmittance ramp filter:
400 to 500 nm, T 500 to 700 nm, T increases linearly from 98%
700 to 800 nm, T > 98% The substrate has index 1.52 and is assumed to have an AR coating on its backside. The incident medium is air. The coating materials are SIO2 and TIO2.
We use the three continuous optimization targets. To find the thinnest possible design, we start with a single thin layer of TIO2 and use TFCalc's needle/tunneling optimization to design the filter from "scratch". Optimizing this design takes only a minute or two on a 2.8 GHz Pentium computer. The performance of the 23-layer design is shown here.
http://www.sspectra.com/designs/ramp1.gif
For the second design, we just replace transmittance by reflectance in the requirements. The performance of the filter, which also has 23 layers, is shown here.
http://www.sspectra.com/designs/ramp2.gif
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