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- #!/bin/bash
- # This test case calculates the differential scattering
- # cross section from a Luneburg lens, as described in:
- # B. R. Johnson, Applied Optics 35 (1996) 3286-3296.
- #
- # The Luneburg lens is a sphere of radius a, with a
- # radially-varying index of refraction, given by:
- # m(r) = [2 - (r/a)**1]**(1/2)
- #
- # For the calculations, the Luneburg lens was approximated
- # as a multilayered sphere with 500 equally spaced layers.
- # The refractive index of each layer is defined to be equal to
- # m(r) at the midpoint of the layer: ml = [2 - (xm/xL)**1]**(1/2),
- # with xm = (xl-1 + xl)/2, for l = 1,2,...,L. The size
- # parameter in the lth layer is xl = l*xL/500. According to
- # geometrical optics theory, the differential cross section
- # can be expressed as:
- # d(Csca)/d(a**2*Omega) = cos(Theta)
- #
- # The differential cross section from wave optics is:
- # d(Csca)/d(a**2*Omega) = S11(Theta)/x**2
- PROGRAM='../../../scattnlay -l'
- L=500
- xL=60
- FULL_PROGRAM="$PROGRAM $L"
- for l in `seq 1 $L`; # Total number of layers
- do
- xlM1=$(echo "scale=2; ($l-1)*$xL/$L" | bc -l)
- xl=$(echo "scale=2; $l*$xL/$L" | bc -l)
- xm=$(echo "scale=2; ($xlM1+$xl)/2" | bc -l)
- ml=$(echo "scale=5; e(0.5*l(2-($xm/$xL)*($xm/$xL)))" | bc -l)
- FULL_PROGRAM="$FULL_PROGRAM $xl $ml 0.0"
- done
- FULL_PROGRAM="$FULL_PROGRAM -t 0.0 180.0 721"
- $FULL_PROGRAM
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