/**
* This operation returns the value of the squared modulus of the specular reflectivity for a
* single wave vector Q.
*
* @param waveVectorQ the value of the wave vector
* @param wavelength the wavelength of the incident neutrons
* @param tiles the list of Tiles that contains the physical parameters needed for the
* calculation, including the scattering densities, absorption parameters and thicknesses.
* @return the squared modulus of the specular reflectivity
*/
public double getModSqrdSpecRef(double waveVectorQ, double wavelength, Tile[] tiles) {
double modSqrdSpecRef = 0.0;
if (wavelength > 0.0) {
// Variables only needed if we are going to do the work, i.e. -
// wavelength > 0.0.
Tile tile;
Complex aNm1Sq,
fNm1N,
rNm1N = new Complex(0.0, 0.0),
one = new Complex(1.0, 0.0),
qN = new Complex(0.0, 0.0),
rNNp1 = new Complex(0.0, 0.0);
// Get the bottom tile
int nLayers = tiles.length;
tile = tiles[nLayers - 1];
// Starting point--no reflected beam in bottom-most (bulk) layer
double qCSq = 16.0 * Math.PI * tile.scatteringLength;
double muLAbs = tile.trueAbsLength;
double mulInc = tile.incAbsLength;
double thickness = tile.thickness;
// Setup other values for the problem
double betaNm1 = 4.0 * Math.PI * (muLAbs + mulInc / wavelength);
Complex qNm1 = new Complex(waveVectorQ * waveVectorQ - qCSq, -2.0 * betaNm1);
qNm1 = qNm1.sqrt();
// Loop through to calculate recursion formula described in Parratt.
// Start at the bottom and work up.
for (int i = nLayers - 1; i > 0; i--) {
// Get the tile above tile[i] (started at the bottom
tile = tiles[i - 1];
// Calculate the normal component of Q for layer and layer-1
qN = qNm1;
qCSq = 16.0 * Math.PI * tile.scatteringLength;
muLAbs = tile.trueAbsLength;
mulInc = tile.incAbsLength;
thickness = tile.thickness;
betaNm1 = 4.0 * Math.PI * (muLAbs + mulInc / wavelength);
qNm1 = new Complex(waveVectorQ * waveVectorQ - qCSq, -2.0 * betaNm1);
qNm1 = qNm1.sqrt();
// Calculate phase factor, e^(-0.5*d*qNm1)
aNm1Sq =
(new Complex(qNm1.getImaginary(), qNm1.getReal()).multiply(-0.5 * thickness)).exp();
// CDiv(qNm1-qN,qNm1+qN)
fNm1N = qNm1.subtract(qN).divide(qNm1.add(qN));
// Calculate the reflectivity amplitude.
// CMult(aNm1Sq, CMult(aNm1Sq, CDiv(CAdd(rNNp1, fNm1N),
// CAdd(CMult(rNNp1, fNm1N), CReal(1)))))
Complex y = rNNp1.multiply(fNm1N).add(one);
Complex z = rNNp1.add(fNm1N);
rNm1N = aNm1Sq.multiply(aNm1Sq).multiply(z.divide((y)));
// Carry over to the next iteration
rNNp1 = rNm1N;
}
modSqrdSpecRef =
rNm1N.getReal() * rNm1N.getReal() + rNm1N.getImaginary() * rNm1N.getImaginary();
}
return modSqrdSpecRef;
}
