// this method builds an R(rho, ft) array and then uses FFT to generate R(rho, t)
private double[] DetermineROfTimeFromROfFtForFixedRho(double rho, IOpticalPropertyRegion[] regions,
out double[] FFTTimeSequence)
{
// get ops of top tissue region
var op0 = regions[0].RegionOP;
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(op0.N);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(op0.N);
var diffusionParameters = GetDiffusionParameters(regions);
var layerThicknesses = GetLayerThicknesses(regions);
int numFreq = 512; // Kienle used 512 and deltaFreq = 0.1
// Kienle says deltaFrequency depends on source-detector separation
var deltaFrequency = 0.1; // 100 MHz
if (rho <= 3)
{
deltaFrequency = 0.5; // so far I've found this value works for smaller rho
}
var F = numFreq * deltaFrequency; // 51 GHz
var deltaTime = 1.0 / (numFreq * deltaFrequency); // 0.02 ns => T = 10 ns
// var homoSDA = new PointSourceSDAForwardSolver(); // debug with h**o SDA
// var rOfTime = new Complex[numFreq]; // debug array
// considerations: 2n datapoint and pad with 0s beyond (deltaTime * numFreq)
var rOfFt = new Complex[numFreq];
double[] ft = Enumerable.Range(0, numFreq).Select(x => x * deltaFrequency).ToArray();
FFTTimeSequence = Enumerable.Range(0, numFreq).Select(x => x * deltaTime).ToArray();
for (int i = 0; i < numFreq; i++)
{
// normalize by F=(numFreq*deltaFrequency)
rOfFt[i] = TemporalFrequencyReflectance(rho, ft[i], diffusionParameters, layerThicknesses, fr1, fr2) * F;
// rOfTime[i] = homoSDA.ROfRhoAndTime(regions[1].RegionOP, rho, t[i]); // debug array
}
// to debug, use R(t) and FFT to see if result R(ft) is close to rOfFt
//var dft2 = new MathNet.Numerics.IntegralTransforms.Algorithms.DiscreteFourierTransform();
//dft2.Radix2Forward(rOfTime, FourierOptions.NoScaling); // convert to R(ft) to compare with rOfFt
//var relDiffReal = Enumerable.Zip(rOfTime, rOfFt, (x, y) => Math.Abs((y.Real - x.Real) / x.Real));
//var relDiffImag = Enumerable.Zip(rOfTime, rOfFt, (x, y) => Math.Abs((y.Imaginary - x.Imaginary) / x.Imaginary));
//var maxReal = relDiffReal.Max();
//var maxImag = relDiffImag.Max();
//var dum1 = maxReal;
//var dum2 = maxImag;
//dft2.Inverse(rOfTime, FourierOptions.NoScaling); // debug convert to R(t)
// end debug code
// FFT R(ft) to R(t)
//var dft = new MathNet.Numerics.IntegralTransforms.Algorithms.DiscreteFourierTransform();
//dft.Inverse(rOfFt, FourierOptions.NoScaling); // convert to R(t)
Fourier.Inverse(rOfFt, FourierOptions.NoScaling);
var rOfTime = new double[FFTTimeSequence.Length];
rOfTime = rOfFt.Select(r => r.Real / (numFreq / 2)).ToArray();
return(rOfTime);
}
// protected methods
/// <summary>
/// Calculates the reflectance based on the integral of the radiance over the backward hemisphere...
/// </summary>
/// <param name="surfaceFluence">diffuse fluence at the surface</param>
/// <param name="surfaceFlux">diffuse flux at the surface</param>
/// <param name="mediaRefractiveIndex">refractive index of the medium</param>
/// <returns></returns>
protected static double GetBackwardHemisphereIntegralDiffuseReflectance(
double surfaceFluence, double surfaceFlux, double mediaRefractiveIndex)
{
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(
mediaRefractiveIndex);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(
mediaRefractiveIndex);
return(GetBackwardHemisphereIntegralDiffuseReflectance(surfaceFluence, surfaceFlux,
fr1, fr2));
}
public override IEnumerable <double> ROfRho(
IEnumerable <OpticalProperties> ops,
IEnumerable <double> rhos)
{
foreach (var op in ops)
{
DiffusionParameters dp = DiffusionParameters.Create(op, this.ForwardModel);
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(op.N);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(op.N);
foreach (var rho in rhos)
{
yield return(StationaryReflectance(dp, rho, fr1, fr2));
}
}
}
public override double ROfFx(IOpticalPropertyRegion[] regions, double fx)
{
// get ops of top tissue region
var op0 = regions[0].RegionOP;
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(op0.N);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(op0.N);
var diffusionParameters = GetDiffusionParameters(regions);
var layerThicknesses = GetLayerThicknesses(regions);
// check that embedded source is within top layer, otherwise solution invalid
if (diffusionParameters[0].zp > layerThicknesses[0])
{
throw new ArgumentException("Top layer thickness must be greater than l* = 1/(mua+musp)");
}
return(SpatialFrequencyReflectance(2 * Math.PI * fx, diffusionParameters, layerThicknesses, fr1, fr2));
}
public override IEnumerable <Complex> ROfRhoAndFt(IEnumerable <OpticalProperties> ops,
IEnumerable <double> rhos, IEnumerable <double> fts)
{
foreach (var op in ops)
{
DiffusionParameters dp = DiffusionParameters.Create(op, this.ForwardModel);
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(op.N);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(op.N);
foreach (var rho in rhos)
{
foreach (var ft in fts)
{
Complex k = ((op.Mua * dp.cn + Complex.ImaginaryOne * ft * 2 * Math.PI) /
(dp.cn * dp.D)).SquareRoot();
yield return(TemporalFrequencyReflectance(dp, rho, k, fr1, fr2));
}
}
}
}
// this method builds an R(fx, ft) array and then uses FFT to generate R(fx, t)
private double[] DetermineROfTimeFromROfFtForFixedFx(double fx, IOpticalPropertyRegion[] regions, out double[] FFTTimeSequence)
{
// get ops of top tissue region
var op0 = regions[0].RegionOP;
var fr1 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder1(op0.N);
var fr2 = CalculatorToolbox.GetCubicFresnelReflectionMomentOfOrder2(op0.N);
var diffusionParameters = GetDiffusionParameters(regions);
var layerThicknesses = GetLayerThicknesses(regions);
int numFreq = 512; // Kienle used 512 and deltaFreq = 0.1
// Kienle says deltaFrequency depends on source-detector separation
var deltaFrequency = 0.5; // 500 MHz good for all fx
var F = numFreq * deltaFrequency; // 51 GHz
var deltaTime = 1.0 / (numFreq * deltaFrequency); // 0.02 ns => T = 10 ns
// considerations: 2n datapoint and pad with 0s beyond (deltaTime * numFreq)
var rOfFt = new Complex[numFreq];
double[] ft = Enumerable.Range(0, numFreq).Select(x => x * deltaFrequency).ToArray();
FFTTimeSequence = Enumerable.Range(0, numFreq).Select(x => x * deltaTime).ToArray();
for (int i = 0; i < numFreq; i++)
{
// normalize by F=(numFreq*deltaFrequency)
rOfFt[i] = SpatialAndTemporalFrequencyReflectance(2 * Math.PI * fx, ft[i], diffusionParameters, layerThicknesses, fr1, fr2) * F;
}
// FFT R(ft) to R(t)
//var dft = new MathNet.Numerics.IntegralTransforms.Algorithms.DiscreteFourierTransform();
//dft.Radix2Inverse(rOfFt, FourierOptions.NoScaling); // convert to R(t)
Fourier.Radix2Inverse(rOfFt, FourierOptions.NoScaling);
var rOfTime = new double[FFTTimeSequence.Length];
rOfTime = rOfFt.Select(r => r.Real / (numFreq / 2)).ToArray();
return(rOfTime);
}