Source Code for Module reflectometry.reduction.fresnel

 1  # This code is public domain 
 2   
 3  """ 
 4  Pure python Fresnel reflectivity calculator. 
 5  """ 
 6   
 7  from numpy import sqrt, exp, real, conj, pi, log, abs, choose 
 8   
 9 -class Fresnel: 
10      """ 
11      Function for computing the Fresnel reflectivity for a single interface. 
12   
13      rho,Vrho 
14          scattering length density of substrate and vacuum 
15      mu,Vmu 
16          absorption of substrate and vacuum (note that we do not correct 
17          for attenuation of the beam through the incident medium since we 
18          do not know the path length). 
19      sigma (angstrom) 
20          interfacial roughness 
21      """ 
22 -    def __init__(self, rho=1e-6, mu=0, sigma=0, Vrho=0, Vmu=0): 
23          self.rho,self.Vrho,self.mu,self.Vmu,self.sigma = rho,Vrho,mu,Vmu,sigma 
24   
25 -    def reflectivity(self, Q, L=1): 
26          """ 
27          Compute the Fresnel reflectivity at the given Q/wavelength. 
28          """ 
29          # If Q < 0, then we are going from substrate into incident medium. 
30          # In that case we must negate the change in scattering length density 
31          # and ignore the absorption. 
32          drho = self.rho-self.Vrho 
33          S = 4*pi*choose(Q<0,(-drho,drho)) \ 
34              + 2j*pi/L*choose(Q<0,(self.Vmu,self.mu)) 
35          kz = abs(Q)/2 
36          f = sqrt(kz**2 - S)  # fresnel coefficient 
37   
38          # Compute reflectivity amplitude, with adjustment for roughness 
39          amp = (kz-f)/(kz+f) * exp(-2*self.sigma**2*kz*f) 
40          # Note: we do not need to check for a divide by zero. 
41          # Qc^2 = 16 pi rho.  Since rho is non-zero then Qc is non-zero. 
42          # For mu = 0: 
43          # * If |Qz| < Qc then f has an imaginary component, so |Qz|+f != 0. 
44          # * If |Qz| > Qc then |Qz| > 0 and f > 0, so |Qz|+f != 0. 
45          # * If |Qz| = Qc then |Qz| != 0 and f = 0, so |Qz|+f != 0. 
46          # For mu != 0: 
47          # * f has an imaginary component, so |Q|+f != 0. 
48   
49          R = real(amp*conj(amp)) 
50          return R 
51   
52      # Make the reflectivity method the default 
53      __call__ = reflectivity 
54   
55 -def test(): 
56      return #TODO: Skip this test until reflectivity.model1d is fixed 
57   
58      # Rough silicon with an anomolously large absorbtion 
59      f = Fresnel(rho=2.07e-6, mu=1e-6, sigma=20) 
60   
61      import numpy 
62      import reflectometry.model1d as reflfit 
63      m = reflfit.Model() 
64      m.incident('Air',rho=0,mu=0) 
65      m.interface(sigma=f.sigma) 
66      m.substrate('Si',rho=f.rho*1e6,mu=f.mu*1e6) 
67   
68      L = 4.75 # Angstrom 
69      Q = numpy.linspace(0,0.1,11,'d') 
70      Rf = f(Q,L) 
71      Rm = m.reflectivity(Q,L,dz=0.01) 
72      #print numpy.vstack((Q,Rf,Rm)).T 
73   
74      # This is failing because reflectometry.model1d is failing; why that 
75      # is so has not yet been determined. 
76      relerr = numpy.linalg.norm((Rf-Rm)/Rm) 
77      assert relerr < 1e-10, "relative error is %g"%relerr 
78   
79  if __name__ == "__main__": test() 
80