Source Code for Module reflectometry.model3d.GSAXS_orthaganal

 1  # Copyright (C) 2008 University of Maryland
 
 2  # All rights reserved.
 
 3  # See LICENSE.txt for details.
 
 4  
 
 5  # Author: Christopher Metting
 
 6  # Starting Date: 4/14/2008
 
 7  
 
 8  
 
 9  from numpy import exp,cumsum,concatenate,empty,sinc,sum,sqrt,cos,sin,pi 
10  from scipy import special 
11  from sys import exit 
12  
 
13  
 
14 -def form_loop(type,feature_form,substrate_form,qx,qy,qz): 
15      Tz_sub,Tz = layer_loop(substrate_form.thickness,feature_form.depth,feature_form.SLD,substrate_form.SLD_sub,qz) 
16      total_form_sub = empty([len(qz),len(qx),len(qy)],'D') 
17      total_form_feature = empty([len(qz),len(qx),len(qy)],'D') 
18  
 
19      for i,qxi in enumerate(qx): 
20          for j,qyj in enumerate(qy): 
21              Txy = orth_shape(qxi,qyj,feature_form.depth,feature_form.Rx,feature_form.Ry,type) 
22              Txy_sub = orth_shape(qxi,qyj,substrate_form.thickness,substrate_form.Dx,substrate_form.Dy,'sub') 
23              total_form_sub[:,i,j] = (Tz_sub*Txy_sub)  
24              total_form_feature[:,i,j] = Tz*Txy 
25              
 
26      return total_form_feature,total_form_sub 
27  
 
28  
 
29 -def layer_loop(thickness,depth,SLD,SLD_sub,qz): 
30      #%:-) calculations for the substrate
 
31      # z_sub contains the positions of the interfaces for the base
 
32      z_sub = cumsum(concatenate(([0],thickness))) 
33      print z_sub 
34      Fz_sub = 0 # Fz  = total integral for rho e^{iQ_z z} over all sections 
35  
 
36      for m in range(len(thickness)): 
37          Fz_sub += z_form(SLD_sub[m], qz, z_sub[m], z_sub[m+1]) 
38      Tz_sub = Fz_sub/(1j*qz) 
39      
 
40      #calculations for the feature
 
41      # z contains the positions of the interfaces for the features
 
42      z = cumsum(concatenate(([sum(thickness)],depth))) 
43      print z 
44      Fz = 0 
45      
 
46      for n in range(len(depth)): 
47          Fz += z_form(SLD[n], qz, z[n], z[n+1]) 
48      Tz = Fz/(1j*qz) 
49      return Tz_sub,Tz 
50  
 
51  
 
52  
 
53  
 
54 -def z_form(rho, Qz,zlo,zhi): 
55      """
 
56      Calculations of \int_zlo^zhi{ rho e^{iQ_z z} dz }
 
57      """ 
58      return rho * (exp(1j * Qz * zhi) - exp(1j*Qz *zlo)) 
59  
 
60 -def orth_shape(qx,qy,depth,Rx,Ry,check): 
61  
 
62      if check == 'sub': 
63          return Rx * Ry * sinc(qx*(Rx/2))* sinc(qy*(Ry/2)) 
64  
 
65      
 
66      elif check == 'parallelepiped': 
67          return Rx * Ry * sinc(qx*(Rx/2))* sinc(qy*(Ry/2)) 
68  
 
69          
 
70      elif check =='prism_3': 
71          fraction = (2*sqrt(3)*exp(-1j*qy*(Rx/2)*sqrt(3)))  /(qx*(qx**2-3*qy**2)) 
72          function = qx * exp(1j*qy*(Rx/2)*sqrt(3)) - qx * cos(qx*(Rx/2))-1j * sqrt(3)*qy*sin(qx*(Rx/2)) 
73          return fraction * function 
74      
 
75      elif check == 'cylinder': 
76          x = sqrt((qx**2)+(qy**2))*(Rx) 
77          return  pi * 2 * ((Rx)**2)*((special.j1(x))/x) 
78      else: 
79          exit("Error: No match for requested feature type") 
80