1 | #pragma rtGlobals=1 // Use modern global access method. |
---|
2 | #pragma IgorVersion=6.1 |
---|
3 | |
---|
4 | //////////////////////////////////////////////////// |
---|
5 | // |
---|
6 | // calculates the scattering from a rectangular solid |
---|
7 | // i.e. a parallelepiped with sides a < b < c |
---|
8 | // |
---|
9 | // - the user must make sure that the constraints are not violated |
---|
10 | // otherwise the calculation will not be correct |
---|
11 | // |
---|
12 | // From: Mittelbach and Porod, Acta Phys. Austriaca 14 (1961) 185-211. |
---|
13 | // equations (1), (13), and (14) (in German!) |
---|
14 | // |
---|
15 | // note that the equations listed in Feigin and Svergun appears |
---|
16 | // to be wrong - they use equation (12), which does not appear to |
---|
17 | // be a complete orientational average (?) |
---|
18 | // |
---|
19 | // a double integral is used, both using Gaussian quadrature |
---|
20 | // routines that are now included with GaussUtils |
---|
21 | // 20-pt quadrature appears to be enough, 76 pt is available |
---|
22 | // by changing the function calls |
---|
23 | // |
---|
24 | //////////////////////////////////////////////////// |
---|
25 | |
---|
26 | //this macro sets up all the necessary parameters and waves that are |
---|
27 | //needed to calculate the model function. |
---|
28 | // |
---|
29 | Proc PlotParallelepiped(num,qmin,qmax) |
---|
30 | Variable num=100, qmin=.001, qmax=.7 |
---|
31 | Prompt num "Enter number of data points for model: " |
---|
32 | Prompt qmin "Enter minimum q-value (A^1) for model: " |
---|
33 | Prompt qmax "Enter maximum q-value (A^1) for model: " |
---|
34 | // |
---|
35 | Make/O/D/n=(num) xwave_Parallelepiped, ywave_Parallelepiped |
---|
36 | xwave_Parallelepiped = alog(log(qmin) + x*((log(qmax)-log(qmin))/num)) |
---|
37 | Make/O/D coef_Parallelepiped = {1,35,75,400,1e-6,6.3e-6,0} //CH#2 |
---|
38 | make/o/t parameters_Parallelepiped = {"Scale Factor","Shortest Edge A (A)","B (A)","Longest Edge C (A)","SLD particle (A^-2)","SLD solvent (A^-2)","Incoherent Bgd (cm-1)"} //CH#3 |
---|
39 | Edit parameters_Parallelepiped, coef_Parallelepiped |
---|
40 | |
---|
41 | Variable/G root:g_Parallelepiped |
---|
42 | g_Parallelepiped := Parallelepiped(coef_Parallelepiped,ywave_Parallelepiped, xwave_Parallelepiped) |
---|
43 | Display ywave_Parallelepiped vs xwave_Parallelepiped |
---|
44 | ModifyGraph marker=29, msize=2, mode=4 |
---|
45 | ModifyGraph log=1 |
---|
46 | Label bottom "q (A\\S-1\\M) " |
---|
47 | Label left "I(q) (cm\\S-1\\M)" |
---|
48 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
49 | |
---|
50 | AddModelToStrings("Parallelepiped","coef_Parallelepiped","parameters_Parallelepiped","Parallelepiped") |
---|
51 | // |
---|
52 | End |
---|
53 | |
---|
54 | // - sets up a dependency to a wrapper, not the actual SmearedModelFunction |
---|
55 | Proc PlotSmearedParallelepiped(str) |
---|
56 | String str |
---|
57 | Prompt str,"Pick the data folder containing the resolution you want",popup,getAList(4) |
---|
58 | |
---|
59 | // if any of the resolution waves are missing => abort |
---|
60 | if(ResolutionWavesMissingDF(str)) //updated to NOT use global strings (in GaussUtils) |
---|
61 | Abort |
---|
62 | endif |
---|
63 | |
---|
64 | SetDataFolder $("root:"+str) |
---|
65 | |
---|
66 | // Setup parameter table for model function |
---|
67 | Make/O/D smear_coef_Parallelepiped = {1,35,75,400,1e-6,6.3e-6,0} //CH#4 |
---|
68 | make/o/t smear_parameters_Parallelepiped = {"Scale Factor","Shortest Edge A (A)","B (A)","Longest Edge C (A)","SLD particle (A^-2)","SLD solvent (A^-2)","Incoherent Bgd (cm-1)"} |
---|
69 | Edit smear_parameters_Parallelepiped,smear_coef_Parallelepiped //display parameters in a table |
---|
70 | |
---|
71 | // output smeared intensity wave, dimensions are identical to experimental QSIG values |
---|
72 | // make extra copy of experimental q-values for easy plotting |
---|
73 | Duplicate/O $(str+"_q") smeared_Parallelepiped,smeared_qvals // |
---|
74 | SetScale d,0,0,"1/cm",smeared_Parallelepiped // |
---|
75 | |
---|
76 | Variable/G gs_Parallelepiped=0 |
---|
77 | gs_Parallelepiped := fSmearedParallelepiped(smear_coef_Parallelepiped,smeared_Parallelepiped,smeared_qvals) //this wrapper fills the STRUCT |
---|
78 | |
---|
79 | Display smeared_Parallelepiped vs smeared_qvals // |
---|
80 | ModifyGraph log=1,marker=29,msize=2,mode=4 |
---|
81 | Label bottom "q (A\\S-1\\M)" |
---|
82 | Label left "I(q) (cm\\S-1\\M)" |
---|
83 | AutoPositionWindow/M=1/R=$(WinName(0,1)) $WinName(0,2) |
---|
84 | |
---|
85 | SetDataFolder root: |
---|
86 | AddModelToStrings("SmearedParallelepiped","smear_coef_Parallelepiped","smear_parameters_Parallelepiped","Parallelepiped") |
---|
87 | End |
---|
88 | |
---|
89 | |
---|
90 | |
---|
91 | //AAO version, uses XOP if available |
---|
92 | // simply calls the original single point calculation with |
---|
93 | // a wave assignment (this will behave nicely if given point ranges) |
---|
94 | Function Parallelepiped(cw,yw,xw) : FitFunc |
---|
95 | Wave cw,yw,xw |
---|
96 | |
---|
97 | #if exists("ParallelepipedX") |
---|
98 | MultiThread yw = ParallelepipedX(cw,xw) |
---|
99 | #else |
---|
100 | yw = fParallelepiped(cw,xw) |
---|
101 | #endif |
---|
102 | return(0) |
---|
103 | End |
---|
104 | |
---|
105 | // calculates the form factor of a rectangular solid |
---|
106 | // - a double integral - choose points wisely |
---|
107 | // |
---|
108 | Function fParallelepiped(w,x) : FitFunc |
---|
109 | Wave w |
---|
110 | Variable x |
---|
111 | // Input (fitting) variables are: |
---|
112 | //[0] scale factor |
---|
113 | //[1] Edge A (A) |
---|
114 | //[2] Edge B (A) |
---|
115 | //[3] Edge C (A) |
---|
116 | //[4] contrast (A^-2) |
---|
117 | //[5] incoherent background (cm^-1) |
---|
118 | // give them nice names |
---|
119 | Variable scale,aa,bb,cc,contr,bkg,inten,qq,ii,arg,mu,sldp,slds |
---|
120 | scale = w[0] |
---|
121 | aa = w[1] |
---|
122 | bb = w[2] |
---|
123 | cc = w[3] |
---|
124 | sldp = w[4] |
---|
125 | slds = w[5] |
---|
126 | bkg = w[6] |
---|
127 | |
---|
128 | contr = sldp - slds |
---|
129 | // mu = bb*x //scale in terms of B |
---|
130 | // aa = aa/bb |
---|
131 | // cc = cc/bb |
---|
132 | |
---|
133 | inten = IntegrateFn20(PP_Outer,0,1,w,x) |
---|
134 | // inten = IntegrateFn76(PP_Outer,0,1,w,x) |
---|
135 | |
---|
136 | inten *= aa*cc*bb //multiply by volume |
---|
137 | inten *= 1e8 //convert to cm^-1 |
---|
138 | inten *= contr*contr |
---|
139 | inten *= scale |
---|
140 | inten += bkg |
---|
141 | |
---|
142 | Return (inten) |
---|
143 | End |
---|
144 | |
---|
145 | // outer integral |
---|
146 | |
---|
147 | // x is the q-value - remember that "mu" in the notation = B*Q |
---|
148 | Function PP_Outer(w,x,dum) |
---|
149 | Wave w |
---|
150 | Variable x,dum |
---|
151 | |
---|
152 | Variable retVal,mu,aa,bb,cc,mudum,arg |
---|
153 | aa = w[1] |
---|
154 | bb = w[2] |
---|
155 | cc = w[3] |
---|
156 | mu = bb*x |
---|
157 | |
---|
158 | mudum = mu*sqrt(1-dum^2) |
---|
159 | retval = IntegrateFn20(PP_inner,0,1,w,mudum) |
---|
160 | // retval = IntegrateFn76(PP_inner,0,1,w,mudum) |
---|
161 | |
---|
162 | cc = cc/bb |
---|
163 | arg = mu*cc*dum/2 |
---|
164 | if(arg==0) |
---|
165 | retval *= 1 |
---|
166 | else |
---|
167 | retval *= sin(arg)*sin(arg)/arg/arg |
---|
168 | endif |
---|
169 | |
---|
170 | return(retVal) |
---|
171 | End |
---|
172 | |
---|
173 | //returns the integrand of the inner integral |
---|
174 | Function PP_Inner(w,mu,uu) |
---|
175 | Wave w |
---|
176 | Variable mu,uu |
---|
177 | |
---|
178 | Variable aa,bb,retVal,arg1,arg2,tmp1,tmp2 |
---|
179 | |
---|
180 | //NVAR mu = root:gEvalQval //already has been converted to S=2*pi*q |
---|
181 | aa = w[1] |
---|
182 | bb = w[2] |
---|
183 | aa = aa/bb |
---|
184 | |
---|
185 | //Mu*(1-x^2)^(0.5) |
---|
186 | |
---|
187 | //handle arg=0 separately, as sin(t)/t -> 1 as t->0 |
---|
188 | arg1 = (mu/2)*cos(Pi*uu/2) |
---|
189 | arg2 = (mu*aa/2)*sin(Pi*uu/2) |
---|
190 | if(arg1==0) |
---|
191 | tmp1 = 1 |
---|
192 | else |
---|
193 | tmp1 = sin(arg1)*sin(arg1)/arg1/arg1 |
---|
194 | endif |
---|
195 | if(arg2==0) |
---|
196 | tmp2 = 1 |
---|
197 | else |
---|
198 | tmp2 = sin(arg2)*sin(arg2)/arg2/arg2 |
---|
199 | endif |
---|
200 | retval = tmp1*tmp2 |
---|
201 | |
---|
202 | return(retVal) |
---|
203 | End |
---|
204 | |
---|
205 | //wrapper to calculate the smeared model as an AAO-Struct |
---|
206 | // fills the struct and calls the ususal function with the STRUCT parameter |
---|
207 | // |
---|
208 | // used only for the dependency, not for fitting |
---|
209 | // |
---|
210 | Function fSmearedParallelepiped(coefW,yW,xW) |
---|
211 | Wave coefW,yW,xW |
---|
212 | |
---|
213 | String str = getWavesDataFolder(yW,0) |
---|
214 | String DF="root:"+str+":" |
---|
215 | |
---|
216 | WAVE resW = $(DF+str+"_res") |
---|
217 | |
---|
218 | STRUCT ResSmearAAOStruct fs |
---|
219 | WAVE fs.coefW = coefW |
---|
220 | WAVE fs.yW = yW |
---|
221 | WAVE fs.xW = xW |
---|
222 | WAVE fs.resW = resW |
---|
223 | |
---|
224 | Variable err |
---|
225 | err = SmearedParallelepiped(fs) |
---|
226 | |
---|
227 | return (0) |
---|
228 | End |
---|
229 | |
---|
230 | // this is all there is to the smeared calculation! |
---|
231 | Function SmearedParallelepiped(s) :FitFunc |
---|
232 | Struct ResSmearAAOStruct &s |
---|
233 | |
---|
234 | // the name of your unsmeared model (AAO) is the first argument |
---|
235 | Smear_Model_20(Parallelepiped,s.coefW,s.xW,s.yW,s.resW) |
---|
236 | |
---|
237 | return(0) |
---|
238 | End |
---|
239 | |
---|
240 | |
---|
241 | |
---|
242 | ////////////For testing |
---|
243 | |
---|
244 | Proc PP_Rg_and_IZero() |
---|
245 | |
---|
246 | variable rg2,iz |
---|
247 | |
---|
248 | iz = coef_Parallelepiped[0] |
---|
249 | iz *= coef_Parallelepiped[1]*coef_Parallelepiped[2]*coef_Parallelepiped[3] |
---|
250 | iz *= (coef_Parallelepiped[4]-coef_Parallelepiped[5])^2 |
---|
251 | iz -= coef_Parallelepiped[6] |
---|
252 | iz *= 1e8 |
---|
253 | |
---|
254 | |
---|
255 | rg2 = coef_Parallelepiped[1]^2 |
---|
256 | rg2 += coef_Parallelepiped[2]^2 |
---|
257 | rg2 += coef_Parallelepiped[3]^2 |
---|
258 | rg2 /= 12 |
---|
259 | |
---|
260 | |
---|
261 | Print "I(q=0) [cm^-1] = ",iz |
---|
262 | Print "Rg [A] = ",sqrt(rg2) |
---|
263 | end |
---|