1 | #pragma rtGlobals=1 // Use modern global access method. |
---|
2 | #pragma version=5.0 |
---|
3 | #pragma IgorVersion=6.1 |
---|
4 | |
---|
5 | |
---|
6 | // |
---|
7 | // resolution calculations for VSANS, under a variety of collimation conditions |
---|
8 | // |
---|
9 | // Partially converted (July 2017) |
---|
10 | // |
---|
11 | // |
---|
12 | // -- still missing a lot of physical dimensions for the SANS (1D) case |
---|
13 | // let alone anything more complex |
---|
14 | // |
---|
15 | // |
---|
16 | // SANS-like (pinhole) conditions are largely copied from the SANS calcuations |
---|
17 | // and are the traditional extra three columns |
---|
18 | // |
---|
19 | // Other conditions, such as white beam, or narrow slit mode, will likely require some |
---|
20 | // format for the resolution information that is different than the three column format. |
---|
21 | // The USANS solution of a "flag" is clunky, and depends entirely on the analysis package to |
---|
22 | // know exactly what to do. |
---|
23 | // |
---|
24 | // the 2D SANS-like resolution calculation is also expected to be similar to SANS, but is |
---|
25 | // unverified at this point (July 2017). 2D errors are also unverified. |
---|
26 | // -- Most importantly for 2D VSANS data, there is no defined output format. |
---|
27 | // |
---|
28 | |
---|
29 | |
---|
30 | // TODO: |
---|
31 | // -- some of the input geometry is hidden in other locations: |
---|
32 | // Sample Aperture to Gate Valve (cm) == /instrument/sample_aperture/distance |
---|
33 | // Sample [position] to Gate Valve (cm) = /instrument/sample_table/offset_distance |
---|
34 | // |
---|
35 | // -- the dimensions and the units for the beam stops are very odd, and what is written to the |
---|
36 | // file is not what is noted in the GUI - so verify the units that I'm actually reading. |
---|
37 | // |
---|
38 | |
---|
39 | |
---|
40 | |
---|
41 | |
---|
42 | //********************** |
---|
43 | // Resolution calculation - used by the averaging routines |
---|
44 | // to calculate the resolution function at each q-value |
---|
45 | // - the return value is not used |
---|
46 | // |
---|
47 | // equivalent to John's routine on the VAX Q_SIGMA_AVE.FOR |
---|
48 | // Incorporates eqn. 3-15 from J. Appl. Cryst. (1995) v. 28 p105-114 |
---|
49 | // |
---|
50 | // - 21 MAR 07 uses projected BS diameter on the detector |
---|
51 | // - APR 07 still need to add resolution with lenses. currently there is no flag in the |
---|
52 | // raw data header to indicate the presence of lenses. |
---|
53 | // |
---|
54 | // - Aug 07 - added input to switch calculation based on lenses (==1 if in) |
---|
55 | // |
---|
56 | // - called by CircSectAvg.ipf and RectAnnulAvg.ipf |
---|
57 | // |
---|
58 | // passed values are read from RealsRead |
---|
59 | // except DDet and apOff, which are set from globals before passing |
---|
60 | // |
---|
61 | // DDet is the detector pixel resolution |
---|
62 | // apOff is the offset between the sample aperture and the sample position |
---|
63 | // |
---|
64 | // |
---|
65 | // INPUT: |
---|
66 | // inQ = q-value [1/A] |
---|
67 | // lambda = wavelength [A] |
---|
68 | // lambdaWidth = [dimensionless] |
---|
69 | // DDet = detector pixel resolution [cm] **assumes square pixel |
---|
70 | // apOff = sample aperture to sample distance [cm] |
---|
71 | // S1 = source aperture diameter [mm] |
---|
72 | // S2 = sample aperture diameter [mm] |
---|
73 | // L1 = source to sample distance [m] |
---|
74 | // L2 = sample to detector distance [m] |
---|
75 | // BS = beam stop diameter [mm] |
---|
76 | // del_r = step size [mm] = binWidth*(mm/pixel) |
---|
77 | // usingLenses = flag for lenses = 0 if no lenses, non-zero if lenses are in-beam |
---|
78 | // |
---|
79 | // OUPUT: |
---|
80 | // SigmaQ |
---|
81 | // QBar |
---|
82 | // fSubS |
---|
83 | // |
---|
84 | // |
---|
85 | Function V_getResolution(inQ,lambda,lambdaWidth,DDet,apOff,S1,S2,L1,L2,BS,del_r,usingLenses,SigmaQ,QBar,fSubS) |
---|
86 | Variable inQ, lambda, lambdaWidth, DDet, apOff, S1, S2, L1, L2, BS, del_r,usingLenses |
---|
87 | Variable &fSubS, &QBar, &SigmaQ //these are the output quantities at the input Q value |
---|
88 | |
---|
89 | //lots of calculation variables |
---|
90 | Variable a2, q_small, lp, v_lambda, v_b, v_d, vz, yg, v_g |
---|
91 | Variable r0, delta, inc_gamma, fr, fv, rmd, v_r1, rm, v_r |
---|
92 | |
---|
93 | //Constants |
---|
94 | Variable vz_1 = 3.956e5 //velocity [cm/s] of 1 A neutron |
---|
95 | Variable g = 981.0 //gravity acceleration [cm/s^2] |
---|
96 | |
---|
97 | |
---|
98 | S1 *= 0.5*0.1 //convert to radius and [cm] |
---|
99 | S2 *= 0.5*0.1 |
---|
100 | |
---|
101 | L1 *= 100.0 // [cm] |
---|
102 | L1 -= apOff //correct the distance |
---|
103 | |
---|
104 | L2 *= 100.0 |
---|
105 | L2 += apOff |
---|
106 | del_r *= 0.1 //width of annulus, convert mm to [cm] |
---|
107 | |
---|
108 | BS *= 0.5*0.1 //nominal BS diameter passed in, convert to radius and [cm] |
---|
109 | // 21 MAR 07 SRK - use the projected BS diameter, based on a point sample aperture |
---|
110 | Variable LB |
---|
111 | LB = 20.1 + 1.61*BS //distance in cm from beamstop to anode plane (empirical) |
---|
112 | BS = bs + bs*lb/(l2-lb) //adjusted diameter of shadow from parallax |
---|
113 | |
---|
114 | //Start resolution calculation |
---|
115 | a2 = S1*L2/L1 + S2*(L1+L2)/L1 |
---|
116 | q_small = 2.0*Pi*(BS-a2)*(1.0-lambdaWidth)/(lambda*L2) |
---|
117 | lp = 1.0/( 1.0/L1 + 1.0/L2) |
---|
118 | |
---|
119 | v_lambda = lambdaWidth^2/6.0 |
---|
120 | |
---|
121 | // if(usingLenses==1) //SRK 2007 |
---|
122 | if(usingLenses != 0) //SRK 2008 allows for the possibility of different numbers of lenses in header |
---|
123 | v_b = 0.25*(S1*L2/L1)^2 +0.25*(2/3)*(lambdaWidth/lambda)^2*(S2*L2/lp)^2 //correction to 2nd term |
---|
124 | else |
---|
125 | v_b = 0.25*(S1*L2/L1)^2 +0.25*(S2*L2/lp)^2 //original form |
---|
126 | endif |
---|
127 | |
---|
128 | v_d = (DDet/2.3548)^2 + del_r^2/12.0 //the 2.3548 is a conversion from FWHM->Gauss, see http://mathworld.wolfram.com/GaussianFunction.html |
---|
129 | vz = vz_1 / lambda |
---|
130 | yg = 0.5*g*L2*(L1+L2)/vz^2 |
---|
131 | v_g = 2.0*(2.0*yg^2*v_lambda) //factor of 2 correction, B. Hammouda, 2007 |
---|
132 | |
---|
133 | r0 = L2*tan(2.0*asin(lambda*inQ/(4.0*Pi) )) |
---|
134 | delta = 0.5*(BS - r0)^2/v_d |
---|
135 | |
---|
136 | if (r0 < BS) |
---|
137 | inc_gamma=exp(gammln(1.5))*(1-gammp(1.5,delta)) |
---|
138 | else |
---|
139 | inc_gamma=exp(gammln(1.5))*(1+gammp(1.5,delta)) |
---|
140 | endif |
---|
141 | |
---|
142 | fSubS = 0.5*(1.0+erf( (r0-BS)/sqrt(2.0*v_d) ) ) |
---|
143 | if (fSubS <= 0.0) |
---|
144 | fSubS = 1.e-10 |
---|
145 | endif |
---|
146 | fr = 1.0 + sqrt(v_d)*exp(-1.0*delta) /(r0*fSubS*sqrt(2.0*Pi)) |
---|
147 | fv = inc_gamma/(fSubS*sqrt(Pi)) - r0^2*(fr-1.0)^2/v_d |
---|
148 | |
---|
149 | rmd = fr*r0 |
---|
150 | v_r1 = v_b + fv*v_d +v_g |
---|
151 | |
---|
152 | rm = rmd + 0.5*v_r1/rmd |
---|
153 | v_r = v_r1 - 0.5*(v_r1/rmd)^2 |
---|
154 | if (v_r < 0.0) |
---|
155 | v_r = 0.0 |
---|
156 | endif |
---|
157 | QBar = (4.0*Pi/lambda)*sin(0.5*atan(rm/L2)) |
---|
158 | SigmaQ = QBar*sqrt(v_r/rmd^2 +v_lambda) |
---|
159 | |
---|
160 | |
---|
161 | // more readable method for calculating the variance in Q |
---|
162 | // EXCEPT - this is calculated for Qo, NOT qBar |
---|
163 | // (otherwise, they are nearly equivalent, except for close to the beam stop) |
---|
164 | // Variable kap,a_val,a_val_l2,m_h |
---|
165 | // g = 981.0 //gravity acceleration [cm/s^2] |
---|
166 | // m_h = 252.8 // m/h [=] s/cm^2 |
---|
167 | // |
---|
168 | // kap = 2*pi/lambda |
---|
169 | // a_val = L2*(L1+L2)*g/2*(m_h)^2 |
---|
170 | // a_val_L2 = a_val/L2*1e-16 //convert 1/cm^2 to 1/A^2 |
---|
171 | // |
---|
172 | // sigmaQ = 0 |
---|
173 | // sigmaQ = 3*(S1/L1)^2 |
---|
174 | // |
---|
175 | // if(usingLenses != 0) |
---|
176 | // sigmaQ += 2*(S2/lp)^2*(lambdaWidth)^2 //2nd term w/ lenses |
---|
177 | // else |
---|
178 | // sigmaQ += 2*(S2/lp)^2 //2nd term w/ no lenses |
---|
179 | // endif |
---|
180 | // |
---|
181 | // sigmaQ += (del_r/L2)^2 |
---|
182 | // sigmaQ += 2*(r0/L2)^2*(lambdaWidth)^2 |
---|
183 | // sigmaQ += 4*(a_val_l2)^2*lambda^4*(lambdaWidth)^2 |
---|
184 | // |
---|
185 | // sigmaQ *= kap^2/12 |
---|
186 | // sigmaQ = sqrt(sigmaQ) |
---|
187 | |
---|
188 | |
---|
189 | Return (0) |
---|
190 | End |
---|
191 | |
---|
192 | |
---|
193 | // |
---|
194 | //********************** |
---|
195 | // 2D resolution function calculation - ***NOT*** in terms of X and Y |
---|
196 | // but written in terms of Parallel and perpendicular to the Q vector at each point |
---|
197 | // |
---|
198 | // -- it is more naturally written this way since the 2D function is an ellipse with its major |
---|
199 | // axis pointing in the direction of Q_parallel. Hence there is no way to properly define the |
---|
200 | // elliptical gaussian in terms of sigmaX and sigmaY |
---|
201 | // |
---|
202 | // For a full description of the gravity effect on the resolution, see: |
---|
203 | // |
---|
204 | // "The effect of gravity on the resolution of small-angle neutron diffraction peaks" |
---|
205 | // D.F.R Mildner, J.G. Barker & S.R. Kline J. Appl. Cryst. (2011). 44, 1127-1129. |
---|
206 | // [ doi:10.1107/S0021889811033322 ] |
---|
207 | // |
---|
208 | // 2/17/12 SRK |
---|
209 | // NOTE: the first 2/3 of this code is the 1D code, copied here just to have the beam stop |
---|
210 | // calculation here, if I decide to implement it. The real calculation is all at the |
---|
211 | // bottom and is quite compact |
---|
212 | // |
---|
213 | // |
---|
214 | // |
---|
215 | // |
---|
216 | // - 21 MAR 07 uses projected BS diameter on the detector |
---|
217 | // - APR 07 still need to add resolution with lenses. currently there is no flag in the |
---|
218 | // raw data header to indicate the presence of lenses. |
---|
219 | // |
---|
220 | // - Aug 07 - added input to switch calculation based on lenses (==1 if in) |
---|
221 | // |
---|
222 | // passed values are read from RealsRead |
---|
223 | // except DDet and apOff, which are set from globals before passing |
---|
224 | // |
---|
225 | // phi is the azimuthal angle, CCW from +x axis |
---|
226 | // r_dist is the real-space distance from ctr of detector to QxQy pixel location |
---|
227 | // |
---|
228 | // MAR 2011 - removed the del_r terms, they don't apply since no bining is done to the 2D data |
---|
229 | // |
---|
230 | Function V_get2DResolution(inQ,phi,lambda,lambdaWidth,DDet,apOff,S1,S2,L1,L2,BS,del_r,usingLenses,r_dist,SigmaQX,SigmaQY,fSubS) |
---|
231 | Variable inQ, phi,lambda, lambdaWidth, DDet, apOff, S1, S2, L1, L2, BS, del_r,usingLenses,r_dist |
---|
232 | Variable &SigmaQX,&SigmaQY,&fSubS //these are the output quantities at the input Q value |
---|
233 | |
---|
234 | //lots of calculation variables |
---|
235 | Variable a2, lp, v_lambda, v_b, v_d, vz, yg, v_g |
---|
236 | Variable r0, delta, inc_gamma, fr, fv, rmd, v_r1, rm, v_r |
---|
237 | |
---|
238 | //Constants |
---|
239 | Variable vz_1 = 3.956e5 //velocity [cm/s] of 1 A neutron |
---|
240 | Variable g = 981.0 //gravity acceleration [cm/s^2] |
---|
241 | Variable m_h = 252.8 // m/h [=] s/cm^2 |
---|
242 | |
---|
243 | |
---|
244 | S1 *= 0.5*0.1 //convert to radius and [cm] |
---|
245 | S2 *= 0.5*0.1 |
---|
246 | |
---|
247 | L1 *= 100.0 // [cm] |
---|
248 | L1 -= apOff //correct the distance |
---|
249 | |
---|
250 | L2 *= 100.0 |
---|
251 | L2 += apOff |
---|
252 | del_r *= 0.1 //width of annulus, convert mm to [cm] |
---|
253 | |
---|
254 | BS *= 0.5*0.1 //nominal BS diameter passed in, convert to radius and [cm] |
---|
255 | // 21 MAR 07 SRK - use the projected BS diameter, based on a point sample aperture |
---|
256 | Variable LB |
---|
257 | LB = 20.1 + 1.61*BS //distance in cm from beamstop to anode plane (empirical) |
---|
258 | BS = bs + bs*lb/(l2-lb) //adjusted diameter of shadow from parallax |
---|
259 | |
---|
260 | //Start resolution calculation |
---|
261 | a2 = S1*L2/L1 + S2*(L1+L2)/L1 |
---|
262 | lp = 1.0/( 1.0/L1 + 1.0/L2) |
---|
263 | |
---|
264 | v_lambda = lambdaWidth^2/6.0 |
---|
265 | |
---|
266 | // if(usingLenses==1) //SRK 2007 |
---|
267 | if(usingLenses != 0) //SRK 2008 allows for the possibility of different numbers of lenses in header |
---|
268 | v_b = 0.25*(S1*L2/L1)^2 +0.25*(2/3)*(lambdaWidth/lambda)^2*(S2*L2/lp)^2 //correction to 2nd term |
---|
269 | else |
---|
270 | v_b = 0.25*(S1*L2/L1)^2 +0.25*(S2*L2/lp)^2 //original form |
---|
271 | endif |
---|
272 | |
---|
273 | v_d = (DDet/2.3548)^2 + del_r^2/12.0 |
---|
274 | vz = vz_1 / lambda |
---|
275 | yg = 0.5*g*L2*(L1+L2)/vz^2 |
---|
276 | v_g = 2.0*(2.0*yg^2*v_lambda) //factor of 2 correction, B. Hammouda, 2007 |
---|
277 | |
---|
278 | r0 = L2*tan(2.0*asin(lambda*inQ/(4.0*Pi) )) |
---|
279 | delta = 0.5*(BS - r0)^2/v_d |
---|
280 | |
---|
281 | if (r0 < BS) |
---|
282 | inc_gamma=exp(gammln(1.5))*(1-gammp(1.5,delta)) |
---|
283 | else |
---|
284 | inc_gamma=exp(gammln(1.5))*(1+gammp(1.5,delta)) |
---|
285 | endif |
---|
286 | |
---|
287 | fSubS = 0.5*(1.0+erf( (r0-BS)/sqrt(2.0*v_d) ) ) |
---|
288 | if (fSubS <= 0.0) |
---|
289 | fSubS = 1.e-10 |
---|
290 | endif |
---|
291 | // fr = 1.0 + sqrt(v_d)*exp(-1.0*delta) /(r0*fSubS*sqrt(2.0*Pi)) |
---|
292 | // fv = inc_gamma/(fSubS*sqrt(Pi)) - r0^2*(fr-1.0)^2/v_d |
---|
293 | // |
---|
294 | // rmd = fr*r0 |
---|
295 | // v_r1 = v_b + fv*v_d +v_g |
---|
296 | // |
---|
297 | // rm = rmd + 0.5*v_r1/rmd |
---|
298 | // v_r = v_r1 - 0.5*(v_r1/rmd)^2 |
---|
299 | // if (v_r < 0.0) |
---|
300 | // v_r = 0.0 |
---|
301 | // endif |
---|
302 | |
---|
303 | Variable kap,a_val,a_val_L2,proj_DDet |
---|
304 | |
---|
305 | kap = 2*pi/lambda |
---|
306 | a_val = L2*(L1+L2)*g/2*(m_h)^2 |
---|
307 | a_val_L2 = a_val/L2*1e-16 //convert 1/cm^2 to 1/A^2 |
---|
308 | |
---|
309 | |
---|
310 | // the detector pixel is square, so correct for phi |
---|
311 | proj_DDet = DDet*cos(phi) + DDet*sin(phi) |
---|
312 | |
---|
313 | |
---|
314 | ///////// OLD - don't use --- |
---|
315 | //in terms of Q_parallel ("x") and Q_perp ("y") - this works, since parallel is in the direction of Q and I |
---|
316 | // can calculate that from the QxQy (I just need the projection) |
---|
317 | //// for test case with no gravity, set a_val = 0 |
---|
318 | //// note that gravity has no wavelength dependence. the lambda^4 cancels out. |
---|
319 | //// |
---|
320 | //// a_val = 0 |
---|
321 | //// a_val_l2 = 0 |
---|
322 | // |
---|
323 | // |
---|
324 | // // this is really sigma_Q_parallel |
---|
325 | // SigmaQX = kap*kap/12 * (3*(S1/L1)^2 + 3*(S2/LP)^2 + (proj_DDet/L2)^2 + (sin(phi))^2*8*(a_val_L2)^2*lambda^4*lambdaWidth^2) |
---|
326 | // SigmaQX += inQ*inQ*v_lambda |
---|
327 | // |
---|
328 | // //this is really sigma_Q_perpendicular |
---|
329 | // proj_DDet = DDet*sin(phi) + DDet*cos(phi) //not necessary, since DDet is the same in both X and Y directions |
---|
330 | // |
---|
331 | // SigmaQY = kap*kap/12 * (3*(S1/L1)^2 + 3*(S2/LP)^2 + (proj_DDet/L2)^2 + (cos(phi))^2*8*(a_val_L2)^2*lambda^4*lambdaWidth^2) |
---|
332 | // |
---|
333 | // SigmaQX = sqrt(SigmaQX) |
---|
334 | // SigmaQy = sqrt(SigmaQY) |
---|
335 | // |
---|
336 | |
---|
337 | ///////////////////////////////////////////////// |
---|
338 | ///// |
---|
339 | // ////// this is all new, inclusion of gravity effect into the parallel component |
---|
340 | // perpendicular component is purely geometric, no gravity component |
---|
341 | // |
---|
342 | // the shadow factor is calculated as above -so keep the above calculations, even though |
---|
343 | // most of them are redundant. |
---|
344 | // |
---|
345 | |
---|
346 | //// // |
---|
347 | Variable yg_d,acc,sdd,ssd,lambda0,DL_L,sig_l |
---|
348 | Variable var_qlx,var_qly,var_ql,qx,qy,sig_perp,sig_para, sig_para_new |
---|
349 | |
---|
350 | G = 981. //! ACCELERATION OF GRAVITY, CM/SEC^2 |
---|
351 | acc = vz_1 // 3.956E5 //! CONVERT WAVELENGTH TO VELOCITY CM/SEC |
---|
352 | SDD = L2 //1317 |
---|
353 | SSD = L1 //1627 //cm |
---|
354 | lambda0 = lambda // 15 |
---|
355 | DL_L = lambdaWidth //0.236 |
---|
356 | SIG_L = DL_L/sqrt(6) |
---|
357 | YG_d = -0.5*G*SDD*(SSD+SDD)*(LAMBDA0/acc)^2 |
---|
358 | ///// Print "DISTANCE BEAM FALLS DUE TO GRAVITY (CM) = ",YG |
---|
359 | // Print "Gravity q* = ",-2*pi/lambda0*2*yg_d/sdd |
---|
360 | |
---|
361 | sig_perp = kap*kap/12 * (3*(S1/L1)^2 + 3*(S2/LP)^2 + (proj_DDet/L2)^2) |
---|
362 | sig_perp = sqrt(sig_perp) |
---|
363 | |
---|
364 | // TODO -- not needed??? |
---|
365 | // FindQxQy(inQ,phi,qx,qy) |
---|
366 | |
---|
367 | |
---|
368 | // missing a factor of 2 here, and the form is different than the paper, so re-write |
---|
369 | // VAR_QLY = SIG_L^2 * (QY+4*PI*YG_d/(2*SDD*LAMBDA0))^2 |
---|
370 | // VAR_QLX = (SIG_L*QX)^2 |
---|
371 | // VAR_QL = VAR_QLY + VAR_QLX //! WAVELENGTH CONTRIBUTION TO VARIANCE |
---|
372 | // sig_para = (sig_perp^2 + VAR_QL)^0.5 |
---|
373 | |
---|
374 | // r_dist is passed in, [=]cm |
---|
375 | // from the paper |
---|
376 | a_val = 0.5*G*SDD*(SSD+SDD)*m_h^2 * 1e-16 //units now are cm /(A^2) |
---|
377 | |
---|
378 | var_QL = 1/6*(kap/SDD)^2*(DL_L)^2*(r_dist^2 - 4*r_dist*a_val*lambda0^2*sin(phi) + 4*a_val^2*lambda0^4) |
---|
379 | sig_para_new = (sig_perp^2 + VAR_QL)^0.5 |
---|
380 | |
---|
381 | |
---|
382 | ///// return values PBR |
---|
383 | SigmaQX = sig_para_new |
---|
384 | SigmaQy = sig_perp |
---|
385 | |
---|
386 | //// |
---|
387 | |
---|
388 | Return (0) |
---|
389 | End |
---|
390 | |
---|
391 | |
---|
392 | |
---|