1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
|
/*
* diffraction.c
*
* Calculate diffraction patterns by Fourier methods
*
* (c) 2006-2010 Thomas White <taw@physics.org>
*
* Part of CrystFEL - crystallography with a FEL
*
*/
#include <stdlib.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <complex.h>
#include "image.h"
#include "utils.h"
#include "cell.h"
#include "diffraction.h"
#include "sfac.h"
#define SAMPLING (1)
static double lattice_factor(struct rvec q, double ax, double ay, double az,
double bx, double by, double bz,
double cx, double cy, double cz,
int na, int nb, int nc)
{
struct rvec Udotq;
double f1, f2, f3;
Udotq.u = ax*q.u + ay*q.v + az*q.w;
Udotq.v = bx*q.u + by*q.v + bz*q.w;
Udotq.w = cx*q.u + cy*q.v + cz*q.w;
/* At exact Bragg condition, f1 = na */
if ( na > 1 ) {
f1 = sin(M_PI*(double)na*Udotq.u) / sin(M_PI*Udotq.u);
} else {
f1 = 1.0;
}
/* At exact Bragg condition, f2 = nb */
if ( nb > 1 ) {
f2 = sin(M_PI*(double)nb*Udotq.v) / sin(M_PI*Udotq.v);
} else {
f2 = 1.0;
}
/* At exact Bragg condition, f3 = nc */
if ( nc > 1 ) {
f3 = sin(M_PI*(double)nc*Udotq.w) / sin(M_PI*Udotq.w);
} else {
f3 = 1.0;
}
/* At exact Bragg condition, this will multiply the molecular
* part of the structure factor by the number of unit cells,
* as desired (more scattering from bigger crystal!) */
return f1 * f2 * f3;
}
/* Look up the structure factor for the nearest Bragg condition */
static double complex molecule_factor(struct molecule *mol, struct rvec q,
double ax, double ay, double az,
double bx, double by, double bz,
double cx, double cy, double cz)
{
double hd, kd, ld;
signed int h, k, l;
double complex r;
hd = q.u * ax + q.v * ay + q.w * az;
kd = q.u * bx + q.v * by + q.w * bz;
ld = q.u * cx + q.v * cy + q.w * cz;
h = (signed int)rint(hd);
k = (signed int)rint(kd);
l = (signed int)rint(ld);
r = lookup_sfac(mol->reflections, h, k, l);
return r;
}
double water_intensity(struct rvec q, double en,
double beam_r, double water_r)
{
double complex fH, fO;
double s, modq;
double width;
double complex ifac;
/* Interatomic distances in water molecule */
const double rOH = 0.09584e-9;
const double rHH = 0.1515e-9;
/* Volume of water column, approximated as:
* (2water_r) * (2beam_r) * smallest(2beam_r, 2water_r)
* neglecting the curvature of the faces of the volume */
if ( beam_r > water_r ) {
width = 2.0 * water_r;
} else {
width = 2.0 * beam_r;
}
const double water_v = 2.0*beam_r * 2.0*water_r * width;
/* Number of water molecules */
const double n_water = water_v * WATER_DENSITY
* (AVOGADRO / WATER_MOLAR_MASS);
/* s = sin(theta)/lambda = 1/2d = |q|/2 */
modq = modulus(q.u, q.v, q.w);
s = modq / 2.0;
fH = get_sfac("H", s, en);
fO = get_sfac("O", s, en);
/* Four O-H cross terms */
ifac = 4.0*fH*fO * sin(2.0*M_PI*modq*rOH)/(2.0*M_PI*modq*rOH);
/* Three H-H cross terms */
ifac += 3.0*fH*fH * sin(2.0*M_PI*modq*rHH)/(2.0*M_PI*modq*rHH);
/* Three diagonal terms */
ifac += 2.0*fH*fH + fO*fO;
return cabs(ifac) * n_water;
}
struct rvec get_q(struct image *image, unsigned int xs, unsigned int ys,
unsigned int sampling, float *ttp)
{
struct rvec q;
float twothetax, twothetay, twotheta, r;
float rx = 0.0;
float ry = 0.0;
int p;
const float k = 1.0/image->lambda;
const unsigned int x = xs / sampling;
const unsigned int y = ys / sampling; /* Integer part only */
for ( p=0; p<image->det.n_panels; p++ ) {
if ( (x >= image->det.panels[p].min_x)
&& (x <= image->det.panels[p].max_x)
&& (y >= image->det.panels[p].min_y)
&& (y <= image->det.panels[p].max_y) ) {
rx = ((float)xs - (sampling*image->det.panels[p].cx))
/ (sampling * image->resolution);
ry = ((float)ys - (sampling*image->det.panels[p].cy))
/ (sampling * image->resolution);
break;
}
}
/* Calculate q-vector for this sub-pixel */
r = sqrt(pow(rx, 2.0) + pow(ry, 2.0));
twothetax = atan2(rx, image->camera_len);
twothetay = atan2(ry, image->camera_len);
twotheta = atan2(r, image->camera_len);
if ( ttp != NULL ) *ttp = twotheta;
q.u = k * sin(twothetax);
q.v = k * sin(twothetay);
q.w = k - k * cos(twotheta);
return quat_rot(q, image->orientation);
}
void get_diffraction(struct image *image, int na, int nb, int nc, int no_sfac)
{
unsigned int xs, ys;
double ax, ay, az;
double bx, by, bz;
double cx, cy, cz;
double a, b, c, d;
if ( image->molecule == NULL ) return;
cell_get_cartesian(image->molecule->cell, &ax, &ay, &az,
&bx, &by, &bz,
&cx, &cy, &cz);
cell_get_parameters(image->molecule->cell,
&a, &b, &c, &d, &d, &d);
STATUS("Particle size = %i x %i x %i (=%5.2f x %5.2f x %5.2f nm)\n",
na, nb, nc, na*a/1.0e-9, nb*b/1.0e-9, nc*c/1.0e-9);
/* Allocate (and zero) the "diffraction array" */
image->sfacs = calloc(image->width * image->height,
sizeof(double complex));
if ( !no_sfac ) {
if ( image->molecule->reflections == NULL ) {
get_reflections_cached(image->molecule,
ph_lambda_to_en(image->lambda));
}
}
/* Needed later for Lorentz calculation */
image->twotheta = malloc(image->width * image->height * sizeof(double));
for ( xs=0; xs<image->width*SAMPLING; xs++ ) {
for ( ys=0; ys<image->height*SAMPLING; ys++ ) {
double f_lattice;
double complex f_molecule;
struct rvec q;
float twotheta;
double sw = 1.0/(SAMPLING*SAMPLING); /* Sample weight */
const unsigned int x = xs / SAMPLING;
const unsigned int y = ys / SAMPLING; /* Integer part only */
q = get_q(image, xs, ys, SAMPLING, &twotheta);
image->twotheta[x + image->width*y] = twotheta;
f_lattice = lattice_factor(q, ax,ay,az,bx,by,bz,cx,cy,cz,
na, nb, nc);
if ( no_sfac ) {
f_molecule = 10000.0;
} else {
f_molecule = molecule_factor(image->molecule, q,
ax,ay,az,bx,by,bz,cx,cy,cz);
}
image->sfacs[x + image->width*y] += sw * f_molecule * f_lattice;
}
progress_bar(xs, SAMPLING*image->width-1, "Calculating lattice factors");
}
}
|
