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/*
* 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 (2)
#define BWSAMPLING (10)
#define BANDWIDTH (0.015)
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, float k)
{
struct rvec q;
float twothetax, twothetay, twotheta, r;
float rx = 0.0;
float ry = 0.0;
int p;
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;
float kc;
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));
kc = 1.0/image->lambda; /* Centre value */
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 */
int kstep;
for ( kstep=0; kstep<BWSAMPLING; kstep++ ) {
float k;
/* Calculate k this time round */
k = kc + (kstep-(BWSAMPLING/2)) *
kc*(BANDWIDTH/BWSAMPLING);
q = get_q(image, xs, ys, SAMPLING, &twotheta, k);
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");
}
}
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