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-rw-r--r--src/diffraction.c464
1 files changed, 464 insertions, 0 deletions
diff --git a/src/diffraction.c b/src/diffraction.c
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+++ b/src/diffraction.c
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+/*
+ * diffraction.c
+ *
+ * Calculate diffraction patterns by Fourier methods
+ *
+ * (c) 2006-2011 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 <assert.h>
+#include <fenv.h>
+
+#include "image.h"
+#include "utils.h"
+#include "cell.h"
+#include "diffraction.h"
+#include "beam-parameters.h"
+#include "symmetry.h"
+#include "pattern_sim.h"
+
+
+#define SAMPLING (4)
+#define BWSAMPLING (10)
+#define DIVSAMPLING (1)
+#define SINC_LUT_ELEMENTS (4096)
+
+
+static double *get_sinc_lut(int n)
+{
+ int i;
+ double *lut;
+
+ lut = malloc(SINC_LUT_ELEMENTS*sizeof(double));
+ lut[0] = n;
+ if ( n == 1 ) {
+ for ( i=1; i<SINC_LUT_ELEMENTS; i++ ) {
+ lut[i] = 1.0;
+ }
+ } else {
+ for ( i=1; i<SINC_LUT_ELEMENTS; i++ ) {
+ double x, val;
+ x = (double)i/SINC_LUT_ELEMENTS;
+ val = fabs(sin(M_PI*n*x)/sin(M_PI*x));
+ lut[i] = val;
+ }
+ }
+
+ return lut;
+}
+
+
+static double interpolate_lut(double *lut, double val)
+{
+ double i, pos, f;
+ unsigned int low, high;
+
+ pos = SINC_LUT_ELEMENTS * modf(fabs(val), &i);
+ low = (int)pos; /* Discard fractional part */
+ high = low + 1;
+ f = modf(pos, &i); /* Fraction */
+ if ( high == SINC_LUT_ELEMENTS ) high = 0;
+
+ return (1.0-f)*lut[low] + f*lut[high];
+}
+
+
+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,
+ double *lut_a, double *lut_b,
+ double *lut_c)
+{
+ 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;
+
+ f1 = interpolate_lut(lut_a, Udotq.u);
+ f2 = interpolate_lut(lut_b, Udotq.v);
+ f3 = interpolate_lut(lut_c, Udotq.w);
+
+ return f1 * f2 * f3;
+}
+
+
+static double sym_lookup_intensity(const double *intensities,
+ const unsigned char *flags,
+ const SymOpList *sym,
+ signed int h, signed int k, signed int l)
+{
+ int i;
+ double ret = 0.0;
+
+ for ( i=0; i<num_equivs(sym, NULL); i++ ) {
+
+ signed int he;
+ signed int ke;
+ signed int le;
+ double f, val;
+
+ get_equiv(sym, NULL, i, h, k, l, &he, &ke, &le);
+
+ f = (double)lookup_flag(flags, he, ke, le);
+ val = lookup_intensity(intensities, he, ke, le);
+
+ ret += f*val;
+
+ }
+
+ return ret;
+}
+
+
+static double sym_lookup_phase(const double *phases,
+ const unsigned char *flags, const SymOpList *sym,
+ signed int h, signed int k, signed int l)
+{
+ int i;
+ double ret = 0.0;
+
+ for ( i=0; i<num_equivs(sym, NULL); i++ ) {
+
+ signed int he;
+ signed int ke;
+ signed int le;
+ double f, val;
+
+ get_equiv(sym, NULL, i, h, k, l, &he, &ke, &le);
+
+ f = (double)lookup_flag(flags, he, ke, le);
+ val = lookup_phase(phases, he, ke, le);
+
+ ret += f*val;
+
+ }
+
+ return ret;
+}
+
+
+static double interpolate_linear(const double *ref, const unsigned char *flags,
+ const SymOpList *sym, float hd,
+ signed int k, signed int l)
+{
+ signed int h;
+ double val1, val2;
+ float f;
+
+ h = (signed int)hd;
+ if ( hd < 0.0 ) h -= 1;
+ f = hd - (float)h;
+ assert(f >= 0.0);
+
+ val1 = sym_lookup_intensity(ref, flags, sym, h, k, l);
+ val2 = sym_lookup_intensity(ref, flags, sym, h+1, k, l);
+
+ val1 = val1;
+ val2 = val2;
+
+ return (1.0-f)*val1 + f*val2;
+}
+
+
+static double interpolate_bilinear(const double *ref,
+ const unsigned char *flags,
+ const SymOpList *sym,
+ float hd, float kd, signed int l)
+{
+ signed int k;
+ double val1, val2;
+ float f;
+
+ k = (signed int)kd;
+ if ( kd < 0.0 ) k -= 1;
+ f = kd - (float)k;
+ assert(f >= 0.0);
+
+ val1 = interpolate_linear(ref, flags, sym, hd, k, l);
+ val2 = interpolate_linear(ref, flags, sym, hd, k+1, l);
+
+ return (1.0-f)*val1 + f*val2;
+}
+
+
+static double interpolate_intensity(const double *ref,
+ const unsigned char *flags,
+ const SymOpList *sym,
+ float hd, float kd, float ld)
+{
+ signed int l;
+ double val1, val2;
+ float f;
+
+ l = (signed int)ld;
+ if ( ld < 0.0 ) l -= 1;
+ f = ld - (float)l;
+ assert(f >= 0.0);
+
+ val1 = interpolate_bilinear(ref, flags, sym, hd, kd, l);
+ val2 = interpolate_bilinear(ref, flags, sym, hd, kd, l+1);
+
+ return (1.0-f)*val1 + f*val2;
+}
+
+
+static double complex interpolate_phased_linear(const double *ref,
+ const double *phases,
+ const unsigned char *flags,
+ const SymOpList *sym,
+ float hd,
+ signed int k, signed int l)
+{
+ signed int h;
+ double val1, val2;
+ float f;
+ double ph1, ph2;
+ double re1, re2, im1, im2;
+ double re, im;
+
+ h = (signed int)hd;
+ if ( hd < 0.0 ) h -= 1;
+ f = hd - (float)h;
+ assert(f >= 0.0);
+
+ val1 = sym_lookup_intensity(ref, flags, sym, h, k, l);
+ val2 = sym_lookup_intensity(ref, flags, sym, h+1, k, l);
+ ph1 = sym_lookup_phase(phases, flags, sym, h, k, l);
+ ph2 = sym_lookup_phase(phases, flags, sym, h+1, k, l);
+
+ val1 = val1;
+ val2 = val2;
+
+ /* Calculate real and imaginary parts */
+ re1 = val1 * cos(ph1);
+ im1 = val1 * sin(ph1);
+ re2 = val2 * cos(ph2);
+ im2 = val2 * sin(ph2);
+
+ re = (1.0-f)*re1 + f*re2;
+ im = (1.0-f)*im1 + f*im2;
+
+ return re + im*I;
+}
+
+
+static double complex interpolate_phased_bilinear(const double *ref,
+ const double *phases,
+ const unsigned char *flags,
+ const SymOpList *sym,
+ float hd, float kd,
+ signed int l)
+{
+ signed int k;
+ double complex val1, val2;
+ float f;
+
+ k = (signed int)kd;
+ if ( kd < 0.0 ) k -= 1;
+ f = kd - (float)k;
+ assert(f >= 0.0);
+
+ val1 = interpolate_phased_linear(ref, phases, flags, sym, hd, k, l);
+ val2 = interpolate_phased_linear(ref, phases, flags, sym, hd, k+1, l);
+
+ return (1.0-f)*val1 + f*val2;
+}
+
+
+static double interpolate_phased_intensity(const double *ref,
+ const double *phases,
+ const unsigned char *flags,
+ const SymOpList *sym,
+ float hd, float kd, float ld)
+{
+ signed int l;
+ double complex val1, val2;
+ float f;
+
+ l = (signed int)ld;
+ if ( ld < 0.0 ) l -= 1;
+ f = ld - (float)l;
+ assert(f >= 0.0);
+
+ val1 = interpolate_phased_bilinear(ref, phases, flags, sym,
+ hd, kd, l);
+ val2 = interpolate_phased_bilinear(ref, phases, flags, sym,
+ hd, kd, l+1);
+
+ return cabs((1.0-f)*val1 + f*val2);
+}
+
+
+/* Look up the structure factor for the nearest Bragg condition */
+static double molecule_factor(const double *intensities, const double *phases,
+ const unsigned char *flags, struct rvec q,
+ double ax, double ay, double az,
+ double bx, double by, double bz,
+ double cx, double cy, double cz,
+ GradientMethod m, const SymOpList *sym)
+{
+ float hd, kd, ld;
+ signed int h, k, l;
+ double 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;
+
+ /* No flags -> flat intensity distribution */
+ if ( flags == NULL ) return 1.0e5;
+
+ switch ( m ) {
+ case GRADIENT_MOSAIC :
+ fesetround(1); /* Round to nearest */
+ h = (signed int)rint(hd);
+ k = (signed int)rint(kd);
+ l = (signed int)rint(ld);
+ if ( abs(h) > INDMAX ) r = 0.0;
+ else if ( abs(k) > INDMAX ) r = 0.0;
+ else if ( abs(l) > INDMAX ) r = 0.0;
+ else r = sym_lookup_intensity(intensities, flags, sym, h, k, l);
+ break;
+ case GRADIENT_INTERPOLATE :
+ r = interpolate_intensity(intensities, flags, sym, hd, kd, ld);
+ break;
+ case GRADIENT_PHASED :
+ r = interpolate_phased_intensity(intensities, phases, flags,
+ sym, hd, kd, ld);
+ break;
+ default:
+ ERROR("This gradient method not implemented yet.\n");
+ exit(1);
+ }
+
+ return r;
+}
+
+
+void get_diffraction(struct image *image, int na, int nb, int nc,
+ const double *intensities, const double *phases,
+ const unsigned char *flags, UnitCell *cell,
+ GradientMethod m, const SymOpList *sym)
+{
+ unsigned int fs, ss;
+ double ax, ay, az;
+ double bx, by, bz;
+ double cx, cy, cz;
+ float klow, khigh, bwstep;
+ double *lut_a;
+ double *lut_b;
+ double *lut_c;
+ double divxlow, divylow, divxstep, divystep;
+
+ cell_get_cartesian(cell, &ax, &ay, &az, &bx, &by, &bz, &cx, &cy, &cz);
+
+ /* Allocate (and zero) the "diffraction array" */
+ image->data = calloc(image->width * image->height, sizeof(float));
+
+ /* Needed later for Lorentz calculation */
+ image->twotheta = malloc(image->width * image->height * sizeof(double));
+
+ klow = 1.0/(image->lambda*(1.0 + image->beam->bandwidth/2.0));
+ khigh = 1.0/(image->lambda*(1.0 - image->beam->bandwidth/2.0));
+ bwstep = (khigh-klow) / BWSAMPLING;
+
+ divxlow = -image->beam->divergence/2.0;
+ divylow = -image->beam->divergence/2.0;
+ divxstep = image->beam->divergence / DIVSAMPLING;
+ divystep = image->beam->divergence / DIVSAMPLING;
+
+ lut_a = get_sinc_lut(na);
+ lut_b = get_sinc_lut(nb);
+ lut_c = get_sinc_lut(nc);
+
+ for ( fs=0; fs<image->width; fs++ ) {
+ for ( ss=0; ss<image->height; ss++ ) {
+
+ int fs_step, ss_step, kstep;
+ int divxval, divyval;
+ int idx = fs + image->width*ss;
+
+ for ( fs_step=0; fs_step<SAMPLING; fs_step++ ) {
+ for ( ss_step=0; ss_step<SAMPLING; ss_step++ ) {
+ for ( kstep=0; kstep<BWSAMPLING; kstep++ ) {
+ for ( divxval=0; divxval<DIVSAMPLING; divxval++ ) {
+ for ( divyval=0; divyval<DIVSAMPLING; divyval++ ) {
+
+ double k;
+ double intensity;
+ double f_lattice, I_lattice;
+ double I_molecule;
+ struct rvec q, qn;
+ double twotheta;
+ const double dfs = (double)fs
+ + ((double)fs_step / SAMPLING);
+ const double dss = (double)ss
+ + ((double)ss_step / SAMPLING);
+
+ double xdiv = divxlow + divxstep*(double)divxval;
+ double ydiv = divylow + divystep*(double)divyval;
+
+ /* Calculate k this time round */
+ k = klow + (double)kstep * bwstep;
+
+ qn = get_q(image, dfs, dss, &twotheta, k);
+
+ /* x divergence */
+ q.u = qn.u*cos(xdiv) +qn.w*sin(xdiv);
+ q.v = qn.v;
+ q.w = -qn.u*sin(xdiv) +qn.w*cos(xdiv);
+
+ qn = q;
+
+ /* y divergence */
+ q.v = qn.v*cos(ydiv) +qn.w*sin(ydiv);
+ q.w = -qn.v*sin(ydiv) +qn.w*cos(ydiv);
+
+ f_lattice = lattice_factor(q, ax, ay, az,
+ bx, by, bz,
+ cx, cy, cz,
+ lut_a, lut_b, lut_c);
+
+ I_molecule = molecule_factor(intensities,
+ phases, flags, q,
+ ax,ay,az,bx,by,bz,cx,cy,cz,
+ m, sym);
+
+ I_lattice = pow(f_lattice, 2.0);
+ intensity = I_lattice * I_molecule;
+
+ image->data[idx] += intensity;
+
+ if ( fs_step + ss_step + kstep == 0 ) {
+ image->twotheta[idx] = twotheta;
+ }
+
+ }
+ }
+ }
+ }
+ }
+
+ image->data[idx] /= (SAMPLING*SAMPLING*BWSAMPLING
+ *DIVSAMPLING*DIVSAMPLING);
+
+
+ }
+ progress_bar(fs, image->width-1, "Calculating diffraction");
+ }
+
+ free(lut_a);
+ free(lut_b);
+ free(lut_c);
+}
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