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/*
* relrod.c
*
* Calculate reflection positions via line-sphere intersection test
*
* (c) 2007-2009 Thomas White <thomas.white@desy.de>
*
* template_index - Indexing diffraction patterns by template matching
*
*/
#include <stdlib.h>
#include <math.h>
#include <stdio.h>
#include "image.h"
#include "utils.h"
#include "cell.h"
static void mapping_rotate(double x, double y, double z,
double *ddx, double *ddy, double *ddz,
double omega, double tilt)
{
double nx, ny, nz;
double x_temp, y_temp, z_temp;
/* First: rotate image clockwise until tilt axis is aligned
* horizontally. */
nx = x*cos(omega) + y*sin(omega);
ny = -x*sin(omega) + y*cos(omega);
nz = z;
/* Now, tilt about the x-axis ANTICLOCKWISE around +x, i.e. the
* "wrong" way. This is because the crystal is rotated in the
* experiment, not the Ewald sphere. */
x_temp = nx; y_temp = ny; z_temp = nz;
nx = x_temp;
ny = cos(tilt)*y_temp + sin(tilt)*z_temp;
nz = -sin(tilt)*y_temp + cos(tilt)*z_temp;
/* Finally, reverse the omega rotation to restore the location of the
* image in 3D space */
x_temp = nx; y_temp = ny; z_temp = nz;
nx = x_temp*cos(-omega) + y_temp*sin(-omega);
ny = -x_temp*sin(-omega) + y_temp*cos(-omega);
nz = z_temp;
*ddx = nx;
*ddy = ny;
*ddz = nz;
}
void get_reflections(struct image *image, UnitCell *cell, double smax)
{
ImageFeatureList *flist;
double tilt, omega, wavenumber;
double nx, ny, nz; /* "normal" vector */
double kx, ky, kz; /* Electron wavevector ("normal" times 1/lambda) */
double ux, uy, uz; /* "up" vector */
double rx, ry, rz; /* "right" vector */
double asx, asy, asz; /* "a*" lattice parameter */
double bsx, bsy, bsz; /* "b*" lattice parameter */
double csx, csy, csz; /* "c*" lattice parameter */
signed int h, k, l;
double res_max;
/* Get the reciprocal unit cell */
cell_get_reciprocal(cell, &asx, &asy, &asz,
&bsx, &bsy, &bsz,
&csx, &csy, &csz);
/* Prepare list and some parameters */
flist = image_feature_list_new();
tilt = image->tilt;
omega = image->omega;
wavenumber = 1.0/image->lambda;
/* Calculate (roughly) the maximum resolution */
if ( image->fmode == FORMULATION_CLEN ) {
double w2, h2;
w2 = image->width/2; h2 = image->height/2;
w2 = pow(w2, 2.0); h2 = pow(h2, 2.0);
res_max = sqrt(w2 + h2) / image->resolution;
res_max *= (wavenumber / image->camera_len);
} else {
fprintf(stderr,
"Unrecognised formulation mode in get_reflections"
" (resolution cutoff calculation)\n");
return;
}
printf("Resolution cutoff is %5.2f nm^-1\n", res_max/1e9);
res_max = pow(res_max, 2.0);
/* Calculate the (normalised) incident electron wavevector */
mapping_rotate(0.0, 0.0, 1.0, &nx, &ny, &nz, omega, tilt);
kx = nx / image->lambda;
ky = ny / image->lambda;
kz = nz / image->lambda; /* This is the centre of the Ewald sphere */
/* Determine where "up" is */
mapping_rotate(0.0, 1.0, 0.0, &ux, &uy, &uz, omega, tilt);
/* Determine where "right" is */
mapping_rotate(1.0, 0.0, 0.0, &rx, &ry, &rz, omega, tilt);
for ( h=-50; h<50; h++ ) {
for ( k=-50; k<50; k++ ) {
for ( l=-50; l<50; l++ ) {
double xl, yl, zl;
double a, b, c;
double s1, s2, s, t;
double g_sq, gn;
/* Get the coordinates of the reciprocal lattice point */
xl = h*asx + k*bsx + l*csx;
yl = h*asy + k*bsy + l*csy;
zl = h*asz + k*bsz + l*csz;
g_sq = modulus_squared(xl, yl, zl);
gn = xl*nx + yl*ny + zl*nz;
/* Early bailout if resolution is clearly too high */
if ( g_sq > res_max ) continue;
/* Next, solve the relrod equation to calculate
* the excitation error */
a = 1.0;
b = 2.0*(wavenumber + gn);
c = -2.0*gn*wavenumber + g_sq;
t = -0.5*(b + sign(b)*sqrt(b*b - 4.0*a*c));
s1 = t/a;
s2 = c/t;
if ( fabs(s1) < fabs(s2) ) s = s1; else s = s2;
/* Skip this reflection if s is large */
if ( fabs(s) <= smax ) {
double xi, yi, zi;
double gx, gy, gz;
double theta;
double x, y;
double dx, dy, psi;
/* Determine the intersection point */
xi = xl + s*nx; yi = yl + s*ny; zi = zl + s*nz;
/* Calculate Bragg angle */
gx = xi - kx;
gy = yi - ky;
gz = zi - kz; /* This is the vector from the centre of
* the sphere to the intersection */
theta = angle_between(-kx, -ky, -kz, gx, gy, gz);
/* Calculate azimuth of point in image
* (anticlockwise from +x) */
dx = xi*rx + yi*ry + zi*rz;
dy = xi*ux + yi*uy + zi*uz;
psi = atan2(dy, dx);
/* Get image coordinates from polar
* representation */
if ( image->fmode == FORMULATION_CLEN ) {
x = image->camera_len*tan(theta)*cos(psi);
y = image->camera_len*tan(theta)*sin(psi);
x *= image->resolution;
y *= image->resolution;
} else if ( image->fmode==FORMULATION_PIXELSIZE ) {
x = tan(theta)*cos(psi) / image->lambda;
y = tan(theta)*sin(psi) / image->lambda;
x /= image->pixel_size;
y /= image->pixel_size;
} else {
fprintf(stderr,
"Unrecognised formulation mode "
"in get_reflections\n");
return;
}
x += image->x_centre;
y += image->y_centre;
/* Sanity check */
if ( (x>=0) && (x<image->width)
&& (y>=0) && (y<image->height) ) {
/* Record the reflection.
* Intensity should be multiplied by relrod
* spike function, except reprojected
* reflections aren't used quantitatively for
* anything. */
image_add_feature(flist, x, y, image, 1.0);
} /* else it's outside the picture somewhere */
} /* else reflection is not excited in this orientation */
}
}
}
image->rflist = flist;
}
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