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/*
* reproject.c
*
* Synthesize diffraction patterns
*
* (c) 2007 Thomas White <taw27@cam.ac.uk>
*
* dtr - Diffraction Tomography Reconstruction
*
*/
#include <stdlib.h>
#include <math.h>
#include "control.h"
#include "reflections.h"
#include "utils.h"
#define MAX_IMAGE_REFLECTIONS 8*1024
ImageReflection *reproject_get_reflections(ImageRecord image, size_t *n, ReflectionList *reflectionlist, ControlContext *ctx) {
ImageReflection *refl;
Reflection *reflection;
int i;
double smax = 0.5e8;
double tilt, omega;
double nx, ny, nz, nxt, nyt, nzt; /* "normal" vector (and calculation intermediates) */
double kx, ky, kz; /* Electron wavevector ("normal" times 1/lambda */
double ux, uy, uz, uxt, uyt, uzt; /* "up" vector (and calculation intermediates) */
//int done_debug = 0;
tilt = deg2rad(image.tilt);
omega = deg2rad(image.omega);
/* Calculate the (normalised) incident electron wavevector
* n is rotated "into" the reconstruction, so only one omega step. */
nxt = 0.0; nyt = 0.0; nzt = 1.0;
nx = nxt; ny = cos(tilt)*nyt + sin(tilt)*nzt; nz = -sin(tilt)*nyt + cos(tilt)*nzt;
nxt = nx; nyt = ny; nzt = nz;
nx = nxt*cos(-omega) + nyt*sin(-omega); ny = -nxt*sin(-omega) + nyt*cos(-omega); nz = nzt;
kx = nx / image.lambda;
ky = ny / image.lambda;
kz = nz / image.lambda; /* This is the centre of the Ewald sphere */
//reflection_add(ctx->reflectionlist, kx, ky, kz, 1, REFLECTION_VECTOR_MARKER_1);
/* Determine where "up" is
* See above. */
uxt = 0.0; uyt = 1.0; uzt = 0.0;
ux = uxt; uy = cos(tilt)*uyt + sin(tilt)*uzt; uz = -sin(tilt)*uyt + cos(tilt)*uzt;
uxt = ux; uyt = uy; uzt = uz;
ux = uxt*cos(-omega) + uyt*-sin(omega); uy = -uxt*sin(omega) + uyt*cos(omega); uz = uzt;
//reflection_add(ctx->reflectionlist, ux*50e9, uy*50e9, uz*50e9, 1, REFLECTION_VECTOR_MARKER_2);
refl = malloc(MAX_IMAGE_REFLECTIONS*sizeof(ImageReflection));
reflection = reflectionlist->reflections;
i = 0;
do {
double xl, yl, zl;
double a, b, c;
double A1, A2, s1, s2, s;
/* Get the coordinates of the reciprocal lattice point */
xl = reflection->x;
yl = reflection->y;
zl = reflection->z;
/* Next, solve the relrod equation to calculate the excitation error */
a = 1.0;
b = -2.0*(xl*nx + yl*ny + zl*nz);
c = xl*xl + yl*yl + zl*zl - 1.0/(image.lambda*image.lambda);
A1 = (-b + sqrt(b*b-4.0*a*c))/(2.0*a);
A2 = (-b - sqrt(b*b-4.0*a*c))/(2.0*a);
s1 = 1.0/image.lambda - A1;
s2 = 1.0/image.lambda - A2;
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 cx, cy, cz;
double theta;
double x, y;
double rx, ry, rz;
/* 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);
if ( theta > 0.0 ) {
double psi, disc;
//reflection_add(ctx->reflectionlist, xl, yl, zl, 1, REFLECTION_GENERATED);
//reflection_add(ctx->reflectionlist, xi, yi, zi, 1, REFLECTION_MARKER);
/* Calculate azimuth of point in image (clockwise from "up", will be changed later) */
cx = yi*nz-zi*ny; cy = nx*zi-nz*xi; cz = ny*xi-nx*yi; /* c = i x n */
psi = angle_between(cx, cy, cz, ux, uy, uz);
/* Finally, resolve the +/- Pi ambiguity from the previous step */
rx = cy*nz-cz*ny; ry = nx*cz-nz*cx; rz = ny*cx-nx*cy; /* r = [i x n] x n */
disc = angle_between(rx, ry, rz, ux, uy, uz);
// if ( (i==20) && !done_debug ) {
// reflection_add(ctx->reflectionlist, xi, yi, zi, 1, REFLECTION_VECTOR_MARKER_3);
// reflection_add(ctx->reflectionlist, cx, cy, cz, 1, REFLECTION_VECTOR_MARKER_4);
// reflection_add(ctx->reflectionlist, rx, ry, rz, 1, REFLECTION_VECTOR_MARKER_4);
// printf("psi=%f deg, disc=%f deg\n", rad2deg(psi), rad2deg(disc));
// }
if ( (psi >= M_PI_2) && (disc >= M_PI_2) ) {
psi -= M_PI_2; /* Case 1 */
// if ( (i==20) && !done_debug ) printf("case 1\n");
} else if ( (psi >= M_PI_2) && (disc < M_PI_2) ) {
psi = 3*M_PI_2 - psi; /* Case 2 */
// if ( (i==20) && !done_debug ) printf("case 2\n");
} else if ( (psi < M_PI_2) && (disc < M_PI_2) ) {
psi = 3*M_PI_2 - psi; /* Case 3 */
// if ( (i==20) && !done_debug ) printf("case 3\n");
} else if ( (psi < M_PI_2) && (disc >= M_PI_2) ) {
psi = 3*M_PI_2 + psi; /* Case 4 */
// if ( (i==20) && !done_debug ) printf("case 4\n");
}
// if ( (i==20) && !done_debug ) printf("final psi=%f clockwise from 'up'\n", rad2deg(psi));
psi = M_PI_2 - psi; /* Anticlockwise from "+x" instead of clockwise from "up" */
// if ( (i==20) && !done_debug ) printf("final psi=%f anticlockwise from +x\n", rad2deg(psi));
psi += omega;
// if ( (i==20) && !done_debug ) printf("final psi=%f anticlockwise from +tilt axis\n", rad2deg(psi));
// if ( (i==20) && !done_debug ) done_debug = 1;
/* Calculate 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 reproject_get_reflections()\n");
return NULL;
}
/* Adjust centre */
x += image.x_centre;
y += image.y_centre;
/* Sanity check */
if ( (x>=0) && (x<image.width) && (y>=0) && (y<image.height) ) {
/* Record the reflection */
refl[i].x = x;
refl[i].y = y;
i++;
if ( i > MAX_IMAGE_REFLECTIONS ) {
fprintf(stderr, "Too many reflections\n");
break;
}
//printf("Reflection %i at %i,%i\n", i, refl[i-1].x, refl[i-1].y);
} /* else it's outside the picture somewhere */
} /* else this is the central beam so don't worry about it */
}
reflection = reflection->next;
} while ( reflection );
//printf("Found %i reflections in image\n", i);
*n = i;
return refl;
}
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