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BTA_utils/wfs_read/zernike.c

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/*
* zernike.c
*
* Copyright 2016 Edward V. Emelianov <eddy@sao.ru, edward.emelianoff@gmail.com>
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
* MA 02110-1301, USA.
*/
#ifndef _GNU_SOURCE
#define _GNU_SOURCE (1) // for math.h
#endif
#include <math.h>
#include <strings.h>
#include <limits.h> // INT_MAX
#include "zernike.h"
#include "usefull_macros.h"
#include "saveimg.h"
#ifndef iabs
#define iabs(a) (((a)<(0)) ? (-a) : (a))
#endif
// scaling factor
static double zscale = 1.;
// coordinate step on a grid
static double coord_step = DEFAULT_CRD_STEP;
// default wavelength for wavefront (650nm) in meters
static double wavelength = DEFAULT_WAVELENGTH;
// default coefficient to transform vawefront from wavelengths into user value
static double wf_coeff = 1.;
// array of factorials 1..100
static double *FK = NULL;
// unit for WF measurement
static char *outpunit = DEFAULT_WF_UNIT;
// amount of first polynomials to reset
static int Zern_zero = 0;
// array with indexes to be reset to 0 (copy of G.tozero)
static int* tozero = NULL;
static int tozerosz = 0; // size of array
// list of additional coefficients
static coeff *addcoefflist = NULL;
static int addcoefsz = 0; // its size
// matrix rotation angle (in radians)
static double rotangle = 0.;
/**
* setter & getter for zscale
*/
void z_set_scale(double s){zscale = s;}
double z_get_scale(){return zscale;}
/**
* Set/get value of Zern_zero
*/
int z_set_Nzero(int val){
if(val > 0) Zern_zero = val;
return Zern_zero;
}
/**
* Fill list of coefficients to be reset
*/
void z_set_tozero(int **val){
if(!val) return;
size_t cur = tozerosz;
while(val[tozerosz]) ++tozerosz;
//printf("2zero: %zd\n", tozerosz);
tozero = realloc(tozero, tozerosz*sizeof(int));
if(!tozero) ERR("realloc()");
while(*val){
tozero[cur++] = **val++;
}
//for(cur = 0; cur < tozerosz; ++cur) printf(":: %d\n", tozero[cur]);
}
/**
* @return size of `tozero` array
* @param idxs (o) - `tozero` itself
*/
int z_get_tozero(int **idxs){
if(!idxs) return -1;
*idxs = tozero;
return tozerosz;
}
// parse additional coefficient record (N=val) and fill data
void parse_coeff(char *rec, coeff *c){
if(!rec) ERRX(_("Empty record"));
char *s = strdup(rec);
if(!s) ERR("strdup()");
char *eq = strchr(s, '=');
if(!eq || *rec == '=')
ERRX(_("Coefficients' records should be like N=val, where N is Znumber, val is its additional value"));
*eq++ = 0;
char *endptr;
long tmp = strtol(s, &endptr, 0);
//printf("tmp=%ld, eptr=%s\n", tmp, endptr);
if(endptr == rec || *endptr != '\0' || tmp < 0 || tmp > INT_MAX)
ERRX(_("Coefficient's index should be a non-negative integer"));
c->idx = (int) tmp;
if(!str2double(&c->addval, eq))
ERRX(_("Wrong coefficient"));
free(s);
}
/**
* Fill list of additional coefficients
*/
void z_set_addcoef(char **list){
if(!list || !*list) return;
size_t cur = addcoefsz;
while(list[addcoefsz]) ++addcoefsz;
//printf("add coeffs: %zd\n", addcoefsz);
addcoefflist = realloc(addcoefflist, addcoefsz*sizeof(coeff));
if(!addcoefflist) ERR("realloc()");
while(*list){
parse_coeff(*list++, &addcoefflist[cur++]);
}
//for(cur = 0; cur < addcoefsz; ++cur) printf("coeff %d += %g\n", addcoefflist[cur].idx, addcoefflist[cur].addval);
}
/**
* @return length of `addcoeflist` array
* @param vals (o) - `addcoeflist` itself
*/
int z_get_addcoef(coeff **vals){
if(!vals) return -1;
*vals = addcoefflist;
return addcoefsz;
}
/**
* Set default coordinate grid step on an unity circle
* @param step - new step
* @return 0 if all OK, -1 or 1 if `step` bad
*/
int z_set_step(double step){
printf("Set step to %g\n", step);
if(step < DBL_EPSILON) return -1;
if(step > 1.) return 1;
coord_step = step;
return 0;
}
double z_get_step(){
return coord_step;
}
/**
* Set value of default wavelength
* @param w - new wavelength (from 100nm to 10um) in meters, microns or nanometers
* @return 0 if all OK
*/
int z_set_wavelength(double w){
if(w > 1e-7 && w < 1e-5) // meters
wavelength = w;
else if(w > 0.1 && w < 10.) // micron
wavelength = w * 1e-6;
else if(w > 100. && w < 10000.) // nanometer
wavelength = w * 1e-9;
else return 1;
return 0;
}
double z_get_wavelength(){
return wavelength;
}
static wf_units wfunits[] = {
{ 1. , (const char * const []){"meter", "m", NULL}},
{1e3 , (const char * const []){"millimeter", "mm", NULL}},
{1e6 , (const char * const []){"micrometer", "um", "u", NULL}},
{1e9 , (const char * const []){"nanometer", "nm", "n", NULL}},
{-1. , (const char * const []){"wavelength", "wave", "lambda", "w", "l", NULL}},
{0. , (const char * const []){NULL}}
};
/**
* Set coefficient `wf_coeff` to user defined unit
*/
int z_set_wfunit(char *U){
wf_units *u = wfunits;
while(u->units[0]){
const char * const * unit = u->units;
while(*unit){
if(strcasecmp(*unit, U) == 0){
wf_coeff = u->wf_coeff;
if(wf_coeff < 0.){ // wavelengths
wf_coeff = 1./wavelength; // in wavelengths
}
outpunit = (char*)u->units[0];
printf("wf_coeff = %g\n", wf_coeff);
return 0;
}
++unit;
}
++u;
}
return 1;
}
char *z_get_wfunit(){
return outpunit;
}
double z_get_wfcoeff(){
return wf_coeff;
}
/**
* Print all wf_units available
*/
void z_print_wfunits(){
wf_units *u = wfunits;
printf(_("Unit (meters)\tAvailable values\n"));
do{
const char * const*unit = u->units;
double val = 1./u->wf_coeff;
if(val > 0.)
printf("%-8g\t", val);
else
printf("(wavelength)\t");
do{
printf("%s ", *unit);
}while(*(++unit));
printf("\n");
}while((++u)->units[0]);
printf("\n");
}
/**
* Convert polynomial order in Noll notation into n/m
* @param p (i) - order of Zernike polynomial in Noll notation
* @param N (o) - order of polynomial
* @param M (o) - angular parameter
*/
void convert_Zidx(int p, int *N, int *M){
int n = (int) floor((-1.+sqrt(1.+8.*p)) / 2.);
if(M) *M = (int)(2.0*(p - n*(n+1.)/2. - 0.5*(double)n));
if(N) *N = n;
}
/**
* Build array with R powers (from 0 to n inclusive)
* @param n - power of Zernike polinomial (array size = n+1)
* @param Sz - size of P array
* @param P (i) - polar coordinates of points
*/
double **build_rpow(int n, int Sz, polar *P){
int i, j, N = n + 1;
double **Rpow = MALLOC(double*, N);
Rpow[0] = MALLOC(double, Sz);
for(i = 0; i < Sz; i++) Rpow[0][i] = 1.; // zero's power
for(i = 1; i < N; i++){ // Rpow - is quater I of cartesian coordinates ('cause other are fully simmetrical)
Rpow[i] = MALLOC(double, Sz);
double *rp = Rpow[i], *rpo = Rpow[i-1];
polar *p = P;
for(j = 0; j < Sz; j++, rp++, rpo++, p++){
*rp = (*rpo) * p->r;
}
}
return Rpow;
}
/**
* Free array of R powers with power n
* @param Rpow (i) - array to free
* @param n - power of Zernike polinomial for that array (array size = n+1)
*/
void free_rpow(double ***Rpow, int n){
int i, N = n+1;
for(i = 0; i < N; i++) FREE((*Rpow)[i]);
FREE(*Rpow);
}
/**
* Free array of coordinates
*/
void free_coords(polcrds *p){
FREE(p->P);
free_rpow(&p->Rpow, p->N);
free(p);
}
/**
* Generate polar coordinates for grid [-1..1] by both coordinates
* with default step. Correct to rotangle
* @return array of coordinates **without any point outside unitary circle**
*/
polcrds *gen_coords(){
int WH = 1 + (int)(2. / coord_step), max_sz = WH * WH, L = 0, idx = -1;
polar *coordinates = malloc(max_sz * sizeof(polar)), *cptr = coordinates;
if(!cptr) return NULL;
double x, y, cmax = 1. + coord_step/2.;
for(y = -1.; y < cmax; y += coord_step){
for(x = -1.; x < cmax; x += coord_step){
double R = sqrt(x*x + y*y);
++idx;
if(R > 1.) continue;
cptr->r = R;
cptr->theta = atan2(y, x) + rotangle;
cptr->idx = idx;
++cptr;
++L;
}
}
DBG("%d points outside circle (ratio = %g, ideal = %g)", max_sz - L, ((double)L)/max_sz, M_PI/4.);
polcrds *crds = MALLOC(polcrds, 1);
crds->P = coordinates;
crds->Sz = L;
crds->N = 40; // start from 40
crds->Rpow = build_rpow(crds->N, L, coordinates);
crds->WH = WH;
return crds;
}
/**
* Build pre-computed array of factorials from 1 to 100
*/
void build_factorial(){
double F = 1.;
int i;
if(FK) return;
FK = MALLOC(double, ZERNIKE_MAX_POWER);
FK[0] = 1.;
for(i = 1; i < ZERNIKE_MAX_POWER; i++)
FK[i] = (F *= (double)i);
}
/**
* Validation check of zernfun parameters
* return 1 in case of error
*/
int check_parameters(int n, int m, polcrds *P){
if(!P || P->Sz < 3 || !P->P || !P->Rpow){
WARNX(_("Size of matrix must be > 2!"));
return 1;
}
if(n > ZERNIKE_MAX_POWER){
WARNX(_("Order of Zernike polynomial must be <= %d!"), ZERNIKE_MAX_POWER);
return 1;
}
int erparm = 0;
if(n < 0) erparm = 1;
if(n < iabs(m)) erparm = 1; // |m| must be <= n
if((n - m) % 2) erparm = 1; // n-m must differ by a prod of 2
if(erparm)
WARNX(_("Wrong parameters of Zernike polynomial (%d, %d)"), n, m);
else
if(!FK) build_factorial();
return erparm;
}
/**
* Zernike function for scattering data
* @param n,m - orders of polynomial
* @param P(i) - array with points coordinates (polar, r<=1)
* @param norm(o) - (optional) norm coefficient
* @return dynamically allocated array with Z(n,m) for given array P
*/
double *zernfun(int n, int m, polcrds *P, double *norm){
if(check_parameters(n, m, P)) return NULL;
int j, k, m_abs = iabs(m), iup = (n-m_abs)/2, Sz = P->Sz;
if(n > P->N){
free_rpow(&P->Rpow, P->N);
P->N = n+10;
P->Rpow = build_rpow(P->N, Sz, P->P);
}
double ZSum = 0.;
// now fill output matrix
double *Zarr = MALLOC(double, Sz); // output matrix
double *Zptr = Zarr;
polar *p = P->P;
double **Rpow = P->Rpow;
for(j = 0; j < Sz; j++, p++, Zptr++){
double Z = 0.;
if(p->r > 1.) continue; // throw out points with R>1
// calculate R_n^m
for(k = 0; k <= iup; k++){ // Sum
double z = (1. - 2. * (k % 2)) * FK[n - k] // (-1)^k * (n-k)!
/(//----------------------------------- ----- -------------------------------
FK[k]*FK[(n+m_abs)/2-k]*FK[(n-m_abs)/2-k] // k!((n+|m|)/2-k)!((n-|m|)/2-k)!
);
Z += z * Rpow[n-2*k][j]; // *R^{n-2k}
}
// normalize
double eps_m = (m) ? 1. : 2.;
Z *= sqrt(2.*(n+1.) / M_PI / eps_m );
double m_theta = (double)m_abs * p->theta;
// multiply to angular function:
if(m){
if(m > 0)
Z *= cos(m_theta);
else
Z *= sin(m_theta);
}
*Zptr = Z;
ZSum += Z*Z;
}
if(norm) *norm = ZSum;
return Zarr;
}
/**
* Restoration of image in points P by Zernike polynomials' coefficients
* @param Zsz (i) - number of actual elements in coefficients array
* @param Zidxs(i) - array with Zernike coefficients
* @param P(i) - points coordinates & R powers
* @return restored image
*/
double *Zcompose(int Zsz, double *Zidxs, polcrds *P){
if(!P || !P->P || !P->Rpow) return NULL;
int i, Sz = P->Sz;
for(i = 0; i < Zern_zero; ++i) Zidxs[i] = 0.;
for(i = 0; i < tozerosz; i++){
int C = tozero[i];
if(C > -1 && C < Zsz) Zidxs[C] = 0.;
else WARNX(_("Not zero idx %d (should be from 0 to %d)"), C, Zsz-1);
}
for(i = 0; i < addcoefsz; i++){
int C = addcoefflist[i].idx;
if(C > -1 && C < Zsz) Zidxs[C] += addcoefflist[i].addval;
else WARNX(_("Not change idx %d (should be from 0 to %d)"), C, Zsz-1);
}
double *image = MALLOC(double, Sz);
for(i = 0; i < Zsz; i++){ // now we fill array
double K = Zidxs[i];
//printf("Z[%d]=%g\n", i, K);
if(fabs(K) < DBL_EPSILON) continue; // 0.0m
int n, m;
convert_Zidx(i, &n, &m);
double *Zcoeff = zernfun(n, m, P, NULL);
if(!Zcoeff){
WARNX(_("Can't compute coefficients for n=%d, m=%d!"), n,m);
continue;
}
int j;
double *iptr = image, *zptr = Zcoeff;
for(j = 0; j < Sz; j++, iptr++, zptr++)
*iptr += K * (*zptr); // add next Zernike polynomial
FREE(Zcoeff);
}
return image;
}
/**
* Save restored wavefront into file `filename`
* @param P (i) - points coordinates & R powers
* @param Z (i) - wavefront shift (in lambdas)
* @param std (i) - std of shift in each point
* @param filename (i) - name of output file
* @return 1 if failed
*/
int z_save_wavefront(polcrds *P, double *Z, double *std, char *fprefix){
int Sz = P->Sz, i, ret = 1;
polar *p = P->P;
if(!P || !p || !Z || Sz < 0 || !fprefix) return 1;
/*************** Step 1 - save points coordinates table ***************/
char *filename = MALLOC(char, strlen(fprefix) + 10);
sprintf(filename, "%s.points", fprefix);
printf("try to save to %s\n", filename);
FILE *f = fopen(filename, "w");
if(!f) goto returning;
int WH = P->WH, max_sz = WH * WH;
double *WF = calloc(max_sz, sizeof(double));
if(!WF) goto returning;
// calculate std & scope by all wavefront
double *z = Z, sum = 0., sum2 = 0., min = 1e12, max = -1e12;
for(i = 0; i < Sz; ++i, ++z){
double pt = *z;
if(pt < min) min = pt;
if(pt > max) max = pt;
sum += pt;
sum2 += pt*pt;
}
double coef = wf_coeff * zscale;
sum2 *= coef, sum *= coef, max *= coef, min *= coef;
fprintf(f, "# Wavefront units: %ss, wavelength: %gnm, std by all WF: %g, Scope: %g, max: %g, min: %g\n",
outpunit, wavelength*1e9, sum2/Sz + sum*sum/Sz/Sz, max - min, max, min);
if(Zern_zero) fprintf(f, "# First %d coefficients were cleared\n", Zern_zero);
fprintf(f, "# X (-1..1)\tY (-1..1)\tZ \tstd_Z\n");
for(i = 0, z = Z; i < Sz; ++i, ++p, ++z, ++std){
double x, y, s, c, r = p->r, zdat = (*z) * coef;
sincos(p->theta - rotangle, &s, &c);
x = r * c, y = r * s;
fprintf(f, "%6.3f\t%6.3f\t%9.3g\t%9.3g\n", x, y, zdat, (*std) * coef);
WF[p->idx] = zdat;
//DBG("WF[%d] = %g; x=%.1f, y=%.1f", p->idx, zdat,x,y);
}
fclose(f);
/*************** Step 2 - save matrix of data ***************/
sprintf(filename, "%s.matrix", fprefix);
printf("try to save to %s\n", filename);
f = fopen(filename, "w");
if(!f) goto returning;
fprintf(f, "# Wavefront data\n# Units: %ss, wavelength: %gnm\n# Step: %g\n",
outpunit, wavelength*1e9, coord_step);
int x, y;
// Invert Y axe to have matrix with right Y direction (towards up)
for(y = WH-1; y > -1; --y){
double *wptr = &WF[y*WH];
for(x = 0; x < WH; ++x, ++wptr)
fprintf(f, "%6.3g\t", *wptr);
fprintf(f, "\n");
}
writeimg(fprefix, WH, WF);
ret = 0;
returning:
FREE(filename);
return ret;
}
/**
* change rotation angle (0..2pi)
*/
void z_set_rotangle(double angle){
angle -= floor(angle/360.) * 360.;
rotangle = angle * M_PI/180.;
printf("angle: %g\n", rotangle*180/M_PI);
}
double z_get_rotangle(){
return rotangle;
}
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