Dopplergram.c

/*-----------------------------------------------------------------------------------------*/
/*                                                                                         */
/* Program to compute Dopplergrams using a MDI-like algorithm                              */
/*(compute the phases of the 1st and 2nd Fourier coefficients)                             */
/* Author: S. Couvidat (based on a code by J. Schou)                                       */
/* Version 1.9 August 24, 2010                                                             */
/*                                                                                         */
/* uses a MDI-like algorithm with 5 or 6 tuning positions                                  */
/* averages the velocities returned by 1st and 2nd Fourier                                 */
/* coefficient, and by LCP and RCP                                                         */
/* the code also estimates the Fe I linewidth, linedepth, and                              */
/* the continuum intensity                                                                 */
/*                                                                                         */
/* FOR THE MEANING OF ROWS AND COLUMNS WE FOLLOW THE CONVENTION:                           */
/* A 2D ARRAY A IN C IS DEFINED AS A[row][column]                                          */
/*                                                                                         */
/* CONVENTION FOR THE VELOCITIES:                                                          */
/* POSITIVE VELOCITIES CORRESPOND TO REDSHIFT (MOVEMENTS AWAY FROM THE OBSERVER)           */
/*-----------------------------------------------------------------------------------------*/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <complex.h>
#include <jsoc_main.h>
#include <omp.h>                      //OpenMP header

#undef I                              //I is the complex number (0,1). We un-define it to avoid confusion

struct parameterDoppler {             //structure to provide some parameters defined in HMIparam.h to Dopplergram()
  double FSRNB;
  double FSRWB;
  double FSRE1;
  double FSRE2;
  double FSRE3;
  double FSRE4;
  double FSRE5;
  double dlamdv;
  int maxVtest;
  int maxNx;
  int ntest;
  double dvtest;
  float MISSINGDATA;
  float MISSINGRESULT;
  double coeff0;
  double coeff1;
  double coeff2;
  double coeff3;
  int QuickLook;
};




/*-----------------------------------------------------------------------------------------*/
/* MDI-like algorithm                                                                      */
/*-----------------------------------------------------------------------------------------*/


int Dopplergram(DRMS_Array_t **arrLev1p,DRMS_Array_t **arrLev15,int framelistSize,DRMS_Array_t *Lookuptable,float Rsun,float X0,float Y0,struct parameterDoppler DopplerParameters,int MISSVALS[5],int *SATVALS,float cdelt1,TIME TargetTime)
{

  double FSR[7];
  double dlamdv;
  int maxVtest;
  int maxNx;
  int ntest;
  double dvtest;
  float MISSINGDATA;
  float MISSINGRESULT;
  int  i,j,iii;                                                       //loop variables
  int QUICKLOOK;
  float ExtraCrop = 50.;//we crop the data at Rsun+ExtraCrop in pixels

  double magnetic = 1.0/(2.0*4.67E-5*0.000061733433*2.5*299792458.0); //Lande factor=2.5 for Fe I line

  //parameters of the Fe I line profiles observed by Roger Ulrich (OBTAINED BY CODE centertolimb.pro; MAKE SURE IT'S THE SAME AS IN lookup.c)
  double cost[3]={1.0,0.70710678,0.5};                    //cos(theta) where theta is the angular distance from disk center
  double minimumCoeffs[2]={0.41922611,0.24190794};        //minimum intensity, assuming the continuum is at 1 (result from a Gaussian fit in the range [-0.055,0.055] Angstroms)
  double FWHMCoeffs[2]={151.34559,-58.521771};            //FWHM of the solar line in Angstrom (result from a Gaussian fit in the range [-0.055,0.055] Angstroms)
  double FWHM,minimum,angulardistance,minimumR,minimumL;
  double coeff[4];                                        //coefficients of the polynomial correction

  FSR[0]=DopplerParameters.FSRNB;
  FSR[1]=DopplerParameters.FSRWB;
  FSR[2]=DopplerParameters.FSRE1;
  FSR[3]=DopplerParameters.FSRE2;
  FSR[4]=DopplerParameters.FSRE3;
  FSR[5]=DopplerParameters.FSRE4;
  FSR[6]=DopplerParameters.FSRE5;
  dlamdv=DopplerParameters.dlamdv;
  maxVtest=DopplerParameters.maxVtest;
  maxNx=DopplerParameters.maxNx;
  ntest=DopplerParameters.ntest;
  dvtest=DopplerParameters.dvtest;
  MISSINGDATA=DopplerParameters.MISSINGDATA;
  MISSINGRESULT=DopplerParameters.MISSINGRESULT;
  coeff[0]=DopplerParameters.coeff0;
  coeff[1]=DopplerParameters.coeff1;
  coeff[2]=DopplerParameters.coeff2;
  coeff[3]=DopplerParameters.coeff3;
  QUICKLOOK=DopplerParameters.QuickLook;

  double vtest[ntest];                                                //internally calculations are done in double precision
  float poly[ntest],poly2[ntest];                                     //for the spatial interpolation of the look-up tables (THE TABLES ARE ASSUMED TO BE OF TYPE FLOAT)

  int  status      = 0; 
  int  error       = 0;                                               //error code returned by the routine: 0=no error, !=0 means error
  int  nRows,nColumns;
  DRMS_Type_t type;
  float distance;

  //check whether or not framelistSize is an even number
  if(framelistSize != 10 && framelistSize != 12 && framelistSize != 16 && framelistSize != 20)
    {
      printf("Error in subroutine computing the Dopplergrams: the framelist size is not 10, 12, 16, or 20\n");
      error=3;
      return error;
    }

  int N=framelistSize/2;                                             //number of different wavelengths
  double *cosi;
  double *sini;
  double *cos2i;
  double *sin2i;
  cosi = (double *)malloc(N*sizeof(double));  
  sini = (double *)malloc(N*sizeof(double));  
  cos2i= (double *)malloc(N*sizeof(double));  
  sin2i= (double *)malloc(N*sizeof(double));  
  if(cosi == NULL || sini == NULL || cos2i == NULL || sin2i == NULL)
    {
      printf("Error: memory could not be allocated in the Dopplergram() function\n");
      exit(EXIT_FAILURE);
    }
  float L[N],R[N]; //NO MALLOCS BECAUSE THEY ARE WRITTEN INSIDE THE OMP LOOP, THE LEVEL 1P DATA ARE ASSUMED TO BE OF TYPE FLOAT
 

  //check that all level 1p data have the same data type (IS THAT NECESSARY?)
  for(i=0;i<framelistSize;++i)
    {
      type    = arrLev1p[i]->type;                                  //float if produced by Jesper's routine
      if (type != DRMS_TYPE_FLOAT)                                  //if the type is not FLOAT
	{
	  printf("Error in subroutine computing the Dopplergrams: data type of level 1p data is not FLOAT\n");
	  error = 1;
	  free(cosi);
	  free(sini);
	  free(cos2i);
	  free(sin2i);
	  return error;
	}
    }
  
  //with C convention Array[row][column], axis[0] is the number of columns 
  nRows    = arrLev1p[0]->axis[1];
  nColumns = arrLev1p[0]->axis[0];

  //check that all filtergrams have the same dimensions (IS THAT NECESSARY?)
  for(i=1;i<framelistSize;++i)
    {
      if (arrLev1p[i]->axis[1] != nRows || arrLev1p[i]->axis[0] != nColumns )//if filtergrams are not nRows*nColumns
	{
	  printf("Error in subroutine computing the Dopplergrams: dimensions of level 1p data are not %d x %d \n",nRows,nColumns);
	  error = 2;
	  free(cosi);
	  free(sini);
	  free(cos2i);
	  free(sin2i);
	  return error;
	}
    }


  //THE LEVEL 1.5 DATA ARE ASSUMED TO BE OF TYPE FLOAT
  double correction=0.0;
  double a0,a1,a2,a3,a4;
  float *lam0g  = arrLev15[0]->data ;                                 //Dopplergram
  float *B0g    = arrLev15[1]->data;                                  //magnetogram
  float *Idg    = arrLev15[2]->data;                                  //linedepth
  float *widthg = arrLev15[3]->data;                                  //linewidth
  float *I0g    = arrLev15[4]->data;                                  //continuum
  float *rawlam0g = arrLev15[5]->data ;                               //raw (uncorrected) Dopplergram

  memset(lam0g,  0.0, drms_array_size(arrLev15[0]));                  //fill the observable arrays with 0
  memset(B0g  ,  0.0, drms_array_size(arrLev15[1]));
  memset(Idg  ,  0.0, drms_array_size(arrLev15[2]));
  memset(widthg, 0.0, drms_array_size(arrLev15[3]));
  memset(I0g   , 0.0, drms_array_size(arrLev15[4]));
  memset(rawlam0g,0.0, drms_array_size(arrLev15[5]));                  //fill the observable arrays with 0
  
  //variables for the MDI-like algorithm
  double FSRNB   = FSR[0];                       //FSR Narrow-Band Michelson, in Angstroms (WILL CHANGE ONCE THE VALUE IS ACCURATELY MEASURED)
  double dtune   = FSRNB/2.5;                    //wavelength separation between each tuning position, nominally 68.8 mA  (SHOULD BE THE SAME FOR 5 OR 6 WAVELENGTHS)
  double dv      = 1.0/dlamdv;                   //conversion factor from wavelength to velocity
  double dvtune  = dtune*dv;
  double *tune   = NULL, *angle=NULL;
  tune=(double *)malloc(N*sizeof(double));
  if(tune == NULL)
    {
      printf("Error: unable to allocate memory to tune\n");
      exit(EXIT_FAILURE);
    }
  angle=(double *)malloc(N*sizeof(double));
  if(angle == NULL)
    {
      printf("Error: unable to allocate memory to angle\n");
      exit(EXIT_FAILURE);
    }


  if(N == 6)
    {
      printf("USING 6 WAVELENGTHS\n");
      tune[0]=+2.5;//I0 (location of the filter)
      tune[1]=+1.5;//I1
      tune[2]=+0.5;//I2
      tune[3]=-0.5;//I3
      tune[4]=-1.5;//I4
      tune[5]=-2.5;//I5
      for(i=0;i<N;++i) angle[i]=tune[i];
    }
  if(N == 5)
    {
      printf("USING 5 WAVELENGTHS\n");
      tune[0]=+2.0;
      tune[1]=+1.0;
      tune[2]= 0.0;
      tune[3]=-1.0;
      tune[4]=-2.0;
      for(i=0;i<N;++i) angle[i]=tune[i];
    }
  if(N == 8)
    {
      printf("USING 8 WAVELENGTHS\n");
      tune[7]=+3.5;//I7
      tune[0]=+2.5;//I0 (location of the filter)
      tune[1]=+1.5;//I1
      tune[2]=+0.5;//I2
      tune[3]=-0.5;//I3
      tune[4]=-1.5;//I4
      tune[5]=-2.5;//I5
      tune[6]=-3.5;//I6
      for(i=0;i<N;++i) angle[i]=tune[i];
    }
  if(N == 10)
    {
      printf("USING 10 WAVELENGTHS\n");
      tune[9]=+4.5;//I9
      tune[7]=+3.5;//I7
      tune[0]=+2.5;//I0 (location of the filter)
      tune[1]=+1.5;//I1
      tune[2]=+0.5;//I2
      tune[3]=-0.5;//I3
      tune[4]=-1.5;//I4
      tune[5]=-2.5;//I5
      tune[6]=-3.5;//I6
      tune[8]=-4.5;//I8
      for(i=0;i<N;++i) angle[i]=tune[i];
    }

  double period = (double)(N-1)*dtune;
  double pv1,pv2;
  double f1LCPc,f1RCPc,f1LCPs,f1RCPs,f2LCPc,f2RCPc,f2LCPs,f2RCPs;
  double vLCP,vRCP,v2LCP,v2RCP;
  double temp,temp2,temp3,tempbis,temp2bis,temp3bis;
  double meanL=0.0,meanR=0.0;

  pv1 = dvtune*(double)(N-1);
  pv2 = pv1/2.;
  
  for(i=0;i<N;++i) 
    {
      tune[i] = tune[i]*dtune;
      angle[i]= angle[i]*2.0*M_PI/(double)N;
      cosi[i] = cos(angle[i]);
      sini[i] = sin(angle[i]);
      cos2i[i]= cos(2.0*angle[i]);
      sin2i[i]= sin(2.0*angle[i]);
    }
  
  
  //array containing the look-up table (type FLOAT)
  float *lookupt = Lookuptable->data ;
  int axist[3];                  //dimensions of the look-up tables
  axist[0]=Lookuptable->axis[0]; //number of input velocities (ntest*2)
  axist[1]=Lookuptable->axis[1]; //number of columns (256)    
  axist[2]=Lookuptable->axis[2]; //number of rows (256)
  printf("Dimensions of the look-up tables: %d %d %d\n",axist[0],axist[1],axist[2]);

  if(axist[0] > maxVtest || axist[1] > maxNx || axist[2] > maxNx)
    {
      printf("Error in subroutine computing the Dopplergrams: dimensions of the look-up tables exceed what is allowed: %d %d %d\n",maxVtest,maxNx,maxNx); //if there is a problem
      error = 4;
      free(cosi);
      free(sini);
      free(cos2i);
      free(sin2i);
      free(tune);
      free(angle);
      return error;        
    }

  //we reconstruct the test (input) velocities used to produce the look-up tables
  //WARNING: MUST BE THE SAME AS IN lookup.c
  for(i=0;i<ntest;++i) vtest[i] = dvtest*((double)i-((double)ntest-1.0)/2.0); 

  int   index_lo=0;
  int   index_hi=ntest-1;
  float RR1,RR2;     //variables for the bilinear interpolation of the look-up tables
  int   x0,y0,x1,y1;
  float xa,xb,ya,yb;
  int   ratio,indexL,indexR,indexL2,indexR2,row,column,step=10;
  long  loc1,loc2,loc3,loc4; //coded 8 bytes
  double Kfourier;
  float *tempvec=NULL;
  Kfourier = dtune/period*2.0;
  ratio = nRows/axist[2];
  float minlookupt1=0.0,maxlookupt1=0.0,minlookupt2=0.0,maxlookupt2=0.0;
  
  int MISSVALS20=0; //the number of missing values (NaN) for Dopplergrams
  int MISSVALS21=0; //the number of missing values (NaN) for magnetograms
  int MISSVALS22=0; //the number of missing values (NaN) for linedepth
  int MISSVALS23=0; //the number of missing values (NaN) for linewidth
  int MISSVALS24=0; //the number of missing values (NaN) for continuum intensity

  int SATVALS2 =0; //number of saturated values
  float offset=((float)ratio-1.0)/2.0; //because the phase maps were rebinned using rebin() which means that pixel 0 is actually (ratio-1)/2 on the initial grid

  /***********************************************************************************************************/
  /*LOOP OVER ALL THE PIXELS OF THE FILTERGRAMS                                                              */
  /***********************************************************************************************************/


#pragma omp parallel default(none) reduction(+:MISSVALS20,MISSVALS21,MISSVALS22,MISSVALS23,MISSVALS24,SATVALS2) shared(step,arrLev1p,cosi,sini,cos2i,sin2i,pv1,pv2,index_lo,index_hi,vtest,period,dtune,dv,I0g,B0g,Idg,lam0g,rawlam0g,widthg,magnetic,axist,ratio,lookupt,nRows,nColumns,MISSINGDATA,MISSINGRESULT,Kfourier,Rsun,X0,Y0,ntest,tune,N,cost,minimumCoeffs,FWHMCoeffs,offset,ExtraCrop,cdelt1,TargetTime,QUICKLOOK,coeff) private(tempvec,iii,L,R,f1LCPc,f1RCPc,f1LCPs,f1RCPs,vLCP,vRCP,f2LCPc,f2RCPc,f2LCPs,f2RCPs,temp,tempbis,temp2,temp2bis,temp3,temp3bis,meanL,meanR,v2LCP,v2RCP,x0,y0,x1,y1,RR1,RR2,i,loc1,loc2,loc3,loc4,xa,xb,ya,yb,indexL,indexR,indexL2,indexR2,poly,poly2,row,column,distance,j,minlookupt1,maxlookupt1,minlookupt2,maxlookupt2,FWHM,minimum,angulardistance,minimumR,minimumL,correction,a0,a1,a2,a3,a4)
 {

#pragma omp for
   for(iii=0;iii<nRows*nColumns;++iii)
	{
	  //with the convention adopted for a 2D array, the index iii is defined as iii=column+row*nColumns
	  row   =iii / nColumns;
	  column=iii % nColumns;

	  distance = sqrt(((float)row-Y0)*((float)row-Y0)+((float)column-X0)*((float)column-X0)); //distance in pixels
	  //printf("%d %d %d %f %f %d %f %f %f\n",iii,row,column,distance,Rsun,nColumns,X0,Y0,tempvec[iii]);

	  if(distance <= (Rsun+ExtraCrop))
		{

		  //CALCULATE THE SOLAR LINE PARAMETER AT THE DISTANCE FROM DISK CENTER (USING A LAW DERIVED FROM THE 3 Fe I PROFILES PROVIDED BY ROGER ULRICH)
		  //if(distance <= Rsun) angulardistance=cos(asin(distance/Rsun)); //convert projected angular distance from disk center to cos(angle) between the solar surface normal and the l.o.s. to the observer (INFINITE DISTANCE APPROXIMATION)
		  //else angulardistance=0.0;
		  //FWHM=FWHMCoeffs[0]+FWHMCoeffs[1]*angulardistance;
		  //FWHM=FWHM/2.0/sqrt(log(2.0))/1000.; //we convert from FWHM in mA to sigma in A
		  //minimum=minimumCoeffs[0]+minimumCoeffs[1]*angulardistance; //minimum intensity Id


		  //CALCULATE THE SOLAR LINE PARAMETER AT THE DISTANCE FROM DISK CENTER (USING A LAW DERIVED FROM A LINEWIDTH MAP OBTAINED WITH THE MDI-LIKE ALGORITHM)
		  distance=distance*cdelt1; //convert from pixels to arcsecs
		  FWHM=100.67102+0.015037016*distance-0.00010128197*distance*distance+3.1548385E-7*distance*distance*distance-3.7298102E-10*distance*distance*distance*distance+1.7275788E-13*distance*distance*distance*distance*distance;
		  FWHM=FWHM/2.0/sqrt(log(2.0))/1000.; //we convert from FWHM in mA to sigma in A

		  /*-------------------------------------------------------------*/
		  /* MDI-like algorithm                                          */
		  /*-------------------------------------------------------------*/

		  for(i=0;i<N;++i) 
		    {
		      tempvec=(float *)arrLev1p[i*2]->data;   //LCP (ASSUMES THE LEVEL 1p DATA ARE STORED LCP/RCP BACK-TO-BACK) IN THE ORDER I0, I1, I2, I3, I4, and I5
		      L[i]= tempvec[iii] ;
		      tempvec=(float *)arrLev1p[i*2+1]->data; //RCP
		      R[i]= tempvec[iii] ;		      
		    }

		  //First and Second Fourier coefficients
		  f1LCPc=0.0;
		  f1RCPc=0.0;
		  f1LCPs=0.0;
		  f1RCPs=0.0;
		  f2LCPc=0.0;
		  f2RCPc=0.0;
		  f2LCPs=0.0;
		  f2RCPs=0.0;
		  for(i=0;i<N;++i) 
		    {
		      f1LCPc += cosi[i] *(double)L[i];
		      f1RCPc += cosi[i] *(double)R[i];
		      f1LCPs += sini[i] *(double)L[i];
		      f1RCPs += sini[i] *(double)R[i];
		      f2LCPc += cos2i[i]*(double)L[i];
		      f2RCPc += cos2i[i]*(double)R[i];
		      f2LCPs += sin2i[i]*(double)L[i];
		      f2RCPs += sin2i[i]*(double)R[i];
		    }
 		  
		  vLCP    = atan2(-f1LCPs,-f1LCPc)*pv1/2.0/M_PI; //-f1LCPs and -f1LCPc so that the jump is at 180 degrees and not 0 degrees
		  vRCP    = atan2(-f1RCPs,-f1RCPc)*pv1/2.0/M_PI;
      		  v2LCP   = atan2(-f2LCPs,-f2LCPc)*pv2/2.0/M_PI;
		  v2RCP   = atan2(-f2RCPs,-f2RCPc)*pv2/2.0/M_PI;
		  v2LCP   = fmod((v2LCP-vLCP+10.5*pv2),pv2)-pv2/2.0+vLCP; //we use the uncorrected velocity, i.e. phase, of the 1st Fourier coefficient to correct for the estimate of v2LCP and v2RCP, because the range of velocities obtained with the second Fourier coefficient is half the range of the first Fourier coefficient
		  v2RCP   = fmod((v2RCP-vRCP+10.5*pv2),pv2)-pv2/2.0+vRCP; 

		  if(isnan(f1LCPc) || isnan(f1RCPc) || isnan(f1LCPs) || isnan(f1RCPs))
		    {
		      MISSVALS20 +=1;
		      MISSVALS21 +=1;
		      MISSVALS22 +=1;
		      MISSVALS23 +=1;
		      MISSVALS24 +=1;
		      lam0g[iii]  = MISSINGRESULT;
		      B0g[iii]    = MISSINGRESULT;
		      widthg[iii] = MISSINGRESULT;
		      Idg[iii]    = MISSINGRESULT;
		      I0g[iii]    = MISSINGRESULT;
		      rawlam0g[iii]  = MISSINGRESULT;
		      continue;
		    }



		  /*-------------------------------------------------------------*/
		  /* bilinear interpolation of the look-up tables at pixel (x,y) */
		  /*-------------------------------------------------------------*/
		  		  
		  //NB: it depends on how the filtergrams rebinning from 4096*4096 to axist[1]*axist[2] was done in phasemaps.c
		  //find the 4 neighbors (x0,y0), (x0,y1), (x1,y0), and (x1,y1) of (column,row) on the grid of the look-up tables, and deal with boundary problems

		  //x0 = (column/ratio); //a column number
		  //y0 = (row/ratio);    //a row number
		  x0 = floor( ((float)column-offset)/(float)ratio); //a column number
		  y0 = floor( ((float)row-offset)/(float)ratio);    //a row number
		  x1 = x0+1;
		  y1 = y0+1;

		  if(x1 >= axist[1])
		    {
		      x0 = x0-1;
		      x1 = x1-1;
		    }
		  if(y1 >= axist[2])
		    {
		      y0 = y0-1;
		      y1 = y1-1;
		    }

		  //xa = ((float)x1-(float)(column % ratio)/(float)ratio-(float)x0);
		  //xb = ((float)(column % ratio)/(float)ratio);
		  //ya = ((float)y1-(float)(row % ratio)/(float)ratio-(float)y0);
		  //yb = ((float)(row % ratio)/(float)ratio);

		  xb = (((float)column-offset)-(float)x0*(float)ratio)/(float)ratio;
		  yb = (((float)row-offset)-(float)y0*(float)ratio)/(float)ratio;
		  xa = 1.0-xb;
		  ya = 1.0-yb;

		  //perform the bilinear interpolation
		  //NB: make sure x0*axist[0]+y0*axist[0]*axist[1] can be coded on 4 bytes 
		  //with the convention adopted for a 2D array, the index iii is defined as iii=vtest+column*Nvtest+row*Nvtest*nColumns
		  loc1=x0*axist[0]+y0*axist[0]*axist[1];
		  loc2=x1*axist[0]+y0*axist[0]*axist[1];
		  loc3=x0*axist[0]+y1*axist[0]*axist[1];
		  loc4=x1*axist[0]+y1*axist[0]*axist[1];
		  
		  indexL =ntest+1;
		  indexR =ntest+1;
		  indexL2=ntest+1;
		  indexR2=ntest+1;

		  //initializes arrays (NOT NEEDED ACTUALLY)
		  memset(poly,0.0,sizeof(poly));
		  memset(poly2,0.0,sizeof(poly2));

		  poly[0]  =ya*(lookupt[loc1]*xa+lookupt[loc2]*xb)+yb*(lookupt[loc3]*xa+lookupt[loc4]*xb);                          //for 1st Fourier coefficient
		  poly2[0] =ya*(lookupt[loc1+ntest]*xa+lookupt[loc2+ntest]*xb)+yb*(lookupt[loc3+ntest]*xa+lookupt[loc4+ntest]*xb);  //for 2nd Fourier coefficient
		  minlookupt1 = poly[0];
		  minlookupt2 = poly2[0];

		  poly[ntest-1]=ya*(lookupt[loc1+ntest-1]*xa+lookupt[loc2+ntest-1]*xb)+yb*(lookupt[loc3+ntest-1]*xa+lookupt[loc4+ntest-1]*xb);          //for 1st Fourier coefficient
		  poly2[ntest-1]=ya*(lookupt[loc1+2*ntest-1]*xa+lookupt[loc2+2*ntest-1]*xb)+yb*(lookupt[loc3+2*ntest-1]*xa+lookupt[loc4+2*ntest-1]*xb);  //for 2nd Fourier coefficient
		  maxlookupt1 = poly[ntest-1];
		  maxlookupt2 = poly2[ntest-1];

		  for(i=step;i<ntest;i=i+step) //make sure (ntest-1)/step is an integer
		    {
		      poly[i]  =ya*(lookupt[loc1+i]*xa+lookupt[loc2+i]*xb)+yb*(lookupt[loc3+i]*xa+lookupt[loc4+i]*xb);                          //for 1st Fourier coefficient
		      poly2[i] =ya*(lookupt[loc1+i+ntest]*xa+lookupt[loc2+i+ntest]*xb)+yb*(lookupt[loc3+i+ntest]*xa+lookupt[loc4+i+ntest]*xb);  //for 2nd Fourier coefficient
		      if(poly[i] > vLCP && poly[i-step]   <= vLCP)
			{
			  for(j=i-step+1;j<=i;j++)
			    {
			      poly[j]  =ya*(lookupt[loc1+j]*xa+lookupt[loc2+j]*xb)+yb*(lookupt[loc3+j]*xa+lookupt[loc4+j]*xb);                          //for 1st Fourier coefficient
			      if(poly[j] > vLCP && poly[j-1]   <= vLCP) indexL = j-1;
			    }
			}
		      if(poly[i] > vRCP && poly[i-step]   <= vRCP)
			{
			  for(j=i-step+1;j<=i;j++)
			    {
			      poly[j]  =ya*(lookupt[loc1+j]*xa+lookupt[loc2+j]*xb)+yb*(lookupt[loc3+j]*xa+lookupt[loc4+j]*xb);                          //for 1st Fourier coefficient
			      if(poly[j] > vRCP && poly[j-1]   <= vRCP) indexR = j-1;
			    }
			}
		      if(poly2[i]> v2LCP && poly2[i-step] <= v2LCP)
			{
			  for(j=i-step+1;j<=i;j++)
			    {
			      poly2[j] =ya*(lookupt[loc1+j+ntest]*xa+lookupt[loc2+j+ntest]*xb)+yb*(lookupt[loc3+j+ntest]*xa+lookupt[loc4+j+ntest]*xb);  //for 2nd Fourier coefficient
			      if(poly2[j] > v2LCP && poly2[j-1]   <= v2LCP) indexL2 = j-1;
			    }
			}
		      if(poly2[i]> v2RCP && poly2[i-step] <= v2RCP)
			{
			  for(j=i-step+1;j<=i;j++)
			    {
			      poly2[j] =ya*(lookupt[loc1+j+ntest]*xa+lookupt[loc2+j+ntest]*xb)+yb*(lookupt[loc3+j+ntest]*xa+lookupt[loc4+j+ntest]*xb);  //for 2nd Fourier coefficient
			      if(poly2[j] > v2RCP && poly2[j-1]   <= v2RCP) indexR2 = j-1;
			    } 
			}
		    }


		  //TO DEAL WITH SATURATION
		  if(vLCP < minlookupt1)
		    { 
		      vLCP=vtest[0];
		      indexL=ntest+1;
		      //printf("take1 %f %f %f %f\n",vLCP,minlookupt1,vRCP,distance);
		    }
		  if(vLCP > maxlookupt1)
		    {
		      vLCP=vtest[ntest-1];
		      indexL=ntest+1;
		      //printf("take2 %f %f %f %f\n",vLCP,maxlookupt1,vRCP,distance);
		    }
		  if(vRCP < minlookupt1)
		    { 
		      vRCP=vtest[0];
		      indexR=ntest+1;
		      //printf("take3 %f %f %f %f\n",vRCP,minlookupt1,vLCP,distance);
		    }
		  if(vRCP > maxlookupt1)
		    {
		      vRCP=vtest[ntest-1];
		      indexR=ntest+1;
		      //printf("take4 %f %f %f %f\n",vRCP,maxlookupt1,vLCP,distance);
		    }
		  if(v2LCP < minlookupt2)
		    { 
		      v2LCP=vtest[0];
		      indexL2=ntest+1;
		    }
		  if(v2LCP > maxlookupt2)
		    {
		      v2LCP=vtest[ntest-1];
		      indexL2=ntest+1;
		    }
		  if(v2RCP < minlookupt2)
		    { 
		      v2RCP=vtest[0];
		      indexR2=ntest+1;
		    }
		  if(v2RCP > maxlookupt2)
		    {
		      v2RCP=vtest[ntest-1];
		      indexR2=ntest+1;
		    }

		  if(indexL == ntest+1 || indexR == ntest+1 || indexL2 == ntest+1 || indexR2 == ntest+1)
		    {
		      //printf("Error FINAL: the Doppler velocity calculated at pixel %d %d is spurious: %f %f %f %f. Distance: %f\n",column,row,vLCP,vRCP,v2LCP,v2RCP,distance);
		      //lam0g[iii]  = MISSINGRESULT;
		      //B0g[iii]    = MISSINGRESULT;
		      //widthg[iii] = MISSINGRESULT;
		      //Idg[iii]    = MISSINGRESULT;
		      //I0g[iii]    = MISSINGRESULT;
		      SATVALS2   += 1;
		    }
		  //else
		  //{

		      //We linearly interpolate in the look-up table for the 1st Fourier coefficient to retrieve the actual velocities
		      if(indexL != ntest+1)  vLCP   = vtest[indexL] +(vLCP-(double)poly[indexL])   *(vtest[indexL+1] -vtest[indexL]) /((double)poly[indexL+1]  -(double)poly[indexL]  );
		      if(indexR != ntest+1)  vRCP   = vtest[indexR] +(vRCP-(double)poly[indexR])   *(vtest[indexR+1] -vtest[indexR]) /((double)poly[indexR+1]  -(double)poly[indexR]  );
		      //We linearly interpolate in the look-up table for the 2nd Fourier coefficient to retrieve the actual velocities
		      if(indexL2 != ntest+1) v2LCP  = vtest[indexL2]+(v2LCP-(double)poly2[indexL2])*(vtest[indexL2+1]-vtest[indexL2])/((double)poly2[indexL2+1]-(double)poly2[indexL2]);
		      if(indexR2 != ntest+1) v2RCP  = vtest[indexR2]+(v2RCP-(double)poly2[indexR2])*(vtest[indexR2+1]-vtest[indexR2])/((double)poly2[indexR2+1]-(double)poly2[indexR2]);

		      /*-------------------------------------------------------------*/
		      /* Calculation of observables                                  */
		      /*-------------------------------------------------------------*/
		      
		      f1LCPc = f1LCPc*Kfourier;
		      f1RCPc = f1RCPc*Kfourier;
		      f1LCPs = f1LCPs*Kfourier;
		      f1RCPs = f1RCPs*Kfourier;
		      f2LCPc = f2LCPc*Kfourier;
		      f2RCPc = f2RCPc*Kfourier;
		      f2LCPs = f2LCPs*Kfourier;
		      f2RCPs = f2RCPs*Kfourier;

		      //We compute the uncorrected (raw) Doppler velocity
		      //lam0g[iii]  = (float)((vLCP+vRCP+v2LCP+v2RCP)/4.);//simple average. Need weights? REMINDER: SIGN CONVENTION: v<0 FOR MOTION TOWARD THE OBSERVER (BLUESHIFT)
		      rawlam0g[iii]  = (float)((vLCP+vRCP)/2.);

		      
		      //THE FOLLOWING CORRECTION COEFFICIENTS WERE OBTAINED WITH correction_calibration.pro
		      //CORRECTION OF DOPPLER VELOCITY USING 4th-ORDER POLYNOMIAL FIT OF DATAMEDN-OBS_VR AS A FUNCTION OF DATAMEDN, AND OF ORDER 2 AS A FUNCTION OF TIME, FOR CALIBRATION NUMBER 11,
		      //FOR EXCLUSIVE USE WITH LOOKUP TABLE FSN_REC=4875802 OF 2010.05.06_17:24:55_TAI
		      /*a0=265411.80-0.00050880079*TargetTime+2.4391071e-13*TargetTime*TargetTime;
		      a1=22.670838-4.3274090e-08*TargetTime+2.0647957e-17*TargetTime*TargetTime;
		      a2=0.017577257-3.3413066e-11*TargetTime+1.5876568e-20*TargetTime*TargetTime;
		      a3=8.5101490e-07-1.6010385e-15*TargetTime+7.5321212e-25*TargetTime*TargetTime;
		      a4=-2.6222007e-09+4.9728844e-18*TargetTime-2.3575677e-27*TargetTime*TargetTime;
		      correction=a0+a1*vLCP+a2*vLCP*vLCP+a3*vLCP*vLCP*vLCP+a4*vLCP*vLCP*vLCP*vLCP;
		      vLCP-=(float)correction;
		      correction=a0+a1*vRCP+a2*vRCP*vRCP+a3*vRCP*vRCP*vRCP+a4*vRCP*vRCP*vRCP*vRCP;
		      vRCP-=(float)correction;*/

		      //CORRECTION OF DOPPLER VELOCITY USING 3th-ORDER POLYNOMIAL FIT OF DATAMEDN-OBS_VR AS A FUNCTION OF DATAMEDN, AND OF ORDER 2 AS A FUNCTION OF TIME, FOR CALIBRATION NUMBER 11,
		      //FOR EXCLUSIVE USE WITH LOOKUP TABLE FSN_REC=4875802 OF 2010.05.06_17:24:55_TAI
		      //a0=258788.69-0.00049651774*TargetTime+2.3821631e-13*TargetTime*TargetTime;
		      //a1=18.190058-3.4845204e-08*TargetTime+1.6683954e-17*TargetTime*TargetTime;
		      //a2=0.016656463-3.1637538e-11*TargetTime+1.5021447e-20*TargetTime*TargetTime;
		      //a3=8.4964346e-07-1.5652946e-15*TargetTime+7.2073361e-25*TargetTime*TargetTime;
		      //correction=a0+a1*vLCP+a2*vLCP*vLCP+a3*vLCP*vLCP*vLCP;
		      //vLCP-=(float)correction;
		      //correction=a0+a1*vRCP+a2*vRCP*vRCP+a3*vRCP*vRCP*vRCP;
		      //vRCP-=(float)correction;


		      //CORRECTION OF DOPPLER VELOCITY USING 3th-ORDER POLYNOMIAL FIT OF DATAMEDN-OBS_VR AS A FUNCTION OF DATAMEDN, AND OF ORDER 3 AS A FUNCTION OF TIME, FOR CALIBRATION NUMBER 11,
		      //FOR EXCLUSIVE USE WITH LOOKUP TABLE FSN_REC=4875802 OF 2010.05.06_17:24:55_TAI
		      /*a0= 2.64020347158473e+06-7.27688397303985e-03 *TargetTime  +6.67317235565747e-12*TargetTime*TargetTime    -2.03569322602522e-21*TargetTime*TargetTime*TargetTime;
		      a1= 9.11624927549143e+03     -2.58756688458379e-05*TargetTime  +2.44813299402635e-14*TargetTime*TargetTime    -7.72051926398669e-24*TargetTime*TargetTime*TargetTime;
		      a2= 1.54511810557473     -4.37364794268721e-09*TargetTime  +4.12654116717364e-18*TargetTime*TargetTime    -1.29774420683466e-27*TargetTime*TargetTime*TargetTime;
		      a3= -1.06133437236275e-03 +3.01513184952562e-12*TargetTime  -2.85515025959781e-21*TargetTime*TargetTime    +9.01198337961537e-31*TargetTime*TargetTime*TargetTime;
		      correction=a0+a1*vLCP+a2*vLCP*vLCP+a3*vLCP*vLCP*vLCP;
		      vLCP-=(float)correction;
		      correction=a0+a1*vRCP+a2*vRCP*vRCP+a3*vRCP*vRCP*vRCP;
		      vRCP-=(float)correction;*/

		      //CORRECTION SUGGESTED BY CHARLIE LINDSEY FOR CALIBRATION 11, WITH LOOKUP TABLE FSN_REC=4875802, AND FOR APRIL 10-11, 2010 ONLY (17:45 to 17:45)
		      //vLCP=100.0+1.11912*(vLCP-100.0)-416.927*log((7000.0+vLCP-100.0)/(7000.0-vLCP+100.0));
		      //vRCP=100.0+1.11912*(vRCP-100.0)-416.927*log((7000.0+vRCP-100.0)/(7000.0-vRCP+100.0));

		      //vLCP=31.2+1.13056*(vLCP-100.0)-421.19*log((7000.0+vLCP-100.0)/(7000.0-vLCP+100.0));
		      //vRCP=31.2+1.13056*(vRCP-100.0)-421.19*log((7000.0+vRCP-100.0)/(7000.0-vRCP+100.0));


		      //CORRECTION USING THE POLYNOMIAL COEFFICIENTS FROM hmi.coefficients[]
		      //if(!QUICKLOOK)
		      //{
		      correction=coeff[0]+coeff[1]*vLCP+coeff[2]*vLCP*vLCP+coeff[3]*vLCP*vLCP*vLCP;
		      vLCP-=(float)correction;
		      correction=coeff[0]+coeff[1]*vRCP+coeff[2]*vRCP*vRCP+coeff[3]*vRCP*vRCP*vRCP;
		      vRCP-=(float)correction;
		      //} 
		      
		      //We compute the Doppler velocity
		      //lam0g[iii]  = (float)((vLCP+vRCP+v2LCP+v2RCP)/4.);//simple average. Need weights? REMINDER: SIGN CONVENTION: v<0 FOR MOTION TOWARD THE OBSERVER (BLUESHIFT)
		      lam0g[iii]  = (float)((vLCP+vRCP)/2.);
		      if(isnan(lam0g[iii])) MISSVALS20 += 1;


		      //We compute the l.o.s. magnetic field
		      //B0g[iii]    = (float)((vLCP-vRCP+v2LCP-v2RCP)/2.0*magnetic);
		      B0g[iii]    = (float)((vLCP-vRCP)*magnetic);
		      if(isnan(B0g[iii])) MISSVALS21 += 1;

		      //We compute the linewidth (in Angstroms)
		      temp        = period/M_PI*sqrt(1.0/6.0*log((f1LCPc*f1LCPc+f1LCPs*f1LCPs)/(f2LCPc*f2LCPc+f2LCPs*f2LCPs)));
		      tempbis     = period/M_PI*sqrt(1.0/6.0*log((f1RCPc*f1RCPc+f1RCPs*f1RCPs)/(f2RCPc*f2RCPc+f2RCPs*f2RCPs)));
		      widthg[iii] = (float)((temp+tempbis)*sqrt(log(2.0)))*1000.; //we want the FWHM not the sigma of the Gaussian, in milliAngstoms	      
		      if(isnan(widthg[iii])) MISSVALS23 += 1;
		      
		      //We compute the linedepth
		      //temp2       = period/2.0*sqrt(f1LCPc*f1LCPc+f1LCPs*f1LCPs)/sqrt(M_PI)/temp*exp(M_PI*M_PI*temp*temp/period/period);
		      //temp2bis    = period/2.0*sqrt(f1RCPc*f1RCPc+f1RCPs*f1RCPs)/sqrt(M_PI)/tempbis*exp(M_PI*M_PI*tempbis*tempbis/period/period);
		      //Idg[iii]    = (float)((temp2+temp2bis)/2.0);
		      
		      //We compute the linedepth (alternative formula)
		      //temp2       = period/2.0/sqrt(M_PI)/temp   *pow((f1LCPc*f1LCPc+f1LCPs*f1LCPs),2./3.)/pow((f2LCPc*f2LCPc+f2LCPs*f2LCPs),1./6.);
		      //temp2bis    = period/2.0/sqrt(M_PI)/tempbis*pow((f1RCPc*f1RCPc+f1RCPs*f1RCPs),2./3.)/pow((f2RCPc*f2RCPc+f2RCPs*f2RCPs),1./6.);
		      temp2       = period/2.0*sqrt(f1LCPc*f1LCPc+f1LCPs*f1LCPs)/sqrt(M_PI)/FWHM*exp(M_PI*M_PI*FWHM*FWHM/period/period);  //to not use the second Fourier coefficient
		      temp2bis    = period/2.0*sqrt(f1RCPc*f1RCPc+f1RCPs*f1RCPs)/sqrt(M_PI)/FWHM*exp(M_PI*M_PI*FWHM*FWHM/period/period);
		      Idg[iii]    = (float)((temp2+temp2bis)/2.0);
		      if(isnan(Idg[iii])) MISSVALS22 += 1;

		      //We compute the continuum intensity
		      //temp3       = (vLCP+v2LCP)/2.0/dv;
		      //temp3bis    = (vRCP+v2RCP)/2.0/dv;
		      //meanL=0.0;
		      //meanR=0.0;
		      //for(i=0;i<N;++i)
		      //{
		      //  meanL      += L[i];
		      //	  meanR      += R[i];
		      //}
		      //meanL=meanL/(double)N;
		      //meanR=meanR/(double)N;
		      //for(i=0;i<N;++i)
		      //{
		      //  meanL      += (temp2   /(double)N*exp(-(tune[i]-temp3)   *(tune[i]-temp3)   /temp   /temp));
		      //  meanR      += (temp2bis/(double)N*exp(-(tune[i]-temp3bis)*(tune[i]-temp3bis)/tempbis/tempbis));
		      //}
		      //
		      //I0g[iii]    = (float)((meanL+meanR)/2.0);

		      temp3       = vLCP/dv;
		      temp3bis    = vRCP/dv;
		      meanL=0.0;
		      meanR=0.0;
		      for(i=0;i<N;++i)
			{
			  meanL      += L[i];
			  meanR      += R[i];
			}
		      meanL=meanL/(double)N;
		      meanR=meanR/(double)N;
		      //minimumL=(L[0]+L[N-1])/2.*minimum/(double)N; //(L[0]+L[N-1])/2. estimate of the continuum
		      //minimumR=(R[0]+R[N-1])/2.*minimum/(double)N;
		      for(i=0;i<N;++i)
			{
			  //meanL      += (minimumL*exp(-(tune[i]-temp3)   *(tune[i]-temp3)   /FWHM/FWHM));
			  //meanR      += (minimumR*exp(-(tune[i]-temp3bis)*(tune[i]-temp3bis)/FWHM/FWHM));
			  meanL      += (temp2   /(double)N*exp(-(tune[i]-temp3)   *(tune[i]-temp3)   /FWHM/FWHM));
			  meanR      += (temp2bis/(double)N*exp(-(tune[i]-temp3bis)*(tune[i]-temp3bis)/FWHM/FWHM));
			}
		      
		      I0g[iii]    = (float)((meanL+meanR)/2.0);
		      if(isnan(I0g[iii])) MISSVALS24 += 1;

		      // }		  
		  
		}//if (distance <= Rsun)
	      else
		{
		  lam0g[iii]  = MISSINGRESULT;
		  B0g[iii]    = MISSINGRESULT;
		  widthg[iii] = MISSINGRESULT;
		  Idg[iii]    = MISSINGRESULT;
		  I0g[iii]    = MISSINGRESULT;
		  rawlam0g[iii]  = MISSINGRESULT;
		}
	      
	}//for iii
 }//end #pragma omp parallel
  

      free(cosi);
      free(sini);
      free(cos2i);
      free(sin2i);
      free(tune);
      free(angle);

      //fclose(fp);

      MISSVALS[0]=MISSVALS20;
      MISSVALS[1]=MISSVALS21;
      MISSVALS[2]=MISSVALS22;
      MISSVALS[3]=MISSVALS23;
      MISSVALS[4]=MISSVALS24;
      *SATVALS=SATVALS2;
      return error;
      
}//end routine