XMM-Newton Science Analysis System


eposcorr (eposcorr-3.13) [xmmsas_20230412_1735-21.0.0]

Algorithm

   subroutine eposcorr

       read x-ray and optical list

       call find_offset

       call correct_positions 

       IF findrotation == TRUE THEN
         call find_all ! make a three dimensional search
  
       DO i=1, niter
         IF findrotation == TRUE THEN
            call find_rotation
         call find_offsets

        update the grid resolution
        ! for the last iteration a larger grid is used in order to get an error
        ! estimate
       END


       modify/write the x-ray list

   end subroutine  eposcorr

   subroutine find_offset
       
       x_shift= y_shift =0
       LOOP over x_offset grid elements
           LOOP over y_offset grid elements
        
              call subroutine likelihood        
              store likelihood in array
              IF likelihood > best likelihood THEN
                update best likelihood, x_shift=x_offset , y_shift=y_offset 

           END LOOP
       END LOOP

       xm = ym = 0
       total_likelihood = 0
       LOOP over likelihood array elements (= corresponding x_offset, y_offset)
         IF( distance( x/y_offset , x/y_shift ) < 0.5* grid size ) THEN
           xm = xm + likelihood * (x_offset - x_shift)
           ym = ym + likelihood * (y_offset - y_shift)
           total_likelihood = total_likelihood + likelihood
         END IF
       END LOOP

       ! New best offsets:
       x_shift = xm/total_likelihood
       y_shift = ym/total_likelihood

   end subroutine find_offset

   subroutine likelihood

       set likelihood = 0
       set nmatches   = 0
       LOOP over elements X-ray list
           LOOP over elements optical list

               calculate the combined position error (sigma)
               calculate the distance (d) between the optical and X-ray source
                         for given x and y offsets
               IF x-ray source within 5 sigma of optical source THEN
                 nmatches =  nmatches + 1
                 likelihood = likelihood + exp{ -0.5 * (d/sigma)^2 }
               END IF

           END LOOP
       END LOOP

   end subroutine  likelihood