function convolve, image, psf, FT_PSF=psf_FT, FT_IMAGE=imFT, NO_FT=noft, \$ CORRELATE=correlate, AUTO_CORRELATION=auto, \$ NO_PAD = no_pad ;+ ; NAME: ; CONVOLVE ; PURPOSE: ; Convolution of an image with a Point Spread Function (PSF) ; EXPLANATION: ; The default is to compute the convolution using a product of ; Fourier transforms (for speed). ; ; The image is padded with zeros so that a large PSF does not ; overlap one edge of the image with the opposite edge of the image. ; ; This routine is now partially obsolete due to the introduction of the ; intrinsic CONVOL_FFT() function in IDL 8.1 ; ; CALLING SEQUENCE: ; ; imconv = convolve( image1, psf, FT_PSF = psf_FT ) ; or: ; correl = convolve( image1, image2, /CORREL ) ; or: ; correl = convolve( image, /AUTO ) ; ; INPUTS: ; image = 2-D array (matrix) to be convolved with psf ; psf = the Point Spread Function, (size < or = to size of image). ; ; The PSF *must* be symmetric about the point ; FLOOR((n_elements-1)/2), where n_elements is the number of ; elements in each dimension. For Gaussian PSFs, the maximum ; of the PSF must occur in this pixel (otherwise the convolution ; will shift everything in the image). ; ; OPTIONAL INPUT KEYWORDS: ; ; FT_PSF = passes out/in the Fourier transform of the PSF, ; (so that it can be re-used the next time function is called). ; FT_IMAGE = passes out/in the Fourier transform of image. ; ; /CORRELATE uses the conjugate of the Fourier transform of PSF, ; to compute the cross-correlation of image and PSF, ; (equivalent to IDL function convol() with NO rotation of PSF) ; ; /AUTO_CORR computes the auto-correlation function of image using FFT. ; ; /NO_FT overrides the use of FFT, using IDL function convol() instead. ; (then PSF is rotated by 180 degrees to give same result) ; ; /NO_PAD - if set, then do not pad the image to avoid edge effects. ; This will improve memory and speed of the computation at the ; expense of edge effects. This was the default method prior ; to October 2009 ; METHOD: ; When using FFT, PSF is centered & expanded to size of image. ; HISTORY: ; written, Frank Varosi, NASA/GSFC 1992. ; Appropriate precision type for result depending on input image ; Markus Hundertmark February 2006 ; Fix the bug causing the recomputation of FFT(psf) and/or FFT(image) ; Sergey Koposov December 2006 ; Fix the centering bug ; Kyle Penner October 2009 ; Add /No_PAD keyword for better speed and memory usage when edge effects ; are not important. W. Landsman March 2010 ; Add warning when kernel type does not match integer array ; W. Landsman Feb 2012 ; Don't force double precision output W. Landsman July 2014 ;- compile_opt idl2 sp = size( psf_FT,/str ) & sif = size( imFT, /str ) sim = size( image ) if (sim[0] NE 2) || keyword_set( noft ) then begin if keyword_set( auto ) then begin message,"auto-correlation only for images with FFT",/INF return, image endif dtype = size(image,/type) if dtype LE 3 then if size(psf,/type) NE dtype then \$ message,/CON, \$ 'WARNING - ' + size(psf,/TNAME) + \$ ' kernel converted to type ' + size(image,/tname) if keyword_set( correlate ) then \$ return, convol( image, psf ) \$ else return, convol( image, rotate( psf, 2 ) ) endif if keyword_Set(No_Pad) then begin sc = sim/2 & npix = N_elements( image ) if (sif.N_dimensions NE 2) || ((sif.type NE 6) && (sif.type NE 9)) || \$ (sif.dimensions[0] NE sim[1]) || (sif.dimensions[1] NE sim[2]) then imFT = FFT( image,-1 ) if keyword_set( auto ) then \$ return, shift( npix*real_part(FFT( imFT*conj( imFT ),1 )), sc[1],sc[2] ) if (sp.N_dimensions NE 2) || ((sp.type NE 6) && (sp.type NE 9)) || \$ (sp.dimensions[0] NE sim[1]) || (sp.dimensions[1] NE sim[2]) then begin sp = size( psf ) if (sp[0] NE 2) then begin message,"must supply PSF matrix (2nd arg.)",/INFO return, image endif Loc = ( sc - sp/2 ) > 0 ;center PSF in new array, s = (sp/2 - sc) > 0 ;handle all cases: smaller or bigger L = (s + sim-1) < (sp-1) psf_FT = conj(image)*0 ;initialise with correct size+type according ;to logic of conj and set values to 0 (type of psf_FT is conserved) psf_FT[ Loc[1], Loc[2] ] = psf[ s[1]:L[1], s[2]:L[2] ] psf_FT = FFT( psf_FT, -1, /OVERWRITE ) endif if keyword_set( correlate ) then \$ conv = npix * real_part(FFT( imFT * conj( psf_FT ), 1 )) \$ else conv = npix * real_part(FFT( imFT * psf_FT, 1 )) sc = sc + (sim MOD 2) ;shift correction for odd size images. return, shift( conv, sc[1], sc[2] ) endif else begin sc = floor((sim-1)/2) & npix = n_elements(image)*4. ; the spooky factor of 4 in npix is because we're going to pad the image ; with zeros if (sif.N_dimensions NE 2) || ((sif.type NE 6) && (sif.type NE 9)) || \$ (sif.dimensions[0] NE sim[1]) || (sif.dimensions[1] NE sim[2]) then begin ; here is where we make an array with twice the dimensions of image and ; pad with zeros -- thanks to Daniel Eisenstein for this fix image_big = make_array(type = sim[sim[0]+1], sim[1]*2, sim[2]*2) image_big[0:sim[1]-1,0:sim[2]-1] = image imFT = FFT( image_big,-1 ) npix = n_elements(image_big) endif if keyword_set( auto ) then begin intermed = shift( npix*real_part(FFT( imFT*conj( imFT ),1 )), sc[1],sc[2] ) return, intermed[0:sim[1]-1,0:sim[2]-1] endif if (sp.N_dimensions NE 2) || ((sp.type NE 6) && (sp.type NE 9)) OR \$ (sp.dimensions[0] NE sim[1]) || (sp.dimensions[1] NE sim[2]) then begin sp = size( psf ) if (sp[0] NE 2) then begin message,"must supply PSF matrix (2nd arg.)",/INFO return, image endif ; this obfuscated line determines the offset between the center of the ; image and the center of the PSF Loc = ( sc - floor((sp-1)/2) ) > 0 psf_image = make_array(type = sim[sim[0]+1],sim[1]*2,sim[2]*2) psf_image[Loc[1]:Loc[1]+sp[1]-1, Loc[2]:Loc[2]+sp[2]-1] = psf psf_FT = FFT(psf_image, -1) endif if keyword_set( correlate ) then begin conv = npix * real_part(FFT( imFT * conj( psf_FT ), 1 )) conv = shift(conv, sc[1], sc[2]) endif else begin conv = npix * real_part(FFT( imFT * psf_FT, 1 )) conv = shift(conv, -sc[1], -sc[2]) endelse return, conv[0:sim[1]-1,0:sim[2]-1] endelse end