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SExtractor User`s Guide

1. 1 changing the detection threshold which can create a variable bias and 2 irregularities of the isophotal limits which introduces additional noise Measurements performed through a window function an envelope do not have such drawbacks SEXTRACTOR versions 2 4 and above implement windowed versions for most of the measure ments described in Isophotal parameters Equivalent windowed parameters X_IMAGE Y_IMAGE XWIN_IMAGE YWIN_IMAGE ERRA_IMAGE ERRB_IMAGE ERRTHETA_IMAGE ERRAWIN_IMAGE ERRBWIN_IMAGE ERRTHETAWIN_IMAGE A_IMAGE B_IMAGE THETA_IMAGE AWIN_IMAGE BWIN_IMAGE THETAWIN_IMAGE X2_IMAGE Y2_IMAGE XY_IMAGE X2WIN_IMAGE Y2WIN_IMAGE XYWIN_IMAGE CXX_IMAGE CYY_IMAGE CXY_IMAGE CXXWIN_IMAGE CYYWIN_IMAGE CXYWIN_IMAGE The computations involved are the same except that the pixel values are integrated within a circular Gaussian window as opposed to the object s isophotal footprint The Gaussian window is scaled to each object its FWHM is the diameter of the disk that contains half of the object flux Note that in double image mode 3 the window is scaled based on the measurement image Computing windowed parameters can be quite CPU intensive because it is an iterative process Despite this it is recommended to use windowed parameters instead of their isophotal equivalents as the measurements they provide are much less noisy Fig 6 Actually the positional accuracy offered by XWIN_IMAGE and YWIN_IMAGE is close to the one offered
2. To test the effects of deblending on photometry and astrometry measurements we made several simulations of photographic images of double stars with different separations and magnitudes under typical observational conditions fig 4 It is obvious that multiple isophotal techniques fail when there is no saddle point present in profiles i e for distance between stars lt 20 in the case of Gaussian images We measured a magnitude error lt 0 2 mag and a shift of the centroid lt 0 4 pixels for the fainter star in the very worst cases but no other systematic effects were noticeable 0 4 Centroid m 19 4 02 i K A e Fi A Le a sA 0 2 i v4 Centroid error pixels o T 0 4 E 4 0 2 F l Magnitude 7 0 1 4 02 J Magnitude error o T Separation pixels Figure 4 Centroid and corrected isophotal magnitude errors for a simulated 19 magnitude star blended with a 11 15 19 and 21 mag companion as a function of distance expressed in pixels Lines stop at the left when the objects are too close to be deblended The dashed vertical line is the theoretical limit for unsaturated stars with equal magnitudes In the centroid plot the arrow indicates the direction of the neighbour The simulation assumes a 1 hour exposure with the CERGA telescope on a IllaJ plate and Moffat profiles with a seeing FWHM of 3 pixels 2 The user can control the multi thresholding operat
3. in pixels for ASSOC Method for cross matching in ASSOC keep values corresponding to the first match found values corresponding to the nearest match found weighted average values exponentialy weighted average val ues sum values exponentialy sum values keep values corresponding to the match with minimum weight ASSOCSELEC_TYPE BACK_FILTERSIZE BACK_SIZE BACK_TYPE BACK_VALUE BACKPHOTO_THICK BACKPHOTO_TYPE CATALOG_NAME CATALOG_TYPE CHECKIMAGE_NAME MATCHED AUTO 0 0 0 0 24 GLOBAL check fits MAX keyword ALL MATCHED MATCHED integers n lt 2 integers n lt 2 keywords n lt 2 AUTO MANUAL floats n lt 2 integer keyword GLOBAL LOCAL string keyword ASCII ASCII_HEAD ASCII_SKYCAT ASCII_VOTABLE FITS_1 0 FITS_LDAC strings n lt 16 keep values corresponding to the match with maximum weight What sources are printed in the out put catalog in case of ASSOC all detections only matched detections only detections that were not matched Size or Width Height in background meshes of the background filtering mask Size or Width Height in pixels of a background mesh What background is subtracted from the images the internal automatically interpo lated background map a user supplied constant value pro vided in BACK_VALUE in BACK_TYPE MANUAL mode the con stant value
4. 16 32 56 8 2 External flags SEXTRACTOR understands that it must process external flags when IMAFLAGS_ISO or NIMAFLAGS_ISO are present in the catalog parameter file It then looks for a FITS image specified by the FLAG_IMAGE keyword in the configuration file The FITS image must contain the flag map in the form of a 2 dimensional array of 8 16 or 32 bits integers It must have the same size as the image used for detection Such flag maps can be created using for example the Weight Watcher software Bertin 1997 The flag map values for pixels that coincide with the isophotal area of a given detected object are then combined and stored in the catalog as the long integer IMAFLAGS_ISO 5 kinds of combination can be selected using the FLAG_TYPE configuration keyword e OR the result is an arithmetic bit to bit OR of flag map pixels e AND the result is an arithmetic bit to bit AND of non zero flag map pixels MIN the result is the minimum of the signed flag map pixels MAX the result is the maximum of the signed flag map pixels MOST the result is the most frequent non zero flag map pixel value The NIMAFLAGS_ISO catalog parameter contains a number of relevant flag map pixels the num ber of non zero flag map pixels in the case of an OR or AND FLAG_TYPE or the number of pixels with value IMAFLAGS_ISO if the FLAG_TYPE is MIN MAX or MOST 9 Measurements Once sources have been detected and deblended they enter the measu
5. 30 0 will for example set the threshold at 1070 4 27 2 30 13 18 ADUs above the local background DETECT_MINAREA sets the minimum number of pixels a group should have to trigger a detection Obviously this parameter can be used just like DETECT_THRESH to detect only bright and big sources or to increase detection reliability It is however more tricky to manipulate at low detection thresholds because of the complex interplay of object topology noise correlations including those induced by filtering and sampling In most cases it is therefore recommended to keep DETECT_MINAREA at a small value typically 1 to 5 pixels and let DETECT_THRESH and the filter define SEXTRACTOR s sensitivity 6 4 Deblending Each time an object extraction is completed the connected set of pixels passes through a sort of filter that tries to split it into eventual overlapping components This case appears more frequently when the field is crowded or when the detection threshold is set very low The deblending method adopted in SEXTRACTOR is based on multi thresholding and works on any kind of object but it is unable to deblend components that are so close that no saddle is present in their profile However as no assumption has to be made on the shape of the objects it is perfectly suited for galaxies as well as for high galactic latitude stellar fields Typical problematic cases for deblending include patchy extended Sc galaxies which have to be consi
6. be interpolated from the global background map is no longer valid in crowded regions An example is a globular cluster superimposed on a bulge of galaxy SEXTRACTOR offers the possibility to estimate locally the background used to compute magnitudes When this option is switched on BACKPHOTO_TYPE LOCAL instead of GLOBAL the photometric background is estimated within a rectangular annulus around the isophotal limits of the object The thickness of the annulus in pixels can be specified by the user with BACKPHOTO_SIZE 24 is a typical value 9 5 Cross identification within SEXTRACTOR SEXTRACTOR allows one to perform on line cross identification of each detection with an ASCII list Although the cross identification algorithm is not very sophisticated it works in pixel coordinates only it is particularly convenient for assessing SEXTRACTOR performances on image simulations from instance Configuration parameters related to cross identification are prefixed with ASSOC 9 5 1 The ASSOC list The ASSOC process is initiated by requesting in the parameter file at least one of the ASSOC catalog parameters VECTOR_ASSOC and NUMBER_ASSOC Then SEXTRACTOR looks for an ASCII file let s call it the ASSOC list whose file name has to be specified by the ASSOC_NAME configuration keyword The ASSOC list must contain columns of numbers separated by spaces or tabs Each line describes a source that will enter the cross identification
7. by PSF fitting 9 3 Astrometry and WORLD coordinates All SEXTRACTOR measurements related to positions distances and areas in the image like those described above can also be expressed in WORLD coordinates in the output catalog These parameters simply have the WORLD suffix instead of the IMAGE appended to them The conver sion from IMAGE to WORLD coordinates is presently performed by using information found in the FITS header of the measurement image even if the parameter is originally computed from the detection image like the basic shape parameters for instance To understand how this is done in practice let s have a general look at the way the mapping from IMAGE to WORLD coordinates is currently described in a FITS image header First a linear transformation involving most of the time only scaling and possibly rotation and more rarely shear allows one to convert integer pixel positions 1 2 for each axis to some projected coordinate system This is where you might want to stop if your WORLD system is just some kind of simple focal plane coordinate system in meters for instance or for a calibrated wavelength axis spectrum Now the FITS WCS World Coordinate System convention allows you to apply to these projected coordinates a non linear transformation which is in fact a de projection 32 80 T 80 T 0 0 Y 10 0 10 20 20 10 0 10 20 Ax mas Ax mas Figure 6 Comparison bet
8. extended galaxy images a compromise value for the contrast parameter e 0 005 proved to be optimum This should normally exclude to separate objects with a difference in magnitude greater than 6 Density Area Figure 3 A schematic diagram of the method used to deblend a composite object The area profile of the object smooth curve can be described in a tree structured way thick lines The decision to regard or not a branch as a distinct object is determined according to its relative integrated intensity tinted area In that case above the original object shall split into two components A and B Remaining pixels are assigned to their most credible progenitors afterwards The outlying pixels with flux lower than the separation thresholds have to be reallocated to the proper components of the merger To do so we have opted for a statistical approach at each faint pixel we compute the contribution which is expected from each sub object using a bivariate Gaussian fit to its profile and turn it into a probability for that pixel to belong to the sub object For instance a faint pixel lying halfway between two close bright stars having the same magnitude will be appended to one of these with equal probabilities One big advantage 21 of this technique is that the morphology of any object is completely defined simply through its list of pixels
9. flux on stars or compact galaxy profiles around 39 0 06 for default extraction parameters The use of MAG_BEST is now deprecated as MAG_AUTO measurements are much more robust in versions 2 x of SEXTRACTOR The first improvement is a crude subtraction of all the neighbours which have been detected around the measured source the MASK_TYPE BLANK option The second improvement is an automatic correction of parts of the aperture which are suspected from contamination by a neighbour by mirroring the oppo site cleaner side of the measurement ellipse if available the MASK_TYPE CORRECT option which is also the default Figure 7 shows the mean loss of flux measured with isophotal threshold 24 4 mag arsec corrected isophotal and automatic aperture photometries for simulated galaxy By on a typical Schmidt survey plate image Photographic photometry In DETECT_TYPE PHOTO mode SEXTRACTOR assumes that the response of the detector over the dynamic range of the image is logarithmic This is generally a good approximation for photographic density on deep exposures Photometric procedures described above remain unchanged except that for each pixel we apply first the transformation D I 10 107 49 where MAG_GAMMA is the contrast index of the emulsion D the original pixel value from the background subtracted image and Jp is computed from the magnitude zero point mo Y 0 4m Io 10 9 50 07 1n10 50 One advantage of using a
10. minimum of 200MB is recommended Swap space can of course be put to contribution although a strong performance hit is to be expected 1Binaries are available on the WWW see e g http www tass survey org tass software software html sextract 2 2 Obtaining SEXTRACTOR The easiest way to obtain SEXTRACTOR is to download it from http terapix iap fr soft sextractor The current official anonymous FTP site is ftp ftp iap fr pub fromusers bertin sextractor There can be found the latest versions of the program as standard tar gz Unix archives plus some documentation 2 3 Installation To install from the source archive you must first uncompress and unarchive the archive gzip dc sextractor x y tar gz tar xv A new directory called sextractor x y should now appear at the current position on your disk You should then just enter the directory and follow the instructions in the file called INSTALL If you have the root privileges it will generally consist of configure make make install RPM binary archives are also provided for x86 architectures e g Intel AMD In this case SEXTRACTOR can be installed as root using rpm U sextractor x y z rpm 3 Using SEXTRACTOR 3 1 Syntax SEXTRACTOR is run from the shell with the following syntax sex image c configuration file Parameter1 Valuel Parameter2 Value2 The part enclosed within brackets is optional Any Parameter Value statement
11. of glitches 6 2 3 What is filtered and what isn t Although filtering is a benefit for detection it distorts profiles and correlates the noise it is therefore nefast for most measurement tasks Because of this filtering is applied on the fly to the image and directly affects only the detection process and the isophotal parameters described in 89 2 Other catalog parameters are indirectly affected through the exact position of the barycenter and typical object extent but the effect is considerably less Obviously in double image mode filtering is only applied to the detection image 6 2 4 Image boundaries and bad pixels Virtual pixels that lie outside image boundaries are arbitrarily set to zero This makes sense since filtering occurs on a background subtracted image When weighting is applied 7 bad pixels pixels with weight lt WEIGHT_THRESH are interpolated by default 7 5 and should therefore not cause much trouble It is recommended not to turn off interpolation of bad pixels when filtering is on 6 2 5 Configuration parameters Filtering is triggered when the FILTER keyword is set to Y If active a file with name specified by FILTER_NAME is searched for and loaded Filtering with large retinas can be extremely time consuming In many cases one is only interested in filtering pixels whose values stand out from the background noise The FILTER_THRESH keyword can be given to specify the range of pix
12. part of a process called segmentation in the image processing vocabulary Segmentation normally consists of identifying and separating image regions which have different properties brightness colour texture or are delineated by edges In the astronomical context the segmentation process consists of separating objects from the sky background This is however a somewhat imprecise definition as astronomical sources have on the images and even often physically no clear boundaries and may overlap We shall therefore use the following working definition of an object in SEXTRACTOR a group of pixels selected through some detection process and for which the flux contribution of an astronomical source is believed to be dominant over that of other objects Note that this means that a simple x y position vector alone cannot be handled by SEXTRACTOR as a detection most measurement routines require some rough shape information about the objects Segmentation in SEXTRACTOR is achieved through a very simple thresholding process a group of connected pixels that exceed some threshold above the background is identified as a detection But things are a little bit more complicated in practice First on most astronomical images the background is not constant over the frame and its determination can be ambiguous in crowded regions Second the software has to operate on noisy data and some filtering adapted to the characteristics of the image has to b
13. s of the flag image s FLAG_TYPE GAIN INTERP_MAXXLAG INTERP_MAXYLAG INTERP_TYPE MAG_GAMMA MAG_ZEROPOINT MASK_TYPE MEMORY_BUFSIZE MEMORY_OBJSTACK MEMORY_PI XSTACK PARAMETERS_NAME PHOT_APERTURES OR 16 16 ALL CORRECT keyword OR AND MIN MAX MOST float integers n lt 2 integers n lt 2 keywords n lt 2 NONE VAR_ONLY ALL float float keyword NONE BLANK CORRECT integer integer integer string floats n lt 32 10 Combination method for flags on the same object arithmetical OR arithmetical AND minimum of all flag values maximum of all flag values most common flag value Gain conversion factor in e ADU used for error estimates of CCD magnitudes Maximum z gap in pixels allowed in interpolating the input image s Maximum y gap in pixels allowed in interpolating the input image s Interpolation method from the variance map s or weight map s no interpolation interpolate only the variance map detection threshold interpolate both the variance map and the image itself y of the emulsion takes effect in PHOTO mode only Zero point offset to be applied to mag nitudes Method of masking of neighbours for photometry no masking put detected pixels belonging to neighbours to zero replace by values of pixels symetric with respect to
14. the source center Number of scan lines in the image buffer Multiply by 4 the frame width to get equivalent memory space in bytes Maximum number of objects that the object stack can contain Multiply by 300 to get equivalent memory space in bytes Maximum number of pixels that the pixel stack can contain Multiply by 16 to 32 to get equivalent memory space in bytes The name of the file containing the list of parameters that will be computed and put in the catalogue for each ob ject Aperture diameters in pixels used by MAG_APER PHOT_AUTOPARAMS PHOT_AUTOAPERS PHOT_FLUXFRAC PIXEL_SCALE SATUR_LEVEL SEEING_FWHM STARNNW_NAME THRESH_TYPE VERBOSE_TYPE WEIGHT_GAIN WEIGHT_IMAGE WEIGHT_TYPE 0 0 0 0 0 5 RELATIVE NORMAL Y weight fits NONE floats n 2 floats n 2 floats n lt 32 float float float string keywords n lt 2 RELATIVE ABSOLUTE keyword QUIET NORMAL EXTRA_WARNINGS FULL boolean strings n lt 2 keywords n lt 2 NONE BACKGROUND MAP_RMS MAP_VAR MAP_WEIGHT 11 MAG_AUTO controls scaling parameter k of the 1st order moment and mini mum Rmin in units of A and B MAG_AUTO minimum circular aper ture diameters estimation disk and measurement disk Fraction of FLUX_AUTO defining each element of the FLUX_RADIUS vector Pixel size in arcsec for surface brightness parameters FWHM and star galaxy separation on
15. to be subtracted from the images Thickness in pixels of the back ground LOCAL annulus Background used to compute magni tudes taken directly from the background map recomputed in a rectangular annu lus around the object Name of the output catalogue If the name STDOUT is given and CATALOG_TYPE is set to ASCII ASCII HEAD ASCII_SKYCAT or ASCII_VOTABLE the catalogue will be piped to the standard output stdout Format of output catalog ASCII table the simplest but space and time consuming as ASCII preceded by a header con taining information about the content SkyCat ASCII format WCS coordi nates required XML VOTable format with meta data FITS format as in SEXTRACTOR 1 FITS LDAC format the original image header is copied File name for each check image together CHECKIMAGE_TYPE CLEAN CLEAN_PARAM DEBLEND_MINCONT DEBLEND_NTHRESH DETECT _MINAREA DETECT_THRESH DETECT_TYPE FILTER FILTER_NAME FILTER_THRESH FITS_UNSIGNED FLAG_IMAGE NONE CCD flag fits keywords n lt 16 NONE IDENTICAL BACKGROUND BACKGROUND_RMS MINIBACKGROUND MINIBACK_RMS BACKGROUND FILTERED OBJECTS OBJECTS APERTURES SEGMENTATION boolean float float integer integer floats n lt 2 keyword CCD PHOTO boolean string floats n lt 2 boolean strings n lt 4 Type of information to put in
16. Dalcanton et al 1997 and references therein The simplest way to achieve the detection of extended LSB objects in SEXTRACTOR is to work on MINIBACK check images see 827 A second problem may occur because of overlaps with other objects Convolving with a low pass filter the PSF has no negative side lobes diminishes the contrast between objects and makes segmentation less effective in isolating individual sources This can to some extent be recovered by deblending see 86 4 In severely crowded fields however confusion noise becomes the limiting factor for detection and it is then advisable not to filter at all or to use a bandpass filter compensated filter Finally the PSF appears sometimes to be variable across the field The convolution mask should ideally follow these changes in order to allow for optimal detection everywhere in the image However considering approximately Gaussian PSF cores and convolution kernels detectability is a rather slow function of their FWHMs a mismatch as large as 50 between the kernel FWHM and that of the PSF will lead to no more than a 10 loss in peak S N Irwin 1985 Considering that PSF variations are generally much smaller than this filtering in SEXTRACTOR is limited to constant kernels 8Full Width at Hal Maximum 17 6 2 2 Non linear filtering There are many situations in which convolution is of little help filtering of strongly non Gaussian noise extraction of specific image
17. Neural Network based star galaxy classifier Flexible catalogue output of desired parameters only Pixel to pixel photometry in dual image mode Handling of weight maps and flag maps Optimum handling of images with variable S N Special mode for photographic scans XML VOTable compliant catalog output Back in the early nineties the purpose of SEXTRACTOR was to find a compromise between re finement in both detection and measurements and computational speed By today s standards SEXTRACTOR would be more accurately described as a quick and dirty tool 2 Installing the software 2 1 Software and hardware requirements Since the beginning in 1993 the development of SEXTRACTOR was always made on Unix systems successively SUN OS HP UX SUN Solaris Digital Unix and GNU Linux Successful ports by external contributors have been reported on non Unix OSes such as AMIGA OS DEC VMS and even MS DOS Windows95 and NT They are however not currently supported by the author and Unix remains the recommended system for running SEXTRACTOR The software is generally run in ANSI text mode from a shell A window system is therefore unnecessary with present versions On the hardware side memory requirements obviously depend on the size of the images to be processed But to give an idea a typical processing of 1024 x 1024 pixel images should require no more than 8 MB of memory For very large images 32000 x 32000 pixels or more a
18. ONV NORM 5x5 convolution mask of a gaussian PSF with FWHM 2 0 pixels 006319 0 040599 0 075183 0 040599 0 006319 040599 0 260856 0 483068 0 260856 0 040599 075183 0 483068 0 894573 0 483068 0 075183 040599 0 260856 0 483068 0 260856 0 040599 006319 0 040599 0 075183 0 040599 0 006319 Oo O The CONV keyword appearing at the beginning of the first line tells SEXTRACTOR that the file contains the description of a convolution mask kernel It can be followed by NORM if the mask is to be normalized to 1 before being applied or NONORM otherwise The following lines should contain an equal number of kernel coefficients separated by lt space gt of lt TAB gt characters Coefficients in the example above are read from left to right and top to bottom corresponding to increasing NAXIS1 x and NAXIS2 y in the image Formatting is free and number representations like 0 14 0 1400 1 4e 1 or 1 4E 01 are equivalent The width of the kernel is set by the number of values per line and its height is given by the number of lines Lines beginning with are treated as comments In SEXTRACTOR file name extensions are just conventions they are not used by the software to distinguish between different file formats 1f the sum of the kernel coefficients happens to be exactly zero the kernel is normalized to variance unity 19 6 3 Thresholding Thresholding is applied to the background subtracted filtered image to is
19. PTICITY 9 1 8 Position errors ERRX2 ERRY2 ERRXY ERRA ERRB ERRTHETA ERRCXX ERRCGYY ERRCXV 200 aoe ag aes a a auf do Gide ots oe t 9 1 9 Handling of infinitely thin detections Windowed positional parameters o e a a Astrometry and WORLD coordinates 9 3 1 Celestial coordinates 9 3 2 Use of the FITS keywords for astrometry Photometry A LE ro Ses Se HE a Me nt eh a a Cross identification within SEXTRACTOR 9 5 1 The ASSOC list 9 5 2 Controlling the ASSOC process 9 5 3 Output from ASSOC Appendices A 1 FAQ Frequently Asked Questions 1 What is SEXTRACTOR SEXTRACTOR Source Extractor is a program that builds a catalogue of objects from an astro nomical image It is particularly oriented towards reduction of large scale galaxy survey data but it also performs well on moderately crowded star fields Its main features are Support for multi extension FITS Speed typically 1 Mpixel s with a 2GHz processor Ability to work with very large images up to 65k x 65k pixels on 32 bit machines or 2G x 2G pixels on 64 bit machines thanks to buffered image access Robust deblending of overlapping extended objects Real time filtering of images to improve detectability
20. R G 1980 ApJS 43 305 15 Lutz R K 1979 The Computer Journal 23 262 16 Moffat A F J 1969 17 Wells D C Greisen E W Harten R H 1981 A amp AS 44 363 A Appendices A 1 FAQ Frequently Asked Questions Fairly often I am asked by users about the reason for some limitations or choices in the way things are done in SEXTRACTOR In this section I try to justify them 39 Q SEXTRACTOR supports WCS So why isn t it possible to have the ASSOC cross identification working in a 0 or any other world coordinates A The ASSOC list which is used for cross identification can be very long 100 000 objects or more Performing an exhaustive cross id in real time can therefore be extremely slow unless the ASSOC coordinates are sorted in some way beforehand In pixel coordinates such a sorting is simple and very efficient as SEXTRACTOR works line by line but it would be much more difficult in the general WCS context This is why this hasn t been implemented considering it as beyond the scope of SEXTRACTOR Q Why isn t the detection threshold expressed in units of the background noise standard deviation in the FILTERed image A There are two reasons for this First it makes the threshold independent of the choice of a FILTER which is a good thing Second having measured on the FILTERed image may have given un informed users the wrong impression that increasing filtering systematically improves the detectabili
21. SEXTRACTOR v2 5 User s manual E BERTIN Institut d Astrophysique amp Observatoire de Paris Contents 1 What is SEXTRACTOR 5 2 Installing the software 5 2 1 Software and hardware requirements 5 2 2 Obtaining EXTRACTOR 2 ide ia a AA bee SM a 6 23 Installations sui 2 hein es LR ee ns RA GO Ae 20e el 6 3 Using SEXTRACTOR 6 dl Syntax 2 Hd ae Se See da Me 2 eee Ee Ades See a ae a Ae bead ven 6 3 2 The configuration files pa esse gaan ania Bae be Go ee GNA oe ee ee ue 6 A SHOVING yee piven sas de decal by url Ge Gok Rep eke dite dote Base bese es 7 3 2 2 Configuration parameter list T 3 3 The catalog parameter file 12 Sock OEMAL Lo a der Seb eo Grad amp GQ angen ss kg ee es Da es 12 3 4 Example of configuration 12 4 Overview of the software 12 5 Handling of image data 12 6 Detection and segmentation 14 6 1 Background estimation 14 6 1 1 Configuration parameters and tuning 16 Gly CPU COSTS ses aid na a A nn ste WD GA RAR kk ME SEE 16 052 Eller lato id es de ata Od hat e Bak of Edad tte Sok en ee tay ae 16 6 24 Convolution s sad Lars hae ee er we BR a GARE Pos le bee amp 16 6 2 2 Non linear filtering 18 6 2 3 What is filtered and what isn t 18 6 2 4 Image boundar
22. a cross identification It does not require the cz column in ASSOC_PARAMS The first geometrical match encountered while scanning 18The x and y coordinates must comply with the FITS and SEXTRACTOR convention by definition the center of the first pixel in the image array has pixel coordinates 1 0 1 0 37 the ASSOC list is retained as the actual match This can used for catalogs with low spatial density e NEAREST this option does not require the cz column in ASSOC_PARAMS The match is performed with the ASSOC list member the closest in position to the current detection provided that it lies within the ASSOC_RADIUS e SUM all parameters issued from ASSOC list members which geometrically match the current detection are summed cz is not required e MAG_SUM all parameters c issued from ASSOC list members which geometrically match the current detection are combined using the following law 2 5log 3 gt 10794 This option allows one to sum flux contributions from magnitude data cz is not required e MIN among all geometrical matches retains the ASSOC list member which has the smallest Z parameter e MAX among all geometrical matches retains the ASSOC list member which has the largest Z parameter e MEAN all parameters issued from ASSOC list members which geometrically match the cur rent detection are weighted averaged using the Z parameter as the weight e MAG_MEAN all parameters issued from ASSOC list memb
23. a gov Both Basic FITS one single header and one single body and Multi Extension FITS MEF images are recognized Binary SEXTRACTOR catalogs produced from MEF images are MEF files themselves If catalog output is in ASCII format all catalogs from the individual extensions are concatenated in one big file the EXT_NUMBER catalog parameter must be used to tell which extension the source belongs to For images with NAXIS gt 2 only the first data plane is loaded If WCS information Greisen 1 Optional parameter In the text uppercase keywords in typewriter font refer to parameters from the configuration file or from the parameter file 3 Flexible Image Transport System World Coordinate System 12 Pixel stack F Object i stack I I I I Pere eed eg perenne Figure 1 Layout of the main SEXTRACTOR procedures Dashed arrows represent optional inputs amp Calabretta 1995 http www cv nrao edu fits documents wcs wcs all ps is available in the header it is automatically used by SEXTRACTOR to compute astrometric parameters Other astrometric descriptions like AST Starlink format or the solution coefficients of the DSS 5 plates are not recognized by the software In SEXTRACTOR as in all similar programs FITS axis 1 is traditionaly refered as the X axis and FITS axis 2 as the Y axis 6 Detection and segmentation In SEXTRACTOR the detection of sources is
24. alues which must then be separated by commas Integers can be given as decimals in octal form preceded by digit 0 or in hexadecimal preceded by 0x The hexadecimal format is particularly convenient for writing multiplexed bit values such as binary masks Environment variables written as HOME or HOME are expanded and not only for string parameters Some parameters are assigned default values in SEXTRACTOR and can therefore be omitted from the configuration file they are listed in 3 2 2 3 2 2 Configuration parameter list Here is a complete list of all the configuration parameters known to SEXTRACTOR Many of them should be used with their default values Please refer to the next sections for a detailed description of their meaning Parameter default ANALYSIS_THRESH ASSOC_DATA 2 3 4 ASSOC_NAME sky list ASSOC_PARAMS 2 3 4 ASSOC_RADIUS 2 0 ASSOC_TYPE MAG_SUM type floats n lt 2 integers n lt 32 string integers 2 lt n lt 3 float keyword FIRST NEAREST MEAN MAG_MEAN SUM MAG_SUM MIN Description Threshold in surface brightness at which CLASS_STAR and FWHM_ op erate 1 argument relative to Background RMS 2 arguments mu mag arcsec Zero point mag of the columns in the ASSOC file that will be copied to the catalog output Name of the ASSOC ASCII file Nos of the columns in the ASSOC file that will be used as coordinates and weight for cross matching Search radius
25. ations of 32 x 32 pixels background meshes polluted by random Gaussian profiles The true background lies at 0 ADU While being slightly noisier the clipped Mode gives a more robust estimate than a clipped Mean in crowded regions Once the grid is set up a median filter can be applied to suppress possible local overestimations due to bright stars The resulting background map is then simply a natural bicubic spline interpolation between the meshes of the grid In parallel with the making of the background map an RMS background map that is a map of the background noise in the image is produced It will be used if the WEIGHT_TYPE parameter is set different from NONE see 7 1 SObviously in some very unfavorable cases like small meshes falling on bright stars it leads to totally inaccurate results 15 6 1 1 Configuration parameters and tuning The choice of the mesh size BACK_SIZE is very important If it is too small the background estimation is affected by the presence of objects and random noise Most importantly part of the flux of the most extended objects can be absorbed in the background map If the mesh size is too large it cannot reproduce the small scale variations of the background Therefore a good compromise has to be found by the user Typically for reasonably sampled images a width of 32 to 256 pixels works well The user has some control over the background map by specifying the size of the median fi
26. barycenter coordinates can be used to identify asymetrical objects on well sampled images 9 1 4 2nd order moments X2 Y2 XY Centered second order moments are convenient for measuring the spatial spread of a source profile In SEXTRACTOR they are computed with x2 E 2 15 D ies So live 5 ies 2 7 16 gt 16 ies NY La xY 2 T 17 S7 iES These expressions are more subject to roundoff errors than if the 1st order moments were sub tracted before summing but allow both 1st and 2nd order moments to be computed in one pass Roundoff errors are however kept to a negligible value by measuring all positions relative here again to XMIN and YMIN 9 1 5 Basic shape parameters A B THETA These parameters are intended to describe the detected object as an elliptical shape A and B are its semi major and semi minor axis lengths respectively More precisely they represent the maximum and minimum spatial rms of the object profile along any direction THETA is the position angle between the A axis and the NAXIS1 image axis It is counted counter clockwise Here is how they are computed 2nd order moments can easily be expressed in a referential rotated from the x y image coordinate system by an angle 0 a cos 6 x2 sin 6 y2 2 cos O sin 0 Ty y sin 0 x cos 0 y 2 cos O sin 0 Ty 18 Tyo cosbsinO r cosOsin0 y cos 0 sin 0 77 One can find interesting angles 69 for which the var
27. d map SEXTRACTOR makes a first pass through the pixel data computing an estimator for the local background in each mesh of a grid that covers the whole 5 Digital Sky Survey 14 frame The background estimator is a combination of k o clipping and mode estimation similar to the one employed in Stetson s DAOPHOT program see e g Da Costa 1992 Briefly the local background histogram is clipped iteratively until convergence at 30 around its median if is changed by less than 20 during that process we consider that the field is not crowded and we simply take the mean of the clipped histogram as a value for the background otherwise we estimate the mode with Mode 2 5 x Median 1 5 x Mean 1 This expression is different from the usual approximation Mode 3 x Median 2 x Mean 2 e g Kendall and Stuart 1977 but was found to be more accurate with our clipped distri butions from the simulations we made Fig 2 shows that the expression of the mode above is considerably less affected by crowding than a simple clipped mean like the one used in FOCAS Jarvis and Tyson 1981 or by Infante 1987 but is amp 30 noisier For this reason we revert to the mean in non crowded fields 10 ll J 5 A lt o dt SEA si Ea so tt rnd ot i HR Fes peto ss se ba 5 o a O 5 fb il 10 i i L L l 0 5 10 15 20 25 30 Clipped Mean ADU Figure 2 Simul
28. density to intensity transformation relative to the local sky background is that it corrects to some extent large scale inhomogeneities in sensitivity see Bertin 1996 for details 16 Errors on magnitude An estimate of the error is available for each type of magnitude It is computed through Ag FE Am 1 0857 42 m 1 0857 51 where A is the area in pixels over which the total flux F in ADU is summed o the standard deviation of noise in ADU estimated from the background and g the detector gain GAIN parameter in e ADU For corrected isophotal magnitudes a term derived from Eq 46 is quadratically added to take into account the error on the correction itself In DETECT_TYPE PHOTO mode things are slightly more complex Making the assumption that plate noise is the major contributor to photometric errors and that it is roughly constant in density we can write on 10 ny 1 lx y Am 1 0857 52 Y Lay Hz y where I x y is the contribution of pixel x y to the total flux Eq 49 The GAIN is ignored in PHOTO mode lSTmportant this error must be considered only as a lower value since it does not take into account the complex uncertainty on the local background estimate Setting GAIN to 0 in the configuration file is equivalent to g 00 36 Background is the last point relative to photometry The assumption made in 86 1 that the local background associated to an object can
29. dered as single entities and close or interacting pairs of optically faint galaxies which have to be considered as separate objects Basically the multi thresholding algorithm employs a multiple isophotal analysis technique similar to those in use at the APM and the 20 COSMOS machines Beard McGillivray and Thanish 1991 in a first time each extracted set of connected pixels is re thresholded at N levels linearly or exponentially spaced between its primary extraction threshold and its peak value This gives us a sort of 2 dimensional model of the light distribution within the object s which is stored in the form of a tree structure fig 3 Then the algorithm goes downwards from the tips of branches to the trunk and decides at each junction whether it shall extract two or more objects or continue its way down To meet the conditions described earlier the following simple decision criteria are adopted at any junction threshold t any branch will be considered as a separate component if 1 the integrated pixel intensity above t of the branch is greater than a certain fraction e of the total intensity of the composite object 2 condition 1 is verified for at least one more branch at the same level i Note that ideally condition 1 is both flux and scale invariant However for faint poorly resolved objects the efficiency of the deblending is limited mostly by seeing and sampling From the analysis of both small and
30. e applied prior to detection to reduce the contamination by noise peaks Third many sources that overlap on the image are unlikely to be detected separately with a single detection threshold and require a de blending procedure which is actually multi thresholding in SEXTRACTOR Each of these points will now be described in greater detail below It is worth mentioning here that these 3 difficulties could to a large extent be bypassed using a wavelet decomposition e g Bijaoui et al 1998 Although such an algorithm might be implemented in a future version of SEXTRACTOR current constraints in processing speed available memory processing of gigantic images often make the pedestrian approach still more interesting in the case of large scale surveys 6 1 Background estimation The value measured at each pixel is a function of the sum of a background signal and light coming from the objects of interest To be able to detect the faintest of these objects and also to measure accurately their fluxes one needs to have an accurate estimate of the background level in any place of the image a background map Strictly speaking there should be one background map per object that is what would the image look like if that object was absent But at least for detection we may start by assuming that most discrete sources do not overlap too severely which is generally the case for high galactic latitude fields To construct the backgroun
31. e coor dinate system and then converted to WCS if requested 9 1 1 Limits XMIN YMIN XMAX YMAX These coordinates define two corners of a rectangle which encloses the detected object XMIN min Dis 9 YMIN min Yi 10 XMAX max Ti 11 YMAX max yi 12 where x and y are respectively the x coordinate and y coordinate of pixel i 9 1 2 Barycenter X Y Barycenter coordinates generally define the position of the center of a source although this definition can be inadequate or inaccurate if its spatial profile shows a strong skewness or very large wings X and Y are simply computed as the first order moments of the profile E lizi eS Dh eS X Lyi Y 7 XH _ 14 DA 1 S 13 Actually x and y are summed relative to XMIN and YMIN in order to reduce roundoff errors in the summing 9 1 3 Position of the peak XPEAK YPEAK It is sometimes useful to have the position XPEAK YPEAK of the pixel with maximum intensity in a detected object for instance when working with likelihood maps or when searching for 27 artifacts For better robustness PEAK coordinates are computed on filtered profiles if available On symetrical profiles PEAK positions and barycenters coincide within a fraction of pixel XPEAK and YPEAK coordinates are quantized by steps of 1 pixel thus XPEAK_IMAGE and YPEAK_IMAGE are integers This is no longer true for skewed profiles therefore a simple comparison between PEAK and
32. ect Internal flags are produced by the various detection and measurement processes within SEXTRACTOR they tell for instance if an object is saturated or has been truncated at the edge of the image External flags come from flag maps these are images with the same size as the one where objects are detected where integer numbers can be used to flag some pixels for instance bad or noisy pixels Different combinations of flags can be applied within the isophotal area that defines each object to produce a unique value that will be written to the catalog 8 1 Internal flags The internal flags are always computed They are accessible through the FLAGS catalog parame ter which is a short integer FLAGS contains coded in decimal all the extraction flags as a sum of powers of 2 25 1 The object has neighbours bright and close enough to significantly bias the MAG_AUTO photometry or bad pixels more than 10 of the integrated area affected 2 The object was originally blended with another one 4 At least one pixel of the object is saturated or very close to 8 The object is truncated too close to an image boundary 16 Object s aperture data are incomplete or corrupted 32 Object s isophotal data are incomplete or corrupted 64 A memory overflow occurred during deblending 128 A memory overflow occurred during extraction For example an object close to an image border may have FLAGS 16 and perhaps FLAGS 8
33. el values within which retina filtering will be applied in units of background noise standard deviation If one value is given it is interpreted as a lower threshold For instance 9 Enhance Your Extraction 18 FILTER_THRESH 3 0 will allow filtering for pixel values exceeding 30 above the local background whereas FILTER_THRESH 10 0 3 0 will only allow filtering for pixel values between 100 and 30 FILTER_THRESH has no effect on convolution The result of the filtering process can be verified through a FILTERED check image see 6 2 6 CPU cost The SEXTRACTOR filtering routine is particularly optimized for small kernels It thus provides a convenient way of filtering large image data On a 2GHz machine a convolution by a 5 x 5 kernel will contribute less than 1 second to the processing time of a 2048 x 4096 image The numbers for non linear retina filtering depend on the complexity of the neural network but can be a hundred times larger 6 2 7 Filter file formats As described above two kinds of filter files are recognized by SEXTRACTOR convolution files traditionaly suffixed with conv and retina files ret extensions Retina files are written exclusively by the EYE software as FITS binary tables Convolution files are in ASCII format The following example shows the content of the gauss_2 0_5x5 conv file which can be found in the config sub directory of the SEXTRACTOR distribution C
34. erally limited at the faintest flux levels by a background noise The power spectrum of the noise and that of the superimposed signal can be significantly different Some gain in the ability to detect sources may therefore be obtained simply through appropriate linear filtering of the data prior to segmentation In low density fields an optimal convolution kernel h matched filter can be found that maximizes detectability An estimator of detectability is for instance the signal to noise ratio at source position xo yo 0 0 el _ Us h zo yo N nh G where s is the signal to be detected n the noise and x the convolution operator Moving to Fourier space we get sy SH dw i JIWPIHI dw 4 TSEXTRACTOR offers the possibility of rectangular background meshes but it is advised to use square ones except in some very special cases rapidly varying background in one direction for example 16 where S and H are the Fourier transforms of s and h respectively and is the power spectrum of the noise Remarking using Schwartz inequality that f IS 21412 f sra lt yet f HP 5 we see that Sp S ep eee x PS G Equality maximum S N in 5 and 6 is achieved for eae x N H that is 7 IN S 8 H x WE 8 In the case of white noise a valid approximation for many astronomical images especially CCD ones V este the optimal convolution kernel for detecting s
35. ers which geometrically match the current detection are weighted averaged using 107047 as the weight This option is useful for weighting catalog sources with magnitudes 9 5 3 Output from ASSOC Now that we have described the cross identification process let s see how informations coming from the matching with the ASSOC list are propagated to the output SEXTRACTOR catalog The output of ASSOC data in SEXTRACTOR catalog is done through the VECTOR_ASSOC cata log parameter VECTOR_ASSOC is a vector each element of which refers to a column from the input ASSOC list VECTOR_ASSOC contains either ASSOC list member data from the best match if ASSOC_TYPE is FIRST NEAREST MIN or MAX or a combination of ASSOC list member data if ASSOC_TYPE is MEAN MAG_MEAN SUM or MAG_SUM If no match has been found it just con tains zeros The NUMBER_ASSOC contains the number of ASSOC list members that geometrically match the current SEXTRACTOR detection and obviously if different from zero indicates that VECTOR_ASSOCO has a meaningful content The ASSOC_DATA configuration parameter is used to tell SEXTRACTOR to which column refers each element of VECTOR_ASSOC The syntax of ASSOC_DATA is similar to that of ASSOC_PARAMS ASSOC_DATA c1 c2 C3 where the c are the column positions in the ASSOC list The special case ASSOC_DATA 0 tells SEXTRACTOR to propagate all columns from the ASSOC file to the output catalog There are situations
36. iance is minimized or maximized along xp 0x2 0 19 00 de 2 which leads to D 2 cos O sin Oy y2 22 2 cos bo sin 09 Ty 0 20 28 If y2 x2 this implies tan 200 2 21 Ty q y a result which can also be obtained by requiring the covariance TY to be null Over the domain 7 2 7 2 two different angles with opposite signs satisfy 21 By definition THETA is the position angle for which a is maximized THETA is therefore the solution to 21 that has the same sign as the covariance Ty A and B can now simply be expressed as A2 De bras and 22 Barge Y THETA 23 A and B can be computed directly from the 2nd order moments using the following equations derived from 18 after some tedious arithmetics a gt a q y x y _ A E 7 79 24 2 224 y ny Be e 5 Ty 25 Note that A and B are exactly halves the a and b parameters computed by the COSMOS image analyser Stobie 1980 1986 Actually a and 6 are defined by Stobie as the semi major and semi minor axes of an elliptical shape with constant surface brightness which would have the same 2nd order moments as the analysed object 9 1 6 Ellipse parameters CXX CYY CXY A B and THETA are not very convenient to use when for instance one wants to know if a particular SEXTRACTOR detection extends over some position For this kind of application three other ellipse parameter
37. ies and bad pixels 18 6 2 5 Configuration parameters 18 6 26 CPU COSTS sn ee Line a da hk a da be eS galet See ends 4 19 6 2 7 Filter file formats us da dupe BR heal s Gop ant oe hue Ges 19 6 3 Thresholding ts oes pire a A See be 8 date la Bs ee SYS 20 6 3 1 Configuration parameters 20 6 47 Deblending ssid at ese diem dns set D ste dla au Bs Lune 20 7 Weighting 7 1 7 2 7 3 7 4 7 5 Weight map form ts nea A ns Mit a Beas ho ee a a A Weight threshold sarisi i e ania Sak ee ee ee ee ae be es Effect of weighting 4 4 eaw d den a eR ve ee ee Haha Combining weight maps Interpolation 2 ino Ru cpu M ik ti a ek a ae a ee aes 8 Flags 8 1 8 2 Internal flags 2 2 24 a LE eek Ma a MR RI Re we Ae de lid ui Pxternaliflags te doce sa Fae ob Ae hoe de gates amp ME 9 Measurements 9 1 9 2 9 3 9 4 9 5 Positional parameters derived from the isophotal profile 9 1 1 Limits XMIN YMIN XMAX YMAX 9152 Barycenter Xi Yo m sonuni mr tt LS us be ee a te OS ee eS 9 1 3 Position of the peak XPEAK YPEAK 9 1 4 2nd order moments X2 Y2 XY 9 1 5 Basic shape parameters A B THETA 9 1 6 Ellipse parameters CXX CYY CXY 9 1 7 By products of shape parameters ELONGATION ELLI
38. in the command line overrides the corresponding definition in the configuration file or any default value see below Actually two image filenames can be provided separated by a comma sex imagel image2 This syntax makes SEXTRACTOR run in the so called double image mode imagel will be used for detection of sources and image2 for measurements only imagel and image2 must have the same dimensions Changing image2 for another image will not modify the number of detected sources neither affect their positional or basic shape parameters But most photometric parameters plus a few others will use image2 pixel values which allows one to easily measure pixel to pixel colours 3 2 The configuration file SEXTRACTOR needs several files for its configuration If no configuration file name is specified in the command line SEXTRACTOR tries to load a file called default sex from the local directory If default sex is not found it loads default values defined internally The default parameters can be listed with the command sex d 3 2 1 Format The format is ASCII There must be only one parameter set per line following the form Config parameter Value s Extra spaces or linefeeds are ignored Comments must begin with a and end with a linefeed Values can be of different types strings can be enclosed between double quotes floats integers keywords or boolean Y y or N n Some parameters accept zero or several v
39. ion through 3 parameters The first one is the number of deblending thresholds DEBLEND_NTHRESH A good value is 32 Higher values are generally useless except perhaps for images having an unusually high dynamic range In case of memory problems decreasing the number of thresholds to say 8 or even less may be a solution But then of course a degradation of the deblending performances may occur The second parameter is the contrast parameter DEBLEND_MINCONT As described above values from 0 001 to 0 01 give best results Putting DEBLEND_MINCONT to 0 means that even the faintest local peaks in the profile will be considered as separate objects Putting it to 1 means that no deblending will be authorized The last parameter concerns the kind of scale used for the thresholds If the image comes from photographic material then a linear scale has to be used DETECTION_TYPE PHOTO Otherwise for an image obtained with a linear device like a CCD an exponential scale is more appropriate DETECTION_TYPE CCD 22 7 Weighting The noise level in astronomical images is often fairly constant that is constant values for the gain the background noise and the detection thresholds can be used over the whole frame Unfortunately in some cases like strongly vignetted or composited images this approximation is no longer good enough This leads to detecting clusters of detected noise peaks in the noisiest parts of the image or missing obvious objects in the m
40. lter BACK FILTERSIZE A width and height of 1 means that no filtering will be applied to the background grid Usually a size of 3 x 3 is enough but it may be necessary to use larger dimensions especially to compensate in part for small background mesh sizes or in the case of large artefacts in the images Median filtering also helps reducing possible ringing effects of the bicubic spline around bright features In some specific cases it might be desirable to median filter only background meshes whose original values exceed some threshold above the filtered value This differential threshold is set by the BACK_FILTERTHRESH parameter in ADUs It is important to note that all BACK_ configuration parameters also affect the background RMS map By default the computed background map is automatically subtracted from the input image But there are some situations where it is more appropriate to subtract a constant from the image e g images where the background noise distribution is strongly skewed The BACK_TYPE configuration parameter set by default to AUTO can be switched to MANUAL to allow for the value specified by the BACK_DEFAULT parameter to be subtracted from the input image The default value is 0 6 1 2 CPU cost The background estimation operation can take a considerable time on the largest images e g a few minutes minutes for a 32000 x 32000 frame on a 2GHz processor 6 2 Filtering 6 2 1 Convolution Detectability is gen
41. ly Pixel value above which it is consid ered saturated FWHM of stellar images in arcsec only for star galaxy separation Name of the file containing the neural network weights for star galaxy sepa ration Meaning of the DETECT_THRESH and ANALYSIS_THRESH parameters scaling factor to the background RMS absolute level in ADUs or in surface brightness How much SEXTRACTOR comments its operations run silently display warnings and limited info concerning the work in progress like NORMAL plus a few more warn ings if necessary display a more complete information and the principal parameters of all the objects extracted If true weight maps are considered as gain maps File name of the detection and measurement weight image respec tively Weighting scheme for single image or detection and measurement images no weighting variance map derived from the im age itself variance map derived from an exter nal RMS map external variance map variance map derived from an exter nal weight map WRITE_XML N boolean If true meta data will be written in XML VOTable format XMLNAME sex xml string File name for the XML output of SEXTRACTOR 3 3 The catalog parameter file In addition to the configuration file detailed above SEXTRACTOR needs a file containing the list of parameters that will be listed in the output catalog for every detection This allo
42. n supposed that the changes in noise intensities seen over the images are due to gain changes This is the most common case correction for vignetting or coverage depth When this is not the case for instance when changes are purely dominated by those of the read out noise WEIGHT_GAIN shall be set to N 5 Finally pixels with weights beyond WEIGHT_THRESH are treated just like pixels discarded by the MASKing process 7 24 7 4 Combining weight maps All the weighting options listed in 7 1 can be applied separately to detection and measurement images 3 even if some combinations may not always make sense For instance the following set of configuration lines WEIGHT_IMAGE rms fits weight fits WEIGHT_TYPE MAP_RMS MAP_WEIGHT will load the FITS file rms fits and use it as an RMS map for adjusting the detection threshold and CLEANing while the weight fits weight map will only be used for scaling the error estimates on measurements This can be done in single as well as in dual image mode 3 WEIGHT_IMAGEs can be ignored for BACKGROUND WEIGHT_TYPEs It is of course possible to use weight maps for detection or for measurement only The following configuration WEIGHT_IMAGE weight fits WEIGHT_TYPE NONE MAP_WEIGHT will apply weighting only for measurements detection and CLEANing operations will remain unaffected 7 5 Interpolation TBW 8 Flags A set of both internal and external flags is accessible for each obj
43. nates in the native system without any precession correction conversion etc 2 _J2000 coordinates precession corrections are applied in the FK5 system to convert to J2000 coordinates if necessary 3 _B1950 coordinates precession corrections are computed in the FK5 system and transfor mation to B1950 is applied Transformation to J2000 or B1950 is done without taking into account proper motions which are obviously unknown for the detected objects In both cases epoch 2000 0 is assumed 33 Here is a list of catalog parameters currently supporting angular coordinates Image parameters World parameters Angular parameters X_IMAGE Y_IMAGE X_WORLD Y_WORLD ALPHA_SKY DELTA_SKY ALPHA_J2000 DELTA_J2000 ALPHA_B1950 DELTA_B1950 XWIN_IMAGE YWIN_IMAGE XWIN_WORLD YWIN_WORLD ALPHAWIN_SKY DELTAWIN_SKY ALPHAWIN_J2000 DELTAWIN_J2000 ALPHAWIN_B1950 DELTAWIN_B1950 XPEAK_IMAGE YPEAK_IMAGE XPEAK_WORLD YPEAK_WORLD ALPHAPEAK_SKY DELTAPEAK_SKY ALPHAPEAK_J2000 DELTAPEAK_J2000 ALPHAPEAK_B1950 DELTAPEAK_B1950 X2_IMAGE Y2_IMAGE XY_IMAGE X2 WORLD Y2_WORLD XY_WORLD X2WIN_IMAGE Y2WIN_IMAGE XYWIN_IMAGE X2WIN_WORLD Y2WIN_WORLD XYWIN_WORLD CXX_IMAGE CYY_IMAGE CXY_IMAGE CXX WORLD CYY_WORLD CXY_WORLD CXXWIN_IMAGE CYYWIN_IMAGE CXYWIN_IMAGE CXXWIN_WORLD CYYWIN_WORLD CXYWIN_WORLD TBW 9 3 2 Use of the FITS keywords for astrometry TBW 9 4 Photometry SEXTRACTOR has currently the possibility to compute four types of mag
44. nitude isophotal corrected isophotal fixed aperture and adaptive aperture For all magnitudes an additive zero point correction can be applied with the MAG_ZEROPOINT keyword Note that for each MAG_XXXX a magnitude error estimate MAGERR_XXXX a linear FLUX_XXXX measurement and its error estimate FLUXERR_XXXX are also available Isophotal magnitudes MAG_ISO are computed simply using the detection threshold as the lowest isophote Corrected isophotal magnitudes MAG_ISOCOR can be considered as a quick and dirty way for retrieving the fraction of flux lost by isophotal magnitudes Although their use is now depre cated they have been kept in SEXTRACTOR 2 x and above for compatibility with SEXTRACTOR 1 If we make the assumption that the intensity profiles of the faint objects recorded on the plate are roughly Gaussian because of atmospheric blurring then the fraction 7 di of the total flux enclosed within a particular isophote reads see Maddox et al 1990 E 45 n Liso where A is the area and t the threshold related to this isophote Eq 45 is not analytically invertible but a good approximation to 7 error lt 107 for y gt 0 4 can be done with the second order polynomial fit A AN n 1019612 0 7512 46 iso iso A total magnitude Miot estimate is then Metot Miso 2 5 log n 47 Clearly this cheap correction works best with stars and although it is shown to give tolerably accura
45. of detection biases or the contamination by neighbours As SEXTRACTOR does not currently take into account possible correlations between pixels the variances simply write 5 o xi T ERRX2 var z E 32 2 21 eS 5 o yi 7 ERRY2 var y gt 33 4 15Such parameters are dimensionless and therefore do not accept any IMAGE or WORLD suffix 30 Y o 2i T yi Y ERRXY com g gt 34 E L of og 35 1 g is the flux uncertainty estimated for pixel i where op is the local background noise and g the local gain conversion factor for pixel i see 87 for more details Major axis ERRA minor axis ERRB and position angle ERRTHETA of the lo position error ellipse are computed from the covariance matrix exactly like in 9 1 5 for shape parameters var T var y ERRA 36 ae Panne zz var Z var y _ var T var y 7 37 2 2 tan 2 x ERRTHETA 2 00 38 var z var y And the ellipse parameters are 2 2 ERRTHETA ERRTHETA o SS FR 39 ERRA ERRB E oa sin ERRTHETA cos ERRTHETA var Z ERRCYY ERR T ERB a gt 40 ED Ed z y 1 1 ERRCXY 2cosERRTHETA sin ERRTHETA e a m 41 ERRA ERRB 42 9 1 9 Handling of infinitely thin detections Apart from the mathematical singularities that can be found in some of the above equations describing shape parameters and which SEXTRACTOR handle
46. olate connected groups of pixels Each group defines the approximate position and shape of a basic SEXTRACTOR detection that will be processed further in the pipeline Groups are made of pixels whose values exceed the local threshold and which touch each other at their sides or angles 8 connectivity 6 3 1 Configuration parameters Thresholding is mostly controlled through the DETECT_THRESH and DETECT_MINAREA keywords DETECT_THRESH sets the threshold value If one single value is given it is interpreted as a threshold in units of the background s standard deviation For example DETECT_THRESH 1 5 will set the detection threshold at 1 50 above the local background It is important to note that em the standard deviation quoted here is that of the unFILTERed image at the pixel scale Hence on images with white Gaussian background noise for instance a DETECT_THRESH of 3 0 will be close to optimum if low pass FILTERing is turned off but sub optimum too high if it is on On the contrary if the background noise of the image is intrinsically correlated from pixel to pixel a DETECT_THRESH of 3 0 with no FILTERing wil be too low and will result in a poor reliability of the extracted catalog Two numbers can be given as arguments to DETECT_THRESH in which case the first one is interpreted as an absolute threshold in units of magnitudes per square arcsecond and the second as a zero point in the same units DETECT_THRESH 27 2
47. ost sensitive ones SEXTRACTOR is able to handle images with variable noise It does it through weight maps which are frames having the same size as the images where objects are detected or measured and which describe the noise intensity at each pixel These maps are internally stored in units of absolute variance in ADU We employ the generic term weight map because these maps can also be interpreted as quality index maps infinite variance gt 10 by definition in SEXTRACTOR means that the related pixel in the science frame is totally unreliable and should be ignored The variance format was adopted as it linearizes most of the operations done over weight maps see below This means that the noise covariances between pixels are ignored Although raw CCD images have essentially white noise this is not the case for warped images for which resampling may induce a strong correlation between neighbouring pixels In theory all non zero covariances within the geometrical limits of the analysed patterns should be taken into account to derive thresholds or error estimates Fortunately the correlation length of the noise is often smaller than the patterns to be detected or measured and constant over the image In that case one can apply a simple fudge factor to the estimated variance to account for correlations on small scales This proves to be a good approximation in general although it certainly leads to underestimations for the smalles
48. patterns In those cases one would like to extend the concept of a convolution kernel to that of a more general stationnary filter able for instance to mimick boolean like operations on pixels What one wants like is thus a mapping from R to R around each pixel But the more general the filter the more difficult it is to design by hand for each case specifying how input pixel i should be taken into account with respect to input pixel j to form the output etc The solution to this is machine learning Given a training set containing input and output pixels a machine learning software will adapt its internal parameters in order to minimize a cost function generally a y error and converge toward the desired mapping function These parameters can then for example be reloaded by a read only routine to provide the actual filtering SEXTRACTOR implements this kind of read only functionnality in the form of the so called retina filtering The EYE software Bertin 1997 performs neural network learning on input and output images to produce retina files These files contain weights that describe the behaviour of the neural network The neural network can thus be seen as an artificial retina that takes its stimuli from a small rectangular array of pixels and produces a response according to prior learning for more details see the EYE documentation Typical applications of the retina are the identification
49. process Lines with zero characters or beginning with for comments are ignored This means you may use any ASCII catalog generated by a previous SEXTRACTOR run as an ASSOC list To perform the cross identification SEXTRACTOR needs to know what are the columns that con tain the x and y coordinates in the ASSOC list These shall be specified using the ASSOC_PARAMS configuration parameter The syntax is ASSOC_PARAMS c z cy cz where cy and cy are the positions of the columns containing the x and y coordinates the first column has position 1 cz optional specifies an extra column containing some Z parameter that may be used for controlling or weighting the ASSOC process Z will typically be a flux estimate cz is required if ASSOC_TYPE is MIN MAX MEAN or MAG_MEAN see below 9 5 2 Controlling the ASSOC process Two configuration parameters control the ASSOC process The first one ASSOC_RADIUS accepts a decimal number which represents the maximum distance in pixels one should have between the barycenter of the current SEXTRACTOR detection and an ASSOC list member to consider a match This number must of course account for positional uncertainties in both catalogs In most cases a value of a few pixels will do just fine The second configuration parameter ASSOC_TYPE accepts a keyword as argument and selects the kind of identification procedure one wants to operate e FIRST this is the simplest way of performing
50. rement phase There are in SEXTRACTOR two categories of measurements Measurements from the first category are made on the isophotal object profiles Only pixels above the detection threshold are considered Many of these isophotal measurements like X_IMAGE Y_IMAGE etc are necessary for the in ternal operations of SEXTRACTOR and are therefore executed even if they are not requested This flag can be activated only when MAG_AUTO magnitudes are requested This flag is inherited from SEXTRACTOR V1 0 and has been kept for compatibility reasons With SEXTRAC TOR V2 0 having this flag activated doesn t have any consequence for the extracted parameters 26 Measurements from the second category have access to all pixels of the image These measure ments are generally more sophisticated and are done at a later stage of the processing after CLEANing and MASKing 9 1 Positional parameters derived from the isophotal profile The following parameters are derived from the spatial distribution S of pixels detected above the extraction threshold The pixel values I are taken from the filtered detection image Note that unless otherwise noted all parameter names given below are only pre fixes They must be followed by _IMAGE if the results shall be expressed in pixel units see or _WORLD for World Coordinate System WCS units see 9 3 Example THETA THETA_IMAGE In all cases parameters are first computed in the imag
51. rocedures act on the variance map too 23 e MAP_WEIGHT the FITS image specified by the WEIGHT_IMAGE file name must contain a weight map in units of relative weights The data are converted to variance units by defi nition variance x 1 weight and scaled as for MAP_VAR MAP_WEIGHT is the most commonly used type of weight map a flat field for example is generally a good approximation to a perfect weight map 7 2 Weight threshold It may happen that some weights are too low or variances too high to be of any interest it is then more appropriate to discard such pixels than to include them in unweighted measurements such as FLUX_APER To allow discarding these very bad pixels a threshold can be set with the WEIGHT_THRESH parameter The unit in which this threshold should be expressed is that of input data ADUs for BACKGROUND and MAP_RMS maps uncalibrated ADUs for MAP_VAR and uncalibrated weight values for MAP_WEIGHT maps Depending on the weight map type the threshold will set a lower or a higher limit for bad pixel values higher for weights and lower for variances and standard deviations The default value is 0 for weights and 10 for variance and standard deviation maps 7 3 Effect of weighting Weight maps modify the working of SEXTRACTOR in the following respects 1 Bad pixels are discarded from the background statistics If more than 50 of the pixels in a background mesh are bad the local background value and its
52. s of course some detections with very specific shapes may yield quite unphysical parameters namely null values for B ERRB or even A and ERRA Such detections include single pixel objects and horizontal vertical or diagonal lines which are 1 pixel wide They will generally originate from glitches but very undersampled and or low S N genuine sources may also produce such shapes How to handle them For basic shape parameters the following convention was adopted if the light distribution of the object falls on one single pixel or lies on a sufficiently thin line of pixels which we translate mathematically by PPE APS 43 then x and y are incremented by p p is arbitrarily set to 1 12 this is the variance of a 1 dimensional top hat distribution with unit width Therefore 1 V12 represents the typical minor axis values assigned in pixels units to undersampled sources in SEXTRACTOR 31 Positional errors are more difficult to handle as objects with very high signal to noise can yield extremely small position uncertainties just like singular profiles do Therefore SEXTRACTOR first checks that 43 is true If this is the case a new test is conducted var Z var y covar T Y lt p2 44 where pe is arbitrarily set to Dijes 0 Dies Ii If 44 is true then 1 and y are incre mented by pe 9 2 Windowed positional parameters Parameters measured within an object s isophotal limit can be altered in two principal ways
53. s are provided CXX CYY and CXY They do nothing more than describing the same ellipse but in a different way the elliptical shape associated to a detection is now parameterized as CXX x T CYY y y CXY x T y y R 26 where R is a parameter which scales the ellipse in units of A or B Generally the isophotal limit of a detected object is well represented by R 3 Fig 5 Ellipse parameters can be derived from the 2nd order moments 2 2 cos THETA sin THETA y XX c A2 Es B2 es 27 7 ZY 2 2 72 sin THETA cos THETA x OY e a el 28 A B2 mE 352 T2 2 y 1 1 CXY 2cosTHETAsin THETA 2 4 29 A2 RB TY 27 ore 3 Ty 29 THETA_IMAGE CXX_IMAGE x 1 7 CYY_IMAGE x y y CXY_IMAGEx a Z y Y 3 Figure 5 The meaning of basic shape parameters 9 1 7 By products of shape parameters ELONGATION ELLIPTICITY 15 These parameters are directly derived from A and B wl LS ELONGATION and 30 ELLIPTICITY gt w Co E 9 1 8 Position errors ERRX2 ERRY2 ERRXY ERRA ERRB ERRTHETA ERRCXX ERRCYY ERRCXY Uncertainties on the position of the barycenter can be estimated using photon statistics Of course this kind of estimate has to be considered as a lower value of the real error since it does not include for instance the contribution
54. standard deviation are replaced by interpolation of the nearest valid meshes 2 The detection threshold t above the local sky background is adjusted for each pixel i with variance o t DETECT_THRESH x ya where DETECT_THRESH is expressed in units of standard deviations of the background noise Pixels with variance above the threshold set with the WEIGHT_THRESH parameter are therefore simply not detected This may result in splitting objects crossed by a group of bad pixels Interpolation see 7 5 should be used to avoid this problem If convolution filtering is applied for detection the variance map is convolved too This yields optimum scaling of the detection threshold in the case where noise is uncorrelated from pixel to pixel Non linear filtering operations like those offered by artificial retinae are not affected 3 The CLEANing process takes into account the exact individual thresholds assigned to each pixel for deciding about the fate of faint detections 4 Error estimates like FLUXISO_ERR ERRA_IMAGE make use of individual variances too Local background noise standard deviation is simply set to o In addition if the WEIGHT_GAIN parameter is set to Y which is the default it is assumed that the local pixel gain i e the conversion factor from photo electrons to ADUs is inversely proportional to g its median value over the image being set by the GAIN configuration parameter In other words it is the
55. t patterns 7 1 Weight map formats SEXTRACTOR accepts in input and converts to its internal variance format several types of weight maps This is controlled through the WEIGHT_TYPE configuration keyword These weight maps can either be read from a FITS file whose name is specified by the WEIGHT_IMAGE keyword or computed internally Valid WEIGHT_TYPEs are e NONE No weighting is applied The related WEIGHT_IMAGE and WEIGHT_THRESH see below parameters are ignored e BACKGROUND the science image itself is used to compute internally a variance map the related WEIGHT_IMAGE parameter is ignored Robust 30 clipped variance estimates are first computed within the same background meshes as those described in The result ing low resolution variance map is then bicubic spline interpolated on the fly to produce the actual full size variance map A check image with CHECKIMAGE_TYPE MINIBACK_RMS can be requested to examine the low resolution variance map e MAP_RMS the FITS image specified by the WEIGHT_IMAGE file name must contain a weight map in units of absolute standard deviations in ADUs per pixel e MAP_VAR the FITS image specified by the WEIGHT_IMAGE file name must contain a weight map in units of relative variance A robust scaling to the appropriate absolute level is then performed by comparing this variance map to an internal low resolution absolute variance map built from the science image itself The mesh filtering p
56. tars is then the PSF flipped over the x and y directions It may also be described as the cross correlation with the template of the sources to be detected for more details see e g Bijaoui amp Dantel 1970 or Das 1991 There are of course a few problems with this method First of all many sources of unquestionable interest like galaxies appear in a variety of shapes and scales on astronomical images A perfectly optimized detection routine should ultimately apply all relevant convolution kernels one after the other in order to make a complete catalog Approximations to this approach are the isotropic wavelet analysis mentioned earlier or the more empirical ImCat algorithm Kaiser et al 1995 for both of which sources to detect are assumed to be reasonably round The impact on memory usage and processing speed of such refinements is currently judged too severe to be applied in SEXTRACTOR Simple filtering does a good job in general the topological constraints added by the segmentation process make the detection somewhat tolerant towards larger objects Extended very Low Surface Brightness LSB features found in astronomical images are often artifacts flat fielding errors optical ghosts or halos However it is true that some of them can be genuine objects like LSB galaxies or distant galaxy clusters burried in the background noise For detecting those with software like SEXTRACTOR a specific processing is needed see for instance
57. te results with most disk galaxies it fails with ellipticals because of the broader wings of their profiles 34 Fixed aperture magnitudes MAG_APER estimate the flux above the background within a circular aperture The diameter of the aperture in pixels PHOTOM_APERTURES is supplied by the user in fact it does not need to be an integer since each normal pixel is subdivided in 5 x 5 sub pixels before measuring the flux within the aperture If MAG_APER is provided as a vector MAG_APER n at least n apertures must be specified with PHOTOM_APERTURES Automatic aperture magnitudes MAG_AUTO are intended to give the most precise estimate of total magnitudes at least for galaxies SEXTRACTOR s automatic aperture photometry routine is inspired by Kron s first moment algorithm 1980 1 We define an elliptical aperture whose elongation e and position angle 0 are defined by second order moments of the object s light distribution The ellipse is scaled to Rimax Oiso 60iso Which corresponds roughly to 2 isophotal radii 2 Within this aperture we compute the first moment EE 48 LAr Kron 1980 and Infante 1987 have shown that for stars and galaxy profiles convolved with Gaussian seeing gt 90 of the flux is expected to lie within a circular aperture of radius kr if k 2 almost independently of their magnitude This picture remains unchanged if we consider an ellipse with ekr and kr e as principal a
58. the check images no check image identical to input image useful for converting formats full resolution interpolated back ground map full resolution interpolated back ground noise map low resolution background map low resolution background noise map background subtracted image background subtracted filtered im age requires FILTER Y detected objects background subtracted image with detected objects blanked MAG_APER and MAG_AUTO integration limits display patches corresponding to pixels attributed to each object If true a cleaning of the catalogue is done before being written to disk Efficiency of cleaning Minimum contrast parameter for de blending Number of deblending sub thresholds Minimum number of pixels above threshold triggering detection Detection threshold 1 argument ADUs or relative to Background RMS see THRESH_TYPE 2 arguments u mag arcsec Zero point mag Type of device that produced the im age linear detector like CCDs or NIC MOS photographic scan If true filtering is applied to the data before extraction Name of the file containing the filter definition Lower and higher thresholds in back ground standard deviations for a pixel to be considered in filtering used for retina filtering only Force 16 bit FITS input data to be in terpreted as unsigned integers File name
59. ty of any source whereas it depends on scale 40
60. ween isophotal and windowed centroid measurement accuracies on simulated background noise limited images Left histogram of the difference between X_IMAGE and the simulation centroid in x Right histogram of the difference between XWIN_IMAGE and the simulation centroid in x back to local spherical celestial coordinates Many types of projections are allowed by the WCS convention but the traditional tangential gnomonic projection is the most commonly used The last step of the transformation is to convert these local coordinates still relative to a projection reference point to an absolute position in celestial longitude and latitude for instance right ascension and declination For this one needs to know the reference frame of the coordinate system which often requires some information about the equinox or the observation date At this level all transformations are matters of spherical trigonometry 9 3 1 Celestial coordinates We will not describe here the transformations a 6 f x y themselves SEXTRACTOR de projections rely on the WCSlib 2 4 written by Mark Calabretta and all the details concerning those can be found in Greisen amp Calabretta 1995 In addition to the WORLD parameters 3 purely angular world coordinates are available in SEXTRACTOR expressed in decimal degrees 1 _SKY coordinates strictly identical to WORLD coordinates except that the units are ex plicitely degrees They correspond to sky coordi
61. where it might be desirable to keep in the output SEXTRACTOR catalog only those detections that were matched with some ASSOC list member Such a feature is controlled by the ASSOCSELEC_TYPE configuration parameter which accepts one of the three following keywords e ALL keep all SEXTRACTOR detections regardless of matching This is the default 38 e MATCHED keep only SEXTRACTOR detections that were matched with at least one ASSOC list member e MATCHED keep only SEXTRACTOR detections that were not matched with any ASSOC list member Acknowledgements References 1 Beard S M McGillivray H T Thanisch P F 1990 MNRAS 247 311 2 Bertin E E y E 1 1 User s manual 1997 Leiden 3 Bertin E WeightWatcher 1 2 User s manual 1997 ESO 4 Bijaoui A Dantel M 1991 A amp A 6 51 5 Bijaoui A Slezak E Vandame B 1998 in Astrophysics and Algorithms a DIMACS Workshop on Massive Astronomical Data Sets 6 Dalcanton J J Spergel D N Gunn J E Schmidt M Schneider D P 1997 AJ 114 635 7 Das P K 1991 Optical Signal Processing Springer Verlag 8 Greisen E W Calabretta M 1995 ADASS 4 233 9 Infante L 1987 A amp A 183 177 10 Irwin M J 1985 MNRAS 214 575 11 Jarvis J J Tyson J A 1981 AJ 86 476 12 Kaiser N Squires G Broadhurst T 1995 ApJ 449 460 13 Kendall M Stuart K 1977 The Advanced Theory of Statistics Vol 1 Charles Griffin amp Co London 14 Kron
62. ws the soft ware to compute only catalog parameters that are needed The name of this catalog parameter file is traditionally suffixed with param and must be specified using the PARAMETERS NAME config parameter 3 3 1 Format The format of the catalog parameter list is ASCII and there must be only one keyword per line Presently two kinds of keywords are recognized by SEXTRACTOR scalars and vectors Scalars like X_IMAGE yield single numbers in the output catalog Vectors like MAG_APER 4 or VIGNET 15 15 yield arrays of numbers The order in which the parameters will be listed in the catalogue are the same as that of the keywords in the parameter list Comments are allowed they must begin with a Here is a descriptive list of available parameter keywords 3 4 Example of configuration 4 Overview of the software The complete analysis of an image is done in two passes through the data During the first pass a model of the sky background is built and a couple of global statistics are estimated During the second pass the image is background subtracted filtered and thresholded on the fly Detections are then deblended pruned CLEANed photometered classified and finally written to the output catalog The following sections enter a little more into the details of each of these operations 5 Handling of image data SEXTRACTOR accepts images stored in FITS format Wells et al 1981 see also http fits gsfc nas
63. xes k 2 defines a sort of balance between systematic and random errors By choosing a larger k 2 5 the mean fraction of flux lost drops from about 10 to 6 When Signal to Noise is low it may appear that an erroneously small aperture is taken by the algorithm That s why we have to bound the smallest accessible aperture to Rmin typically Rmin 3 4050 The user has full control over the parameters k and Rmin through the configuration parameters PHOT_AUTOPARAMS by defaut PHOT_AUTOPARAMS is set to 2 5 3 5 Isophotal e Automatic Aperture Corrected Isophotal E Measured mag True mag True total magnitude Figure 7 Flux lost expressed as a mean magnitude difference with different faint object pho tometry techniques as a function of total magnitude see text Only isolated galaxies no blends of the simulations have been considered Aperture magnitudes are sensitive to crowding In SEXTRACTOR 1 MAG_AUTO measurements were not very robust in that respect It was therefore suggested to replace the aperture magni tude by the corrected isophotal one when an object is too close to its neighbours 2 isopho tal radii for instance This was done automatically when using the MAG_BEST magnitude MAG_BEST MAG_AUTO when it is sure that no neighbour can bias MAG_AUTO by more than 10 or MAG_BEST MAG_ISOCOR otherwise Experience showed that the MAG_ISOCOR and MAG_AUTO mag nitude would loose about the same fraction of

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