\n",
"
Note
\n",
"\n",
"As you can notice, the aperture photometry is performed on the image values multiplied by _img_F560W.area_.\n",
"\n",
"The area subtended by each pixel on the sky varies as a result of geometric distortion and hence, they have different collecting power. Flat-fielding is designed to produce images with a flat background given a flat stimulus. When the flat-field correction is applied to a science image, the resulting image is characterized by constant surface brightness. However, flat-fielding does not take into account for the different collecting power of pixels due to geometric distortion. For more details, see the discussion
here.\n",
" \n",
"Photometry measured on distorted images as the stage-2 _cal.fits_ files requires a field-dependent correction called the Pixel Area Map (PAM), to ensure that the same sources have the same magnitude regardless of their position within the images. The PAM is obtained from the geometric-distortion correction and is included in the _area_ extention of the JWST data model.\n",
"\n",
"\n",
"
\n",
"
Nota bene
\n",
" \n",
"For stage-2 images (_cal.fits_ files), the WCS information is assigned by the _assign_wcs_ step. This information is saved in an ASDF extension of the FITS file. However, image-display tools such as ds9 do not understand the ASDF encoding. For this reason, an approximation to the WCS is stored in the image header using the SIP (Simple Imaging Polynomial) convention. The SIP-based header does not provide an exact fit: it is accurate to a $\\sim$0.25-pixel level and it is meant for general display purposes (see
here for more information).\n",
"\n",
"
\n",
"
Aperture photometry on stage-3 images
\n",
" \n",
"This notebook can be adapted to perform aperture photometry on stage-3 (_i2d.fits_) images. In this case, with a few expedients the photometric calibration does not need additional files.\n",
" \n",
"First, we choose an aperture radius from the aperture-correction reference file available in the
JWST Calibration Reference Data System (CRDS). For each filter (FILTER), array/subarray (PUPIL) and encircled-energy values (EEFRACTION), this file lists the aperture-correction values needed for correcting observed signals within a finite aperture to the estimated total signal for a source (APCORR), the aperture radius containing the EEFRACTION fraction of the total flux (RADIUS), the inner (SKYIN) and outer (SKYOUT) radii for the sky estimation. The APCORR value is a multiplicative correction that scales the measured flux to infinite aperture.\n",
"\n",
"If we perform aperture photometry using these values of RADIUS, SKYIN and SKYOUT, then, once corrected the flux for the finite aperture, the photometric calibration is straighforward. Indeed, as for stage-2 images, the pixel unit in the stage-3 images is MJy sr$^{-1}$. This is an advantage for the photometric calibration because we can directly obtain magnitudes in the AB system (
Oke 1964; see also Sect. 7 of
Sirianni et al. 2005). The AB magnitude is defined as:\n",
"\n",
"\\begin{equation*}\n",
" m_{\\rm AB} = -2.5 \\log_{10} f_\\nu - 48.60\n",
"\\end{equation*}\n",
"\n",
"with $f_\\nu$ in erg s$^{-1}$ cm$^{-2}$ Hz$^{-1}$, or as:\n",
"\n",
"\\begin{equation*}\n",
" m_{\\rm AB} = -2.5 \\log_{10} f_\\nu + 8.90\n",
"\\end{equation*}\n",
"\n",
"with $f_\\nu$ in Jansky. Therefore, we can simply transform our total flux in MJy sr$^{-1}$ by multiplying it by $10^6$ and by the average pixel area in steradian. The header keyword _PIXAR_SR_ contains the average pixel area in steradian; the corresponding value in the JWST data-model scheme is included in _meta.photometry.pixelarea_steradians_. This value is added in the flux (photometric) calibrations performed by the _Photom_ step of the _calwebb_image2_ pipeline.\n",
"\n",
"AB magnitudes can be converted to VEGA magnitudes by adding the AB-to-Vega magnitude offset available in the corresponding reference file in the CRDS.\n",
" \n",
"
\n",
"
Warning 1
\n",
"\n",
"The APCORR values include a correction for the sky-background subtraction obtained with the specific SKYIN and SKYOUT radii provided in the CRDS reference file. This correction takes into account the contribution of the PSF wings of the star to the local background. If different sky-background radii are used, the APCORR values cannot be used anymore. The best alternative option is to evaluate the sky background in an annulus far enough from the center of each star that the contribution of the PSF wings of the star to the local background is negligible, for example between 25 and 35 pixels as shown in this notebook. In this case, the total flux of a star can be obtained from the flux containging EEFRACTION of the total flux by multiplying it by EEFRACTION$^{-1}$.\n",
"\n",
"\n",
" \n",
"
\n",
"
Warning 2
\n",
"\n",
"No pixel-area map correction is needed with stage-3 images.\n",
"\n",
"\n",
"\n",
"\n",
"
![\"Space](\"https://raw.githubusercontent.com/spacetelescope/notebooks/master/assets/stsci_pri_combo_mark_horizonal_white_bkgd.png\")
"
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