IRAC: Bright Star Rectification

Stars that saturate the IRAC arrays form inverted "crater" peak profiles, losing a significant fraction of their light in the process. Recovery or flux rectification is possible through PSF-fitting of the non-saturated "wings" of the stellar profile, and is the subject of this web page. The iraf tasks and fortran code that is used to fit and recover saturated pixels is described here.

IRAC, Band-1

Star located at (197, 51) in the lower right side of image (see left panel). Note the inverted "crater" peak feature, indicative of saturation.

Star located at (40, 14) in the lower left of image (see left panel). Note the inverted "crater" peak feature, indicative of saturation.

The basic technique is to "fit' the expected PSF to the wings of the target source. The inner region of the star that is saturated is rectified using the PSF, scaled to the fit the wings of the star.

Steps:

1. Identify X-Y center of saturated star
2. Extract sub-image
3. Resample subimage on finer grid, matching the PSF; for IRAC band-1, the expanded sampling is 4x4.
For channels 3/4, mask the "band effect" ghosts that reside to the right of the star center. There are three such artifacts, located 4, 8 and 16 camber pixels respectively from the star center.
4. Match pixel-by-pixel the resampled target and the PSF; this is a scaling between the target and PSF flux (flux ratio)
5. Eliminate flux ratio measurements with S/N < LIMIT
5. Compute statistics for radially-symmetric annuli (mean, RMS and median of flux ratio per annulus)
6. Starting from the outer radius and working inward, compute the mean flux ratio (avoid inner saturated region); compute preliminary median flux ratio and RMS.
7. Recompute flux ratio using entire radial annuli sequence but with n-sigma rejection; iterate until convergence
8. Determine the range in radius in which the fit is applied (this localizes the non-saturated wings)
9. Derive median flux ratio and RMS
10. Now vary the X-Y position by sampling a region that captures the true center position; for each X-Y position, repeat steps 4 to 9.
11. Determine best fit (minimize the RMS dispersion) and derive the final median flux ratio and RMS, and the radii that are fit.
12. Compute the ratio between the target peak flux and the scaled PSF peak flux. Ratios that fall below 50% are almost certainly due to saturation.
13. Rectify the "lost" flux by replacing the inner, saturated pixels (see radial range of wings, above) with the scaled PSF.
14. Recompute flux of rectified source using aperture photometry.
15. Log photometry.

Results

Example 1

Upper Left Panel: Saturated star (IRAC-1) resampled with 4x4 finer gridding to match PSF. Upper Right Panel: PSF scaled to fit "wings" of saturated star Lower Left Panel: Pixel-to-pixel scale fit of PSF to saturated star; outer boundary limited by condition S/N > 10. Lower Right Panel: Rectified star

Ratio of star to PSF flux, normalized to the median value. Each point represents the median of the scaling value per radial annulus (1 pixel wide). The errorbars represent the RMS scatter in the scaling value per annulus. The blue dashed line marks the scaling normalization (unity), while the red dashed lines mark the RMS scatter in the median scaling value determined for the ensemble of median annulus values between the marked radial boundary (9 < Radius < 40). Outer boundary limited by S/N > 10 threshold.

Photometry

The saturated star's integrated flux is measured using a large cicular aperture, radius = 25 PSF units (6.25 BCD units). The flux is converted to a flux density in mJy. Both the before correction ("raw") and after correction ("rectify") are calculated. For comparison, the same star is measured but using the shorter exposure image (and hence, probably not saturated). The results are tabulated below.

radius	npix	Pratio	raw	model	rectify	notes
pix	-	-	mJy	mJy	mJy	-
25.0	1963	0.06	307.5	1037.9	1046.6	IRAC.1.0006581504.0003.0000.2.bcd_fp
-	-	-	-	-	-
radius	npix	Pratio	raw	model	rectify	notes
pix	-	-	mJy	mJy	mJy	-
25.0	1964	0.82	1150.1	1111.6	1190.	IRAC.1.0006581504.0002.0000.2.bcd_fp

Note: the integrated flux using "iracexam" is 1146.5 mJy

Key:

radius = aperture radius in PSF pixel units
npix = total number of pixels within aperture
Pratio = star to PSF ratio of the "peak" pixel
raw = before saturation correction, integrated flux
model = integrated flux of the model PSF scaled to match star wings
rectify = integrated flux of corrected star

Example 2

Upper Left Panel: Saturated star (IRAC-1) resampled with 4x4 finer gridding to match PSF. Upper Right Panel: PSF scaled to fit "wings" of saturated star Lower Left Panel: Pixel-to-pixel scale fit of PSF to saturated star; outer boundary limited by condition S/N > 10. Lower Right Panel: Rectified star

Ratio of star to PSF flux, normalized to the median value. Each point represents the median of the scaling value per radial annulus (1 pixel wide). The errorbars represent the RMS scatter in the scaling value per annulus. The blue dashed line marks the scaling normalization (unity), while the red dashed lines mark the RMS scatter in the median scaling value determined for the ensemble of median annulus values between the marked radial boundary (9 < Radius < 40). Outer boundary limited by S/N > 10 threshold.

Photometry

image	radius	npix	Pratio	raw	model	rectify
-	pix	-	-	mJy	mJy	mJy
IRAC.1.0006581248.0013.0000.2.bcd_fp	25.0	1963	0.02	575.8	3755.7	3768.4
image	radius	npix	Pratio	raw	model	rectify
-	pix	-	-	mJy	mJy	mJy
IRAC.1.0006581248.0012.0000.2.bcd_fp	25.0	1964	0.31	2467.3	3943.9	4032.3

Most of the testing has been with IRAC-1. But the other channels appear to work in a similar fashion, although IRAC-3/4 have interesting quirks that offer a challenge to overcome. See star test.

The cpu cycles needed to run the saturation processor is non-negligible. Consequently, in the pipeline (future implementation) it should *only* be run on saturated stars. (see note below)

The signature of saturation, inverted peak with crater, is relatively easy to identify (see Pratio in table above). But this requires that we go to the trouble of fitting the PSF to the stellar wings. If the star is not saturated, this is wasteful of cpu cycles. Moreover, if the star is not saturated, the method of fitting the PSF to the wings of the star will not be reliable since high S/N is required to firmly match the PSF to the star.

To save cpu cycles, a method that can quickly estimate the saturation level for every source is needed to pre-condition the seedlist used to process saturated stars. See the crater_finder task for a quick way to identify saturated stars.

The original IRAC-1 PSF created by T. Megeath is too narrow compared to IRAC-1 stars by about 10%. The PSF used to correct saturated stars has been adjusted accordingly. The other IRAC band PSFs also seem to be too narrow.

More on the other IRAC channels is given