Point source fitting of IRAC images using a PRF

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Results of tests of PRF fitting

Tests on calibration stars
Sub-pixel response in channels 1 and 2
The Serpens test field
The GLIMPSE test field

One sample AOR was selected for each of the nine brightest IRAC calibration stars (Reach et al. 2005). The selected AORs were from 2005 June 05 to 2006 September. Photometry was performed on the five BCD's in each AOR and the results averaged. BCD uncertainties and imasks were used. The pipeline versions were S14.0-S14.4. The central PRF, modified for APEX use as described above, was used as the stars were close to the center of the array in each of the images.

APEX_1frame was used with current default parameters in the namelists provided in the cdf sub-directory of the current MOPEX distrubution, e.g. apex_1frame_I1.nl etc, with one change. A Normalization Radius for the PRF is needed to correspond to the IRAC calibration radius of 10 pixels. This was placed in the parameter block for sourcestimate: Normalization_Radius = 1000 (since it is in units of PRF pixels, and the sampling is 100x).

We performed aperture photometry using a 10 pixel (calibration) radius for IRAC1 and 2, and a 3 pixel radius for IRAC3 and 4, and a 12-20 pixel background annulus for all. Aperture corrections from the IRAC Data Handbook were applied to IRAC3 and 4. The use of smaller apertures at longer wavelengths is not critical but reduces the effect of background noise. No aperture corrections were needed for IRAC1 and 2 for this aperture/annulus combination as it is used to define the flux calibration. The IRAC1 aperture photometry was divided by the empirical pixel-phase flux correction (IRAC Data Handbook v. 3.0, Eq. 5.14):

(1)

where p is the radial pixel phase, defined as the distance of the centroid of the stellar image from the center of its peak pixel. This corrects to an average pixel phase of pix.

The average PRF-fitted fluxes compared to aperture photometry are shown in Fig. 1. The weighted average differences between PRF fluxes and (corrected) aperture fluxes are shown as long blue dashes.

There are offsets in all four channels between the aperture and fitted fluxes. In IRAC3 and 4, the offset is due to the fact that in these channels, the PSFs are wide and there is significant flux in the 12-20 pixel background annulus subtracted out in the IRAC calibration. APEX does not know about this in its PRF normalization, so the PRF fluxes are too high. We examined the "Core" PRFs obtained from the IRAC PSF page and estimated this factor. The estimated effect of the annulus on the PRF fluxes is shown in Fig. 1 as black short dashes. These are witin 1% of the IRAC3 and 4 estimates from the calibration stars. For IRAC1 and 2, these annulus terms appear to be small, so we assume zero correction for the present time. The annulus correction factors (divide PRF fluxes by these) are 1.022 for IRAC3, and 1.014 for IRAC4 (Table 1).

Sub-Pixel Response in channels 1 and 2

The offset for IRAC1 in Fig. 1 is due to a completely different effect, namely the pixel phase effect described above. Aperture sums on the channel 1 IRAC PRFs match reasonably well the pixel phase relation in Eqn. 1 if we sum a 10 pixel radius aperture.

APEX performs normalization on the ''center-of-pixel'' (pixel phase [0,0]) PRF, and applies this normalization factor to all sub-pixel positions. This results in an offset of the photometry relative to the mean pixel phase of . We need to ''back out'' APEX's center normalization. Setting p=0 in Eqn. 1 gives us the required factor: divide the PRF fluxes by 1.021. Similarly, using the pixel phase slope of 0.0301 in IRAC2 leads to a correction factor of 1.012.

With these corrections, the PRF fitting using these PRFs on single BCDs matches aperture results with any systematics less than a percent in all IRAC bands (Fig. 2). The remaining scatter is most likely due to residual pixel phase effect not removed by the one-dimensional correction applied to teh aperture photometry. The true pixel phase effect has two dimensional structure which is included in the PRF (see also Mighell et al.\ 2008).

Band	PRF aperture corrections			Correction to mean	Total
	From Core PRFs	From Cal Stars	Adopted	pixel phase	correction
IRAC1				1.021	1.021
IRAC2				1.012	1.012
IRAC3				1.000	1.022
IRAC4				1.000	1.014

Divide PRF fluxes by the last column.
Table 1: Correction Factors for PRF Fluxes

Figure 1: PRF fits vs. aperture photometry for selected IRAC calibration star BCDs. The vertical axis is the fractional difference between the PRF fit and corrected aperture photometry. The aperture photometry for IRAC3 and 4 is in a 3 pixel radius with a 12-20 pixel background annulus and an aperture correction factor from the IRAC Data Handbook. For IRAC1 and 2, it is in a 10 pixel radius with the same annulus. Short black dashed lines are the expected annulus correction needed based on the PRFs posted on the IRAC website. Long blue dashed line is the offset estimated from a weighted average of the data. Note this is essentially the expected value for IRAC3 and 4. But IRAC1 and IRAC2, to a lesser extent, require a pixel-phase correction (see text).

Figure 2: Data from Fig. 1, with IRAC3 and 4 corrected for the annulus contribution, and IRAC1 and 2 corrected for the pixel-phase effect.

Data for this test is a ''C2D'' off-cloud field (OC3) near Serpens, AOR 5714944 (S14.0). It is HDR mode (12 and 0.6 sec) in all four IRAC bands. It is 2 repeats of 2 dithers, so the typical coverage is 4. It is a 3x4 map. The field was chosen to be a crowded, predominantly stellar, field. The BCD data were run through the IRAC artifact mitigation software to correct muxbleed, column pulldown/pullup, electronic banding and the first frame effect. No pixel replacement was done. Long and short HDR data were handled separately. The tests here are with the long frames.

APEX multiframe was used with the Hoffmann PRF's, using complete set of 25 array-dependent ones. Note APEX does aperture photometry on the mosaic, but PRF fits on the stack. Final extracted sources shown are those with SNR>~8.

Fig. 3 shows the comparison of PRF-fitted fluxes to aperture-corrected aperture photometry in a 3 pixel radius aperture. For IRAC1 and 2, this is without pixel-phase corrections; for IRAC3 and 4 it is with correction for the PRF aperture (Table 1), but without correction for mosaic smear. Mosaicking involves an interpolation process which smears out point sources. Aperture corrections for aperture photometry off the mosaics need therefore to be made either based on point sources in the mosaic itself, or using values for BCDs with a correction for mosaic smear. The amount of smearing depends on the pixel sampling in the final mosaic.

Figure 3: APEX PRF-fitted photometry in the Serpens test field, with array-position-dependent PRFs vs. aperture photometry. The aperture has a 3 pixel radius, the background annulus is 12-20 pixels. The aperture fluxes have been corrected using the aperture corrections in the IRAC Handbook. The IRAC3 and 4 PRF fluxes have been corrected for annulus contribution.

Figure 4, shows the data with the remaining corrections discussed above applied. PRF fluxes for IRAC1 and 2 were corrected for the pixel phase effect (Table 1). Mosaic smear corrections for the aperture fluxes were determined empirically by comparing BCD and mosaic aperture fluxes, in IRAC 1 and 2 they were negligible, but IRAC3 and 4 fluxes were corrected by 2.8% and 1.5%, respectively.

The results (Fig. 4) show generally good agreement with aperture photometry with any systematic offset ~< 1%.

Figure 4: APEX PRF-fitted photometry with a PRF Map vs. aperture photometry in the Serpens test field. PRF and aperture fluxes have been corrected as described in the text.

We also analysed the GLIMPSE AOR 9225728 ina similar manner. This produced similarly good agreement between the aperture and fitted fluxes. In addition, we stacked the residuals of the brighter sources in an attempt to determine the size of any systematics, and plotted out the ratio of the residuals to the uncertainties for the inner four pixels closest to the source position. No significant residual could be found in a stack of 111 sources with channel 1 fluxes between 50 and 100mJy, corresponding to a limit of ~0.1% on the size of any systematic residual. Similarly, no significant difference could be found for the distribution of the ratio of residual to uncertainty between the pixels near to the peak star position and pixels in the remainder of the image.