4.9 IRAC Point Spread and Point Response Functions
Because the point spread function (PSF) was grossly undersampled by the IRAC pixels, especially in channels 1 and 2, we use the concept of the point response function (PRF). In practice, the PRFs are stored in a table (not an image, though for convenience it is stored as a 2D FITS image file) that combines the information on the PSF, the detector sampling, and the intrapixel sensitivity variation (see Section 4.6), and gives an appropriate PRF depending on where on the pixel the peak of a point source falls. By sampling this table at regular intervals corresponding to single detector pixel increments (for example, taking every fifth pixel for a five-times oversampled PRF), an estimate of the detector point response function (or PRF) can be obtained for a source centered at any given subpixel position. Such PRFs formed from the table are called “point source realizations” (PSRs) in Appendix C.
To build the PRFs, we sampled the PSF with much smaller “pixels.” In the case of IRAC, the oversampling is usually by either a factor of five or a factor of 100. See Appendix C for how to extract the correct PRF from the PRF table for a point source that peaks at a given location on a pixel. Figure 4.9 shows the 5 × oversampled (in row and column direction) IRAC point response function tables.
FITS files of both the core and extended IRAC PRF tables are available in the IRAC section of IRSA’s Spitzer documentation website:
The appropriateness of a given PRF is dependent on the observation sampling and the photometric reduction package used.
Figure 4.9: Images of the IRAC point response function (PRF) tables. These are shown at 3.6 (upper left), 4.5 (middle, top row), 5.8 (left, bottom row), and 8.0 µm (middle, bottom row) from the cryogenic mission and from the warm mission at 3.6 (right, upper row) and 4.5 µm (right, bottom row). The PRFs were generated from models refined with in-flight calibration test data involving a bright calibration star observed at several epochs. The PRFs are shown as they appear with 1/5 the native IRAC pixel sampling of 1.2 arcseconds to highlight the core structure. The PRFs were calculated using the Simfit routine in Hoffmann et al. (2004). The images are 128 × 128 1/5 native IRAC pixels in size (about 31 arcseconds × 31 arcseconds).
The PRFs vary over the IRAC detectors’ field of view due to the Spitzer/IRAC optics, including, but not limited to, the relative position of the optical ghosts (see Section 7.3.3). For this reason, the PRFs available at the Spitzer website at IRSA for use with MOPEX/APEX are given at 25 different positions. The PRF variation over the field of view in channel 1 (as an example) is demonstrated by Figure 4.10 that shows the “best” and “worst” case PRFs over the field of view and Figure 4.11 that shows the corresponding changes in the number of noise pixels. A step-by-step description of IRAC PRF-fitting photometry is given in Appendix C.
Figure 4.10: “Best” (left) and “worst” (right) channel 1 PRF images from the set of PRFs available for the cryogenic mission. A logarithmic stretch was used to highlight the low-level emission. The core of the “worst” image is a larger than the “best” image, and it has a ≈ 60% higher noise pixel value.
Figure 4.11: Distribution of noise pixel values over the channel 1 field of view in the cryogenic mission. The image matches the BCD orientation, with pixel (1,1) in the lower left corner. The mean point source noise pixel values (averaging over many different pixel phases) were measured at the 25 positions indicated by the small squares on the image, and a quadratic surface was fit to the data, plotted here as grayscale and contours. The lowest noise pixel value is 6.79 at (x,y) position (163,128). The highest noise pixel location, in the upper left corner, is 1.6 times this, requiring 1.6 times the integration time to achieve the same signal-to-noise as for the lowest noise pixel position.
4.9.1 Core PRFs
The FITS files of the core PRFs are linked off the IRAC web pages. These core PRFs can be used for PRF-fitting photometry and source extraction in (C)BCDs for all but the brightest sources. We recommend performing aperture photometry instead of PRF fitting in all instances except in crowded fields and regions with a strongly varying background, because aperture photometry is much simpler, more straightforward, and faster to do. In addition, especially in channels 1 and 2, the PSF was undersampled by the native IRAC pixel size, causing further uncertainty to PRF fitting. PRF fitting does not work in image mosaics where the information from the PSFs has been blended together. Aperture photometry is the correct way to perform point source flux density measurements in image mosaics.
The PRFs are provided in two different samplings, 1/5 and 1/100 native pixels. The 1/100th native pixel sampling PRFs were created by interpolating the 1/5th sampled PRFs onto a finer grid. These PRFs were designed to work with the astronomical point source extractor for MOPEX, called APEX (Makovoz & Marleau 2005). The 1/5th pixel sampling versions are the originally derived versions and are appropriate for use with custom PRF-fitting software, but not APEX. For both versions of sampling, the PRFs are provided for 25 positions in a 5x5 grid upon the array for each channel. The PRFs are normalized such that the flux is unity within 12 arcsecond (10 native pixel) radius around each point source with the zero pixel phase instance (centered on a pixel).
4.9.2 Extended PSFs
The FITS files of the extended PSFs can be obtained using the links on IRSA’s IRAC web pages. We will first address the cryogenic IRAC extended PSFs and then explain the procedure to generate the warm IRAC PSFs below. In order to gain high signal-to-noise out to the edge of the arrays, PSFs were generated from a combination of on-board calibration and science observations of stars with different brightness, joined together to produce extended high dynamic range (HDR) observational PSFs. These PSFs have two main components: a core HDR PSF created by the observations of a reference star, and the extended region from observations of a set of bright stars that saturated the IRAC array. They can be used to perform source extraction and PSF-fitting photometry of bright, highly saturated stars with extended wings. The core of the extended PSF was generated using the prf_estimate module of MOPEX, which has been shown to be inadequate for making high-quality PSFs for IRAC. As a result, the extended PSF should not be used for PSF-fitting photometry and source extraction of non-saturated point sources. Instead, the core PRF in Section 4.9.1 is more appropriate for PRF-fitting photometry. Also, note that the detailed structure of the center of saturated sources fitted using the extended PSF will not be correct.
Observations of the stars Vega, Epsilon Eridani, Fomalhaut, Epsilon Indi, and Sirius were used in the construction of the extended portion of the PSF. Each star was observed with a sequence of 12 second IRAC full frames, using a 12-point Reuleaux dither pattern (cf. Section 3.4) with repeats to obtain the required total integration time (the stars were typically observed for 20 - 60 minutes during each epoch). The images were aligned, rescaled to the observation of Vega, and then averaged together with a sigma-clipping algorithm to reject background stars.
These extended HDR PSFs have a pixel size of 0.2 IRAC pixels, or ≈ 0.24 arcseconds. The size of each PSF image is 1281x1281 pixels, covering an area of ≈ 5.1 arcminutes x 5.1 arcminutes. The PSFs are centered within each image. The PSFs are calibrated in MJy/sr. The PSFs represent an unsaturated, very high SNR image calibrated to Vega, and the flux density contained within a 10 native IRAC pixel aperture radius (50 HDR PSF pixels), with the sky level estimated in a radial annulus from 12 to 20 native IRAC pixels, is equal to the flux density of Vega. The pedestal level was set to zero in the corners of each PSF.
To produce the core portion of the HDR PSF, 300 HDR observations of a calibration star were obtained during three separate epochs, each observation consisting of short exposures (0.6 seconds/1.2 seconds) and long exposures (12 seconds/30 seconds). The HDR PSFs were generated by first combining short-exposure frames and long-exposure frames separately. The short frames enabled the cores to be constructed without a saturation problem, while the long exposures allowed the construction of a higher signal-to-noise PSF in the wings out to 15 arcseconds. The assembly required the replacement of any saturated areas in the long-exposure frames with unsaturated data from the same pixel area of the short-exposure frames. It also required the replacement of a few pixels in the long-exposure frames by the corresponding pixels in the short-exposure frames to mitigate the non-linear bandwidth effect in channels 3 and 4.
The core HDR PSFs were aligned and rescaled to the extended portion of the PSF by matching their overlapping areas. The alignment was done at best to an accuracy of ≈ 0.1 arcseconds. The rescaling was made by forcing the cores to have the same flux density, that of Vega, within a 10 native IRAC pixel radius aperture. The stitching was made using a mask with a smooth 1/r transition zone, 2.4 arcseconds wide, between the core (contributing where the extended portion PSF data were missing due to saturation cutoff), and the extended portion of the PSF. The merged PSFs were then cropped to a final 5.1 arcminutes x 5.1 arcminutes size, and a pedestal level was removed in order to have a surface brightness as close as possible to zero in the corners of the images.
The warm mission extended PSFs were created in a similar way, except that 22 A -M V stars (PID 40976) were used, along with 122 observations of NPM1 +67.0536 from the IRAC calibration program. The original BCDs were corrected for pinstriping (see Section 7.2.2), and residual images were masked. Mosaics of each star were created with IRACproc (Schuster et al. 2006) on a 0.24 arcseconds/pix scale. All pixels above 50% of the saturation level were masked, and the mosaics aligned to a common center (with a typical accuracy ≈ 0.03 arcseconds) using the diffraction spikes of the images. The pedestal level and normalization levels were then fit by minimizing the chi-squared value of the difference in the binned radial profiles between the observation and the Vega calibration measurement. The aligned and normalized mosaics were averaged with sigma-clipping to remove outliers (background stars, other artifacts) to produce a normalized PSF image. This procedure was repeated for the observations that were not saturated in the core, and the core and extended PSFs were aligned and smoothly merged to produce the final PSF for each channel.
All of the extended PSFs are available at IRSA’s Spitzer/IRAC documentation website at
Figure 4.12:The IRAC extended PSFs. The cryogenic PSFs are shown on the left, with channel 1 PSF in upper left, channel 2 PSF in the middle (upper row), channel 3 in lower left, and channel 4 in the middle (lower row). The warm extended PSFs are shown on the right, with channel 1 on top and channel 2 at the bottom. See the text for how these were constructed.
4.10 Calculation of IRAC zmags
Some software packages, such as IRAF's phot task, require specifying zmag. For IRAC data, you need to know the pixel size of the IRAC image being analyzed in order to convert surface brightness to flux density. The zmag can be evaluated from 2.5xlog10 (F0/C), where F0 is the zero magnitude flux density in Jy for the relevant channel, tabulated in Table 4.2, and C is the conversion factor from MJy/sr to μJy/pixel, e.g., 8.461595 for 0.6 arcsecond x 0.6 arcsecond pixels (the value of C will be different depending on the pixel size).
To understand where the IRAC zmag comes from, you can start with the fundamental equation between magnitudes and flux densities. In one incarnation, it becomes
m - M0 = –2.5*log10(F/F0).
(4.16)
Here m is the magnitude of the source you want to measure, M0 is the zero magnitude (= 0), F is the flux density in Jy of the source you want to measure and F0 is the flux density of a zero magnitude source. For IRAC channel 1, F0 = 280.9 Jy. Expanded out,
m = –2.5*log10(F) +2.5*log10(F0).
(4.17)
Here zmag = 2.5*log10(F0). Now, because the IRAC images are in units of MJy/sr, we have to do some manipulation to get the equation to this form. Specifically, the measurable F that we have in IRAC images is the surface brightness, not the flux density. Therefore, the equation becomes
m = –2.5*log10(SB x C) + 2.5*log10(F0)
(4.18)
where SB is the measured surface brightness in the image in MJy/sr and C is a conversion factor from MJy/sr to Jy/pixel. For IRAC channel 1 mosaics with 0.6 arcsecond x 0.6 arcsecond pixels it equals C = 8.461595 x 10-6 Jy/pixel/(MJy/sr). Therefore, the equation becomes
m = –2.5*log10(SB) + 2.5*log10(F0/C)
(4.19)
where zmag now corresponds to the latter term, +2.5*log10(F0/C). Inserting the values of F0 and C mentioned above, we get zmag = 2.5*log10(280.9/8.461595E-06)= 18.80 mag in channel 1.
Please remember that this is true only for the 0.6 arcseconds x 0.6 arcseconds pixel scale mosaics. For other pixel scales you will get a different value. Also, please remember the required corrections (e.g., aperture correction) that are needed for high accuracy photometry
