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Photometry of near- and far-UV images using visible priors

A Bayesian approach enables accurate multicolor UV photometry in crowded fields of galaxies.
19 July 2010, SPIE Newsroom. DOI: 10.1117/2.1201006.002951

Measuring positions and brightnesses of stars and planets has always been of great importance in astronomy. Similarly, accurate photometry (in multiple passbands) of astronomical objects is crucial to answer many open questions in contemporary astrophysics. In this context, major challenges include the huge range in luminosity and the exponentially increasing number of sources per unit surface area with decreasing brightness. Consequently, the need to measure fluxes of faint stars and/or galaxies in crowded fields has spawned a large variety of photometric measurement techniques. Most are based on either fitting the point-spread function (PSF) or flux integration in predefined apertures.

We recently developed a novel photometric method to measure the brightnesses of large numbers of faint galaxies observed at optical as well as near- and far-UV wavelengths across large fields. The procedure uses a high-resolution (0.2 arcsecond) image obtained at visible wavelengths to determine the brightnesses of all galaxies blended in the low-resolution (1.5 arcsec) UV field (see Figure 1). (In astronomy, brightnesses are measured on a logarithmic scale as ‘magnitudes,’ m, for a given wavelength interval. For a source of brightness I, , where I0 is the brightness of a standard star of magnitude 0 in the same wavelength range. Note the negative sign, which implies that fainter sources have larger magnitudes.)

Figure 1. (top) Visible and (bottom) near-UV observations of a given field. Following object extraction from the former, their UV fluxes are measured in the latter. In the UV range, the extended point-spread function and extremely low flux levels induce a characteristic granularity in photon-limited images.

Launched in 2003, NASA's Galaxy Evolution eXplorer (GALEX)1 satellite observed large sky areas in the far- and near-UV wavelength ranges (spanning 135–175 and 170–275nm, respectively). The telescope continuously scanned a large number of circular areas (field of view: 1.25° diameter) covering the entire sky using a 2D photon-counting device. Precise knowledge of the rosetta-shaped path swept by the scanning algorithm enables reconstruction of a circular image for each area, which is included in the resulting square image frame of 3820 × 3820 pixels, with a resolution of 1.5 arcsec/pixel. The full width at half maximum of the GALEX PSF is 1.35 pixels. The PSF exhibits very faint but extended wings out to 40 pixels. All fields are crowded and contain many extragalactic sources. Most are unresolved and look like point sources. At best, they are poorly resolved as elliptical patches of a few pixels wide. Consequently, blends of objects occur frequently. Classical photometric measurement procedures (based on matching UV-detected sources with catalogs obtained in visible bands) lead to numerous ambiguities and mismatches and are not very sensitive to faint magnitudes (m > 24mag). Therefore, the commonly used SExtractor tool2 misses many objects and its results are characterized by significant object confusion, while DAOPHOT3 uses priors and assumes that images are composed of unresolved objects and Gaussian noise. It is, therefore, not optimized to detect objects in photon-limited GALEX images. In our new method, we use high-resolution visible images as priors by applying a Bayesian approach appropriate for low-flux-level images. In addition, we require nonnegative model results.

The morphological similarity between the UV and visible images forms the basis of our method.4 Each object in the visible image is a prior for a (most likely blended) object in the corresponding UV image. We assume that all UV objects have one visible counterpart and that the relation between visible and UV objects depends only on the common PSF, H(i, j) (for the entire UV field) and the specific weighting factor a(k) for each object (k) at coordinates (i, j). The UV field, F(i, j), can be modeled as the sum, μ(i, j), of individual objects, O(i, j; k), convolved with the PSF, H(m−i, n−j), of the GALEX imaging system and scaled by a(k). Consequently, we set out to determine a(k).

To solve this inverse problem, we compare our model to the real observations using parametric maximum-likelihood estimates of a(k). Each pixel in the field depends on the set of a(k)parameters. We define the Poissonian-statistics model (P) with mean μ(i, j) for the observed UV image:

where b is the background-flux level and G is the result of a linear convolution of the object and the PSF,


We use an iterative maximum-likelihood procedure. Each iteration consists of two steps, estimation—the value of each pixel is determined using the last estimate of the set {a(k)}—and maximization: a new set {a(k)(n+1)} results from {a(k)(n)} using the correction factor derived for each k. This correction factor is the ratio of the total flux of the objects to the total flux of the weighted objects (at UV resolution),

where the weights are defined as


To obtain accurate results, we need a very precise PSF. Astronomical objects exhibit a large dynamic range (>1:1000). Therefore, determination of the PSF with the highest-possible accuracy is a preliminary and crucial step. We used a modified StarFinder5 procedure to find the PSF of our UV fields. Second, our model is based on the assumption that b is constant and known. In practice, b is replaced by a position-dependent value b(i, j), defined independently.6 This requires strong photometric decoupling between the galaxies and the background flux.6 Figure 2 shows a small part of a UV field and the corresponding residuals after object subtraction.

Figure 2. (top) Part of a UV-observed field and (bottom) the same field after object subtraction. The Poissonian (statistical) noise shows up clearly in the subtracted field, as do residual morphology errors for some of the brightest objects.

Our new method improves the sensitivity compared to the GALEX data-reduction pipeline by more than two magnitudes,6,7 corresponding to an increase of 25% of measured sources. We determined the photometric performance of our algorithm (see Figure 3) by randomly adding a set of simulated stars to the original UV images and measuring the combined frames as if they were original images. This procedure is presently included in the standard GALEX pipeline. Our future work aims at improving and validating the background estimation, increasing the accuracy of PSF determination, and extension of this new method to spectroscopic tomography.

Figure 3. Mean and standard errors (expressed in magnitudes) for (top) the near- and (bottom) the far-UV field as a function of object magnitude. Std dev: Standard deviation.

The authors are grateful for financial support from CNRS, the Centre National d'Etudes Spatiales (CNES), and the University of the Provence (Marseille). We also thank S. Conseil for testing and graphics.

Antoine Llebaria, Didier Vibert
Laboratoire d'Astrophysique de Marseille (LAM)-CNRS
Marseille, France

Antoine Llebaria is an image scientist. He received his PhD in optics and image processing from the University of Aix-Marseille (France) in 1988. From 1978 to 1998 he headed the LAM Image Processing Department. He is an author of more than 50 papers on astrophysical image processing.

Didier Vibert has been a staff research engineer since 2008. He has worked on several image-processing projects for astronomical satellites, including GALEX, Hershel, FireBall, and Rosetta. He obtained his PhD in image processing in 1997 on the 3D reconstruction of the solar corona.

Mireille Guillaume
Fresnel Institute
University of the Provence (Marseille)-CNRS
Marseille, France

Mireille Guillaume is an assistant professor at the École Centrale de Marseille (France), as well as a researcher at the Fresnel Institute. She obtained her PhD degree in theoretical physics and her Habilitation à Diriger des Recherches (a qualification to supervise research) in signal processing. Her research focuses on multicomponent and hyperspectral-image analysis, and astronomical faint-object reconstruction.