Recently, we have developed and calibrated the Synthetic Field Method (SFM) to derive the total extinction through disk galaxies. The method is based on the number counts and colors of distant background field galaxies that can be seen through the foreground object, and has been successfully applied to NGC 4536 and NGC 3664, two late-type galaxies located, respectively, at 16 and 11 Mpc. Here, we study the applicability of the SFM to HST images of galaxies in the Local Group, and show that background galaxies cannot be easily identified through these nearby objects, even with the best resolution available today. In the case of M 31, each pixel in the HST images contains 50 to 100 stars, and the background galaxies cannot be seen because of the intrinsic granularity due to strong surface brightness fluctuations. In the LMC, on the other hand, there is only about one star every six linear pixels, and the lack of detectable background galaxies results from a ``secondary'' granularity, introduced by structure in the wings of the point spread function. The success of the SFM in NGC 4536 and NGC 3664 is a natural consequence of the reduction of the intensity of surface brightness fluctuations with distance. When the dominant confusion factor is structure in the PSF wings, as is the case of HST images of the LMC, and would happen in M 31 images obtained with a 10-m diffraction- limited optical telescope, it becomes in principle possible to improve the detectability of background galaxies by subtracting the stars in the foreground object. However, a much better characterization of optical PSFs than is currently available would be required for an adequate subtraction of the wings. Given the importance of determining the dust content of Local Group galaxies, efforts should be made in that direction.
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