The opacity of nearby galaxies from colors and counts of background galaxies.: I.: The synthetic field method and its application to NGC 4536 and NGC 3664

We describe a new direct method for determining the opacity of foreground galaxies that does not require any a priori assumptions about the spatial distribution or the reddening law of the obscuring material. The method is to measure the colors and counts of background galaxies that can be identified through the foreground system. The method is calibrated and the effects of confusion and obscuration are decoupled by adding various versions of a suitable deep-reference frame containing only held galaxies with known properties into the image of the foreground galaxy and analyzing these "synthetic field" images in the same way as the real images. We test the method on Hubble Space Telescope Wide Field Planetary Camera 2 archived images of two galaxies that are quite different: NGC 4536 is a large Sc spiral, and NGC 3664 is a small Magellanic irregular. The reference frames are taken from the Hubble Deep Field. From the background galaxy counts, NGC 4536 shows an extinction of A(I) similar to 1 mag in the northwestern arm region and A(I) < 0.5 mag in the corresponding interarm region (no correction for inclination has been attempted). However, from the galaxy colors, the same reddening of E(V - I) similar to 0.2 is observed in both the arm and the interarm regions. In the interarm region, the combination of extinction and reddening can be explained by a diffuse component with a Galactic reddening law (R-V approximate to 3). In the spiral arm, however, the same diffuse, low-opacity component seems to coexist with regions of much higher opacity. Since the exposures are shorter, the results for NGC 3664 are less clear but also appear to be consistent with a two-component distribution.