Interstellar grains, within our Galaxy, along the line of sight to a nearby galaxy, or within the galaxy being studied, will each result in light being selectively scattered and absorbed. If any one of these components of extinction is not accounted for, a Cepheid in an external galaxy will appear fainter and more distant than it actually is, and at the same time it will appear redder and cooler than it truly is. Systematic errors will thereby creep into the distance scale.
Accounting for the Galactic foreground component associated with dust in the plane of our own Milky Way is relatively straightforward and will not be discussed here in any detail. The use of foreground stars and/or reddening maps, generated from galaxy counts in combination with neutral hydrogen studies (see Burstein & Heiles 1984) appears to be quite reliable and is widely used. Since most external galaxies subtend an angular size small in comparison to expected variations of extinction across the line of sight, and since most extragalactic studies are also done at fairly high Galactic latitudes, these foreground Galactic extinction corrections are relatively small and of low variance.
Dealing with the reddening internal to the parent galaxy itself is more problematic. In the earliest studies it was simply ignored. Even if this simplification had proven true for the first few specific cases, there is no reason to believe that it would have obtained in general.
To illustrate the systematic effects of reddening on the observed PL and PLC relations, we consider the following example. Suppose for the moment that the instability strip is intrinsically very narrow both in color and in magnitude at fixed period. Now consider a sample of Cepheids drawn from this strip in a nearby galaxy, where on average the reddening is E (B-V) = 0.2 mag, with a standard deviation of ± 0.1 mag. These stars, differentially obscured, would be observed to have a period-color relation with a full (± two-sigma) color width of ~ 0.4 mag, a B period-luminosity relation with a magnitude width of 1.7 mag and a V period-luminosity relation with a width of 1.3 mag (for a ratio of AV / E (B-V) = 3.3). As ``predicted'' from a general consideration of the theoretical PLC, the deviations in the period-luminosity relation would be found to be correlated, with residuals from the period-color relation, apparently confirming the theory. But none of this correlation would be intrinsic, of course, despite it being very well defined. Unfortunately too, solutions for distances would be systematically in error since the ridge line of the data (defining the mean PL relations) would be displaced from the intrinsic strip by AB = 4.3 E (B-V), always towards larger apparent distances.
The above example is extreme, but it illustrates the point that any attempt to disentangle the effects of differential reddening and true color deviations within the instability strip must rely first on a precise and thoroughly independent determination of the intrinsic structure of the Period-Luminosity-Color relation. In order to achieve that calibration high-quality, independent reddenings and distances to individual calibrator Cepheids must be available. The uncertainty involved in undertaking this first step will affect all future results based on those assumptions. Below we discuss old methods that have been adopted to deal with the reddening problem, and emphasize new methods that have been brought to bear with the introduction of panoramic, digital detectors operating at optical and now at near-infrared wavelengths.