Effects Of Substrate Scattering On Bar-Code Scanning Signals

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Abstract
When a beam of light strikes a piece of paper or similar substrate, a portion of its energy penetrates into the bulk and, due to multiple scattering, may re-emerge at some distance from the point of entry. We refer to this phenomenon as substrate scattering. In this paper we describe a general model for scattering substrates and, using linear systems theory, we investigate its implications for bar-code scanning. We show that the effects of substrate scattering can be represented as a modified reflectance distribution associated with the original printed reflectance pattern. This effective distribution is shown to be independent of the details of scanning system configuration. We show that under a broad range of conditions substrate scattering will decrease modulation and will cause scanners to overestimate barwidths. A specific diffusion model of the scattering process is developed, providing a family of functions which can be used in empirical studies. We conclude that the scattering distributions will not even be approximately Gaussian. Experimental results are presented which are consistent with this conclusion and inconsistent with a Gaussian model. Further experimental results are presented which show that, for typical substrates, depth of modulation may be decreased by 20 percent or more and perceived bar-width increases will be on the order of one mil.

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