Transmitted intensity follows I = I₀ × e^(−εcl), where ε is the dye's extinction coefficient, c the concentration and l the path length, which is the section thickness. In optical density, OD = εcl. That straight line between OD and concentration is what makes brightfield quantification possible. Measure the OD of a DAB-stained region and you have a number proportional to the DAB chromogen deposited, and so to the target antigen, with many caveats about staining kinetics and saturation.
Most biological tissue is nearly transparent: unless stained, it absorbs very little visible light. That is why H&E was developed. Hematoxylin binds DNA and other acidic structures (nuclei) and eosin binds basic proteins (cytoplasm), and the two colors make tissue architecture visible. Without staining, a thin section in brightfield shows almost nothing.
Brightfield is subtractive: it takes some light away from a bright source. Fluorescence is additive: it emits light against a dark background. Fluorescence has the higher contrast for molecular targets, because the target is the only thing that glows, while brightfield shows the overall tissue architecture. Modern immuno-oncology uses both, brightfield H&E for morphology and multiplex fluorescence for molecular profiling.
A standard RGB camera records three channels, so color deconvolution can separate three stains at most. RGB is also perceptually nonlinear: equal steps in RGB value don't look like equal steps in color. For quantitative analysis, optical density or a perceptual color space (Lab, HSV) gives measurements with more biological meaning.
Stains remove specific wavelengths from white light, and what is left forms the colored image. The Beer-Lambert law says the light absorbed is proportional to the stain present, which makes measurement possible, in optical density rather than raw RGB. Brightfield shows tissue architecture that fluorescence cannot, so the two complement each other.
