Beer-Lambert law (Pawley): Transmitted intensity follows I = I₀ × e^(−εcl), where ε is the extinction coefficient (dye-specific), c is the concentration, and l is the path length (section thickness). In optical density: OD = εcl. This linear relationship between OD and concentration is what makes brightfield quantification possible — if you measure the OD of a DAB-stained region, it's proportional to the amount of DAB chromogen deposited, which is proportional to the amount of target antigen (with many caveats about staining kinetics and saturation).
Contrast mechanisms (Pawley): Most biological tissue is nearly transparent in brightfield — it absorbs very little visible light unless stained. This is why H&E was developed: hematoxylin binds DNA and other acidic structures (nuclei), eosin binds basic proteins (cytoplasm), creating the color contrast that makes tissue architecture visible. Without staining, brightfield microscopy would show essentially nothing in thin tissue sections.
Absorption vs. fluorescence trade-off: Brightfield absorbs some light from a bright source (subtractive), while fluorescence emits light against a dark background (additive). Fluorescence has inherently higher contrast for molecular targets (the target is the only thing that glows), but brightfield reveals tissue architecture (the overall structure is visible). This complementarity is why modern immuno-oncology combines both: brightfield H&E for morphology and fluorescence multiplex for molecular profiling.
Color space limitations: Standard RGB cameras capture three channels (red, green, blue), limiting color deconvolution to separating three or fewer stains. Gonzalez & Woods note that RGB is "perceptually nonlinear" — equal changes in RGB values don't produce equal perceived color changes. For quantitative analysis, converting to optical density or perceptual color spaces (Lab, HSV) provides more biologically meaningful measurements.
Brightfield contrast comes from absorption — stains remove specific wavelengths from white light, and the remaining light forms the colored image. The Beer-Lambert law says the amount of light absorbed is proportional to the amount of stain present, enabling quantitative measurement (in optical density, not raw RGB). Brightfield shows tissue architecture that fluorescence cannot, which is why the two modalities complement each other.
