A Model based Survey of Colour Deconvolution in Diagnostic Brightfield Microscopy: Error Estimation and Spectral Consideration

Colour deconvolution is a method used in diagnostic brightfield microscopy to transform colour images of multiple stained biological samples into images representing the stain concentrations. It is applied by decomposing the absorbance values of stain mixtures into absorbance values of single stains. The method assumes a linear relation between stain concentration and absorbance, which is only valid under monochromatic conditions. Diagnostic applications, in turn, are often performed under polychromatic conditions, for which an accurate deconvolution result cannot be achieved. To show this, we establish a mathematical model to calculate non-monochromatic absorbance values based on imaging equipment typically used in histology and use this simulated data as the ground truth to evaluate the accuracy of colour deconvolution. We show the non-linear characteristics of the absorbance formation and demonstrate how it leads to significant deconvolution errors. In particular, our calculations reveal that polychromatic illumination causes 10-times higher deconvolution errors than sequential monochromatic LED illumination. In conclusion, our model can be used for a quantitative assessment of system components - and also to assess and compare colour deconvolution methods.