Black box linearization for greater linear dynamic range: the effect of power transforms on the representation of data.

Power transformations are commonly used in image processing techniques to manipulate image contrast. Many analytical results, including chromatograms, are essentially presented as images, often to convey qualitative information. Power transformations have remarkable effects on the appearance of the image, in chromatography, for example, increasing apparent resolution between peaks by the factor √n and apparent column efficiency (plate counts) by a factor of n for an nth-power transform. The profile of a Gaussian peak is not qualitatively changed, but the peak becomes narrower, whereas for an exponentially tailing peak, asymmetry at the 10% peak height level changes markedly. Using several examples we show that power transforms also increase signal-to-noise ratio and make it easier to discern an event of detection. However, they may not improve the limit of detection. Power responses are intrinsic to some detection schemes, and in others they are imbedded in instrument firmware to increase apparent linear range that the casual user may not be aware of. The consequences are demonstrated and discussed.