Fluorescence Ratio Imaging

In this paper, the properties of the mean and variance of three estimators of the ratio between two random variables x, y are discussed. Given n samples of x and y we can construct two different estimators. One is biased and the other is asymptotically unbiased. Using the noise characteristics (variance, covariance) a third, unbiased estimator can be constructed. 1. Introduction In fluorescence microscopy, ratio imaging is applied in a number of applications. In ratio labeling, the ratio between the intensities of different fluorochromes is used to expand the number of labels for an in situ hybridization procedure [1]. This number is normally restricted by the number of fluorochromes that can be spectrally separated by fluorescence microscopy. Fluorescence ratio imaging is also used to measure spatial and temporal differences in ion concentrations within a single cell. This is achieved by using fluorochromes whose excitation or emission spectrum change as function of the Ca ++ or pH concentration [2]. In a third application of ratio imaging, known as Comparative Genome Hybridization (CGH) [3,4], one tries to estimate the DNA sequence copy number as a function of the chromosomal location. This is achieved by measuring the ratio between " tumor " DNA and " normal " DNA to detect gene amplifications and deletions.