With the emergence of diffuse optical tomography (DOT) as a non-invasive imaging modality, there is a requirement to evaluate the performance of the developed DOT systems on clinically relevant tasks. One such important task is the detection of high-absorption signals in the tissue. To investigate signal detectability in DOT systems for system optimization, an appropriate approach is to use the Bayesian ideal observer, but this observer is computationally very intensive. It has been shown that the Fisher information can be used as a surrogate figure of merit (SFoM) that approximates the ideal observer performance. In this paper, we present a theoretical framework to use the Fisher information for investigating signal detectability in DOT systems. The usage of Fisher information requires evaluating the gradient of the photon distribution function with respect to the absorption coefficients. We derive the expressions to compute the gradient of the photon distribution function with respect to the scattering and absorption coefficients. We find that computing these gradients simply requires executing the radiative transport equation with a different source term. We then demonstrate the application of the SFoM to investigate signal detectability in DOT by performing various simulation studies, which help to validate the proposed framework and also present some insights on signal detectability in DOT.
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