Existence, uniqueness, and efficiency of numerically unbiased attenuation pathlength estimators for photon counting detectors at low count rates

If arbitrarily thick objects are permitted, an unbiased attenuation pathlength estimator does not exist. If the maximum thickness is restricted, an unbiased estimator exists but is not unique. An optimal estimator can be selected that minimizes variance, but a bias-variance tradeoff exists where a larger domain of unbiased behavior requires increased variance.