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It is shown that the applicability conditions for the inverse Bernoullitransform method for solving the inverse problem of photocount statistics aredetermined by the fulfillment of the associativity condition for multiplyingthe matrices included in this transformation. A general criterion forevaluating the photocount distributions $Q_{m}$ in the case of few-photonlight, which makes it possible to establish whether the solution to the inverseproblem of photocount statistics by inverse Bernoulli transform method isapplicable for $\eta<0.5$, is found. As an example of application of theobtained criterion, the critical quantum efficiency $\eta_{cr}$ is found forcompound Poisson distribution, below which the solution of the inverse problemof photocount statistics becomes incorrect. Additionally it is shown that thenormalization of $Q_{m}$ is not sufficient to obtain a correct solution usingthe inverse Bernoulli transform.

Existence Criterion of Solutions to the Inverse Problem of Photocount Statistics Obtained by the Inverse Bernoulli Transform