The probability relationships between bubble sizes and chord lengths in an heterogeneously bubbling system have been analyzed. A forward transform of chord length distribution for a given bubble size density distribution affecting the probe under a heterogeneously bubbling condition has been demonstrated. Three backward transform techniques, an analytical, a general, and a numerical, have been developed to infer bubble sizes from the chord length data in heterogeneously bubbling system. Both the analytical and the general backward transforms were based on the representation of the bubble population density function as a product of two functions which depend on bubble size and chord length. The techniques were tested and compared using Monte-Carlo simulations.