Argon microbubbles will exist in the primary sodium of the next generation of sodium-cooled fast reactors (SFR). Due to its opacity, acoustic methods will be used for the in-service inspection in these reactors, but the presence of such bubbles will greatly affect ultrasonic wave propagation. Moreover, these bubbles can lead to the formation of gas pockets in the reactor and impact cavitation and boiling phenomena. It is therefore necessary to characterise what is called the 'microbubble cloud' by providing the volume fraction and the bubble size distribution. Safety requirements in this field call for robust inspection methods based on very few assumptions about the bubble populations. The objective of this study is to assess the performance of spectroscopic methods in the presence of bubbles with high polydispersity and to monitor an evolving cloud of microbubbles. The histogram and void fractions were estimated according to the regularised inversion of the complex wave number's integral equation. To reduce the need for prior information on the bubble cloud, a specific procedure was used to estimate the maximum radius of the population. The results are presented on the basis of the experimental data obtained and then compared with optical measurements.