On the integrating cavity transfer function and decay time

Abstract

A novel method for deriving the integrating cavity transfer function, where the average electromagnetic radiation intensity decay time in the cavity has been found as the final result, is presented, and where a uniform photon distribution inside the cavity was assumed. Instead of the beam reflection analysis, the method is based on employing the energy conservation law inside the integrating cavity. The obtained result for the decay time is slightly different from other results obtained elsewhere but still in relatively good agreement with them. In order to verify the obtained result, we performed a similar analysis based on the photon number conservation law. This analysis gives the same result for the decay time as the first one. Finally, in order to confirm the obtained result, we statistically analyzed the average lifetime of a photon inside the cavity after the radiation source switch-off, i.e. the average time between the radiation source switch-off and its absorption by the cavity inner walls. The result for the decay time obtained in this way is identical to the results obtained using the above-presented methods. At the end, the transfer function of the integrating cavity filled with a weak absorbing material is derived. Based on the obtained result, a novel method for the absorption coefficient measurement is proposed.