We study the spontaneous Raman emission in an ensemble of laser-cooled three-level Λ-type atoms confined inside a hollow-core photonic-bandgap fiber using a novel approach to observe the process. Instead of detecting the emitted light, we measure the number of atoms in the ground state as a function of Raman pump time, which eliminates the need to suppress the pump photons with a high-resolution filter. We describe how this measurement can be used to detect superradiant emission from the atomic ensembles and estimate the number of atoms required to observe Raman superradiance in atomic clouds inside a hollow-core fiber.