## 1 Introduction
On the other hand, a disadvantage of this technique is related to sufficient changes in the probe light intensity in the course of the pumping current modulation; however, this disadvantage is minimized due to application of average-intensity-normalized statistical characteristics of the multiple-scattered light fields (such as, e.g., a contrast as a standard deviation of intensity fluctuations normalized by the average intensity) as the diagnostic parameters. The abovementioned approaches are primarily based on application of the narrow-band probing radiation with a controllable coherence length for illumination of the characterized multiple-scattering system with a follow-up spatially resolvable detection of the scattered partially coherent light. On the other hand, the principle of the narrow-band spectral selection of the detected scattered radiation under a wide-band illumination of a probed object can be applied to provide the necessaryconditions for stochastic interference of light waves contributing to the multiple-scattered light field in the probed medium. Moreover, this probing light field can be induced by fluorescence of the medium due to continuous-wave (CW) laser pumping in the presence of the natural or artificially added fluorophores. The spectral selection can be provided using a monochromator between the light-collecting optics with a high spatial resolution and a photodetector; the effective coherence length of the detected light is determined as \(l_{c}\approx\overline{\lambda}^{2}/\Delta\lambda\), where \(\overline{\lambda}\) is the central wavelength in the spectral interval selected by the monochromator, and \(\Delta\lambda\) is the interval width defined by the spectral resolution of the monochromator. This approach was discussed in Ref. [29]; the combined light-collecting, wavelength-selecting, and photo-detecting unit was based on the Raman microscope Horiba Jobin Ivon LabRam HR800 and provided a remarkably high spectral (\(\Delta\lambda\approx 0.052\) nanometers) and spatial resolution. As the random modulation of the detected optical signal is caused by the stochastic interference of spectrally selected, or band-limited multiple-scattered light waves, the discussed technique can be defined as the band-limited reference-free speckle spectroscopy. For further development of this technique and expansion of the area of possible applications, it is important to examine its operational ability in the case of almost total suppression of the stochastic interference modulation in the detected signal because of the low spectral and spatial resolution of the light-collecting unit. Under these conditions, the factual content of the detected signal becomes strongly corrupted by the intrinsic noise of the system, and the main problem related to the workability of the system under these conditions is to recover this factual content. In particular, this problem occurs when the detection conditions are far from ideal and the band-limiting unit (the monochromator) in the reference-free speckle-spectroscopic system provides a relatively small coherence length \(l_{c}\) of the detected radiation, whereas the average propagation path \(\langle s\rangle\) of the probe light in the medium becomes sufficiently larger compared with \(l_{c}\). The goal of this work is to examine the workability of the band-limited reference-free speckle spectroscopy (BLRFS) applied as the probing technique for the CW-pumped fluorescent random media in the case of a strong damping of the detected signal due to non-ideal detection conditions and data corruption by an intrinsic noise of the speckle-spectroscopic system. In addition, the discussed technique of data recovery is verified in the experiments with the dye-doped fluorescent random media consisting of densely packed oxide (titania and silica) particles. It should be noted that the physical principles of the BLRFS probing are generally similar to the principles used in the previously discussed reference-free path length interferometry of random media [29].