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Optical interferometry has proven extremely powerful to investigate some ofthe most fundamental laws of physics, using light with very preciselycontrolled geometry. In the past few decades, various speckle metrology methodshave emerged to harness the interferometric properties of strongly disorderedlight instead, using time-domain analysis of speckle patterns at a maximum ratelimited by the frequency of image acquisition. The present work is based onusing a centimeter-sized quartz-powder cavity with an arbitrary shape that isengineered with very high Lambertian reflectivity. When filled with a coherentmonochromatic photon gas, a statistically isotropic and homogeneous 3D speckleinterference pattern is obtained. A single-mode fiber is then used incombination with photon number autocorrelation analysis to detect minutechanges of the speckle decorrelation spectrum, caused either by cavitydeformations or fluctuations of the dielectric tensor field inside. Thedecorrelation spectrum is acquired over 8 to 10 frequency decades below 100MHz, with a sensitivity that is only limited by the intrinsic photon statisticsand the extrinsic instrumental noises. With typically 1700 reflections and anaverage photon transit path length of 62m, our 3D stochastic interferometeryields a typical finesse of 10500, and cavity deformations are detected in anergodic fashion over a six-decade dynamic range with a power noise floor of4x{10}^{-3} pm^2 which corresponds to 2.7 pm at 1 kHz. The cavity also operatesas a speckle fluctuation amplifier that reveals decorrelation spectra due topicometric thermal motions of colloids in both single and multiple scatteringregimes with a typical 100-fold sensitivity gain compared to conventional lightscattering techniques.

3D stochastic interferometer detects picometer deformations and minute dielectric fluctuations of its optical volume