Optical interferometry, with applications ranging from measuring the speed of light to detecting gravitational waves, is a powerful metrology tool. Traditional methods often require precise optical geometries. Speckle metrology offers an alternative, using the interferometric properties of disordered light to achieve high sensitivity, but it's typically limited by time-domain analysis and image acquisition rates. This research introduces a novel 3D stochastic interferometer that uses a frequency-domain approach to overcome these limitations. By employing a centimeter-sized, arbitrarily shaped cavity with high Lambertian reflectivity and filling it with a coherent monochromatic photon gas, the researchers create a 3D speckle field sensitive to minute fluctuations in the optical volume. This approach enables the detection of picometer-scale deformations and dielectric fluctuations with significantly enhanced sensitivity compared to existing techniques, opening new possibilities in various fields of metrology and materials science.

Existing speckle metrology methods rely on time-domain analysis of speckle patterns, limiting their frequency response to the image acquisition rate. The authors cite examples of speckle metrology's use in wavelength determination, spectral analysis, small angle and displacement metrology, and refractive index sensing. However, they highlight the lack of frequency-domain approaches in existing speckle metrology, which restricts the analysis to the limitations of image acquisition rates. The study aims to address this gap by developing a frequency-domain approach capable of detecting high-frequency fluctuations.

The researchers constructed a 3D stochastic interferometer using a centimeter-sized cavity with walls made of compressed quartz powder, providing uniform Lambertian reflectivity and high albedo. A single-frequency laser (λ = 660 nm, λcoh = 95 m) was coupled into the cavity, creating a 3D speckle field. The intensity fluctuations of a single speckle grain were measured using a single-mode fiber that splits the light to two avalanche photodiodes and a digital correlator, providing the intensity autocorrelation function. The cavity's high reflectivity (finesse of 10,500) and long average photon transit path (62 m) amplify the sensitivity. Experiments involved measuring the interferometric response to harmonic cavity deformations using piezo actuators and to minute dielectric fluctuations using various scattering samples (jammed emulsions and suspensions of PMMA spheres). The normalized intensity autocorrelation function was analyzed to quantify the decorrelation caused by these perturbations. The data acquisition and analysis procedures, including baseline subtraction, normalization, and signal-to-noise ratio calculation, are detailed. The authors use a 16/8 multi-tau correlation scheme, addressing dead-time and afterpulse artifacts through cross-correlation between two photodiodes. A comprehensive explanation of the construction and optical properties of the quartz powder cavities is provided, along with details of the optical setup, environmental control, and specific experimental parameters for the piezo-actuator and intra-cavity sample experiments.

The 3D stochastic interferometer demonstrated exceptional sensitivity. Cavity deformations were detected with a power noise floor of 4 × 10⁻³ pm², corresponding to a 2.7 pm sensitivity at 1 kHz. The frequency spectrum was sensitive to volume deformations across 8–10 frequency decades below 100 MHz. Probing thermal motions of scattering colloids, the interferometer showed a 100-fold sensitivity gain compared to conventional light scattering techniques. The interferometer's response to picometer deformations was linear up to approximately 1 nm. For jammed emulsions of oil-in-water droplets, the speckle intensity decorrelation scaled linearly with the mean-square displacement of the droplets, showcasing the ability to measure sub-nanometer thermal motions. Experiments with PMMA microsphere suspensions in water showed a sensitivity to 1 nm rms displacements, with a significantly improved dynamic range compared to conventional dynamic light scattering (DLS) techniques. The sensitivity is explained through the amplification of the signal by multiple scattering in the cavity, which acts as a random paths integrator for geometric and dielectric fluctuations within the optical volume.

The findings demonstrate that the 3D stochastic interferometer offers a significant advance in sensitivity and frequency range compared to existing speckle metrology and light scattering techniques. The non-local nature of the measurement, where the detector probes all perturbations regardless of location, is a key advantage. The high sensitivity stems from the long photon path length and high reflectivity of the cavity, effectively amplifying the signal. The observed picometer sensitivity validates the theoretical predictions, while the discrepancies are attributed to the simplifications in the theoretical model (e.g., neglecting the effect of the fiber's shadow on the 3D Berry field). The enhanced sensitivity for measuring thermal motions of colloids opens possibilities for studying the dynamics of soft matter and biological systems. The work also highlights the need for further theoretical development to fully understand the amplification mechanisms of light scattering in the cavity and to better define the concept of “optical volume”.

This research successfully demonstrated a novel 3D stochastic interferometer capable of highly sensitive picometer-level detection of both cavity deformations and dielectric fluctuations. The frequency-domain approach overcomes limitations of previous time-domain speckle techniques. Future work should focus on refining the theoretical model to fully account for the observed amplification effects and exploring applications in diverse areas, such as ultrasensitive dielectric spectroscopy, dynamic light scattering of diluted samples, and force field detection.

The theoretical model simplifies the complex 3D speckle field by considering only the 2D projection onto the fiber's aperture. This simplification may lead to an underestimation of the interferometer's sensitivity. The fiber itself perturbs the spherical symmetry of the speckle field, affecting the measurements. The dynamic range is ultimately limited by the noise floor and the unity decorrelation ceiling. Furthermore, the sensitivity may be dependent on the specific nature and position of the perturbation inside the cavity.