Wavelength sensitivity of the speckle patterns produced by an integrating sphere

TL;DR

This paper models how speckle patterns from an integrating sphere respond to wavelength changes, revealing high sensitivity influenced by sphere size and reflectivity, with potential advantages over fiber-based methods.

Contribution

It provides the first comprehensive model of wavelength sensitivity in speckle patterns generated by integrating spheres, highlighting key parameters affecting sensitivity.

Findings

Sensitivity is mainly governed by sphere radius and reflectivity.

Integrating spheres outperform multimode fibers in wavelength sensitivity by three orders of magnitude.

Analogies with Fabry-Pérot interferometers are discussed.

Abstract

Speckle metrology is a powerful tool in the measurement of wavelength and spectra. Recently, speckle produced by multiple reflections inside an integrating sphere has been proposed and showed high performance. However, to our knowledge, a complete characterisation of speckle sensitivity to wavelength in that geometry has not been performed to date. In this work, we derive a general model predicting the variation in a speckle pattern as a result of a generic transformation. Applying this to a shift in the incident wavelength, we show that the speckle sensitivity is mainly governed by the radius and surface reflectivity of the sphere. We show that integrating spheres offer sensitivity three orders of magnitude above that of multimode fibres of a similar size, and discuss analogies with the transmission line of a Fabry-P\'erot interferometer.