Abstract
Laser speckle is generated by the multiple interference of light through a disordered medium. Here we study the premise that the speckle pattern retains information about the polarisation state of the incident field. We analytically verify that a linear relation exists between the Stokes vector of the light and the resulting speckle pattern. As a result, the polarisation state of a beam can be measured from the speckle pattern using a transmission matrix approach. We perform a quantitative analysis of the accuracy of the transmission matrix method to measure randomly time-varying polarisation states. In experiment, we find that the Stokes parameters of light from a diode laser can be retrieved with an uncertainty of 0.05 using speckle images of 150×150 pixels and 17 training states. We show both analytically and in experiment that this approach may be extended to the case of more than one laser field, demonstrating the measurement of the Stokes parameters of two laser beams simultaneously from a single speckle pattern and achieving the same uncertainty of 0.05.
Highlights
When coherent light is diffused by a disordered medium, it produces a typical granular pattern called speckle
We provide a demonstration verifying the linearity between the Stokes vector of the input beam and the resulting speckle pattern, and extend this result to the case of multiple beams
We derive an expression for the linearity that exists between the polarisation state and the speckle pattern, which is at the core of the transmission matrix method
Summary
When coherent light is diffused by a disordered medium, it produces a typical granular pattern called speckle. This has been applied to many types of measurements, such as displacement [2,3,4,5], vibration and sound [6,7], and blood flow mapping in tissues [8], among many others Another approach is to consider the diffuser to be constant in time, in which case the speckle pattern can be harnessed to probe properties of the incident light. We extend the method to show that the polarisation state of multiple beams can be measured simultaneously from one single speckle pattern We demonstrate this experimentally for the case of two light fields. Such an approach may have applications in optical telecommunications, optical manipulation of birefringent particles and polarisation microscopy
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