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 four orders of magnitude above that of multimode fibres of a similar size, and discuss analogies with the transmission profile of a Fabry–Pérot interferometer.

Many areas of optical science require an accurate measurement of optical spectra. Devices based on laser speckle promise compact wavelength measurement, with attometer-level sensitivity demonstrated for single wavelength laser fields. The measurement of multimode spectra using this approach would be attractive, yet this is currently limited to picometer resolution. Here, we present a method to improve the resolution and precision of speckle-based multi-wavelength measurements. We measure multiple wavelengths simultaneously, in a device comprising a single 1 m-long stepindex multimode fiber and a fast camera. Independent wavelengths separated by as little as 1 fm are retrieved with 0.2 fm precision using Principal Component Analysis. The method offers a viable way to measure sparse spectra containing multiple individual lines and is likely to find application in the tracking of multiple lasers in fields such as portable quantum technologies and optical telecommunications.The speckle produced when coherent light is scattered by a rough surface can provide a surprising method with which one can track the properties of the incoming light. The precise speckle pattern produced by this multipleinterference is uniquely determined by the beam parameters, and can therefore be used as a fingerprint for linewidth [1], polarization [2], beam position [3] or transverse mode characteristics [4]. Broadband spectrometers have been constructed which extract the spectrum of light from the speckle, by using either the transmission matrix method ([5-8]) or deep learning [9], achieving a spectral resolution limited by speckle correlation. Typically, this speckle correlation limit is on the picometerscale. For monochromatic light, speckle wavemeters utilizing Principal Component Analysis (PCA) [10-12], Poincaré descriptors [13] and convolutional neural networks [14] have greatly surpassed this limit, measuring an isolated wavelength with a resolution down to the attometer-scale. It remains an open challenge to simultaneously measure multiple wavelengths or spectra at such high resolution using speckle. A successful method promises applicability in laser stabilization for portable cold atoms experiments, wavelength-division multiplexed telecommunications and chemical sensing.In this letter, we demonstrate that the high resolution achieved by using PCA to analyze speckle can be extended beyond a single laser-line, to measure sparse spectra composed of multiple laser wavelengths. We establish that wavelength measurements of lasers separated by 1 fm, five orders of magnitude less than the speckle correlation limit, can be performed simultaneously and with an accuracy of 0.2 fm. Simultaneous measurement of up to ten laser lines is demonstrated.The principle of measurement is outlined in Fig. 1. A single scattering element is illuminated by a beam composed of multiple wavelengths; each wavelength is * gdb2@st-andrews.ac.uk l 1 + l 2 FIG. 1. Principle of multi-wavelength measurement in a speckle wavemeter. Laser beams are overlapped and illum...

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.

Aims. We aim to study the presence of superoscillations in coronal magnetoacoustic (MHD) waves and their possible role in heating coronal loops through the strong and localised gradients that they generate on the wave. Methods. An analytic model is built for the transition between sausage and kink wave modes propagating along field lines in the corona. We compute in this model the local frequencies, the wave gradients, and the associated heating rates due to compressive viscosity. Results. We find superoscillations associated with the transition between wave modes accompanying the wave dislocation that shifts through the wave domain. Frequencies ten times higher than the normal frequency are found. This means that a typical three-minute coronal wave will oscillate locally in 10 to 20 s. Such high frequencies bring up strong gradients that efficiently dissipate the wave through compressive viscosity. We compute the associated heating rates; locally, they are very strong, largely compensating typical radiative losses. Conclusions. We find a new heating mechanism associated to magnetoacoustic waves in the corona. Heating due to superoscillations only happens along particular field lines with small cross sections, comparable in size to coronal loops, inside the much larger magnetic flux tubes and wave propagation domain.