It is found that the exact equations governing motion of Foucault pendulum take a simpler form when describing pendulum's position as complex number evolving in plane. In this description, three notable effects (the intrinsic precession, and Crane effect) appear natural solutions without prior assumptions on their precessional nature. The pedagogical value problem discussed, emphasizing its connections to time-reversal symmetry use numbers two-dimensional problems.

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 showed high performance. However, to our knowledge, complete characterisation sensitivity that geometry not performed date. In this work, we derive general model predicting variation pattern as result generic transformation. Applying shift incident wavelength, show mainly governed radius surface reflectivity...

Highly resolved determination of refractive index is vital in fields ranging from biosensing through to laser range finding. Laser speckle known be a sensitive probe the properties light and environment, but date speckle-based measurements have been restricted 10-6 resolution. In this work we identify strategy optimize sensitivity changes, namely, by maximizing width distribution optical path lengths medium. We show that can realized experimentally encapsulating medium interest within an...

As the fields of optical microscopy, semiconductor technology and fundamental science increasingly aim for precision at or below nanoscale, there is a burgeoning demand sub-nanometric displacement position sensing. We show that speckle patterns produced by multiple reflections light inside an integrating sphere provide exceptionally sensitive probe displacement. use split into two independent hemispheres, one which free to move in any given direction. The relative motion hemispheres produces...

Many areas of optical science require an accurate measurement spectra. Devices based on laser speckle promise compact wavelength measurement, with attometer-level sensitivity demonstrated for single fields. The multimode spectra using this approach would be attractive, yet is currently limited to picometer resolution. Here, we present a method improve the resolution and precision speckle-based multi-wavelength measurements. We measure multiple wavelengths simultaneously, in device comprising...

Laser speckle is generated by the multiple interference of light through a disordered medium. Here we study premise that pattern retains information about polarisation state incident field. We analytically verify linear relation exists between Stokes vector and resulting pattern. As result, beam can be measured from using transmission matrix approach. perform quantitative analysis accuracy method to measure randomly time-varying states. In experiment, find parameters diode laser retrieved...

Aims: To study the presence of superoscillations in coronal magnetoacoustic waves and its possible role heating loops through strong localized gradients they generate on wave. Methods: An analytic model is built for transition between a sausage kink wave modes propagating along field lines corona. We compute this local frequencies, associated rates due to compressive viscosity. Results: find with accompanying dislocation that shifts domain. Frequencies 10 times higher than normal frequency...

Speckle patterns are a powerful tool for high-precision metrology, as they allow remarkable performance in relatively simple setups. Nonetheless, researchers this field follow rather distinct paths due to underappreciated general principles underlying speckle phenomena. Here, we advise on universal metric of intrinsic sensitivity, and the advantages disadvantages multiple scattering. This will catalyse progress metrology but also translate other domains disordered optics which undergoing...

Speckle patterns are sensitive to wavelength variations, and can be used measure such variations. Recently, a new way of producing speckles have been introduced, using an integrating sphere. Here, we derive general model predicting the change occurring in speckle pattern as result generic transformation this particular geometry. Applying variation, show that sensitivity is mainly governed by two parameters: radius surface reflectivity We analytically experimentally spheres offer four orders...

As the fields of optical microscopy, semiconductor technology and fundamental science increasingly aim for precision at or below nanoscale, there is a burgeoning demand sub-nanometric displacement position sensing. We show that speckle patterns produced by multiple reflections light inside an integrating sphere provide exceptionally sensitive probe displacement. use split into two equal independent hemispheres, one which free to move in any given direction. The relative motion hemispheres...

Speckle, the granular interference pattern produced when coherent light is scattered by a rough surface, commonly thought to be detrimental optical systems. But scattering processes are entirely linear, and speckle can therefore used as surprisingly sensitive probe of properties light, environment scatterer. We review current progress in measuring wavelength, polarisation topological charge light; refractive index environment; displacement surface. In particular, we show how sensitivity...

Speckle patterns have proven to be a versatile tool in various areas of metrology. Different levels resolution been achieved depending on how the speckles are produced and analysis method that is employed. We show three particular applications speckle metrology: measurement refractive index variation (10^-10 uncertainty), wavelength variations (10^-18 m displacement (10^-11 where uncertainties made very low by an appropriate choice scattering geometry method. explore this both analytically...

Highly-resolved determination of refractive index is vital in fields ranging from biosensing through to laser range-finding. Laser speckle known be a sensitive probe the properties light and environment, but date speckle-based measurements have been restricted $10^{-6}$ resolution. In this work we identify strategy optimise sensitivity changes, namely by maximising width distribution optical path lengths medium. We show that can realised experimentally encapsulating medium interest within an...