Troubleshooting sketchup Stokes problems using spectroscopic Stokes additional parameter based on the Fourier transform spectrometer partition method

Author(s): Fernanda Cipriano

[1]The Navier-Stokes (N-S) equations are solved in 3D incompressible viscous flow problems with and without through-flow boundaries using an alternate vector potential formulation. The application of boundary conditions for through-flow borders and the numerical treatment of fourth-order partial differential equations are challenging aspects of the vector potential formulation. On the other hand, benefits include decoupling pressure from velocity and automated fulfilment of the continuity equation. The purpose of this study is to introduce the proper gauge and boundary conditions to the localised meshless vector potential formulation. A Coulomb gauge condition is imposed on the vector potential to guarantee its existence and singularity analytically, handling the divergence-free quality. For measuring the spectroscopic Stokes parameters with a Fourier transform spectrometer, two approaches are suggested. [2]It is intended for single point measurement in the first approach. Using an optical set-up that includes a white light source, a polarizer set to 0, a quarter-wave plate, and a scanning Michelson interferometer, the parameters are recovered. The parameters for the suggested method are taken from the interferogram intensity distributions obtained with the quarter-wave plate rotated to 0°, 22.5°, 45°, and 45°, respectively. For the second strategy, a specific angle design in a polarizer and a quarter-wave plate can be used to create a full-field and dynamic measurement based on the first technique. Consequently, using a pixelated phaseretarder and polarizer, it is also possible to simultaneously extract the interferograms of two-dimensional detection. Based on a multi-channel analogue to digital converter and parallel read-out circuit with a high-speed CCD camera. As a result, a full-field, dynamic Stokes polarimetry without any spinning parts may be created. Both numerical and experimental evidence is presented to support the efficacy of the suggested strategies. According to the authors’ knowledge, this might be the most straightforward optical setup for obtaining the spectral Stokes parameters. It’s significant that the latter technique avoids the necessity for rotating optical system components and so offers a simple experimental method for obtaining the dynamic spectral Stokes parameters.