3D mapping in optical trapping of polystyrene particles applying the Gerchberg-Saxton modified with 2D Legendre polynomials

We are focused on the phase retrieval and 3D profiles of microparticles (MP), analyzed in optical trapping. To this aim, we use several image segmentation procedures of MP from an optical trapping video. Moreover, we implement different procedures to remove several errors in the segmented image by means of algorithms based on the Legendre polynomials to enhance the MP image quality, as well as the errors caused by the drift inducing a shift in the MP (considering different MP with drift by shift, static, trapped and untrapped). Once the image corrections are conducted considering these errors, we propose some processes to recover the irradiance distribution of the MP in the image, from which it is possible to retrieve the MP phase to show their 3D profiles as 3D objects. Finally, we analyze the image in gray tones and use different retrieval methods with 2D Legendre polynomials, Gerchberg-Saxton (GS), Goldstein, and Quality Guided. We propose some modifications to such algorithms using Legendre polynomials, resulting in the deformation re-scaling iterative algorithm, ModI-LP, and a modified GS using the 2D-LP code to optimize our results.