The detection of the longitudinal component of a highly focused electromagnetic beam is not a simple task. Although in recent years several methods have been reported in the literature, this measure is still not routinely performed. This paper describes a method that allows us to estimate and visualize the longitudinal component of the field in a relatively simple way. First, we measure the transverse components of the focused field in several planes normal to the optical axis. Then, we determine the complex amplitude of the two transverse field components: the phase is obtained using a phase recovery algorithm, while the phase difference between the two components is determined from the Stokes parameters. Finally, the longitudinal component is estimated using the Gauss’s theorem. Experimental results show an excellent agreement with theoretical predictions.

We introduce an algorithm able to map arbitrary complex values into an arbitrary modulation curve using the K-Nearest Neighbor algorithm. The proposed algorithm is around 80 times faster than the conventional calculation.

Document signature is a powerful technique used to determine whether a message is tampered or valid. Recently, this concept was extended to optical codes: we demonstrated that the combined use of optical techniques and machine learning algorithms might be able to distinguish among different classes of samples. In the present work, we produce nano particle encoded optical codes with predetermined designs synthesized with a 3D printer. We used conventional polylactic acid filament filled with metallic powder to include the effect of nano-encoding for unique polarimetric signatures. We investigated an interesting real-world scenario, that is, we demonstrate how a single class of codes is distinguished among a group of samples to be rejected. This is a difficult unbalanced problem since the number of polarimetric signatures that characterize the true class is small compared to the complete dataset. Each sample is characterized by analyzing the polarization state of the emerging light. Using the one class-support vector machine algorithm we found high accuracy figures in the recognition of the true class codes. To the best of our knowledge, this is the first report on implementing optical codes with nano particle encoded materials using 3D printing technology.

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This chapter describes an efficient approach to generating light beams with arbitrary intensity profile and phase distribution. Accordingly, a fast method is described to characterize liquid crystal displays based on the Mach-Zehnder interferometer and fringe analysis in the Fourier domain. Then, the double-pixel hologram Arrizón’s approach is reviewed. This approach is able to generate an on-axis computer-generated hologram into a low-resolution twisted-nematic liquid crystal for encoding arbitrary complex modulations. Furthermore, a fast algorithm to map holographic cells based on the k-nearest neighbor (k-NN) classifier is introduced in order to generate computer-generated holograms faster than the conventional calculation. Finally, two beam profiles are produced with the described approach and assessed at the entrance pupil and the depth of focus of a high-NA microscope objective.