## 3 PS-DHI Applications
### Microelectronics and Nanophotonic Quantitative Phase Imaging  
Since PS-DHI has been introduced in the literature, it has been applied on samples with well-known SoP, such as bent fiber [16], stressed polymer [15], waveplates [39; 40], or liquid crystals (LCs) [47], just to confirm the potentiality offered by this technique. Among these applications, LC seems to be the most interestingly due to their uses in the display. For example, [PERSON] et al. [49] measured the spatially resolved Jones matrix components of the light passing through the single pixel of a liquid-crystal display (LCD) as a function of the applied voltage to the LCD panel by using PS-DHI. However, in the proposed setup, the authors need to acquire four independent interferograms with two different polarization states to reconstruct Jones matrix components map from a sample, thus the properties of PS-DHI are not fully exploited. In the published work, an in-plane switching liquid-crystal display (IPS-LCD) was characterized. However, the same approach can be used to feature also other types of LCDs--for example, full RGB channels of LCD pixels can be characterized in terms of their Jones matrix components using a DH setup with multiple lasers or in spectroscopic modality. An LC depolarizer was characterized using PS-DHI with the scheme reported in Figure 5b by [PERSON] et al. [47]. In this case, the LC depolarizer consists in a collection of HWPs with optical axes randomly distributed and the Stokes parameters distribution of the output beams for a linear incident polarized beam with \(\theta=\pi/4\) and for left-handed circularly polarized incident beam were measured, confirming the depolarizing effect induced by LC [47]. Regarding nanophotonics applications, images obtained with DHI have the disadvantage of being limited by the diffraction limit and, thus, a device in the nanometres size typically covers just a few camera pixels leading to a low resolution. On the other hand, a full field radiation pattern (i.e., polarization, amplitude, and phase) measurement at all angles gives a complete polarizability tomography of nanophotonic devices such as metasurfaces and nanoantennae. For this reason, [PERSON] et al. [53] have combined Fourier microscopy, polarimetry, and digital holography, generating a signal over an entire CCD chip, for angle-resolved amplitude, polarization, and phase imaging of single nano-objects. In particular, the authors analyzed the orbital angular momentum (OAM) content of light scattered by a family of plasmonic spirals. In Figure 7 results obtained in Ref. [53] are summarized; the intensity radiation distribution is recorded by a Fourier microscope (Figure 7a--logarithmic scale). Then, the Stokes parameters are determined by polarization-resolved imaging; these parameters completely define the SoP of the wavefront for each wave vector in the radiation pattern and, consequently, can be transformed in the polarization ellipse parameters--namely, the ellipticity and the orientation angles (Appendix A, Equation (A5)). The evaluated ellipse parameters are shown in Figure 7b and a complete helicity conversion in a doughnut-like pattern with five spiraling arms around it can be observed. Finally, by using DHI the individual phase profiles of two orthogonally polarized field components were retrieved; in Figure 7c the representation in the Fourier transform domain of a hologram corresponding to an m = \(-5\) spiral in circular co-polarization is reported, while in Figure 7d the two evaluated phase maps related to the co- and cross-polarized channel are shown and for this latter channel, the helical shape around the optical axis is clearly visible. As suggested by [PERSON] et al.