## 4 Conclusions  
PS-DHI is a flexible, useful development of DHI; indeed, only a few changes to the standard DH setup are required to obtain polarization-based imaging. However, innovative solutions were also developed. The requirement of a single-shot imaging and high processing speed significantly improve the operation of the measurement process making this approach more appropriate for real-time multiple analyses. Moreover, the full SoP and phase distribution for an arbitrary light field can be easily and quickly measured by PS-DHI based on the geometric phase.  
In this context, this review paper presents a brief introduction to the basic principles underlying PS-DHI and an overview of some enhancements in its technology development. To the best of our knowledge, there are no other reviews on this topic. Therefore, it is our belief that this work could help researchers who work in this field. Even if PS-DHI is a fairly established research line (the first work proving its feasibility dates back to 1999 [17], while in the past 20 years, many works have been published to introduce improvements to the technique), there are currently only a few applications presented in the literature. Among these, the most promising are in the fields of microelectronics, photonics and biomedical imaging. Since it has been demonstrated with other more complex techniques that birefringence and, in general, SoP modification induced by biological and electronics samples can  
Figure 9: Illustration of quantitative fourth-generation optics microscopy (Q4 GOM). (**a**) Experimental setup using 4G optics module connected to microscope with a polarization adapted interference objective. P\({}_{1}\): input polarizer; L\({}_{1}\), IL\({}_{2}\): illumination lenses; MMO: Mirau microscope objective; BS\({}_{1}\): pellicle beam splitter; QWP\({}_{1}\), QWP\({}_{2}\), QWP\({}_{3}\): quarter-wave plates; M: reference mirror; BS\({}_{2}\): beam splitter cube; TL: tube lens; GPG: geometric-phase grating; L\({}_{1}\): first Fourier lens; P\({}_{2}\): analyzer; L\({}_{2}\): second Fourier lens; CCD: charged coupled device. (**b**) Polarization-adapted Mirau microscope objective (MMO) used for imaging of isotropic samples. (**c**) Polarization sensitive transformation of light by geometric phase grating. (**d**) The quantitative phase retardance imaging of human cheek cells. At the top a comparison of the quantitative phase imaging (left) and bright field image (right) of the marked area (adapted from [PERSON] et al. [76]).  
indicate their status (e.g., the healthy state of some cells [54; 55; 56; 69; 70] or the stress-strain induced in some materials [15; 16]), and considering the achievements of PS-DHI in microelectronics, photonics, and biomedical imaging of the past few years, new technological developments, such as the use of quantum holography, which is a recent fascinating line of research, and new potential applications are expected in the next years.  
Conceptualization, M.A.F. and G.C.; investigation, M.A.F. and G.C.; data curation, M.A.F. and G.C.; writing--original draft preparation, M.A.F. and G.C.; writing--review and editing, M.A.F. and G.C.; supervision, M.A.F. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.