Polarization is one of the fundamental properties of light waves and an important carrier of information. The technique of measuring polarization is known as polarimetry. Compared with traditional intensity detection methods, polarimetry can significantly enhance the ability to acquire and analyze target information by fully utilizing the polarization characteristics of light waves. Due to its unique advantages, polarimetry has been widely used in various fields such as remote sensing, industrial inspection, biomedical, and environmental monitoring.

The key to polarimetry is to obtain the Stokes vector of the measured light waves or the Mueller matrix of the measured sample, which correspond to the Stokes polarimetry and Mueller matrix polarimetry, respectively. Several methods have been proposed for achieving Stokes polarimetry and Mueller matrix polarimetry, including multi-channel polarimetry, temporally modulated polarimetry, spectral polarization modulated polarimetry, and spatially modulated polarimetry. In the multi-channel method, the incident beam is split into several channels with different polarization optics for analyzing the polarization state. In the last three methods, the incident light is modulated in the time domain, spectral domain, or spatial domain for measuring polarization information. The multi-channel scheme is competent for real-time monitoring, but its configuration is usually complicated to adjust. The configuration of temporally modulated polarimetry is compact, but it is restricted by poor stability and slow measurement speed. The spectral polarization modulated polarimetry obtains polarization information at a single integration interval without rotating or active components, but its measurement accuracy is limited, and its wave band is narrow. In contrast, spatially modulated polarimetry modulates the polarization information at different spatial locations by using the spatial modulation components, and it has the advantage of stability, rapidness, and compactness, so it is a promising technique for polarization measurement.

Numerous review articles have provided comprehensive summaries of multi-channel polarimetry, temporally modulated polarimetry, and spectral polarization modulated polarimetry. However, little attention has been given to spatially modulated polarimetry. With the increasing maturity of micro-nano fabrication and optical field control technologies, various spatial modulation devices such as vortex retarders, azimuthal polarizers, and S-waveplates have been fabricated with high quality and have gained important applications in the field of polarization detection. Therefore, it is crucial and imperative to consolidate the current research about spatially modulated polarimetry to guide the future development of this field more rationally.

Firstly, the working principles and technical characteristics of various spatially modulated Stokes polarimeters and Mueller matrix polarimeters are analyzed and summarized. In these spatially modulated polarimeters, vector optical beams with spatially inhomogeneous polarization distributions or spatial polarization modulation components such as micro-polarizer arrays, polarization grating, azimuthal or radial polarizers, Savart polariscopes, and handmade axisymmetric quarter-wave plates have been utilized to modulate the spatial distribution of light intensity. This enables the measurement of polarization information in a stable, rapid, and compact way. However, it should be noted that the existing spatially modulated polarimetry is limited by the hard fabrication, poor modulation quality of the spatial polarization modulation components, complex processing procedures, and low accuracy. In particular, there is no configuration yet that can realize accurate Mueller matrix measurement experimentally with the spatial polarization modulation technique.

Secondly, in order to overcome the drawbacks of the traditional spatially modulated polarimeters, vortex retarders with the advantages of mature fabricating processes, good wavelength and temperature stability, high modulation quality, and low cost are utilized to construct the high-performance spatially modulated polarimeter. The vortex half-wave retarder-based Stokes polarimeter (Fig. 9) can achieve polarization measurement in a single shot, and it is fast, stable, and easy to implement. However, the measurement accuracy of the vortex retarder-based Stokes polarimeter is limited by various error sources. In order to reduce the measurement error, an efficient calibration method is proposed by analyzing the general effects of the different error sources on the intensity modulation curve of the incident waves with the Stokes-Mueller formalism. The error calibration method can effectively reduce the measurement error from about 0.05 to less than 0.01 (Fig. 12). The proposed vortex half-wave-based Stokes polarimeter lacks the capability of detecting circular polarization components because the fourth Stokes parameter is calculated indirectly, and the handedness of the input light cannot be recognized. In order to directly measure all the Stokes parameters, a vortex quarter-wave retarder is employed to substitute the vortex half-wave retarder, and experiments show that the measurement accuracy of the vortex quarter-wave retarder-based polarimeter is less than 0.035 (Fig. 13). Based on the vortex retarder-based Stokes polarimeter, a complete dual vortex retarder Mueller matrix polarimetry (Fig. 14) is proposed and experimentally verified by using two vortex quarter wave retarders with different orders in polarization state generation (PSG) arm and polarization state analyzer (PSA) arm, and the maximum absolute error is less than 0.04 (Fig. 16).

The spatially modulated polarimetry has the advantages of simple optical structure, good stability, fast measurement speed, and high accuracy, and it is promising in target detection and recognition, industrial and biochemical detection, and many other fields. As for the perspective of spatially modulated polarimetry, one direction may be smart polarimetry, which is expected to improve the speed and accuracy of image processing and reduce the prior information of the sample and the technical requirements for operators in polarimetry. In addition, the metasurfaces can be utilized to achieve polarization measurement in a compact size. Furthermore, spatially modulated polarimeters should overcome the limitations in spatial resolution and spectral measurement to expand their application fields.