A computer-controlled Mueller matrix polarimeter with dual rotating retarders is described. Bulk properties of optical materials are determined by controlling the input-polarization state and measuring the output-polarization state. The Mueller matrix of a sample is obtained from polarimetric measurements, and polarization properties, i.e., diattenuation and retardance as well as depolarization, are extracted from the Mueller matrix. Further, fundamental electro- and magneto-optical material properties such as the electro-optical tensor coefficients may be obtained from Mueller matrices measured with applied fields. The polarimeter is currently configured to operate over the 3- to 12-microm spectral region.

Mueller matrix dual-rotating retarder polarimeter

Polarimetry is one of the most promising types of remote sensing for improved characterization of atmospheric aerosol. Indeed, aerosol particles constitute a highly variable atmospheric component characterized by a large number of parameters describing particle sizes, morphologies (including shape and internal structure), absorption and scattering properties, amounts, horizontal and vertical distribution, etc. Reliable monitoring of all these parameters is very challenging, and therefore the aerosol effects on climate and environment are considered to be among the most uncertain factors in climate and environmental research. In this regard, observations that provide both the angular distribution of the scattered atmospheric radiation as well as its polarization state at multiple wavelengths covering the UV–SWIR spectral range carry substantial implicit information on the atmospheric composition. Therefore, high expectations in improving aerosol characterization are associated with detailed passive photopolarimetric observations. The critical need to use space-borne polarimetry for global accurate monitoring of detailed aerosol properties was first articulated in the late 1980s and early 1990s. By now, several orbital instruments have already provided polarization observations from space, and a number of advanced missions are scheduled for launch in the coming years by international and national space agencies. The first and most extensive record of polarimetric imagery was provided by POLDER-I, POLDER-II, and POLDER/PARASOL multi-angle multi-spectral polarization sensors. Polarimetric observations with the POLDER-like design intended for collecting extensive multi-angular multi-spectral measurements will be provided by several instruments, such as the MAI/TG-2, CAPI/TanSat, and DPC/GF-5 sensors recently launched by the Chinese Space Agency. Instruments such as the 3MI/MetOp-SG, MAIA, SpexOne and HARP2 on PACE, POSP, SMAC, PCF, DPC–Lidar, ScanPol and MSIP/Aerosol-UA, MAP/Copernicus CO2 Monitoring, etc. are planned to be launched by different space agencies in the coming decade. The concepts of these future instruments, their technical designs, and the accompanying algorithm development have been tested intensively and analyzed using diverse airborne prototypes. Certain polarimetric capabilities have also been implemented in such satellite sensors as GOME-2/MetOp and SGLI/GCOM-C. A number of aerosol retrieval products have been developed based on the available measurements and successfully used for different scientific applications. However, the completeness and accuracy of aerosol data operationally derived from polarimetry do not yet appear to have reached the accuracy levels implied by theoretical sensitivity studies that analyzed the potential information content of satellite polarimetry. As a result, the dataset provided by MODIS is still most frequently used by the scientific community, yet this sensor has neither polarimetric nor multi-angular capabilities. Admittedly polarimetric multi-angular observations are highly complex and have extra sensitivities to aerosol particle morphology, vertical variability of aerosol properties, polarization of surface reflectance, etc. As such, they necessitate state-of-the-art forward modeling based on first-principles physics which remains rare, and conventional retrieval approaches based on look-up tables turn out to be unsuitable to fully exploit the information implicit in the measurements. Several new-generation retrieval approaches have recently been proposed to address these challenges. These methods use improved forward modeling of atmospheric (polarized) radiances and implement a search in the continuous space of solutions using rigorous statistically optimized inversions. Such techniques provide more accurate retrievals of the main aerosol parameters such as aerosol optical thickness and yield additional parameters such as aerosol absorption. However, the operational implementation of advanced retrieval approaches generally requires a significant extra effort, and the forward-modeling part of such retrievals still needs to be substantially improved. Ground-based passive polarimetric measurements have also been evolving over the past decade. Although polarimetry helps improve aerosol characterization, especially of the fine aerosol mode, the operators of major observational networks such as AERONET remain reluctant to include polarimetric measurements as part of routine retrievals owing to their high complexity and notable increase in effort required to acquire and interpret polarization data. In addition to remote-sensing observations, polarimetric characteristics of aerosol scattering have been measured in situ as well as in the laboratory using polar nephelometers. Such measurements constitute direct observations of single scattering with no contributions from multiple scattering effects and therefore provide unique data for the validation of aerosol optical models and retrieval concepts. This article overviews the above-mentioned polarimetric observations, their history and expected developments, and the state of resulting aerosol products. It also discusses the main achievements and challenges in the exploitation of polarimetry for the improved characterization of atmospheric aerosols.

https://hal.archives-ouvertes.fr/hal-03009287/document

Polarimetric remote sensing of atmospheric aerosols: Instruments, methodologies, results, and perspectives

Utilization of Mueller matrix formalism to obtain optical targets depolarization and polarization properties

The Air Force Institute of Technology

Preface Acknowledgements 1. Introduction 2. The macroscopic Maxwell equations and monochromatic fields 3. Fundamental homogeneous-medium solutions of the macroscopic Maxwell equations 4. Basic theory of frequency-domain electromagnetic scattering by a fixed finite object 5. Far-field scattering 6. The Foldy equations 7. The Stokes parameters 8. Poynting-Stokes tensor 9. Polychromatic electromagnetic fields 10. Polychromatic scattering by fixed and randomly changing objects 11. Measurement of electromagnetic energy flow 12. Measurement of the Stokes parameters 13. Description of far-field scattering in terms of actual optical observables 14. Electromagnetic scattering by a small random group of sparsely distributed particles 15. Statistically isotropic and mirror-symmetric random particles 16. Numerical computations and laboratory measurements of electromagnetic scattering 17. Far-field observables: qualitative and quantitative traits 18. Electromagnetic scattering by discrete random media: far field 19. Near-field scattering by a sparse discrete random medium: microphysical radiative transfer theory 20. Radiative transfer in plane-parallel particulate media 21. Weak localization 22. Epilogue Appendix A. Dyads and dyadics Appendix B. Free-space dyadic Green's function Appendix C. Euler rotation angles Appendix D. Spherical-wave expansion of a plane wave in the far zone Appendix E. Integration quadrature formulas Appendix F. Wigner d-functions Appendix G. Stationary phase evolution of a double integral Appendix H. Hints and answers to selected problems Appendix I. List of acronyms References Index.

Electromagnetic Scattering by Particles and Particle Groups: An Introduction

Polarized Light, Second Edition explores polarized light, its production, and its use, facilitating self-study without prior knowledge of Maxwell's equations. This comprehensive second edition includes more than 2500 thoroughly updated figures and equations for easier understanding and application across various industries. It features new chapters on polarization by refraction and reflection, polarization elements, anisotropic materials, Stokes polarimetry, Mueller matrix polarimetry, the mathematics of the Mueller matrix. This edition also offers updated and expanded material on the derivation of the Fresnel equations with plots of the magnitude and phase of the reflection coefficients.

Polarized Light, Revised and Expanded

We report the results of high-accuracy controlled laboratory measurements of the Stokes reflection matrix for suspensions of submicrometer-sized latex particles in water and compare them with the results of a numerically exact computer solution of the vector radiative transfer equation (VRTE). The quantitative performance of the VRTE is monitored by increasing the volume packing density of the latex particles from 2% to 10%. Our results indicate that the VRTE can be applied safely to random particulate media with packing densities up to ∼2%. VRTE results for packing densities of the order of 5% should be taken with caution, whereas the polarized bidirectional reflectivity of suspensions with larger packing densities cannot be accurately predicted. We demonstrate that a simple modification of the phase matrix entering the VRTE based on the so-called static structure factor can be a promising remedy that deserves further examination.

/pdf/radiative-transfer-theory-verified-by-controlled-laboratory-2yniqdpy2m.pdf

Radiative transfer theory verified by controlled laboratory experiments

The images introduced to an optical pattern recognition system are normally an amplitude representation of the original intensity images. We define a method of encoding intensity images as phase-only images, and we demonstrate that the performance of the correlation is generally substantially better than that of the correlation performed with amplitude inputs. Energy in the correlation peak is about a factor of 20 greater for the phase-encoded input image method. These performance and energy advantages are particularly useful when designing filters that incorporate various degrees and types of invariance. We give examples and numerical results for the correlation process with ternary and 15-phase-state plus zero-amplitude filters with varying spans of invariance. We suggest practical implementations for this technique.

Phase-encoding input images for optical pattern recognition

/pdf/polarization-measurement-analysis-and-remote-sensing-ix-5cb7wbg447.pdf

Polarization: Measurement, Analysis, and Remote Sensing IX

A commercial PLZT modulator is characterized at wavelengths from 0.6328 μm to the limits of its IR transmission around 9 μm. Laser polarimetry and IR spectropolarimetry are the characterization techniques used. Polarization measurement results include diattenuation and retardation. The PLZT modulator is found to be an electrically controllable polarizer as well as an electrically controllable retarder.

Dennis H. Goldstein

Papers

Polarized Light, Revised and Expanded

Radiative transfer theory verified by controlled laboratory experiments

Phase-encoding input images for optical pattern recognition

Polarization: Measurement, Analysis, and Remote Sensing IX

PLZT modulator characterization