Matrix Fourier optics enables a compact full-Stokes polarization camera

INTRODUCTION

Polarization describes the path along which light’s electric field vector oscillates. An essential quality of electromagnetic radiation, polarization is often omitted in its mathematical treatment. Nevertheless, polarization and its measurement are of interest in almost every area of science, as well as in imaging technology. Traditional cameras are sensitive to intensity alone, but in a variety of contexts, knowledge of polarization can reveal features that are otherwise invisible. Determination of the full-Stokes vector—the most complete description of light’s polarization—necessitates at least four individual measurements. This results in optical systems that are often bulky, reliant on moving parts, and limited in time resolution.

RATIONALE

We introduce a formalism—matrix Fourier optics—for treating polarization in paraxial diffractive optics. This formalism is a powerful generalization of a large body of past work on optical elements in which polarization may vary spatially. Moreover, it suggests a path to realizing many polarization devices in parallel using a single optical element. We can then design diffraction gratings whose orders behave as polarizers for an arbitrarily selected set of polarization states, a new class of optical element. The intensity of light on a set of diffraction orders is then dictated by the polarization of the illuminating light, making these gratings immediately applicable to full-Stokes polarization imaging.

RESULTS

We theoretically investigate these gratings and develop an optimization scheme for their design. Our diffraction gratings were realized with dielectric metasurfaces in which subwavelength, anisotropic structures provide for tunable polarization control at visible frequencies. Characterization of the fabricated gratings shows that they perform as designed. Notably, an arbitrary set of polarizations may be analyzed by a single unit cell, in contrast to past approaches that relied on interlacing of several individually designed diffraction gratings, increasing the flexibility of these devices.

These gratings enable a snapshot, full-Stokes polarization camera—a camera acquiring images in which the full polarization state is known at each pixel—with no traditional polarization optics and no moving parts (see panel A of the figure). Polarized light from a photographic scene is incident on the grating inside of a camera. The polarization is “sorted” by the specially designed subwavelength metasurface grating. When combined with imaging optics (a lens) and a sensor, four copies of the image corresponding to four diffraction orders are formed on the imaging sensor. These copies have each, effectively, passed through a different polarizer whose functions are embedded in the metasurface. The four images can be analyzed pixel-wise to reconstruct the four-element Stokes vector across the scene. Several examples are shown at 532 nm, both indoors and outdoors. The figure depicts an example photograph of two injection-molded plastic pieces, a ruler and a spoon (illuminated by a linearly polarized backlight), that show in-built stresses (see panels C to E of the figure) that are not evident in a traditional photograph (panel B). The camera is compact, requiring only the grating (which is flat and monolithically integrated, handling all the polarization analysis in the system), a lens, and a conventional CMOS (complementary metal–oxide–semiconductor) sensor.

CONCLUSION

Metasurfaces can therefore simplify and compactify the footprint of optical systems relying on polarization optics. Our design formalism suggests future research directions in polarization optics. Moreover, it enables a snapshot, full-Stokes polarization imaging system with no moving parts, no bulk polarization optics, and no specially patterned camera pixels that is not altogether more complicated than a conventional imaging system. Our hardware may enable the adoption of polarization imaging in applications (remote sensing, atmospheric science, machine vision, and even onboard autonomous vehicles) where its complexity might otherwise prove prohibitive.

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