Direct discrimination of structured light by humans

Abstract

We predict and experimentally verify an entoptic phenomenon through which humans are able to perceive and discriminate optical spin-orbit states. Direct perception and discrimination of these particular states of light with polarization-coupled spatial modes is possible through the observation of distinct profiles induced by the interaction between polarization topologies and the radially symmetric dichroic elements that are centered on the foveola in the macula of the human eye. A psychophysical study was conducted where optical states with a superposition of right and left circular polarization coupled to two different orbital angular momentum (OAM) values ([Formula: see text] and [Formula: see text]) were directed onto the retina of participants. The number of azimuthal fringes that a human sees when viewing the spin-orbit states is shown to be equal to the number (N) of radial lines in the corresponding polarization profile of the beam, where [Formula: see text] The participants were able to correctly discriminate between two states carrying OAM [Formula: see text] and differentiated by [Formula: see text] and [Formula: see text], with an average success probability of 77.6% (average sensitivity [Formula: see text], [Formula: see text], [Formula: see text]). These results enable methods of robustly characterizing the structure of the macula, probing retina signaling pathways, and conducting experiments with human detectors and optical states with nonseparable modes.

Keywords: human perception; orbital angular momentum; spin–orbit coupling.

Fig. 1.

(A) Pictorial representation of a spin–orbit beam, composed of a coherent superposition of a planar right-circularly polarized state and a helical left-circularly polarized state, being directed onto the retina of an observer. The helical state carries OAM, and its phase varies along the azimuthal coordinate $\varphi$. The depicted example corresponds to Eq. 1 with ${\ell }_1=0$ and ${\ell }_2=-1$. (B) In the macula of the human eye, the macular pigment molecules (green) are bound to the radially oriented Henle fibers (red) that surround the foveola. The radial symmetry of these dichroic elements (polarization filter direction as a function of the azimuthal coordinate is shown by black arrows) coincides with the symmetry of the polarization-coupled OAM beams shown in A. (C) The number of azimuthal fringes that a human sees when viewing the spin–orbit beams is equal to the number of radial lines (N) in the corresponding polarization profile of the beam, where $N=|\left({\ell }_1-{\ell }_2\right)-2|$. Shown are the examples for $N=2$ where ${\ell }_1={\ell }_2=0$, $N=3$ where ${\ell }_1=-1,{\ell }_2=0$, $N=5$ where ${\ell }_1=7,{\ell }_2=0$, and $N=9$ where ${\ell }_1=0,{\ell }_2=7$. The size of the central region increases with propagation. The $N=2$ case depicts the Haidinger’s brush profile when horizontally polarized light is observed.

Fig. 2.

Schematic of the experimental setup where a Michelson interferometer along with an SPP and standard polarization optics components are used to prepare the spin–orbit states that are directed onto the retina of the participants in the study. For a complete description of the setup, see Setup and Stimuli. Translating the mirror along the beam path direction varies $\theta \left(t\right)$ in Eq. 5, while the two orientations of the outer QWP, $\beta \in \left[\mathrm{0,18}{0}^{○}\right]$ around the vertical axis, correspond to the two states ($|{\mathrm{\Psi }}_{+}\mathrm{\rangle }$ and $|{\mathrm{\Psi }}_{-}\mathrm{\rangle }$) of Eq. 5. (i) The images observed by a complementary metal–oxide semiconductor (CMOS) camera placed before the user lens, for both $|{\mathrm{\Psi }}_{+}\mathrm{\rangle }$ and $|{\mathrm{\Psi }}_{-}\mathrm{\rangle }$. It can be noted that azimuthal fringes are not present. The ring features are artifacts from SPP machining, and they are equally present in both images. (ii) The images observed by a CMOS camera placed before the user lens when a linear polarizer (LP) is placed in front of the camera. The seven azimuthal fringes correspond to the helical (OAM = 7) phase structure of $|{\mathrm{\Psi }}_{+}\mathrm{\rangle }$ and $|{\mathrm{\Psi }}_{-}\mathrm{\rangle }$, the only notable difference being the $180^{○}$ azimuthal phase shift. The attenuators were removed to obtain the images shown in i and ii, and the camera gain was correspondingly optimized. In the study, the participants only observed beams shown in i, and the red circles bound the area ($\sim 2^{○}$ of field of vision) with good intensity and high-quality phase structure that the participants were instructed to observe. The two simulated profiles of what the participants were expected to observe are shown in Fig. 1C under the labels “$N=5$” for $|{\mathrm{\Psi }}_{+}\mathrm{\rangle }$ and “$N=9$” for $|{\mathrm{\Psi }}_{-}\mathrm{\rangle }$. Note that the characteristic spherical phase of a Michelson interferometer caused the azimuthal fringes to wind.

Fig. 3.

Sensitivity and accuracy for the discrimination task. Each participant performed 100 trials over two sessions. The dashed line indicates chance performance. Open bars show individual participant performance. Circular symbols show group mean sensitivity (blue: left ordinate) and accuracy (black: right ordinate). Error bars show 95$\%$ CIs. Participants were highly sensitive to the difference between both trial types, performing significantly better than chance.

Fig. 4.

Comparison of spin–orbit states generated with the setup of Fig. 2 using a SLM in place of the SPP. The topological charge of the fork dislocation pattern on the SLM sets the OAM value of the diffraction orders. Imaged is the intensity between the first diffraction order and the reference beam (Top) without a linear polarizer before the camera and (Bottom) with a linear polarizer before the camera. Shown are the examples for ${\ell }_1=0,{\ell }_2=3$, ${\ell }_1=0,{\ell }_2=7$, and ${\ell }_1=0,{\ell }_2=-7$. Note that only the stimuli shown in Fig. 2 were presented to the observers during the study.