Position errors in far-field optical imaging

The most basic function of an optical microscope is imaging the position of an object. But if the object is too small, the diffraction-limited optics blur the image. Superresolution imaging techniques, however, can turn that blurry information into a position with nanometer-scale accuracy (see Physics Today, December 2014, page 18 ).

Now, in a collaboration between the University of Innsbruck, the Institute of Quantum Optics and Quantum Information, and the Technical University of Vienna, Arno Rauschenbeutel and coworkers have identified another fundamental source of imaging errors: elliptically polarized light. If the object under study emits circularly polarized light, such as an ion undergoing a dipole transition, it produces spiral wavefronts, as shown in the figure. When the light is collected by the imaging optics, the pitch of the spiral tilts the wavefront with respect to the optical axis. That tilt shifts the peak of the intensity distribution on the imaging screen, thereby shifting the image’s apparent position. According to the researchers’ analysis, the effect can be exacerbated or reduced by changing the light’s elliptical polarization, and it applies to any kind of wave that carries orbital angular momentum.

To test their predictions for a polarization-dependent image shift, the researchers used two systems: a barium ion trapped by electric fields and a gold nanoparticle placed on an optical fiber. When imaging circularly polarized light, both systems displayed position shifts of about 150 nm, in agreement with the researchers’ expectations. When elliptically polarized light was used, that value increased to as much as 430 nm for the nanoparticle, more than four times its diameter.

Such large systematic shifts can be a problem when precisely determining an object’s position. If the object scatters or emits elliptically polarized light, measuring its position requires detailed knowledge about the light’s polarization. On the bright side, the effect can also yield information about the polarization of the light itself. (G. Araneda et al., Nat. Phys., 2018, doi:10.1038/s41567-018-0301-y .)