Photon orbital angular momentum and torque metrics for single telescopes and interferometers

National Radio Astronomy Observatory, P.V. Domenici Science Operations Center, PO Box O, 1003 Lopezville Road, Socorro, NM 87801-0387, USA ^⋆

Received: 4 January 2012
Accepted: 8 March 2012

Abstract

Context. Photon orbital angular momentum (POAM) is normally invoked in a quantum mechanical context. It can, however, also be adapted to the classical regime, which includes observational astronomy.

Aims. I explain why POAM quantities are excellent metrics for describing the end-to-end behavior of astronomical systems. To demonstrate their utility, I calculate POAM probabilities and torques from holography measurements of EVLA antenna surfaces.

Methods. With previously defined concepts and calculi, I present generic expressions for POAM spectra, total POAM, torque spectra, and total torque in the image plane. I extend these functional forms to describe the specific POAM behavior of both single telescopes and interferometers.

Results. POAM probabilities of spatially uncorrelated astronomical sources are symmetric in quantum number. Such objects thus have zero intrinsic total POAM on the celestial sphere, which means that the total POAM in the image plane is identical to the total torque induced by aberrations within propagation media and instrumentation. The total torque can be divided into source- independent and dependent components, and the latter can be written in terms of three illustrative forms. For interferometers, complications arise from discrete sampling of synthesized apertures, but they can be overcome. POAM also manifests itself in the apodization of each telescope in an array. Holography measurements of EVLA antennas observing a point source indicate that  ~ 10% of photons in the n = 0 state are torqued to n  ≠  0 states.

Conclusions. POAM quantities represent excellent metrics for characterizing instruments because they are based on real physics and are used to simultaneously describe amplitude and phase aberrations. In contrast, Zernike polynomials are just solutions of a differential equation that happen to  ~ correspond to specific types of aberrations (e.g., tip-tilt, focus, etc.) and are typically employed to fit only phases. Possible future studies include forming POAM quantities with real interferometry visibility data, modeling instrumental aberrations and turbulence of the troposphere/ionosphere in terms of POAM, POAM-based imaging algorithms and constraints, POAM-based super resolution imaging, and POAM observations of astrophysically important sources.