Photon orbital angular momentum in astronomy

Context. Photon orbital angular momentum (POAM) has been created in the laboratory, yet it is still relatively unknown. How does POAM manifest itself in astronomy? Are there any applications for measuring astrophysical POAM? Aims. In this paper, I 1) explain POAM in an astronomical context; 2) define the POAM observables for astronomy; 3) create generic systems-based calculi that describe how POAM propagates from celestial sphere to detector; 4) use the calculi with several astronomical instruments as examples of their utility; 5) demonstrate an application for astrophysical POAM measurements; and 6) relate POAM to existing astronomical instruments and concepts. Methods. Electric fields are expanded into azimuthal Fourier components, and the intensities are expanded into correlations or rancors. The source electric fields are spatially incoherent. In the systems-based calculi, the inputs are located on the celestial sphere, the system is represented by propagation through free space and instrument, and the outputs are located in a specific plane. The diffraction and point-spread function expansions are very generic and can be used with any type of instrument. I employ these examples to demonstrate the calculi (in order of increasing difficulty): free space, single telescopes, interferometers, coronagraphs, and rancorimeters. Results. The azimuthal Fourier components of the electric field correspond to POAM vortex states. Rancors contain less information than correlations, yet they are easier to measure and can be used in many applications. Propagation through an aberrated telescope applies external torque, which may be expressed in terms of Zernike polynomials. I prove that a sectored phase mask in a focal-plane coronagraph applies torque to the low-order states, producing a null. Also, I prove that a Michelson interferometer is inherently capable of filtering POAM; e. g., tracking 180. from the central fringe eliminates even states, producing a null. A limited rancorimeter can be created by placing a focal-plane wedge mask in a coronagraph. The resulting rancors can be used to perform super-Rayleigh observations of unresolved unresolved objects, such as binary stars. There are three types of source POAM: intrinsic, structure, and pointing. Instrumental POAM, which must be calibrated, includes optical aberrations and atmospheric turbulence. Conclusions. This paper represents the starting point for future research: 1) making a priori predictions about the intrinsic POAM of astronomical sources; 2) designing ground-and space-based POAM-measuring instruments; 3) understanding existing instruments in terms of POAM; 4) minimizing the effects of random noise on POAM; and 5) calibrating all types of instrumental POAM.