25,161 research outputs found
Photon orbital angular momentum and torque metrics for single telescopes and interferometers
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 single telescopes and interferometers.
Results. POAM probabilities of spatially uncorrelated astronomical sources
are symmetric in quantum number. Such objects 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 &
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
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 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 and are typically employed to fit only phases
Combined calculi for photon orbital and spin angular momenta
Context. Wavelength, photon spin angular momentum (PSAM), and photon orbital
angular momentum (POAM), completely describe the state of a photon or an
electric field (an ensemble of photons). Wavelength relates directly to energy
and linear momentum, the corresponding kinetic quantities. PSAMand POAM,
themselves kinetic quantities, are colloquially known as polarization and
optical vortices, respectively. Astrophysical sources emit photons that carry
this information. Aims. PSAM characteristics of an electric field (intensity)
are compactly described by the Jones (Stokes/Mueller) calculus. Similarly, I
created calculi to represent POAM characteristics of electric fields and
intensities in an astrophysical context. Adding wavelength dependence to all of
these calculi is trivial. The next logical steps are to 1) form photon total
angular momentum (PTAM = POAM + PSAM) calculi; 2) prove their validity using
operators and expectation values; and 3) show that instrumental PSAM can affect
measured POAM values for certain types electric fields. Methods. I derive the
PTAM calculi of electric fields and intensities by combining the POAM and PSAM
calculi. I show how these quantities propagate from celestial sphere to image
plane. I also form the PTAMoperator (the sum of the POAMand PSAMoperators),
with and without instrumental PSAM, and calculate the corresponding expectation
values. Results. Apart from the vector, matrix, dot product, and direct product
symbols, the PTAM and POAM calculi appear superficially identical. I provide
tables with all possible forms of PTAM calculi. I prove that PTAM expectation
values are correct for instruments with and without instrumental PSAM. I also
show that POAM measurements of "unfactored" PTAM electric fields passing
through non-zero instrumental circular PSAM can be biased. Conclusions. The
combined PTAM calculi provide insight into how to mathematically model PTAM
sources and calibrate POAMand PSAM- induced POAM measurement errors
Dual and complex formulations of thin shell equations
Dual and mixed formulations of thin shell equations using displacements and stress function
A dual formulation of thin shell theory
Differential equations formulated for stress functions, and thin elastic shell
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