  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.
