The method of constructing the tomographic probability distributions
describing quantum states in parallel with density operators is presented.
Known examples of Husimi-Kano quasi-distribution and photon number tomography
are reconsidered in the new setting. New tomographic schemes based on coherent
states and nonlinear coherent states of deformed oscillators, including
q-oscillators, are suggested. The associated identity decompositions providing
Gram-Schmidt operators are explicitly given, and contact with the Agarwal-Wolf
Ω-operator ordering theory is made.Comment: A slightly enlarged version in which contact with the Agarwal-Wolf
Ω-operator ordering theory is mad