We present direct measurement of Kirkwood-Rihaczek (KR) distribution for
spatial properties of coherent light beam in terms of position and momentum
(angle) coordinates. We employ a two-local oscillator (LO) balanced heterodyne
detection (BHD) to simultaneously extract distribution of transverse position
and momentum of a light beam. The two-LO BHD could measure KR distribution for
any complex wave field (including quantum mechanical wave function) without
applying tomography methods (inverse Radon transformation). Transformation of
KR distribution to Wigner, Glauber Sudarshan P- and Husimi or Q- distributions
in spatial coordinates are illustrated through experimental data. The direct
measurement of KR distribution could provide local information of wave field,
which is suitable for studying particle properties of a quantum system. While
Wigner function is suitable for studying wave properties such as interference,
and hence provides nonlocal information of the wave field. The method developed
here can be used for exploring spatial quantum state for quantum mapping and
computing, optical phase space imaging for biomedical applications.Comment: 27 pages, 14 figure
