A Hermitian operator conjugate to two-mode number-difference operator

For the Shapiro-Wagner-Hradil phase detection description the canonical commutation relation between phase angle psi and two-mode number-difference operator D = a dagger a - b dagger b is constructed. Departing from [psi, D] = -i, the phase angle Hermitian operator is derived in the newly obtained representation [xi\, where \xi] is the common eigenket of a + b dagger and b + a dagger.