A Hermitian Opetator Conjugate to Two-Mode Number-Difference Operator

For the Shapiro-Wagner-Hradil phase detection description the canonical commutation relation between phase angle ψ and two-mode number-difference operator D = a^†a - b^†b is constructed. Departing from ψ, D = -i, the phase angle Hermitian operator is derived in the newly obtained representation < ξ |, where | ξ > is the common eigenket of a + b^† and b + a^†.