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

For the Shapiro-Wagner-Hradil phase detection description the canonical commutation relation between phase angleψand 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^(†).