Following the model independent approach to deuteron photodisintegration with linearly polarized \(\gamma-\)rays, we show that the measurements of the tensor analyzing powers on aligned deuterons along with the differential cross section involve five different linear combinations of the isovector \(E1^j_v; j=0,1,2\) amplitudes interfering with the isoscalar \(M1_s\) and \(E2_s\) amplitudes. This is of current interest in view of the recent experimental finding \cite{blackston1} that the three \(E1^j_v\) amplitudes are distinct and also the reported experimental observation \cite{sawatzky} on the front-back (polar angle) asymmetry in the differential cross section.