Constraint condition of applying the formula ‖vr‖/Ba to the azimuth resolution calculation for bistatic SAR with arbitrary geometry configuration

According to several mathematical models related to slant range and Doppler of the bistatic SAR with arbitrary geometry configuration, the concept of equivalent velocity is presented and the equivalent velocity divided by the Doppler bandwidth B can be used for calculating the azimuth resolution. The quantitative relation between the equivalent velocity and the receiver velocity parvoarrpar is studied and the service condition of the formula parvoarrpar/B_a for calculating the azimuth resolution is obtained. For the translational invariant configuration the two equivalent service conditions are obtained by simplifying the constraint relation from the scalar and vector angle, respectively. The analysis of the constraint relation for the translational variant configuration demonstrates that the formula parvoarrpar/B_a is not appropriate for most cases except the stationary-transmitter case.