“…The relationship between the two can be found, in this case, by defining a new integration variable for , which we here denote by q : In terms of this variable we have where γ ⊥ is essentially a constant, as is x in . The differential form of is With this change of variable, becomes In terms of the Doppler shift of the deflector z d , since points towards the observer, we have , so the bending angle by a moving deflector in terms of the same deflector at rest is This result is in agreement with Frittelli et al (2002), where a significantly different method was used, and the deflector was assumed not to move across the line of sight. An important point to emphasize is the fact that the transverse motion of the deflector has no effect on the bending angle, as long as it is approximately uniform, as noted by Pyne & Birkinshaw (1993).…”