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Assuming a bi-static Radar or LIDAR with a stationary transmitter and a stationary target and a stationary receiver, with a sweeping RADAR/LIDAR beam reflecting off a stationary target:

Why would the receiver not see a Doppler shift, because the reflected wavelength is shortened/lengthened by the constant motion of the sweeping beam, similar to how a non-stationary target would produce a real Doppler shift?

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  • $\begingroup$ The sweeping beam isn't real. For the same reason that the beam can sweep an arc that "moves faster than the speed of light". $\endgroup$
    – Aron
    Commented Feb 22, 2015 at 18:40
  • $\begingroup$ To expand on @Aron's point, the beam is not a thing that moves. The things that move are the components of the beam (disturbances in the EM field classically, or photons in the QT picture), and those only move outward (and then reflect back toward the detector). $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Feb 22, 2015 at 18:55
  • $\begingroup$ @dmckee nor can individual components of the beam affect other parts of the beam (a simple argument on SR space time diagram can show this). $\endgroup$
    – Aron
    Commented Feb 22, 2015 at 19:01

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It depends on what you mean by sweeping. If by "sweeping" you mean motion in cross-range (orthogonal to radial) then at least in the non-relativistic regime there should not be any Doppler shift because (the length of) the range transmitter/reflector/receiver is constant, that is the number of wave-crests per unit time does not change. To see Doppler shift you need to have that range change with time, so either the transmitter to reflector, or the reflector to receiver range (or both) should change. This range change could be induced by any radial motion be that of the transmitter, or of the target, or of the receiver. And if by sweeping you mean a frequency chirp then again you get no range variation, hence no Doppler shift.

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  • $\begingroup$ If, instead of a sweeping beam, the beam had orbital angular momentum, would this create radial motion between photon and reflector, resulting in a Doppler shift? $\endgroup$
    – Jim Lewis
    Commented Feb 23, 2015 at 4:18
  • $\begingroup$ what would you be changing if as you said "the beam had orbital angular momentum", where is the motion?. $\endgroup$
    – hyportnex
    Commented Feb 23, 2015 at 21:34
  • $\begingroup$ It was wondering if there would be a Doppler shift for Orbital Angular Momentum twisted light and it seems there is a Doppler shift for both OAM and circularly polarized light if I understand correctly Physical Review Letters, 30 Nov 1998, "Rotational Frequency Shift of a Light Beam". $\endgroup$
    – Jim Lewis
    Commented Feb 25, 2015 at 2:23
  • $\begingroup$ This Physical Review article states "The shift is equal to the total angular momentum per photon multiplied by the angular velocity between the source and observer." $\endgroup$
    – Jim Lewis
    Commented Feb 25, 2015 at 2:30

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