ALL Experts Redux: Radar Telescopes & Asteroids

 Question:

Would you be so kind as to simply explain to me this statement I found in an astronomy text about radar telescopes and asteroids:

"The ability to produce delay-Doppler images of asteroids is exciting but a bit perplexing.  Clearly there is a lot of information in these images, but, because radar forms images in a way that is quite different from the way our eyes work, delay-Doppler images are not very intuitive"

Answer -

All this means is that RADAR ('Radio Detection and Ranging') provides an indirect means of assembling the image of an asteroid, compared to say an optical image that one would obtain using a telescope.

To get an optical image, one would either:

a) look directly at the object through the telescope and see it as it is,

or

b) take a photograph of it through the telescope - which essentially
amounts to collecting the incident light rays and fixing them on a
negative or emulsion

In the case of radar, you don't look directly but rather transmit a wave
(radio wave) toward the object. You can't "see" radio waves, since they are many times larger than light waves. (Hence outside the visible spectrum) So, you have to wait for the transmitted radio waves to bounce back to you- which you can then pick up with a radar antenna.

Next, you want to measure how long it takes for each of these reflected radio waves to get back to your antenna. Each such time delay gives a rough idea of the asteroid's surface.

For example, imagine a small 'mountain' on the asteroid, its peak in the rough direction of your antenna. Obviously, the peak is closer to you than the mountain’s  base.

In one instant, say at time t1 - you get the reflection of the wave from
the base. In the next, at time t2, you get a reflection from the peak.

You find: t2 <  t1 (t2 is less than time t1)

Thus, you can conclude that the second radio wave (corresponding to time t2)  hit a part of the asteroid that was CLOSER to you. You continue doing this procedure until you receive no further reflected signals. (I.e. the asteroid  has passed out of your transmitted beam).

Now, if the asteroid or part thereof is ALSO moving - with respect to
you - then the frequency of the bounced off radio wave will change.  This is the 'Doppler delay' part of the observation.  Note the strength of the radar  return signal is proportional to the inverse fourth-power of the distance.  Thus, if a part of the asteroid is moving AWAY from you at the time the radio wave hits it, then bounces back - you will pick up a LOWER frequency signal. (Call it f1)

On the other hand, if a part of the asteroid is moving TOWARD you at the time the radio wave hits it, then bounces back - you will pick up a HIGHER frequency signal.(Call it f2)  Measuring each of these Doppler shifts (f2 - f1) or difference in
frequency, and comparing them with the time-delays allows you to form a two-dimensional delay-Doppler image.

Obviously, since this is based on times and frequencies (actually frequency differences) it can't possibly be the same as the way our eyes work (since they function, like telescopes, in the optical region of the spectrum - as I noted already).