# azimuth extent for range migration algorithm

Is it true that in the Range Migration Algorithm for synthetic aperture radar, the azimuth extent can be said to span the length of the flight path?

This makes sense but also does not make sense. Because what if the scene being imaged is 1 km, then won't the flight have to travel a ridiculously long extent?

Illustration:

So in the final step of the RMA, an inverse FFT is taken on a phase that has the form (after stolt interpolation): $\phi(K_X, K_R) = -K_XX_t + K_Y(R_B-R_S)$

Where:

$K_X = azimuth\ spatial\ frequency\ \epsilon\ [\frac{-\pi}{\Delta X}, \frac{\pi}{\Delta X}]$

$K_Y = ground\ range\ direction\ frequency\$

$X_t = scatterer\ azimuth\ location$

$R_B - R_S = scatterer\ ground\ range\ displacement$

After this step, my question is what the span of $X_t$ would be. i.e. how to calculate the azimuth axes.

• I think a quick hand drawing will go a looooong way here :) But, yeah I think you're right, but I'm not sure I 100% accurately understand you. – Marcus Müller Jun 28 '18 at 8:58
• thanks! i have clarified the portion of the rma equation that is not clear at this point – matthew Jun 29 '18 at 0:37