When measuring the radar cross section (RCS) of a target the incident wave at the target must be planar or close to planar. As explained in for example: Kouyoumjian R.G. and Peters L. jr., 1965, "Range Requirements in Radar Cross-Section Measurements", a maximum deviation of pi/8 from a planar phase for the phase front over the extend of the target is still permittable. Using this pi/8 -criteria for a target with maximum dimmension L one can find the well-known formula R_min = 2 x L^2 / lambda, as is also explaned in aforementioned paper.
However, with some other publications, see for example Geldsetzer T., Mead J.B. e.a., 2007, "Surface-based polarimetric C-band scatterometer for field measurements of sea ice", the antenna's maximum apperture dimension D is used instead in the same equation R_min = 2 x D^2 / lambda to calculate the far field.
Is there a reason why one would use the antenna apeture dimmension D instead of that of the target L?
I am gratefull for your comments/answers,
Jan Hofste
University of Twente (Netherlands)
I imagine it has something to do with the application. The former 2*L^2/lambda is the quiet-zone/far-zone criterion for RCS measurements. I've seen it most often applied to indoor compact RCS ranges and anechoic chambers.
The latter 2*D^2/lambda is the criterion to be in the far zone with respect to the antenna. This seems appropriate for remote sensing where the object of interest (sea ice in your reference) is electrically huge and doesn't have a well-defined L.
Thanks for your reply. Have been reading some more on the subject myself. I agree with you. The 2L^2 / lambda can be used as a worst-case estimation of the minimum distance R required during RCS measurements. Worst case since it assumes a point source antenna with a spherical wavefront. When using any antenna with a good amount of directivity the phase front is already quite planar even close to the antenna. An antenna with good directivity implies the aperture dimension D being large compared to the wavelength. If that is the case the equation 2D^2 /lambda applies. I also found some literature giving better estimations on when usage of 2D^2 / lambda is allowd: see for example Bansal, 1999, "The far-field, how far is far enough?"
2D^2/lambda is the distance from the antenna by which the antenna pattern has settled down so that the wave front is roughly spherical and the gain and beam-shape are well defined by the standard aperture formulae.
2D^2/lambda gives the far field distance. Beyond the far field distance the antenna radiation pattern, i.e. Relative intensity over angle from antenna boresight, remains constant. The absolute intensity still decreases with R^-2 of course.
@ Malcolm WHite: Say you compare the wavefronts of two antennas. One large (D >> lambda) and one small (D = lambda). Is then the wavefront coming from the large antenna not more planar, or less spherical, than the wavefront coming from the small antenna? Or is this not true. At a large enough distance the wavefront from any (finite size) antenna is spherical. I think the latter is the case, so I agree with you.
Hi Jan Hofste
Very close to a large antenna the wavefront is (may be) planar (used in near-field measurement ranges), but then it gets more confused out to D^2/lambda, where it starts becoming regular again, and at twice this range it more or less looks like it is coming from a point source. The only difference a large antenna makes at this point is the angular width of beam. Even then, "supergain" antennas make this not generally true!
There are some interesting plots of fields near a focus in Born and Wolf, which is the inverse problem, and looking at the fields of the first order Gaussian beam around the waist is very instructive - they have very simple forms given by clear formulae. Highly tapered aperture distributions can give fields like this.
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