In the limit. (Was " Is there an actual definition for 'direction of arrival'?")

John Monro wrote:
Jerry Avins wrote:

John Monro wrote:

Jerry Avins wrote:

I meant that the transmitter seems like a point source to the receiver, and that it is sufficiently remote that the bearing to it is the same from every point on the receiving array. If these conditions are met, they would also be met if the role of receiver and transmitter were interchanged. "Plane wave" encompasses these conditions, but doesn't serve well as a definition. "Point source" and "plane wave" are in fact mutually contradictory, but serve well as local approximations. A true plane wave doesn't have inverse-square intensity.



Jerry,
Another way of looking at it is this:

Those two terms: "point source" and "plane wave" are not mutually contradictory if you take into account the 'optical' location of the source.

If you trace back the 'nearly' plane-wave radiated by a large dish or array, the wave appears to be coming from a point that is located well behind the antenna. The less curvature you have on that wave-front the further behind the antenna the source appears to be.

In the case of a theoretical-perfect plane-wave, the source appears to be located at an infinite distance behind the antenna aperture. As the apparent distance between the signal source and the receiving antenna is already infinite it is not possible to change this distance to any significant degree by changing the physical separation between the antennas. The inverse-square law is working correctly when it shows us that there is no change in received signal under these circumstances.



Sure. I'll say it two more ways.

When the curvature of the wavefront is infinitesimal, the distance to the point radiator is infinite.

The radius of curvature is the reciprocal of the curvature.

Jerry


Because of the fact that: "when the curvature of the wavefront is infinitesimal, the distance to the point radiator is infinite", it is incorrect to say that "a true plane wave doesn't have inverse-square intensity."

Here on earth, the light from Betelgeuse might as well be plane, but we (think we) know the distance to the star and can calculate the departure from planarity. There will always be a difference between what can be measured and what can be calculated from theory. That difference is a common cause of discussions at cross purposes here on comp.dsp. I, for one, have grown gun shy and try to dot the i's and cross the t's.

Jerry
--
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