Is there an actual definition for "direction of arrival"?

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
-- 
Engineering is the art of making what you want from things you can get.
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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."

Regards,
John

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
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Jerry Avins wrote:

> 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.

Well, yes, and that's how it has to be. No theories fit the real world
perfectly, and no real-world measurement comply 100% with any given
theory. Knowing to what extent a theory fits, and the nature of the
discrepancy, is the key to get anything done what "practical" DSP
is concerned.

> I, for
> one, have grown gun shy and try to dot the i's and cross the t's.

Don't know what you mean by that, but it is always a good idea to
make clear what the basis of one's arguments is.

Rune

Rune Allnor wrote:
> Jerry Avins wrote:
> 
> 
>>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.
> 
> 
> Well, yes, and that's how it has to be. No theories fit the real world
> perfectly, and no real-world measurement comply 100% with any given
> theory. Knowing to what extent a theory fits, and the nature of the
> discrepancy, is the key to get anything done what "practical" DSP
> is concerned.

One can calculate that the sagitta of a kilometer-long chord across a 
wavefront is a few �ngstroms, but such a result defies measurement.

>>I, for
>>one, have grown gun shy and try to dot the i's and cross the t's.
> 
> 
> Don't know what you mean by that, but it is always a good idea to
> make clear what the basis of one's arguments is.

It means that (when I remember) I try to make constraints and 
assumptions explicit. It can seem boring and pedantic -- some would have 
it anal retentive -- but the extra words usually save words in the long 
run (this occasion being an exception).

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������