1. ### vinven7

51
Suppose there is a set of twenty tiny radio sources that are distributed randomly in an area of 1 mm2. What is the best way to locate each of these sources - as in identify them and their locations? We can suppose that all of them are of the same frequency of 1 Mhz. Thus if the radio telescope was inverted - with its size reduced considerably and it was pointing at this area instead of the sky. how would we realize it?

2. ### davenn

4,369
At that frequency ( 1MHz) you wouldn't have the resolution to separate 2 sources within let alone 10 or 20 sources

I would venture further, and some one is sure to correct me if I am wrong, that on a surface of several metres square you would not be able to accurately resolve in which 1mm2 box within that surface a 1MHz source would be located

resolving ability and wavelength are closely related

hence why we see details of deep space objects much better with optical telescopes than what we do with radio telescopes

Dave

3. ### mishima

405
Not sure if there is a practical way to accomplish that. Your wavelength of interest is around 300 meters according to

c = λ $\nu$

speed of light is wavelength times frequency

If the receiving antenna was 1 cm from your sample, a resolution of well under 0.1 radians would be required.

s = r $\theta$

s the width of your sample, r the distance from antenna to sample. s would actually be much smaller in your example, probably on the order of microns.

This would make the diameter of the antenna 3 kilometers at the very least, just to resolve the 1 mm^2...

$\theta$ ~ $\lambda$ / diameter

### Staff: Mentor

What is the application?

As said, you will not be able to be any distance away from those low-frequency closely-spaced sources. You may be able to do an x-y physical scan at close distance to find them, though.

5. ### f95toli

2,473
It might be possible if you were allowed to use a near-field probe. Near field effects can be used to "beat" the usual resolution limit, which is why microwave microscopes can reach spatial resolutions of about a micrometer.

However, near-field in this case means that you would have to put the probe very close, you would need a proper scanning-probe setup.

6. ### sophiecentaur

14,730
It comes down to the measurement of relative phases of signals. mm wavelengths and micron resolution (13:1) is one thing but 300m wavelength and 0.3mm spacing is significantly harder to achieve. (106:1). But, in the end, it would be down to the signal to noise ratio that you would be working with - so I couldn't say there's no chance).

@vinven7
Btw, is this just an idle bit of exploratory thought (I have no problem with that) or is there some application you had in mind?

7. ### Baluncore

3,305
This problem is usually encountered when trying to reverse engineer programmed semiconductors by reading the protected memory contents. One solution is to use a scanning electron microscope with a probe. If you could lower the frequency from 1 MHz to 1kHz then it would make SEM easier.

There is a rule of thumb. If you want to image an object, you must use radiation that has a wavelength shorter than the dimension of the detail you want in the image. That precludes using 1 MHz radiation for images smaller than 300 metres.

8. ### sophiecentaur

14,730
With the right processing, you can image a lot finer than that. You need a long time ( many cycles) in order to resolve tiny phase changes - and as I wrote earlier- a good SNR.

9. ### Baluncore

3,305
That is the problem.
If they were all pure sine waves with different frequencies they could be separated using interferometry without too much processing.

Before the advent of optical interferometers, microwave VLBI had an unfair baseline advantage and gave better resolution than optical systems. I don't know which is now the best.