Are there limitations to detecting small objects using sound and light?

[nickek]

Hi!
In a book, there is stated that the least detectable object by a bat is when the object is λ/2 of the sound wavelength emitted by the bat. I know there is resolution criteria for light microscopes too, which concerns the wavelength of the light.

My question is: Are these criteria about the phenomena of interference of waves or something else? Or maybe it is possible to detect the objects smaller than this size, but we can not get any information about size or form from them if the wavelength is too long?

 

[Drakkith]

The basic idea revolves around the interference of the light wave with itself as it converges to a point. Basically, the more of the wave you can get to converge, the more the light wave constructively interferes with itself at the point of focus, resulting in a smaller spot. This is why larger telescopes with larger diameters have a higher angular resolution. You can read more here:
http://en.wikipedia.org/wiki/Diffraction-limited_system
http://en.wikipedia.org/wiki/Angular_resolution

 

[Andy Resnick]

<snip>My question is: Are these criteria about the phenomena of interference of waves or something else? Or maybe it is possible to detect the objects smaller than this size, but we can not get any information about size or form from them if the wavelength is too long?

There's at least one important difference between 'detecting' and 'resolving'- while 'resolving' does involve the wavelength of light (or sound), 'detecting' does not- detection only depends on the signal-to-noise ratio, which can be quite high even for subresolution objects. Also, it is true that detection of a subresolution object does not provide any information about the size/shape/etc. of the object.

 

[glappkaeft]

One good example is stars. Naked eye resolution is about 1 arc minute (60 arc minutes = 1 degree) so we can only resolve one star (the sun at ~30 arc minutes) but there are thousands of stars we can detect given reasonably dark skies (good SNR).

 

[nickek]

Thanks for answers, everyone. Now I have a starting point for curious students asking about this task.

 

[sophiecentaur]

Bats have a significant amount of brain power and they can deduce a lot about what their target is without needing a high resolution sonar image. They can detect a target and know its distance. The strength of the return signal is a good indication of size because the reflectivity of their prey species will be much of a muchness (unlike the range of brightnesses of stars, for instance). They can then go closer and 'investigate' - unlike astronomers with their stars.

Diffraction (resolution) limits, optical and sonar are a bigger problem when it comes to deciding whether it's one or two objects you are looking at. The eye can see many points of light up in the night sky which are, in fact two or more bright objects.