Measurement of a particle's position using photons

[Frank Castle]

I've read that a particle's position can be measured by firing a photon at it, but how does one actually determine the position of the particle by doing this? What is the maths behind it (is it calculated from momentum conservation)? Furthermore, I've read that increasing the energy of the photon fired at the particle increases the accuracy of the position measurement, why is this so?

 

[vanhees71]

Measuring the position of something with light is what we do all the time in everyday life. The shorter the wave length the better is the resolution due to the diffraction limit (Abbe et al):

https://en.wikipedia.org/wiki/Diffraction-limited_system

 

[Frank Castle]

Measuring the position of something with light is what we do all the time in everyday life. The shorter the wave length the better is the resolution due to the diffraction limit (Abbe et al):

https://en.wikipedia.org/wiki/Diffraction-limited_system

Thanks for the link.

How does one measure the position though, is it related to the scattering angle of the photon?

 

[Vanadium 50]

Hold up a ruler to it and compare the scattered light from the object to the scattered light from the ruler. We do this with our eyes all the time.

 

[Frank Castle]

Hold up a ruler to it and compare the scattered light from the object to the scattered light from the ruler. We do this with our eyes all the time.

I'm not sure what you mean by that? It that we now the angle that the incident light was emitted at and then we can infer from its scattering angle the location of the particle?

 

[Vanadium 50]

How do you use light, a ruler, and your eyes to determine the size of a pencil?

 

[Khashishi]

You can't really measure much with a single photon. But if you fire a whole bunch of photons, you can take an image using a camera.

 

[Frank Castle]

How do you use light, a ruler, and your eyes to determine the size of a pencil?

Ah, stupid me, I see what you mean. The incident light scatters off the top and bottom of the pencil and yours eyes absorb these incoming photons and determine from the angle that they arrive at what point on the ruler they came from, right?

 

[Frank Castle]

You can't really measure much with a single photon. But if you fire a whole bunch of photons, you can take an image using a camera.

True, but what about determining locations of particles?

Is the idea that we emit a large number of photons from some source, and a fraction of these will scatter of off the particle. These photons will be reflected back to our source, where a detector is located, and from the angular distribution of the reflected photons detected we can reconstruct their paths to determine a location for the particle. The accuracy of the measurement is determined by the aperture of the detector - the smaller the aperture, the better the resolution. However, longer wavelength light will be diffracted more for smaller apertures and so the accuracy of the postion available from the incoming data will be reduced. Hence, decreasing the wavelength of the incident photons (correspondingly, increasing their energy) will mean that they diffract less for smaller apertures and hence the resolution increases.

Would this be correct at all?

 

[Vanadium 50]

right?

Right.

 

[Frank Castle]

Right.

Actually, I've thought about this a bit more. Is it that one puts the ruler next to the pencil, such that the one can compare the angle of the light scattered from the top and the bottom of the pencil with the angle of light scattered from the ruler. From this one can determine the length of the pencil as the angles measured for the top and bottom of the pencil should correlate to the scattering angles of light scattering off of particular lengths along the ruler.

In the case of measuring the position of a particle, is the idea that one scatters light off of it and uses a detector to detect this scattered light. Is the idea that one can use this information (angles the scattered light is detected at) to reconstruct the path they took, and thus where they diverged from, giving a measurement for the position of the particle?

Also, I now know of the diffraction limit thanks to Vanhees, but is there an intuitive way to understand why light of shorter wavelength increases the accuracy of the measurement? Is it due to the incident light being diffracted less as it scatters off of the structure off the particle?