Wavelength and resolution

[ledamage]

Hi there!

What is meant by saying that a photon of smaller wavelength can resolve smaller distances?

I know from scattering theory that the form factor is the Fourier transform of the charge distribution and that knowing the form factor at high momentum transfers gives a better overall picture of the distribution. But without information from measurements at long wavelengths, the distribution can't be reconstructed either, can it?

I also know the "argument" using the uncertainty relation. But the UR connects the typical length scale and momentum uncertainty of one single wavefunction but in this context it is used in the way that $\Delta x$ is related to the target's extension whereas $\Delta p$ is the photon's momentum. I simply don't get it.

Thanks to you all!
ledamage

 

[Creator]

Hi there!

What is meant by saying that a photon of smaller wavelength can resolve smaller distances?
\
l

Limits on angular resolution with wavelength are best descibed by wave mechanics using the concept of diffraction limitations, and is given by the Rayleigh criterion.

see...http://hyperphysics.phy-astr.gsu.edu/Hbase/phyopt/Raylei.html

 

[Entropia]

Hi ledamage,

Thank you for your question! Wavelength and resolution are closely related in the context of imaging and scattering experiments. In general, the resolution of an imaging or scattering experiment refers to the smallest feature or distance that can be distinguished or resolved by the measurement. This is often limited by the wavelength of the probe used in the experiment.

In the case of photons, their wavelength is inversely proportional to their momentum. This means that a photon with a smaller wavelength will have a higher momentum. In imaging and scattering experiments, this higher momentum allows the photon to probe smaller distances or features in the target material. This is because the high momentum of the photon allows it to interact with smaller structures in the target, providing more detailed information about the distribution of the material.

The uncertainty principle also plays a role in this relationship between wavelength and resolution. As you mentioned, the uncertainty principle relates the uncertainty in position (Δx) and momentum (Δp) of a particle. In the context of imaging and scattering, this means that a photon with a smaller wavelength (Δx) will have a higher momentum (Δp). This higher momentum allows for more precise measurements of the target's extension, leading to better resolution.

In summary, a photon with a smaller wavelength can resolve smaller distances because of its higher momentum, which allows it to interact with smaller structures in the target. This is also supported by the uncertainty principle, which relates the wavelength of the photon to its momentum and the ability to measure small distances. I hope this helps clarify the relationship between wavelength and resolution in the context of imaging and scattering experiments. Keep asking great questions and happy experimenting!