Calculating Particle Spacing in a Lattice Using Fourier Transform

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SUMMARY

This discussion focuses on calculating the average distance between particles in a lattice using Fourier Transform (FT) techniques. The user encounters challenges in converting reciprocal space pixel size into real space measurements, specifically needing to apply the formula 2π/d, where d represents the particle spacing. The presence of an Airy pattern complicates the analysis, indicating that the particles may not form a perfect lattice. The discussion suggests leveraging the locations of aliases in the FT to determine spacing if the lattice structure is regular.

PREREQUISITES
  • Fourier Transform (FT) principles
  • Understanding of Airy patterns in imaging
  • Knowledge of lattice structures (rectangular, triangular, etc.)
  • Image scaling in pixels and microns
NEXT STEPS
  • Research the application of Fourier Transform in particle analysis
  • Learn about the significance of Airy disks in imaging
  • Study methods for identifying aliases in Fourier Transform results
  • Explore techniques for converting pixel measurements to physical distances
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Researchers in materials science, physicists analyzing particle distributions, and anyone involved in imaging techniques that utilize Fourier Transform for spatial analysis.

indie452
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Homework Statement



Okay so i am applying a FT to an image of particles that are forming a lattice, and i need to find the average distance between the particles

because its not a perfect lattice, I am getting an airy pattern and i believe that the distance to the first ring is the average distance between the particle.

But, i don't know how to convert reciprocal space pixel size into normal space.
I believe i need to use the 2pi/d where d is the spacing between 2 particles, but i don't know how many pixels are in 2pi/d

note: i know the scale of my image width and height in pixels and microns
 
Physics news on Phys.org
An Airy disk results from transforming a circular disk. Are your particles contained within a disk? You may be looking at the envelope.

Is your lattice regular (e.g., rectangular, triangular, etc.)? If so, then you can find the spacing from the location of aliases, that is, replications of the primary Airy disk.
 

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