Fourier Transform

Question 1

Basic FT Principle in CryoEM

Answer 1

• electron beam shot through sample and scattered
• image is FT of sample
• lense creates inverse FT of electrons to form image

Question 2

Wave Components

Answer 2

1. frequency (or wavelength)
2. amplitude
3. phase shift

Question 3

Reciprocal Space

Answer 3

• wavelength and frequency are reciprocal
• waves can be represented in frequency/reciprocal space
• amplitude and phase represented as a function of frequency

Question 4

Fourier Transform

Answer 4

• essentially teasing apart composite waves into discrete sine wave components
• calculates component sine waves of composite (distinct frequencies/amplitudes)
• inverse FT puts components back together

Question 5

DC Components

Answer 5

• straight horizontal line
• constant
• infinite wavelength with frequency of 0

Question 6

2D Waves

Answer 6

• amplitude, phase, and 2D frequency component
• oscillating in two directions (a,b)
• detect frequency along a and b axes
• DC of 0,0
• plot wave component and DC component (Friedl pairs)
  eg. frequency of 2 along a and 0 along b will give 0,0 and -2,0 and 2,0
• amplitude of Friedl pairs sum to amplitude of single wave

Question 7

Composite 2D Waves

Answer 7

• each component wave forms individual spot coordinates

- black spots have no image contribution

Question 8

Fourier Transform Definition

Answer 8

decompose complex composite waves into component 2D sine waves with given 2D frequency/phase/amplitudes corresponding to these frequencies

• inverse FT to get back to original image
• each pixel represents amplitudes of each 2D sine ave in image
• changing one pixel in original image changes every fourier component

Question 9

Process of Image Creation

Answer 9

• image FT into pixel image
• extract individual FT components
• inverse fourier transform into waves
• build image from layering waves

Question 10

Filters

Answer 10

• applied in reciprocal space
• low pass filter: low spatial filter
• high pass filter: removes dc component/high spatial frequency

Question 11

3D Waves

Answer 11

• X,Y,Z fourier components in sine waves
• can visualise 3D composite wave of a molecule
• go from 3D image to waves with specific phases/amplitudes with respect to wave frequency