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Correct Sampling

Correct Sampling. What is SAMPLING?. Intensity [a.u.]. X [µm]. 1. 2. 3. 4. 5. 6. Intensity [a.u.]. 2. 3. 4. 5. 6. Aliasing … suppose it is a sine-wave. There are many sine-waves, SAMPLED with the same measurements. Which is the correct one?. Intensity. Spatial Coordinate.

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Correct Sampling

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  1. Correct Sampling

  2. What is SAMPLING? Intensity [a.u.] X [µm] 1 2 3 4 5 6

  3. Intensity [a.u.] 2 3 4 5 6 Aliasing … suppose it is a sine-wave There are many sine-waves, SAMPLED with the same measurements.Which is the correct one?

  4. Intensity Spatial Coordinate Aliasing … suppose it is a sine-wave … maybe we can know! Object: Microscope Image: Intensity Spatial Coordinate

  5. ½ Sampling Frequency Aliased Frequencies Aliasing in Fourier-space Fourier-transform of Image Intensity ½ Nyquist Frequencies

  6. Pixel sensitivity Convolution of pixel form factor with sampling positions  Multiplication in Fourier-space  Reduced sensitivity at high spatial frequency Intensity [a.u.] X [µm] 1 2 3 4 5 6

  7. rectange form-factor specimen sampled Optical Transfer Function contrast 1 0 |kx,y| [1/m] Cut-off limit

  8. Consequences of high sampling Confocal: high Zoom more bleaching? No! if laser is dimmed or scan-speed adjusted bad signal to noise ratio? Yes, but photon positions are only measured more accurately binning still possible high SNR. Readout noise is a problem at high spatial sampling (CCD)

  9. Optimal Sampling?

  10. Multiplied in real spacewith band-limited information Regular sampling Reciprocal d-Sampling Grid Real-space sampling:

  11. Widefield Sampling • In-Plane sampling distance •  Axial sampling distance

  12. Confocal Sampling • In-Plane sampling distance (very small pinhole) • else use widefield equation •  Axial sampling distance

  13. Confocal OTFs in-plane, in-focus OTF1.4 NA Objective WF Limit 1 AU 0.3 AU WF

  14. Reciprocal d-Sampling Grid Multiplied in real spacewith band-limited information Hexagonal sampling Real-space sampling: Advantage: ~17%+ less ‚almost empty‘ information collected+ less readout-noiseapproximation in confocal; 3D: ABA, ABC stacking

  15. 63× 1.4 NA Oil Objective (n=1.516), excitation at 488 nm, emission at 520 nm  leff = 251.75 nm, a = 67.44 deg widefield in-plane: dxy < 92.8 nm  maximal CCD pixelsize: 63×92.8 = 5.85 µm confocal in-plane: dxy < 54.9 nm widefield axial: dz < 278.2 nm confocal axial: dz < 134.6 nm Fluorescence Sampling Example

  16. OTF is not zero but very small(e.g. confocal in-plane frequency) Object possesses no higher frequencies You are only interested in certain frequencies (e.g. in counting cells, serious under-sampling is acceptable) Reasons for Undersampling

  17. Detector generates high-frequency noise? Measure this noise (e.g. dark exposure and 2D FFT) Avoid aliasing by sampling above this noise frequency. Traps and Pitfalls

  18. FFT of dark CCD exposure (2 µs)

  19. If you need high resolution or need to detect small samples  sample your image correctly along all dimensions Sampling Summary

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