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Homework: Now due Monday, 12pm on the 25 th at 364 LLP.

Homework: Now due Monday, 12pm on the 25 th at 364 LLP. There will be another HW assigned on Monday, Oct 28, due Tuesday Nov 5 th . Following Tuesday: Tom Kuhlman talking on Following Thursday (31 st ): Tour of optical and magnetic traps (and fluorescence)

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Homework: Now due Monday, 12pm on the 25 th at 364 LLP.

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  1. Homework: Now due Monday, 12pm on the 25that 364 LLP. There will be another HW assigned on Monday, Oct 28, due Tuesday Nov 5th. Following Tuesday: Tom Kuhlman talking on Following Thursday (31st): Tour of optical and magnetic traps (and fluorescence) We’ll go over Fourier Transforms and start Fluorescence today.

  2. Drag force γ = 6πηr Brownian motion as test force Langevin equation: ≈0 kBT Trap force Inertia term (ma) Fluctuating Brownian force Inertia term for um-sized objects is always small (…for bacteria) Brownian force: There is power on the bead at all frequencies

  3. You can put one frequency at a time, and measure the response, and then scan through the frequencies. Or you can put in all frequencies and find the resulting signal General form: Fourier Transform –put in a square wave, see result, or modify the result.

  4. Can add more “base” or treble to music. Fig. 1.25: Illustration of the addition of sine waves to approximate a square wave. http://en.wikibooks.org/wiki/Basic_Physics_of_Digital_Radiography/The_Basics

  5. 1st two Fourier components http://cnx.org/content/m32423/latest/

  6. Fundamental F~1; A ~1 1st Harmonic F ~ 3x; A=1/3 2nd Harmonic F ~ 5x; A=1/5 Fig.2 http://www.techmind.org/dsp/index.html

  7. 1st 3 components (terms)

  8. 1st 11 components The representation to include up to the eleventh harmonic. In this case, the power contained in the eleven terms is 0.966W, and hence the error in this case is reduced to 3.4 %.

  9. Test your brain: What does the Magnitude as a function of Frequency look like for the 2nd graph?

  10. Filtering as a function of wavelength Use in music…

  11. Can add more “base” or treble to music. Fig. 1.25: Illustration of the addition of sine waves to approximate a square wave. http://en.wikibooks.org/wiki/Basic_Physics_of_Digital_Radiography/The_Basics

  12. A simple Radiogram: Enhanced Resolution by FFT 1.23: A profile plot for the yellow line indicated in the radiograph. Can think of spectra as the intensity as a function of position or a function of frequency.  Fourier Transforms http://en.wikibooks.org/wiki/Basic_Physics_of_Digital_Radiography/The_Basics

  13. A fundamental feature of Fourier methods is that they can be used to demonstrate that any waveform can be approximated by the sum of a large number of sine waves of different frequencies and amplitudes. The converse is also true, i.e. that a composite waveform can be broken into an infinite number of constituent sine waves.

  14. 2D spatial Filter with Fourier Transforms Fig. 1.27: 2D-FFT for a wrist radiograph showing increasing spatial frequency for the x- and y-dimensions, fx and fy, increasing towards the origin. http://en.wikibooks.org/wiki/Basic_Physics_of_Digital_Radiography/The_Basics

  15. (a) Radiograph of the wrist. (b) The wrist radiograph processed by attenuating periodic structures of size between 1 and 10 pixels. (c): The wrist radiograph processed by attenuating periodic structures of size between 5 and 20 pixels. (d): The wrist radiograph processed by attenuating periodic structures of size between 20 and 50 pixels.

  16. Beginning of microscopes Microscope must produce a magnified image of the specimen, separate the details in the image, and render the details visible to the human eye or camera. www.olympusmicro.com

  17. You can get beautiful pictures www.invitrogen.com

  18. How much can you see?Fluorescence (single molecule)Light microscopy– amount of contrastFluorescence microscopy is much more sensitive than standard microscopy How small can you see– limited to l/2

  19. Why can you see so little w fluorescence? I weighed myself. (130 lbs). I then shaved and wanted to know how much lighter I was. Two methods. 1. Weigh myself again. Take difference. 2. Weigh just the hair. Which is more accurate? Why? Answer: #2: you are subtracting off two big #’s in method 1, each of which has some noise (uncertainty) roughly proportional to the signal (or ≈√Signal). What counts is Signal to Noise

  20. Noise Why can’t you see starlight in the day? (The stars are just as bright during the day as at night.) You have a “bright” background (sun)... which has a lot of noise. If you have N photons, then you have √N noise. (This is important to remember!) Example: Sun puts out a 106 photons/sec. Noise = 103 photons/sec Therefore: if star puts out 103 photons/sec, can just barely “see it” with Signal/Noise =1 (Really want to “see it” with S/N of at least a few >2-5))

  21. Example of Noise con’t Let’s say star puts out 100 photon/sec. (It turns out you (your eye) can see about 1 photon!!) S/N day? At night? Fluorescence vs. standard light Microscopy

  22. Class evaluation • What was the most interesting thing you learned in class today? • 2. What are you confused about? • 3. Related to today’s subject, what would you like to know more about? • 4. Any helpful comments. Answer, and turn in at the end of class.

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