Limits of Detection:Report Requirements

• Before you go to the lab, read the optical trapping lab manual and the the Atomic Force Microscopy lab manual
• Attend an optical trap lab session during the week of 11/28-12/3.
• Attend an AFM lab session during the week of 12/5-12/9.
• Submit your report in PDF format to Stellar before midnight on 12/13.
• Name the file: <lastname>DetectionLimitReport.pdf. (Substitute your surname for "<lastname>")
• The report should be answer-book style, like a problem set.
• Submit all the computer code (.m files) that you used in your analysis as a single, separate zip file to Stellar.

You will gather data as a group; however, reports must be individually authored. Everything in your report, including computer code, must be entirely your own work.

Answer the following questions:

1. Optical trap calibration
   1. What is the responsivity of the QPD in microns per Volt? Plot the raw data and linearized detector response on the same set of axes for one representative power level. Plot QPD responsivity versus power. Over what range of displacements is the detector response reasonably approximated by a line?
   2. What is your estimate of the trap stiffness as a function of power as determined by the three different calibration methods (equipartition, PSD roll-off, and Stokes drag)? Plot stiffness versus power for each method on the same set of axes.
      1. For the PSD method: plot a representative power spectrum and the corresponding model fit on the same set of axes.
      2. For the Stokes method: plot a representative displacement versus velocity dataset and the corresponding regression model on the same set of axes.
   3. Which method is superior? Explain why.
   4. What is the minimum detectable force as a function of power and bandwidth?

1. AFM
   1. What is the stiffness of the cantilever you measured? Plot the spectrum you measured and the model fit on one set of axes.
   2. How does the stiffness computed from the cantilever's material properties compare to the value measured by the Sader method?
   3. What is the smallest force you could measure using that cantilever?