20.309: Biological Instrumentation and Measurement
This assignment has 3 parts.
Submit your work on Stellar in a single PDF file with the naming convention <Lastname><Firstname>Assignment2.pdf.

Here is a comprehensive list of what you need to turn in:
Part 1 (individually)
 What percentage of the results fall with one, two, and three standard deviations? Is it reasonable to approximate this situation as a normal distribution?
 Produce a loglog plot of standard deviation of the number of photons emitted as a function of the average number of photons emitted for probability of photon emission equal to the values: 1E6, 1E5, 1E4, 1E3, and 1E2. Hints:
 Use a nested loop.
 Speed things up by getting rid of the plotting inside the loop and only run 100 simulations for each probability.
 What is the relationship between the number of photons detected and the noise (standard deviation)?
 Repeat the simulation for a detector that has only a 25% chance of detecting a photon and a light source that is 4 time brighter.
 Turn in the code you used to generate the plots
 On one set of axes, plot the average variance vs. mean for exposure times of 10^{4}, 10^{3}, 10^{2}, 10^{1}, 10^{0} seconds.
 In what situations is dark current noise a significant problem?
Parts 2 & 3 (as a team)
 Choose focal lengths for L3, L4 and L5 so that the laser beam diameter matches the FOV of the CCD camera.
 Sketch a block diagram of the illumination path. Make sure to indicate
 your chosen focal lengths for L3L5,
 the correct lens orientations, and
 distances between components (if not important, leave blank).
 For each bead sample, include the original, reference, and flatfield corrected images in your lab report. In the caption note the exposure and gain settings used for each image.
 For one set of images (either the 0.84 or 3.6 μm beads and their corresponding dark and reference images), include the MATLAB code you used to calculate the flatfield correction.

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