Assignment 2: fluorescence microscopy

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20.309: Biological Instrumentation and Measurement

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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

  1. Turn in your plot of simulation results
    • Find the interval [ $ \mu - s $, $ \mu + s $ ] that contains about 68% of the simulation results.
    • Turn in the code you used to find the interval.
  2. On the same plot, plot the PDF of a normal distribution with the same mean and standard deviation as the simulation results. Multiply the PDF by a constant so that it has the same vertical scale as the histogram.
  3. Is the Poisson distribution a good approximation of shot noise?
    • What percentage of the results fall with one, two, and three standard deviations?
    • Produce a log-log 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: 10-6, 10-5, 10-4, 10-3, and 10-2.
    • Hints: Use a nested loop. Use the poissrnd function instead of the line containing rand. 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)?
    • Turn in the code you used to generate the plots
  4. On one set of axes, plot the variance vs. mean for exposure times of 10-4, 10-3, 10-2, 10-1, and 100 seconds.
  5. Using the camera measurements provided:
    1. Plot the raw data from the static scene measurements and the model best fit on one set of axes.
    2. Calibrate the gain setting: make a plot of the actual camera gain in electrons per ADU versus the software setting.
    3. Provide a formula for converting the camera gain setting to the actual gain value.
    4. Plot dark current versus exposure time and determine the value of ID in units of electrons per pixel per second.
    5. Determine the read noise standard deviation.
    6. Under what circumstances is each of the three noise terms is dominant?

Parts 2 & 3

  1. Draw a block diagram of the LED epi-illumination path. Indicate the focal lengths of all lenses, the correct lens orientation, and all important distances between components.
  2. Lenses L3 and L4 make an image of the LED. Assuming the initial size of the LED is 1.3 mm, what is the size of the LED image made by lens L3?
  3. For each bead sample, include the original, reference, and flat-field corrected images in your lab report. In the caption note the exposure and gain settings used for each image.
  4. 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 flat-field correction.

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