20.309 Lab Report 1: Optical Microscopy
Emily Prentice, Mimi Yen, Kelly Drinkwater
October 17, 2010
Microscope Stability Characterization
Top Left: Sum trajectory of two stationary particles, obtained by taking ((x1+x2)/2, (y1+y2)/2) for all
x and y in the individual trajectories of each particle. Top Right: Mean squared displacement vs. time
interval for the sum trajectory. Bottom Left: Difference trajectory, obtained by taking ((x1-x2)/2, (y1y2)/2) for all x and y in the individual trajectories. Bottom Right: Mean squared displacement vs time
interval for the difference trajectory. For both trajectories, MSD was calculated for time intervals up to
10% of the total time the particles were tracked.
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We tracked the motion of two stationary particles in a dry sample in order to characterize the
stability of our microscope. These particles should move as little as possible.
The sum trajectory highlights common mode vibration, i.e. motions that move all particle
centroids identically (building vibration, jostles to the apparatus, etc.).
The difference trajectory deemphasizes common-mode vibrations and focuses on noise effects
that move the two particle centroids differently (camera shot noise, uneven illumination, dust,
etc.).
The top right graph in the figure shows a clear periodic common-mode vibration with a period
of about 1 sec, likely a building vibration.
For a time interval of 1 second, the mean squared displacement of the difference trajectory was
less than 0.01µm2. For a time interval of 14 seconds (the longest interval calculated), the mean
squared displacement was less than 0.08µm2.
See section 4 for a description of the MSD calculation.