Changes

[[Image:Screenshot2.png|center|300px|Matlab code used for image analysis]]

[[Image:Screenshot2.png|center|300px|Matlab code used for image analysis]]

    

    

The parameters p(1) to p(6) are, in numerical order, (1) the amplitude of the function, (2) x location, (3)sigma x, (4) y location, (5) sigma y, and (6) an offset applied to eliminate background noise.  The function takes user inputs as an initial guess, then loops the search process to find more accurate values for the parameters.  Arbitrary values are chosen for p(1), p(3), p(5) and p(6) to begin, and are then readjusted based on the first output parameters.  Typically, the closer these fit parameters are to the true parameters, the better the function is at defining p(2) an p(4).

The parameters p(1) and p(2) are the x and y locations for the test point, respectfully.  Suitable shape and amplitude parameters for the flare spots were chosen based on analysis of individual images.  Once the fit is complete, the program put the x and y location for an image in a matrix called pars, with the x location in column 1 and the y locations in column 2.  The program loops this fitting procedure until all the images have been fit.  Once the fit is complete, the mean value for the x and y positions are subtracted from their respective columns and the data points are scaled (using the data received from the camera calibration) to obtain the deflection of the glass from center.   

By knowing the change in pixel location between photos, as well as th angular displacement, a value for pixel change per mrad in the x diection can be determined.  This process is then repeated for the y direction. Once these two parameters are known, the video analysis can be used to find both frequency and amplitude.

 

[[Image:deflection_plot.jpeg|center|400px|Plot of the amplitude of vibration versus time for the simulated diamond wafer]]

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