New Gaussian Fit on the temperature curve due to the YAG laser

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New Gaussian Fit on the temperature curve due to the YAG laser

Post  Alessandro on Fri Oct 09, 2009 8:52 pm

The Fit exposed in a previous topic is wrong.

The function Fit applied is the sum of two Gaussian functions.
The initial values of the parameters were set after several trials.
The curve is on the distribution of temperature on the surface of the mirror, so it is different from a single Gaussian!

Graph of best fit, with the function Fit used:



The parameter d1 is the temperature limit for the maximum radius of the mirror.

We can see how the fit is perfect, this is confirmed by the following data:

General model (the function Fit):
f(x) = a1*exp(-((x-b1)/c1)^2)+a2*exp(-((x-b2)/c2)^2)+d1

Coefficients (with 95% confidence bounds):
a1 = 1.028 (1.009, 1.047)
a2 = 0.5202 (0.5037, 0.5366)
b1 = -1.072e-011 (-5.76e-005, 5.76e-005)
b2 = 4.605e-011 (-0.000182, 0.000182)
c1 = 0.04721 (0.0469, 0.04752)
c2 = 0.09443 (0.09259, 0.09627)
d1 = 295.2 (295.2, 295.2)

Goodness of fit:
SSE: 0.001488
R-square: 1
Adjusted R-square: 1
RMSE: 0.00277 (Confirmation of the quality of the Fit!)

Comments:

  • We note that the two Gaussians are centered on x = 0 (center of the mirror).
  • Their amplitude (intensity) is real and implementable.
  • The Gaussian differ in amplitude and width (Sigma, C1 and C2).
  • New possibility for the DRC method with the cones cut.
  • Subsequent tests with ANSYS for confirmation.
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Alessandro

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