ELOG - Beam Profiling Results

40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop

40m Log

Not logged in

List | Find | Login | Help

Wed May 17 18:08:45 2017, Dhruva, Update, Optical Levers, Beam Profiling Setup

Mon May 22 10:53:02 2017, Dhruva, Update, Optical Levers, Beam Profiling Results 6x

Tue May 23 10:27:24 2017, Dhruva, Update, Optical Levers, Beam Profiling Results 6x

Tue May 23 15:22:04 2017, rana, Update, Optical Levers, Beam Profiling Results

Tue May 30 18:31:54 2017, Dhruva, Update, Optical Levers, Beam Profiling Results

Thu Jun 8 12:43:42 2017, Dhruva, Update, Optical Levers, Beam Profiling Results

Tue May 23 16:33:00 2017, Steve, Update, Optical Levers, Beam Profiling Results

Message ID: 13053 Entry time: Thu Jun 8 12:43:42 2017 In reply to: 13021

Author:	Dhruva
Type:	Update
Category:	Optical Levers
Subject:	Beam Profiling Results

Quote:

Updates in the He-Ne beam profiling experiment.

New and improved plots for the He-Ne profiling experiment

Font size has been increased to 30.

The plots are maximum size (Following Rana's advice, I saved the plots as eps files(maximized) and converted them to pdf later).

There is a shaded region around the trendline that represents the parameter error.

Function that I fit my data to (should have mentioned this in my earlier elog entries)

$P = \dfrac{P_0}{2}\Bigg[1+erf\Big(\dfrac{\sqrt2(X-X_0)}{w}\Big) \Bigg]$

Description of my error analysis -

1. I have assumed a 20% deviation from markings in the micrometer error.

2. Using the error in the micrometer, I have calculated the propogated error in the beam power :

$\delta P = \sqrt{\dfrac{2}{\pi}}{P_0}\dfrac{\delta x}{w}\exp\Bigg({\frac{-2(X-X_0)^2}{w^2}}\Bigg)$

I added this error to the stastistical error due to the fluctuation of the oscilloscope reading to obtain the total error in power.

3. I found the Fisher Matrix by numerically differentiating the function at different data points $P_b$ with respect to the parameters $p_i =$ $P_0, X_0$ and $w$ .

$F_{ij} = \sum_{b} {\frac{\partial P_b}{\partial p_i}\frac{\partial P_b}{\partial p_j}}$ $\frac{1}{\sigma^2_b}$

I then found the covariance matrix by inverting the Fisher Matrix and found the error in spot size estimation.

EDIT : Residuals added to plots and all axes made equal

Attachment 1:

profile.pdf 955 kB Uploaded Thu Jun 8 20:35:49 2017 | Hide | Hide all

ELOG V3.1.3-