About
Developed by E. Behringer
This set of exercises guides the student to model the results of an experiment to determine the profile of a laser beam using a knifeedge technique. It requires the development of the model of the knifeedge profile, and fitting of the model profile to experimental data. Here, the computational tasks are handled by builtin functions of the computational tool being used to complete these exercises.
Subject Area  Waves & Optics 

Level  Beyond the First Year 
Available Implementation  Python 
Learning Objectives 
Students who complete this set of exercises will be able to

Time to Complete  120 min 
EXERCISE 3: THE KNIFEEDGE PROFILE
You can experimentally determine the value of the parameter that describes the width of the beam by measuring the profile of the laser beam using a knifeedge mounted on a linear translation stage together with an optical detector connected to a power meter. The idea is that you allow the laser beam to enter the detector while you translate the knifeedge across the beam and monitor the power meter reading. Initially, when the beam is not blocked, the reading gives the total power of the beam; finally, the beam is completely blocked from entering the detector by the knifeedge and the reading would be zero (in the absence of background light). A schematic is shown below; we assume the beam is centered on the origin.
Imagine that the knifeedge travels in the direction, and that the position of the knifeedge is . Then the power received by the detector is
where is the total power of the laser beam. Show that this expression is equivalent to
where is the error function. Calculate and plot this quantity versus , the position of the knife edge, when mm and for .
#
# Beam_Profile_Exercise_3.py
#
# This file will generate a plot of
# the predicted knifeedge beam profile
# for the TEM00 laser mode
#
# Written by:
#
# Ernest R. Behringer
# Department of Physics and Astronomy
# Eastern Michigan University
# Ypsilanti, MI 48197
# (734) 4878799
# This email address is being protected from spambots. You need JavaScript enabled to view it.
#
# 20160614 by ERB
#
# import the commands needed to make the plot and fit the data
from pylab import xlim,xlabel,ylim,ylabel,grid,show,plot,title
from numpy import linspace,sqrt
from scipy.special import erf
# inputs
npts = 200 # number of intervals in x
w0 = 0.5 # beam width [mm]
# calculated quantity
x_max = 3.0*w0
# set up the array of knifeedge positions
x = linspace(x_max,x_max,npts+1)
# calculate the scaled power
scaled_P = 0.5*(1.0  erf(sqrt(2.0)*x/w0))
# Define the limits of the horizontal axis
xlim(x_max,x_max)
# Label the horizontal axis, with units
xlabel("Knifeedge position \(x\) [mm]", size = 16)
# Define the limits of the vertical axis
ylim(0.1,1.1)
# Label the vertical axis, with units
ylabel("Scaled transmitted power \(P(x)/P_0\)", size = 16)
# Make a grid on the plot
grid(True)
# Make the title
title('Normalized knifeedge profile for \(w_0 = \)%s mm'%w0)
# Generate the plot. The line color is magenta (m).
plot(x,scaled_P,"m")
show()
For Teachers
Translations
Software Requirements
Android  iOS  Windows  MacOS  
with best with  Chrome  Chrome  Chrome  Chrome 
support fullscreen?  Yes. Chrome/Opera No. Firefox/ Samsung Internet  Not yet  Yes  Yes 
cannot work on  some mobile browser that don't understand JavaScript such as.....  cannot work on Internet Explorer 9 and below 
Credits
Fremont Teng; Loo Kang Wee; based on codes by E. Behringer
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Sample Learning Goals
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For Teachers
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Research
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Video
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Version:
 https://www.compadre.org/PICUP/exercises/exercise.cfm?I=134&A=laser_beam_profile
 http://weelookang.blogspot.com/2018/06/laserbeamprofileexercise3knife.html
Other Resources
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