Changes

The pupose of this page is to describe the work being done in the construction of a tabletop Michelson Interferometer.  The purpose of this device in the scope of the project is two fold.  First, the interferometer can be used to analyze the vibrational characteristics of a diamond wafer suspended from a wire frame.  Second, the interferometer can be used to study the surface profile of a diamond wafer, allowing us to see the effects that different cutting and mounting techniques have on the final product.  The main work does this semester has been on the vibrational aspects of the diamond mounting.

 

All atoms are made up of protons and neutrons, which are in turn comprised of quarks.  The particles “gluing” the quarks together are known as [http://en.wikipedia.org/wiki/Gluons gluons].  The interaction of quarks and gluons is still not entirely understood, specifically how they are confined in the nucleus such that lone quarks are never seen.  The nuclear physics group at the University of Connecticut is part of the [http://dustbunny.physics.indiana.edu/HallD/GlueX/Home.html GlueX Experiment], which hopes to probe directly the gluon bond and understand its mechanical properties.  The probe used by GlueX is a high energy (small wavelength), polarized photon (particle of light) generated by a technique known as coherent bremsstrahlung .  This technique involves radiation of photons as a high energy electron beam passes through a carefully oriented diamond wafer. Because of the potential for contamination, it is necessary to suspend the diamond wafer rather than mount on a ridged mount.  The diamond is currently suspended on  thin tungsten wires.  Proper orientation ensures a high degree of polarization, which requires stable mounting of the diamond.  The goal of my research is to investigate the mechanical properties of the mount and eliminate the possibility of vibration of the crystal.

 

The pupose of this page is to describe the work being done on the development of a system to analyze these vibrations.  Two different techniques will be used to determine the amplitude and frequency of these vibrations.  First, a direct imaging technique will be used.  A [http://en.wikipedia.org/wiki/Michelson_interferometer Michelson interferometer] will also be constructed, and will be used in not only the vibrational research, but also in the analysis of the diamond surface structure.

== Construction ==  

== Construction ==  

| || Kinematic Mirror Mount || Adjustable Kinematic mount for 1" holder

| || Kinematic Mirror Mount || Adjustable Kinematic mount for 1" holder

|-  

|-  

| Light Source || 532nm Green laser Module || 5mW, 5mm spot size, <1.4 mrad div.  

| Light Source || 532nm Green laser Module [[Media:5_milli_watt_circuit.pdf|Circuit Layout]]  || 5mW, 5mm spot size, <1.4 mrad div.  

|-

|-

| || Kinematic V-Mount || Small Mount with Attached Clamping Arm

| || Kinematic V-Mount || Small Mount with Attached Clamping Arm

| Safety Equipment || Laser Safety Glasses || Green and Blue laser beam protection

| Safety Equipment || Laser Safety Glasses || Green and Blue laser beam protection

|}

|}

=== Estimating Camera Sensitivity ===

=== Estimating Camera Sensitivity ===

It is critical to understand the sensitivity of the camera to light from the interferometer, given the high intended image acquisition speed. The camera purchased for this setup, Casio EX-F1, has a movie frame rate capability of 1200&nbsp;Hz. The following information allows an order of magnitude estimate of the sensitivity. (The camera uses a CMOS sensor. Note that lx=lm&middot;m²)

Originally the parts list called for a 1mW laser.  There was a concern, however, that this laser would not be powerful enough to produce interferograms.  It is critical to understand the sensitivity of the camera to light from the interferometer, given the high intended image acquisition speed. The camera purchased for this setup, Casio EX-F1, has a movie frame rate capability of 1200&nbsp;Hz. The following information allows an order of magnitude estimate of the sensitivity. (The camera uses a CMOS sensor. Note that lx=lm&middot;m²)

* a sample CMOS chip, Micron's MT9P401, has sensitivity of 1.4&nbsp;V/lx&middot;s and supply voltage of 2.8&nbsp;V yielding 2&nbsp;lx&middot;s of light energy to saturation.

* a sample CMOS chip, Micron's MT9P401, has sensitivity of 1.4&nbsp;V/lx&middot;s and supply voltage of 2.8&nbsp;V yielding 2&nbsp;lx&middot;s of light energy to saturation.

The two order of magnitude shortfall means that very little of the dynamic range of the sensor will be used, leading to a low signal to noise ratio. For this reason, a 5mW laser was chosen over a 1mW.

The two order of magnitude shortfall means that very little of the dynamic range of the sensor will be used, leading to a low signal to noise ratio. For this reason, a 5mW laser was chosen over a 1mW.

=== Choosing a pinhole ===

 

It is crucial that any spherical aberration are removed by way of pinhole.  The laser spot is passed through a pinhole, which acts to expand the beam. This expansion creates a patter known as an [http://en.wikipedia.org/wiki/Airy_disk Airy pattern]. To correctly remove the spherical aberrations, the beam must be expanded such that the only the first ring is sent through the second lens, and the rest is blocked off.  To determine the proper pinhole size for the design, [[Huygens Principle for a Planar Source|the following analysis was performed]].

== Camera Calibration ==

Analysis of videos taken of the vibration of the diamond wafer can lead to information about both the frequency and the amplitude of vibration.  To perform simultaneous measurements of both parameters, a precise camera calibration was necessary.

 

=== Calibration Set-Up ===

The following is an image of the device used for the camera calibration:

 

 

This calibration device was used to determine the change in pixel location of the center of the lens flares based on angular displacement.  To do this, the camera was mounted horizontally on a 1.40m long bar.  The camera end was free to rotate about a pivot located at the opposite end of the rod, above which a mirror was mounted.  A linear micro-adjustment translation stage was placed below the camera end.

 

 

[[Image:Screenshot.jpg|center|Matlab code used for image analysis]]

 

The first line imports the image, in this case IMAG0001.jpg, converts it to a matrix, and separates the green channel.  Next, this matrix is imaged in false color in terms of intensity from blue(low) to red(hgh).

The last line is the actual search function. The search functions by finding the location with the smallest difference between the intensity(a(m,n)) and the fit function we apply to image.  We use a gaussian distribution with user defined parameters as our fit.  The code for this function is:

      function out=gauss2(x,y,p)

 

        [xx,yy]=meshgrid(x,y);

 

        out=p(1)*exp(-0.5*((xx-p(2))/p(3)).^2-0.5*((yy-p(4))/p(5)).^2) + p(6);

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).

== Design of a mounting device for diamond surface analysis ==

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. 

==Video analysis ==

   

During the last test as [http://www.chess.cornell.edu/ CHESS] it was determined that the wire mount was not suitable for diamond analysis because the rocking curve was skewed by the high vibrational frequency of the diamond-wire system.  In order to perform the surface analysis, a new mounting device is in development.  

* [[Interferograms]]

[[Image:Mylar mount.jpg|center|Mount which will be used at the next run at CHESS]]

* [[Analysis of heat equation for diamond mounting]]

In order to use this mount in the diamond analysis, the center area of the mylar must be sufficiently flat.  To ensure this flatness, a large sheet of mylar (100 <math> \mu m</math>, most likely 24" x 24") will be placed over and attached to a drum with an 18" diameter.  The large diameter will ensure that any small wrinkles at the edges will not propagate all the way to the center region.  The mount will then be glued to the mylar and while the glue is still tacky, the mylar will be stretched. The mylar will be stretched by placing a weighted container (approximately 100 pounds) on top of it. To verify that the center region is flat, the mount will be placed in the interferometer, and the interferogram will be analyzed using the process found [http://zeus.phys.uconn.edu/wiki/index.php/Analysis_of_Michelson_interference_images here].  This will give us an image of the surface of the mylar.