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Message ID: 62     Entry time: Thu Jul 1 09:40:13 2010
Author: James Kunert 
Type: Misc 
Category: Hartmann sensor 
Subject: SURF Log 8 -- more SLED characterization 

As I started setting up my next experiment, I noticed that the beam size from the SLED appeared to be larger than expected from previous analysis. It was therefore necessary to conduct further experiments to characterize the divergence angle of the beam.

First, I set up the photodetector attached to an SLED and mounted a razor blade on a translational stage, in the same manner as done previously. All of these components were the exact same ones used in the previous beam size experiment. The only differences in the components of the apparatus were as follows: first, the photodetector was placed considerably closer to the SLED source than was done previously. Second, a different lens was used to focus the light onto the photodetector. Lens LX082 from the lenskit was used, which is a one-inch lens of focal length f=50.20mm.

Experiment 1: Columnated Beam Size Measurement

Before repeating the previous experiment, the following experiment was done: the beam was columnated by placing the lens 50.20mm away from the source and then adjusting until columnation was observed. Columnation was confirmed by setting a mirror in the optical path of the beam directing it to the other side of the room. The position of the lens along the optical axis was adjusted until the beam exiting the lens did not change in size across the length of the table and appeared to be roughly the same size as the spot on the opposite side of the room (as gauged roughly by the apparent size on an IR card and through an IR viewer).

Then,the translational stage onto with the laser was mounted was placed after the lens against the ruler clamped to the table, and beam size was measured using the same experimental procedure used to find the width in the previous experiment. The only variation in the experimental procedure was that measurements were not taken strictly at 0.5V intervals; rather, intensity readings were taken for 28 different intensity outputs. The following measurements were collected:

x(mm)   V(V)
13.00  7.25
12.00  7.24
10.80   7.18
10.15   7.09
9.50   6.92
9.30   6.86
9.00   6.74
8.75   6.61
8.50   6.47
8.25   6.31
8.00   6.12
7.75   5.92
7.50   5.69
7.30   5.49
7.15   5.33
7.00   5.17
6.75   4.88
6.50   4.58
6.25   4.27
6.00   3.95
5.75   3.63
5.50   3.32
5.25   3.02
5.00   2.729
4.60   2.306
4.50   2.205
4.25   1.981
4.00 1.770
ambient 0.585

When fit to gsbeam.m using lsqcurvefit, this yielded a width of 4.232mm. Since the beam is columnated through the lens, we know that it is approximately f=50.2mm from the source. Thus the divergence angle is approximately 0.084.

At this point, to double-check that the discrepency between this value and the previous experiment was not a result of a mistake in the function, I wrote a simpler function to go through the steps of using lsqcurvefit and plotting the fit curve versus the data automatically, 'manualbeam.m' (attached), which simply fits a curve to one set of data from a constant z-value. Using this one-by-one on each z-value in the previous experiment, it was shown that the slope of the widths was still ~0.05, so this discrepency was not the result of a mistake in the previous function somewhere.

Experiment 2: Blocked Beam Analysis 2

I then placed the razor before the lens in the beampath and repeated the previous experiment exactly. See the previous eLog for details on experimental procedure. Sets of measurements were taken at 6 different z-values, and widths were found using manualbeam.m in MATLAB. A curve of the calculated widths versus the z-position of the stage on the ruler is below:


Note that this appears to be consistant with the first experiment.

Experiment 3: Direct Beam Measurements on CCD

The front-plate of the Hartmann sensor was replaced with the new invar design (on a related note, the thread on the front plate needs a larger chamfer). In doing this, the Hartmann plate was removed. The sensor was moved much closer to the SLED along the optical axis, and an optical filter of OD 0.7 was screwed into the new frontplate. This setup allows for the direct imaging of the intensity of the beam, as shown below:


The spots and distortions on the image are from dust and other blemishes on the optical filter, as was confirmed by rotating the filter and observing the subsequent rotation of each feature.

Note that in some images, there may be a jump in intensity in the middle of the image. This is believed to be due to a inconsistant gain between the two sides of the image.

The means of the intensities of each row and each column will be Gaussian, and thus can be fit to a Gaussian using lsqcurvefit. Function 'gauss_beam1D.m' was written and this function was fit to using function 'autogaussfit1', which automatically imports the data from .raw files, fits Gaussians to the means of each row and column, and plots everything.

An example of the fit for the means of the columns of one image is as follows:


 And for the rows:


Note that for all the fits, the fitting generally looks a little better along the row than along the column (which is true here, as well).

The following procedure was used to calculate the change of the beam width as a function of distance: the left edge of the base of the Hartmann sensor was measured against a ruler which was clamped to the table. The ruler position z was recorded. Then, preliminary images would be taken and the exposure time would be adjusted as needed. The exposure time was then noted. Then, an image was taken and curves were fit to it, and the width was calculated. This was done for 15 different positions of the Hartmann sensor along the optical axis.

The calculated widths vs. displacements plot from this can be seen below:


Note that the row width and column width are not the same, implying that the beam is not circularly symmetric and is thusly probably off alignment by a little bit. Also, the calculated slopes are different than the value of 0.085 acquired from the previous two measurements. Further investigation into the beam size and divergence angle is required to finally put this question to rest.

Attachment 6: manualbeam.m  710 Bytes  Uploaded Thu Jul 1 10:41:23 2010  | Hide | Hide all
function x=manualbeam(M,guess)
    grid on
    xlabel('Stage Translation (mm)')
    ylabel('Photodetector Output (V)')
    text(0.8,0.2,['A = ' num2str(x(1))],'FontSize',12,'Interpreter','none','Units','normalized');
    text(0.8,0.15,['x0 = ' num2str(x(2))],'FontSize',12,'Interpreter','none','Units','normalized');
    text(0.8,0.1,['w = ' num2str(x(3))],'FontSize',12,'Interpreter','none','Units','normalized');
... 7 more lines ...
Attachment 7: gauss_beam1D.m  253 Bytes  Uploaded Thu Jul 1 10:41:44 2010  | Hide | Hide all
function result = gauss_beam1D(x0, xdata)
% x0(1) = offset
% x0(2) = amplitude
% x0(3) = x centroid location
% x0(4) = x width

result = x0(1) + x0(2).*exp(-2.0.*( ...
                           ((xdata - x0(3)).^2)/(x0(4).^2)));
Attachment 8: autogaussfit1.m  2 kB  Uploaded Thu Jul 1 10:42:42 2010  | Hide | Hide all
function [x y wx wy]=autogaussfit1(imgname,guess,imgdetails)
%guess = [offset amplitude centroidlocation width]
%imgdetails = [HWSrulerlocation exp.time]
%output vectors same format as guess

rulerz = imgdetails(1,1);
exposure = imgdetails(1,2);

... 56 more lines ...
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