Mie-Scattering Experiment for the Classroom Manufactured by 3D Printing: Supplementary Material Christian Scholz, Achim Sack, Michael Heckel, and Thorsten Pöschel Institute for Multiscale Simulations, Friedrich-Alexander-Universtätt Erlangen-Nürnberg Build and perform a low cost Mie-scattering experiment Table of contents: 1. Mie-scattering 2. Hardware 3. Setup
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Mie-Scattering Experiment for the Classroom Manufactured by 3D Printing: SupplementaryMaterial
Christian Scholz, Achim Sack, Michael Heckel, and Thorsten PöschelInstitute for Multiscale Simulations, Friedrich-Alexander-Universtätt Erlangen-Nürnberg
Build and perform a low cost Mie-scattering experiment
Table of contents:1. Mie-scattering 2. Hardware 3. Setup
4. Software 5. Preparation of the calibration sample 6. Preparation of the samples 7. Calibration and measurement 8. Analyzing the data 9. Reference s 10.Resources 11.FAQ
1. Mie-scatteringMie-scattering is light scattering on particles with diameters in the order of the wavelength of the light. An every day example for this is for example the light scattering on small water droplets in clouds and fog. The light is scattered multiple times on particles of different sizes resulting in white and opaque areas.
Scattering monochromatic light, i.e. light of one wavelength, on monodisperse spherical particles cause a characteristic scattering pattern like scattering on a grid. Using this pattern one can calculatethe size of the particles.
We show here a cost-efficient experiment, using 3D printing and embedded computing (Arduino Uno), which is capable of measuring Mie scattering on monodisperse particle suspensions quantitatively with high precision.
2. Hardware• Servo motor small, e.g. www.conrad.de, article 209089-62 (~7 €)
• Servo motor large, e.g. www.conrad.de, article 404753-62 (~6 €)
• LASER, e.g. www.roithner-laser.com, article LM-101-C4 (~6 €)
• Photodiode, e.g. www.reichelt.de, article SFH 203 P (~1 €)
• Arduino board, e.g. www.amazon.de, article Arduino Uno R3 (~6 €)
• Polarizer, e.g. www.polfilter24.com, article 110580 (~6 €)
• Wires, e.g. www.elv.de, article 68008417 (~4 €)
• Screws, e.g. www.amazon.de, article M3*10 (~2 €)
• Power supply, e.g. www.reichelt.de, article GS12E05-P1I (10 €)
• Filament for 3D printing, e.g. www.filamentworld.de (~2 € per pc; 25 € per kg)
(STL and SCAD files can be found at the Resources)
All links to parts are examples with prices from end of 2015 (total of 50 €). All parts can be found atwebstores such as amazon, ebay and similar, too.
Here an example list from www.amazon.com (e.g. for US citizens). If you know better shops, feel free to use them. Please check all specifications and dimensions again carefully, as the experiment
Linux: Connect to the serial device (e.g. /dev/ttyACM0) with 9600 baud, e.g. :
screen /dev/ttyACM0 9600
Available commands
• Moving the servos
x $ANGLE (lower servo)y $ANGLE (upper servo; polfilter)e.g.: x 90
• Turning the LASER on/off
O (LASER off)o (LASER on)
• Reading background, LASER intensity, and difference between both
m • Set the number of measurements to average over
N $NUMBERe.g.: N 200
Each command is sent by pressing ENTER at the end.
Software on the measurement computerHere we use python and Matlab / octave for the automatic measurement. Therefore Matlab / octave and python has to be installed as well as the python packages numpy, matplotlib and python-serial.
Linux: In Linux the packages can be installed e.g. via
sudo apt get install python python-numpy python-matplotlib python-serial octave
The python code is started via command line with
python ArduMie.py
All files can be found under Resources.
Matlab / octave scripts for analysis is able to:
• Calculate the theoretical Mie-scattering
• Determine the positions of the extrema from the measurement
• Compare the theoretical and experimental extrema
• Determine particle diameter from look-up table
All files can be found under Resources (Arduino firmware, python and Matlab / octave scripts).
5. Preparation of calibration sample1. Peel off the reflection layer from a CD with a track distance of 1.5 µm (CD-R 80 min) with cellotape (try different manufactures if you experience problems).
7. Calibration and measurementThe calibration and the measurement is done almost automatically. The calibration sample has to bechanged for the actual sample during the run. At the end the measurement values are compared against the theoretical values and a few graphs as well as the recognized samples diameters are printed.
The experiment is started via
python ArduMie.py
The program will ask you to insert the calibration sample. Then a calibration run for the motors willbe performed. At the end a graph will be presented and you’ll be asked to enter the the value of parallel (maximum) and perpendicular (minimum) position.
Next, the script will ask you to insert the actual sample to be measured and will then start the actual measurement. The setup will first measure the parallel scattering intensity and then rotate the polarizer and measure the perpendicular scattering intensity. The resulting data will be saved in two text files called Mie_scattering_parallel.dat and Mie_scattering_perpendicular.dat.
ArduMie.py and all other files can be found under Resources.
8. Analyzing the dataTo analyze the data and get the particle diameter, the data must be first smoothed to find the local maxima. This is done by using the Matlab / octave script called smooth.m. Measurement, spline fit and position of extrema are shown in the following image:
The next step is calculating the theoretical values and compare them the measured data. This is doneby the Matlab / octave script called Mie_table.m. In the end you’ll receive the measured particle diameter in your sample (see the point marked by the arrow in the figure; here for two different particle sizes). 5.9 µm sized monodisperse spheres can be bought for example here [5].
All Matlab / octave scripts can be found under Resources.
9. References1. S. Prahl. Mie scattering. http://omlc.org/software/mie/ 2. C. Mätzler. MATLAB Functions for Mie Scattering and Absorption Version 2. IAP Res.
Rep., 2002 3. C. Scholz, A. Sack, M. Heckel, and T. Pöschel. Mie-Scattering Experiment for the
Classroom Manufactured by 3D Printing. Submitted, 2016 4. C. Aguilera. extrema.m. Math-Central. 2007 5. Polysciences, Inc. Polybead® Microspheres 6.00µm. http://www.polysciences.com
1. Find a local Fab lab (cost est. $5) 2. Build parts from cardboard [Pepakura] [Unfold] 3. Use an online 3d-printing service [shapeways] [meltwork] (cost est. $50)
B) Where to get cheap particle suspensions?
For testing you can use suspensions of milk etc. Suspensions of monodisperse particles are typicallysold in (relatively) large quantities (~ 15 ml). Since you only need a small droplet, try to ask at a local research facility, e.g. chemistry or physics departments of your nearby university.