B.4 Appendix - Benchmarking different machines
C.1.2 METTLE flash
The energy output (Joule per microsecond) of the 600 Ws METTLE flash is measured. For detecting light intensity, the Thorlabs SV2-FC high speed photodiode was used. The light yield amounts to 31.55 mJ per 1 µs. This is a factor of 1182 higher than the 6 times overdriven LED.
The formula to obtain the incident light power P for the photodiode is stated in Eq. C.1 Because the METTLE flash emits a spectrum, the formula has to be written as
Vout =Rload·P·
A normalized black body spectrum of daylight temperature (5777 K) was assumed forP(λ)of the METTLE flash lamp:
The flash was set to highest power ("6.0"). It was triggered via a TTL signal that made a FET-transistor close circuit the two poles of the "sync" connection. The maximum voltage of the photodiode pulse was measured by the oscilloscope’s cursor function. The waveform of the pulse was found to be the one in Fig. C.8.
0
photodiode voltage [mV] photodiode voltage [mV] of pulse 2
time [ms]
pulses of METTLE 600 DR flash, measured at different spots read via imagej
pulse 1 pulse 2
Fig. C.8: Pulse characteristics of the photodiode voltage when using METTLE flash at highest power.
The setup was kept as simple as in Fig. C.2 and run manually. The light emission was measured along the diameter of the reflector shield, approximately8.5cm±0.3cm above the reflector rim.
The measurement values obtained are shown in Fig. C.9.
0
profile of the METTLE flash
METTLE
Fig. C.9: Raw measurement values
In order to correlate the voltage of the maximum height of the flash pulse with the emitted energy, first of all the value of the integral of Eq. C.6 had to be determined. For this, the spectrumR(λ)of the data-sheet of the photodiode was multiplied withP(λ)of Eq. C.7. The result is shown in Fig. C.10. The integral values to
Z
Responsivity Rλ [A/W] normalized daylight spec. and multiplied spec. [a.u.]
wavelenght [nm]
R(λ) normalized black body at T=5777 K multiplied spectra
Fig. C.10: Spectra of the SV2-FC photodiode, the normalized daylight black body radiation and the two multiplied together.
which is slightly lower than the value for the red LEDs. With this value and Eq. C.1 the wave-forms Ui(t) of the pulses of Fig. C.8 were then transformed into values of light power per
photodiode active area (Ø0.4mm)
Those energies were correlated to the maximum voltage of the respective waveform (integration of the waveform by midpoint rule)
e1 ↔ U1,max= 2385.67mV ⇒ e1 The second factor of value 1.36091 seems to be reasonably lower because the second pulse was not recorded till the end (Fig. C.8 - green line). That is why the first conversion factor of 2.07227·10−4mV cmJ 2 was taken.
This conversion factor was used to convert the raw measurement values of Fig. C.9 to energy values. The results including a triple Gaussian fit function are shown in Fig. C.11.
0
converted light energy [J/cm2 ] photodiode voltage [mV]
Energy emission by METTLE flash at highest power converted
fit
Fig. C.11: Converted measurement values and Gaussian fit functions The fit function is:
where the offset of all terms is fixed to 10 cm, theσi are the widths of the Gaussian packages and theAi are the amplitudes. Fit parameters are shown in Table C.2.
value unit Table C.2: Fit parameters for Gaussian fits.
Assuming rotational symmetry, a two-dimensional intensity function I(x, y)was created from Eq. C.9 to extrapolate to the whole field of flash emission:
I(x, y) =
The plot is shown in Fig. C.12.
intensity [J/cm2]
In order to finally receive the Joule output, Eq. C.10 was numerically integrated. The python script is found again in the repository B.3. It was run with
python integrate.py -a "-12" -b 12 -c "-12" -d 12 -s 100 \ -e 10000 -t 1e-5
to find the final result:
I
M ET T LE= 122.86 J
In order to compare the Energy output of the METTLE-Blitz to the LED DOPPEL-Blitz, a 1 µs window was taken out of each pulse signal where the amplitude is highest. The maximum of the pulse lasts about 78 µs, so we can assume power stability over the 1 µs window. This leads to a conversion factor of
e3 = 1.59279·10−7 J
π(0.2mm)2 ↔ U3,max= 2385,67mV
⇒ e3
U3,maxπ(0.2mm)2 = 5.31297·10−8 J
mV cm2. (C.11)
The new fit parameters are shown in Tab. C.3. The final result is:
I
M ET T LE,1µs= 31.55 mJ
which is still by a factor of 1,000 higher than the Energy from the LEDs.
value unit
σx1 4.09533 cm σx2 4.07853 cm σx3 3.83306 cm
A1 0.447996 J/cm2 A2 -0.475446 J/cm2 A3 0.0275761 J/cm2 Table C.3: Fit parameters for the 1 µs Gaussian fits.
Here is the space for honesty.
I deeply thank Dr. Robert Mettin and Prof. Dr. Werner Lauterborn for their motivating guidance in the work with bubbles all those years. The humour, exceptional knowledge and pressure-less leadership of Robert Mettin made me feel home and at the same time very produc-tive. I thank Werner Lauterborn for his restless support, motivation and universe of experience that motivated even in paper rejection times.
A heartfelt thanks goes to the bubble guys and girls: Dr. Christiane Lechner, the one who solves any equation and algorithm problem even if unsolvable and whom I may call colleague, friend and supervisor at the same time, Juan M. Rosselló (called J or Dr. Nobody), Ferenc Heged˝us, Julian Eisener who went to the battlefields of lab moving with me, Hendrik Söhnholz, Dwayne Stephens and Ekim Büsra Sarac, Fabian Reuter, Julia Schneider, Matti Tervo, Bern-hard Lindinger, Roxana Vargas, the secretaries Sabine Huhnold and Elke Zech, the IT support Thomas Geiling, the workshop guys Dieter Hille and Team, Markus Schönekeß and Team and Simon Bahl and Prof. Dr. Ulrich Parlitz for his year long loyalty to the DPI-Team. Altogether the best team, ever.
Special thanks go to Claus-Dieter Ohl, who made it possible that I may have worked on a workstation in the home office during Corona time.
Enormous thanks go to my father Andreas Koch, mother Ursula Koch and brother Henry Koch for their yearlong support and endurance.
I deeply, gratefully thank my wife Sunny Ursa Liebscher-Koch for her love and energy support. Without her patience and care for the strangeness of the ideas of academic minds, I
would still not touch the ground.
Official acknowledgements
The funding for this project by the Deutsche Forschungsgemeinschaft (German Research Foun-dation) under contract Me 1645/8-1 is gratefully acknowledged.
I hereby confirm that my thesis entitledLaser cavitation bubbles at objects: Merging numerical and experimental methods is the result of my own work. I did not receive any help or support from commercial consultants. All sources and / or materials applied are specified in the thesis.
Furthermore, I confirm that this thesis has not yet been submitted as part of another exami-nation process neither in identical nor in similar form.
Göttingen, 21. Nov. 2020