1. Calibration of Sensors for Acoustic Detection of Neutrinos
M. Ardid, M. Bou-Cabo, V. Espinosa,
J. Martínez-Mora, F. Camarena, J. Alba,
Departament de Física Aplicada, E.P.S. Gandia, Universitat Politècnica de València

2. Contents
Absolute calibration of the sensitivity using the reciprocity method
Description
Studies using different kind of signals
MLS, TSP, white noise, tone burst
Studies using different propagation conditions
Tank, Butterfly configuration, Tube, Coupler
Generation of neutrino-like signals using transducers
Without equalisation
Equalisation
Comparison
Convolution with MLS + inverse filter
Summary

3. Absolute calibration of the sensitivity using the reciprocity method
Motivation:
The reciprocity calibration method for acoustic sensors is a simple method, in which calibrated hydrophones are not needed.
Usually the free field configuration is used, but it is not easy to have it a small lab. If we could avoid these limitations, it would be accessible for any lab, and could be used extensively for the sensor studies needed in a neutrino telescope.
Here, we present some studies, using different calibration signals and different configurations trying to go further in this technique
Moreover, the reciprocity method could be used to calibrate the sensors of a neutrino telescope just by using themselves (reciprocally)

4. Absolute calibration of the sensitivity using the reciprocity method
Absolute calibration of the sensitivity using the reciprocity method. Description
Based on the electrical reciprocity theorem.
It is possible to measure the absolute sensitivity of a transducer (c), with just 3 steps (four measurements) involving three non-calibrated transducers J
J: reciprocity parameter. Depends on the acoustic propagation conditions:
spherical: J=2d/(rf)
cylindrical: J=2A/(rc)
coupler: J=wC=2pfV/(rc2)

5. Absolute calibration of the sensitivity using the reciprocity method
Absolute calibration of the sensitivity using the reciprocity method. Studies using different kind of signals
Different signals can be used to feed the transducers and obtain the sensitivity:
White noise
Tone bursts
Maximum Length Sequence (MLS): Pseudorandom signal, consisting of the values 1 and -1, with period P=2N-1, where N is the "order of the sequence“. It has a flat frequency content, and the circular autocorrelation provides a delta function.
Sine sweep, or Time Streched Pulses (TSP): the circular convolution provides a delta function

6. Absolute calibration of the sensitivity using the reciprocity method
Absolute calibration of the sensitivity using the reciprocity method. Studies using different kind of signals
EXPERIMENTAL SETUP
Assuming J spherical and free field
Transducers
c: Reson TC4034 a,b: Airmar Tech. P319
Computer
Soundcard
HDSP9632
Sampling Frequency: 192 kHz
Cool Edit + Aurora
Matlab
Tank
1.10x0.85x0.80 m3

7. Absolute calibration of the sensitivity using the reciprocity method
Absolute calibration of the sensitivity using the reciprocity method. Studies using different kind of signals
RESULTS (PRELIMINARY):
Although the results are quite similar and the uncertainty is still large, some differences are observed: MLS and sine sweep seems to be more convenient for this calibration.

8. Absolute calibration of the sensitivity using the reciprocity method
Absolute calibration of the sensitivity using the reciprocity method. Studies using different propagation conditions
Additional to the tank study, we have tried different configurations
Butterfly configuration: trying to avoid the reflections
Cylindrical tube: L=170cm, d=8 cm, methacrylate, J=2A/(rc)
Coupler (cylindrical): L=25 cm, d=8 cm, methacrylate, J=wC=2pfV/(rc2)
Study using MLS signal, order 19

9. Absolute calibration of the sensitivity using the reciprocity method
Absolute calibration of the sensitivity using the reciprocity method. Studies using different propagation conditions
RESULTS (PRELIMINARY):
The tank gives better results. Avoiding reflections in a small tank with the butterfly setup is not easy (the reduction of volume plays a larger role). The tube has large loses for high frequency, and the coupler seems promising (not bad considering the limitations of the self-made coupler)

10. Absolute calibration of the sensitivity using the reciprocity method
Absolute calibration of the sensitivity using the reciprocity method. Conclusions to the studies
Conclusions:
These preliminary results have shown that the election of the signal for calibration of the sensitivity of a sensor by reciprocity could play a role. In this sense, MLS and TSP seem to be very promising.
The configuration study has given us hints about the validity of this technique in different configurations with different reciprocity parameters. Additionally to the free field reciprocity, which could be much more expensive, the coupler could be a solution.
Moreover, the reciprocity technique could be used to calibrate the sensors of a telescope just by using themselves (if we are able to know, or measure the reciprocity parameter)
Work in progress:
We are trying to take advantage of the properties of MLS and TSP to overcome some limitations of the tank configuration (trying to eliminate the effects of the reflections).
We are improving our experimental setups for the different configurations, especially for the case of the coupler. For the simplicity of this configuration, it would be a good candidate for calibration of sensors for neutrino telescopes in the lab

11. Generation of neutrino-like signals using transducers
Motivation:
Generation of neutrino-like signals is necessary to calibrate acoustic neutrino sensors and telescope
Probably, the most convenient way to generate these signals is from transducers directly.
Since transducers do not usually have a flat frequency response, distortion is produced, and it could be difficult to achieve.
We present some equalization techniques to offset this effect.
Setup: the same as the reciprocity study in the tank (a-c configuration)
The pressure pulse for a 1.2 × 1011 GeV shower in sea water at a distance of 1 km. The angle with the plane transverse to the shower direction is zero degrees.

12. Generation of neutrino-like signals using transducers
Generation of neutrino-like signals using transducers. Without equalisation
First attempt: feed the transducer with the neutrino-like signal directly
Emitted: neutrino-like signal
Received
The received signal is distorted, there is a kind of inertia.
The sampling frequency (192 kHz) could be considered low. However, we have preferred to do these study under these conditions because signals are still observed and lower rates are preferred in neutrino telescopes.

13. Generation of neutrino-like signals using transducers
Generation of neutrino-like signals using transducers. Without equalisation
Other signals
Emitted: slow neutrino-like signal
Received
Emitted: 1 cycle 10 kHz sinus
Received

14. Generation of neutrino-like signals using transducers. Equalisation
Question: if feeding with the original signal, this is not received. Could I feed with another signal in order to obtain the original signal in the receiver position?
This is an inverse problem, The first step is to know the transfer function.
Using the MLS, we could obtain the impulse response, and therefore the transfer function
Flatten spectrum: creates an inverse filter inverting only the Minimum Phase component of it, that is the Magnitude of the Transfer Function is inverted
Inverse filter: inverts mixed-phase impulse response following the Mourjopoulos least-squares technique
Once the filter is obtained the original signal is convolved with the filter.
Feeding with this signal, hopefully the original signal is received

15. Generation of neutrino-like signals using transducers. Equalisation
Getting the filter
Impulse response
Flatten spectrum filter
Impulse response (peak zoom)
Inverse filter

16. Generation of neutrino-like signals using transducers. Equalisation
Neutrino-like signals obtained using equalisation
Signal emitted (Flatten spectrum)
Signal obtained (Flatten spectrum)
Signal emitted (Inverse filter)
Signal obtained (Inverse filter)

17. Generation of neutrino-like signals using transducers. Comparison
Original Signal
Signal obtained (Flatten spectrum)
Signal obtained (without equalisation)
Signal obtained (Inverse filter)

18. Generation of neutrino-like signals using transducers. Comparison
Slow neutrino-like signals
Original Signal
Signal obtained (Flatten spectrum)
Signal obtained (without equalisation)
Signal obtained (Inverse filter)

19. Generation of neutrino-like signals using transducers. Comparison
1 cycle 10 kHz sinus
Original Signal
Signal obtained (Flatten spectrum)
Signal obtained (without equalisation)
Signal obtained (Inverse filter)

20. Generation of neutrino-like signals using transducers. Comparison
Conclusions:
The received signal without equalisation is highly distorted
It is possible to make improvements if we know the transfer function
There is a small improvement with the flatten spectrum
Much better results are obtained using the inverse filter based in the Morjopoulos technique
Future work:
The generation of neutrino-like signal for calibration of telescopes, which has not only the temporal shape, but also the directivity pattern.
Next step: study the use of array of transducer to get neutrino-like signals with the same directivity as neutrino events

21. Generation of neutrino-like signals using transducers
Generation of neutrino-like signals using transducers. Convolution with MLS + Inv. Filter
Convolution with MLS + Inverse Filter
Original Signal
Signal received
Signal emitted
(convolved with MLS+ Inverse filter)
Signal obtained (MLS + Inverse filter, after deconvolution)

22. Generation of neutrino-like signals using transducers
Generation of neutrino-like signals using transducers. Convolution with MLS + Inv. Filter
This technique of calibration could have a series of advantages in a telescope:
Better signal to noise ratio, because of the large average
Less amplification is needed, or in other point of view, can be used for larger distances
It is possible to calibrate at the same time as measuring: the signal appears only after deconvolution with the MLS (the only effect could be a little increase of the noise, but normally negligible)
The same sensors for detection could be used also for calibration, generating this kind of signals

23. Summary
We have presented some studies of the absolute calibration of the sensitivity of transducers using the reciprocity method.
Although the results are preliminary, it seems that the election of the signal could play a role, being worthwhile to consider MLS and TSP signals.
Different propagation conditions have tried with different reciprocity parameters. Additionally to the free field configuration the coupler seems that could give good results.
The work in the generation of neutrino-like signals using transducers have been shown
In usual transducers, equalisation is needed. Results have been presented using the flatten spectrum and the inverse filter based in the Morjopoulos method. The last gives the better results
Finally the convolution with MLS + inverse filter is proposed for calibration techniques