Optical Transition-Edge Sensors Single Photon Pulse ... - IEEE Xplore

IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 21, NO. 3, JUNE 2011

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Optical Transition-Edge Sensors Single Photon Pulse Analysis D. Alberto, Student Member, IEEE, M. Rajteri, E. Taralli, L. Lolli, C. Portesi, E. Monticone, Y. Jia, R. Garello, Senior Member, IEEE, and M. Greco

Abstract—Transition-edge sensors (TES) are detectors able to count single photons from x-ray to infrared, generating pulses with amplitudes proportional to the absorbed photon energy. The TES performance depends on the sensor parameters and also on the noise level. The evaluation of the energy resolution is thus dependent on the type of signal analysis applied. In this work we report the results of an off-line analysis applied to pulses measured with a TiAu TES for the optical region. The pulses were acquired with a digital oscilloscope and further elaborated with numerical methods. Different kinds of digital filters were applied for improving the TES energy resolution, starting from simple Savitzky-Golay filters to more complex Wiener filters. Particular attention was paid both to time-domain and frequency-domain analyses. The first aims to extract features of interest as the photon pulse amplitude, arrival time and time jitter. The second can help for better energy resolution, aiming to identify and enhance only the photon pulse frequency components and reducing the noisy ones. Index Terms—Photodetectors, signal analysis, spectral analysis, superconducting radiation detectors.

I. INTRODUCTION ICROCALORIMETERS based on transition-edge sensors (TESs) are extremely sensitive, capable of counting single photons from x-ray to infrared [1]. TESs have a sharp transition between the superconducting and the normal phase with very low transition temperatures (100–300 mK). The main advantage of TESs is their intrinsic energy resolution, i.e. the response is proportional to the absorbed photon energy, that allows photon-number resolving capability when the photon energy is known. The energy resolution is a very important parameter that strongly depends on how it is evaluated

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and what kind of signal processing is carried out. Some solutions to obtain an optimal filter that take into account the different noise source contributions have been presented [2]–[4] and also a bit simpler algorithm to quickly estimate the pulse parameters [5]; nevertheless generally little information is given on how the energy resolution is computed. In this work we report the results of an off-line analysis applied to pulses measured with a TiAu TES for the optical region. The pulses are acquired with a digital oscilloscope and analysed with numerical software using a Matlab [6], [7] platform. II. EXPERIMENTAL SETUP The experimental data analysed in this work have been obtained at INRiM with a TiAu TES, whose fabrication process has been described in [8]. The photons are absorbed directly and by the TiAu layer with an active area of . The signals, with a response time of 3.5 , are read out with a dc-SQUID with a bandwidth of 6 MHz. The TES is operated inside a dilution refrigerator and coupled to a 1310 nm pulsed diode laser with a fiber optic [9]. The laser was pulsed at a repetition rate of 50 kHz with a pulse width of 100 ns, well below the response time of our detector, and the intensity was controlled with an optical attenuator. The traces of the triggered pulses produced from the absorbed photons are monitored and saved in a binary format by means of a digital oscilloscope, without any kind of filtering. A collection of pulses of the order of tens of thousands traces are typically saved for different experimental conditions, e.g. light intensity and bias point. III. SIGNAL ANALYSIS

Manuscript received August 02, 2010; accepted October 05, 2010. Date of publication November 11, 2010; date of current version May 27, 2011. This work was supported by the European Community’s Seventh Framework Programme, ERA-NET Plus, under Grant Agreement 217257 and “Associazione per la Promozione dello Sviluppo Scientifico e Tecnologico del Piemonte” (ASP). D. Alberto is with the Dipartimento di Fisica Generale-Università di Torino, INFN-Sezione di Torino, 10125 Torino, Italy. He is also with Dipartimento di Elettronica, Politecnico di Torino, 10129 Torino, Italy (e-mail: [email protected]). M. Rajteri, E. Taralli, L. Lolli, C. Portesi, and E. Monticone are with the Istituto Nazionale di Ricerca Metrologica (INRiM), 10135 Torino, Italy (e-mail: [email protected]). Y. Jia and R. Garello are with the Dipartimento di Elettronica, Politecnico di Torino, 10129 Torino, Italy (e-mail: [email protected]). M. Greco is with the Dipartimento di Fisica Generale-Università di Torino, INFN-Sezione di Torino, 10125 Torino, Italy (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASC.2010.2087736

The nature of the TES signal noise (mainly Johnson, phonon, etc.) makes it preferable to carry out a signal analysis after data acquisition to improve the most important TES waveform features. In this section we present two complementary analyses aiming to enhance the Signal-to-Noise Ratio (SNR), the energy resolution and to reduce the time jitter. A. Frequency Domain Elaboration On the complete set of noisy signals, as first approach, we determined the minimum amplitudes, detected in the 2 time slot after the trigger signal. Representing these values with a histogram (the absolute values of the amplitudes are considered in all the histograms presented in this work) (Fig. 1), we can signals are predominant and that the level of observe that noise is high enough not to easily distinguish complete sub-sets

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Fig. 1. Amplitude histogram of pulses. The inset reports the 2 signal averaged in a region of 1.5 standard deviations around the mean value of the third peak.

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Fig. 2. Histogram of cross-correlation between the 2 reference signal and all noisy waveforms.

of waveforms carrying a specified number of (i.e. 1, 2, etc.). With respect to Fig. 1, in a region of 1.5 standard deviations around the mean value of the third peak ( signals) we can confidently isolate an ensemble of some thousands of noisy signals carrying . Since the distribution of amplitudes of different signals for the same sample can be considered Gaussian, the average of this sub-set can contribute to a reference signal (inset of Fig. 1) representative of all noisy signals carrying . Calculating the maximum of each cross-correlation between this built waveform and all acquired signals, the histogram reported in Fig. 2 can be obtained. The relative minima among all peaks are highly reduced. By means of this new distribution a set of reference signals can be easily produced with the averaging technique (Fig. 3). Since the TES response may be slightly non-linear, we chose to identify different reference pulse signals (instead of using

Fig. 3. All 5 reference signals for the Wiener filter. These waveforms are obtained with the averaging technique, based on the cross-correlation histogram.

Fig. 4. Example of a TES noisy signal (cian), its reference (green) for the Wiener filter, Savitzky-Golay (blue) and Wiener (red) filter outputs. SNR comparisons are also reported.

multiple of the elementary one). Reference signals presented in Fig. 3 can be used to feed a Wiener filter. This filter is able to optimize the SNR of every pulse signal waveform [7]. Working on a Matlab [6] platform, our best results have been obtained with a 30th order Wiener filter. In Fig. 4 this filter’s output is reported and compared with a Savitzky-Golay 3rd order (window 101 samples) filter elaboration [10] and the original unfiltered trace. Savitzky-Golay filters are Low Pass filters that work very well in noise reduction preserving peak amplitude information. The Power Spectral Density (PSD) of a TES noisy signal, of its Savitzky-Golay filtering and of its Wiener elaboration, are reported in Fig. 5. Both filters reduce the noise components in the range 1–5 MHz while Wiener enhances better the desired components at low frequency ( 1 MHz).

ALBERTO et al.: OPTICAL TRANSITION-EDGE SENSORS SINGLE PHOTON PULSE ANALYSIS

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TABLE II TIME JITTER ESTIMATE

Fig. 5. PSD of the same noisy (green) signal presented in Fig. 4, of Wiener (red) and of Savitzky-Golay (cian) filter outputs. The inset shows a detailed behavior at low frequency.

TABLE I SNR EVALUATION

Fig. 6. Noisy signal amplitudes histogram (dots) and fit (line). No processing has been applied. The 0 peak has been isolated and neglected using the crosscorrelation information.

B. Time Domain Analysis In the time domain two significant features that can be calculated are the SNR and the time jitter. The SNR is an index that expresses the ratio between the signal and the noise power, it is used to control the capability of a filter to reduce noise components in a measured signal, the higher it is, the easier the signal features extraction is. In Table I there are reported SNR evaluations for noisy data, Savitzky-Golay and Wiener filtered signals subdivided in groups carrying the same photon numbers. We chose to define the SNR ratio as:

of time values at half amplitude in a sub-set of waveforms carrying the same number of photons. From the results presented in Table II, we can conclude that neither Savitzky-Golay nor Wiener reduce the time jitter and that, fixed the filter, the time jitter estimate is sensitive to the SNR. Increasing the number of photons, the SNR increases and time jitter decreases, even in case of not elaborated noisy sigthe time jitter is the nals. When the SNR is the lowest highest, with values out of any proportion with the estimates conduced on sub-sets carrying 2 or more photons. IV. RESULTS AND DISCUSSIONS is one of the most important The energy resolution parameters characterizing TESs. A possible way to estimate is:

where is the amplitude of the considered signal and is the RMS of noisy values of every acquired waveform before trigger. Note that the noise amplitude distribution has been considered Gaussian and the coefficient 4 corresponds to the 95% amplitude band of the aforementioned distribution. The SNR values reported in Table I indicate that Wiener works better than Savitzky-Golay in the SNR improvement. The reason is that the SNR evaluation here presented highly depends on peak-to-peak amplitude measurement and on the enhancement of the desired low-frequency components. In a TES signal detection, another important feature is the time jitter. It has been calculated as the time fluctuation (RMS)

where: is the energy carried by one photon (in our case is the mean value of signals amplitudes 0.95 eV); is the mean value of signals ampliexpressed in mV; is the Full Width at Half tudes expressed in mV; Maximum expressed in mV and calculated as , being the RMS common to all peaks and obtained fitting an amplitude histogram. In Fig. 6 original noisy data have been used to build a histogram whose fit (Poisson distribution convolved with Gaussian

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The best result is given by the Wiener filter, the corresponding amplitude histogram is reported in Fig. 8 together with its fit. is 0.22 eV and is less than half of the original The resolution value obtained from noisy measurements. V. CONCLUSIONS An analysis in both frequency and time domains has been performed. Filtering techniques are necessary to significantly enhance the most important features in triggered TES acquisitions with known wavelength, as the energy resolution and the reduction of peak tails superposition in amplitude histograms. Time jitter is not reduced neither by Savitzky-Golay nor by Wiener filters, while the Wiener filter optimizes the SNR. However, the Wiener filter allows us to gain a factor 2 in the energy resolution making the superposition between two consecutive peaks negligible. Fig. 7. Savitzky-Golay filtered signal amplitudes histogram (dots) and fit (line). 0 peak is neglected in the discussed way.

ACKNOWLEDGMENT The authors thank J. Beyer for providing the dc-SQUID. REFERENCES

Fig. 8. Wiener filtered signals amplitude histogram (dots) and fit (line). 0 peak is neglected in the aforementioned way.

functions) allowed us to estimate a of 0.46 eV with the aforementioned procedure. Applying the same technique to amplitude estimates after a is 0.39 eV. Savitzky-Golay filtering (Fig. 7), the resolution

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