Initial On-Sky Performance testing of the Single-Photon Imager for Nanosecond Astrophysics (SPINA) system

We use the PS-SiPM model PSS 11-3030-S from the Novel Device Laboratory in the SPINA system. When a photon is detected by the PS-SiPM detector, a photo-electron (P.E.) is excited and multiplied into a charge pulse. We refer to each charge pulse in our 8 ns time window as a single event. However, when more than one photon converts to a P.E. in a single event, this is called “electron pile-up”. The signal is greater for more P.E., and so we can use the pulse strength to determine how many P.E. counts were in an event. Therefore, the number of events indicates how many charge pulses are received, and ideally, the number of counts in each event indicates the number of detected photons.

Each charge pulse is then collected by the four anodes, one along each of the four sides of the PS-SiPM [13]. By comparing pulse strengths on the four anodes, the SPINA system estimates the position of each event and records this position in a 7-bit number each for x and y, and an associated time in 8ns steps. These data are transmitted to the data acquisition computer through an Ethernet interface.

We cool down the detector to reduce dark current using a thermoelectric cooler. We calibrated the dark events rate ($D$) versus the temperature curve prior to the on-sky testing and found:

We needed a mechanical framework for our components that would mount on an instrument port of the Nazarbayev University Transient Telescope at the Assy-Turgen Astrophysical Observatory (NUTTelA-TAO) [15]. We connected a mounting ring to a small optical breadboard that would serve as a mounting platform for our components. The PS-SiPM detector chip and its cooling system are mounted on top of the platform. All control electronics are mounted on the bottom of the platform, which acts as a grounded electromagnetic shield.

An optical shield made with painted aluminum sheets covers the testing platform to isolate the SPINA system from stray light.

While we were doing our experiments at the observatory, we found substantial electromagnetic interference (EMI) noise when the telescope mount motors were switched on. To reduce the interference, we built a grounded metallic shield to protect the readout system from EMI, shown in Fig.3.

We performed the first On-Sky test of the SPINA system on the NUTTelA-TAO telescope. The specifications of the telescope are given in Table III in Appendix A. The SPINA PS-SiPM has a 2.2716’$\times$2.2716’ field of view on this telescope.

We performed observations during the local nighttime of UT Jul 10. There was a strong thunderstorm at the Assy-Turgen Observatory from UT Jul 10 15:00 to 17:00. The sky became partly clear with some high-level clouds and haze after UT Jul 10 17:30. Our observations began at UT Jul 10 18:56, and last till UT Jul 10 19:55. During observation, the humidity was $90\%$ near the ground, the ambient temperature was $10^{\circ}$C, and the radiometric sky temperature (measured with a Boltwood Cloud detector II) was $-25^{\circ}C\pm 5^{\circ}C$, indicating a partly cloudy or hazy sky. The astronomical twilight begins at UT Jul 10 21:07, which did not interfere with our observation. There were also strong wind gusts up to $7ms^{-1}$. Small sections of the sunset sky can make a relatively uniform source of illumination, and can therefore be used to correct non-uniform response of detectors, a ”flat field” correction. Since the sky was cloudy and therefore non-uniform, we could not make the observations for such corrections.

The moon phase was 93.5%, leading to a bright sky background. The moon was near the Southern horizon during the observation time. Therefore, we pointed the telescope to the Northern sky near the zenith to minimize the effect of the moon, air mass, and the milky way.

We first focused the system on a relatively bright star just below saturation. We then measured a nearby group of stars near the constellation Draco with a wide range of apparent magnitudes. All stars were within a 5-degree area, and all measurements were performed within 1 hour to minimize atmospheric effects. We chose a sky area without a star brighter than magnitude 18 (Empty Field) to measure the sky background and performed the dark reference measurement with the telescope shutter closed. The observation log is presented in Table I. We acquired at least 16 million recorded events in each dataset to ensure an adequate signal-to-noise ratio (SNR).

Throughout the observations, the thermoelectric cooling module kept the detector temperature at $-50\pm 0.003^{\circ}C$. We made regular visual inspections to make sure that there was no condensation or frost on the detector’s surface or the cooling chamber’s window.

The detector was located at the focal plane of the telescope for the measurements. We pointed our system to a 3.58 mag star HIP94376, just below saturation ($\sim 3$ mag), for focusing.

The instrument is focused via the telescope focuser, which moves the instrument along the optical path with a travel of 30mm in micron steps. We set an initial position of $15000\mu m$. We captured an image of HIP94376 at multiple positions, fit the star’s full-width half-maximum (FWHM) versus the focuser position, as shown in Fig. 4. We found the best focus position to be $\sim 22500\mu m$. We frequently checked the focus during the measurements of dimmer stars, and we found no noticeable deviation.

In an ideal photon detector, the histogram of output pulse strength should be in discrete steps, as P.E. counts are quantized. In reality, the recorded pulse strength is affected by gain variations across the detector, electronic noise, and imperfect pile-up of photons. Hence the discrete pulse strengths broaden into a mixture of Gaussian distributions. To correctly distinguish the P.E. counts per event, we performed a Gaussian Mixture Model (GMM) fitting on N peaks [16]:

Where $s$ is the pulse strength, $A_{n}$, $\mu_{n}$, and $\sigma_{n}$ are the amplitude, location, and standard deviation of each Gaussian peak. We reduced the number of dependent parameters of GMM fitting by assuming (1) linear response from the PS-SiPM, (2) standard deviation of each Gaussian peak, $\sigma_{n}$, growing linearly with the peak number, and (3) higher P.E. events coming from coincidence and crosstalk probability [17]. These assumptions are shown in the following equations:

1. 1.

   $\mu_{n}=(\mu_{1}-\mu_{0})*n+\mu_{0}$, where $\mu_{0}$ is an offset from readout system electronics.

2. 2.

   $\sigma_{n}=\sigma_{1}*n$,

3. 3.

   $A_{n}=A_{1}*C^{n}$, where $C$ is a constant indicating height ratio of each peak to the previous one.

By applying these assumptions, we can reduce the number of dependent parameters from $3N$ to $5$ ($\mu_{0}$, $\mu_{1}$, $\sigma_{1}$, $A_{1}$ and $C$).

The fitting was performed using a non-linear least squares fit algorithm. After fitting the GMM parameters, we matched the strength of each recorded pulse to the most probable number of P.E. counts. Fitting results show that the algorithm works well from dark testing data to the brightest star near saturation, as shown in Fig. 6 and 7.

After P.E. identification, the data can be treated as a stream of P.E. counts with spatial information. We reduced the data to 2D images by integrating the P.E. counts according to their pixel position.

The empty field data contain information on detector dark counts and sky background. We subtracted the integrated empty field data from the integrated star field data to obtain a reduced image. The difference in exposure time is compensated with the following equation:

Where $I_{star}$, $I_{empty}$, and $I_{reduced}$ represent integrated images of star field data, empty field data, and subtraction output, respectively. $t_{star}$ and $t_{empty}$ represent the integration time of star and empty field data. A data subtraction sample is shown in Fig. 8.

After calculating the reduced data, we ran a star fitting and identification algorithm. Assuming the star shape is a 2D round Gaussian with an offset (residue sky background from the above subtraction), we obtain the following equation for Gaussian fitting of P.E. counts :

Where $A$ is the amplitude, $\mu_{x}$, and $\mu_{y}$ are the center position of the star, k is the residual background counts, and $\sigma$ is the standard deviation of Gaussian. We performed the fitting with a non-linear least squares fit algorithm. A sample star of 11.46 mag is shown in Fig. 8, the R-squared value of Gaussian fitting is 0.925, indicating the Gaussian profile fits well.

We obtained the Dark Reference data with the telescope shutter closed (Dark Reference in Table I). We recorded $1.6790161\times 10^{7}$ events within 81.804s, or $205,248\pm 50$ events per second. This recorded value is higher than our expectation, as we expected $3396\times e^{-50\times 0.0616}\simeq 1.56\times 10^{5}$ events per second from Eq. 1.

The excess dark events possibly originated from the scattered moonlight, as the moon was near full (moon phase $93.5\%$), and there were clouds to scatter moonlight. The scattered moonlight may leak into our system through the gaps between photon shield panels.

We also pointed our system to an area in the sky without a star brighter than 18 mag (Empty Field in Table I). We recorded $1.6791428\times 10^{7}$ events in 61.043$s$, or $275,116\pm 67$ events per second. This background flux comes from the detector noise plus the sky background.

Considering the digitized pixel size of $25\mu m\times 25\mu m$ from the SPINA system output, we obtained an average overall single-pixel background flux of $19.105$ events per second per pixel. Calculating the P.E. counts per event, we got an average overall single-pixel background flux of 28.898 counts per second ($cps$).

We calculated the signal strength of each target star from the fitted Gaussian parameters in Sec. IV-C. The calibrated star flux (in cps) can be calculated with the following function:

Where $A$ and $\sigma$ correspond to the amplitude and standard deviation of the fitted Gaussian in Eq. 4, $t_{bright}$ corresponds to the exposure time of the star, and $E(AM,AOD)$ corresponds to the extinction calculated with the atmospheric extinction model [18, 19]:

Where $h=2750m$ is the altitude of the observatory, $\lambda=420nm$ is the observation wavelength, which we took to be the PS-SiPM sensitivity peak. AM corresponds to the airmass recorded during observation, and AOD is the aerosol optical depth. Unfortunately, there are no real-time AOD data available, so we can only estimate it: a typical value of $AOD\sim 0.7-1$ [19] for most observatory sites during a hazy night. Following Eq. 6, we can see the AOD value contributes linearly to the extinction magnitude. All of our observations span a small range of AM ($1.12\pm 0.02$). Changing $AOD$ from $1$ to $0.7$ would change the extinction by $0.5$ mag. The effect on linearity, however, is negligible. Therefore, we choose a mean value of $AOD=0.85$ in the following analysis.

The multi-P.E. events detected by the PS-SiPM either come from the intrinsic crosstalk of the detector itself or the natural coincidence of multiple photons arriving at our detector concurrently.

When intrinsic crosstalk occurs in a PS-SiPM, one detected photon will give a multi-P.E. event. We cannot distinguish this multi-P.E. event from a real multiple photon detection [20].

We created a crosstalk probability map using the Dark Reference data set, as shown in Fig. 9. The crosstalk probability is $\sim 0.18$ near the center while reaching $\sim 0.5$ near the detector edges. The extra crosstalk near the detector edges possibly comes from photon localization errors near readout electrodes.

We compared our recorded flux to the Gaia DR2 BP-band data, which is sensitive near the blue end of the visible spectrum.

We plotted our calibrated detector flux versus the Gaia BP-band flux to obtain the sensitivity of our system, as shown in Fig. 10. We reported the standard flux of Gaia BP-band and our calibrated detector flux in Table IV in Appendix B.

In the following sensitivity estimations, we took the best values from the above measurements: $FWHM=232\mu m$, crosstalk probability= $0.18$ and an overall single-pixel ($25\mu m\times 25\mu m$) background (dark + sky) flux of 19.105 events per second or 28.898 counts per second ($cps$).

We first calculate the FWHM integrated background flux (integrating all background flux within FWHM) $=19.105\pi\left(\frac{232}{2\times 25}\right)^{2}=1219$ events per second, or $1914cps$ considering multi-P.E. events.

Now we can directly calculate the $5\sigma$ detection limit (in $cps$) for long exposures. The signal-to-noise ratio for one second of integration can be calculated with the following equation:

Solving with $SNR=5$, and using $\sigma^{2}_{dark+sky}=$ the dark counts and the sky background flux we calculated above, gives a detection limit of $S=231.063\ cps$, or $1424.56e^{-}s^{-1}$ Gaia BP-band flux. This corresponds to a limiting magnitude of $17.45$ in the Gaia BP-band (assuming no atmospheric extinction), or $15.68$ mag for $AM=1$ and $AOD=0.85$.

The motivation for developing the SPINA system is the measurement of very short timescale transient events. During the on-sky measurements, as expected, no significant brightness change was observed in the stars. Here, we calculate the detection limits of $10ms$ and $1\mu s$ transients with one false alarm per $5\times 10^{4}s$ ($\sim 1$ night) and one false alarm per $5\times 10^{6}s$ ($\sim 100$ night).

For a $10ms$ bin and a desired false alarm rate of 1 false alarm per $\sim 100$ night, we can accept less than one false alarm per $5\times 10^{9}$ bins, or a false alarm probability of $<2\times 10^{-10}$ per bin. From Poisson statistics and the 19.14 background counts in one FWHM aperture, this false alarm probability gives a detection limit of 52 counts per 10 ms. From the calibration in Fig. 10, the transient should give at least $320.59e^{-}$ in Gaia BP-band in 10ms, corresponding to a 14.06 mag burst for 10ms. If we loosen the accepted false alarm rate to one false alarm per night (false alarm probability of $<2\times 10^{-8}$ per bin), we will need a detection limit of $47$ counts per 10ms bin, corresponding to a 14.18 mag burst within 10ms in Gaia BP-band.

For fast transient events within a $1\mu s$ bin, we consider the FWHM integrated background flux of $1219$ events per second (we used events instead of counts here to avoid double counting the crosstalk effect). We expect an average of only one event per $\sim 800$ $1\mu s$ bins. However, the crosstalk effect will limit our detection potential. We recorded a minimum crosstalk probability of $\sim 0.18$ near the center of the detector, which is much higher than the possibility of having a count in the time bin. Therefore, we need to calculate the crosstalk effect with the geometric statistic [20]. For a desired false alarm rate of 1 false alarm per $\sim 100$ nights, we can accept less than one false alarm per $5\times 10^{13}$ bins, or a false alarm probability of $2\times 10^{-14}$ per bin. We can then calculate: $1.219\times 10^{-3}\times(0.18)^{N}\leq 2\times 10^{-14}$, where $N$ is the minimum counts detected in a bin for triggering. Solving gives a trigger threshold of at least 15 counts detected within a $1\mu s$ bin. If we loosen the accepted false alarm rate to one false alarm per night (false alarm probability of $<2\times 10^{-12}$ per bin), we will need a detection limit of 12 counts detected within a $1\mu s$ bin.

Even at the current $-50^{\circ}C$ detector temperature, there is still a significant dark count rate from the PS-SiPM detector. We would therefore like to increase the cooling system capacity. We plan to install a $100W$ thermoelectric cooler and aim to get the detector temperature to $-70^{\circ}C$. We expect a roughly 4-fold improvement of dark counts to $<50kcps$. Further cooling may also help reduce the crosstalk probability.

We found more dark counts in the Dark Reference measurement than expected. We suspect the extra dark counts came from scattered moonlight, which might leak into the system through slits and feed-through holes between optical shields. To avoid this, we are designing an improved optical shield to be made with a single piece of aluminum tube, directly connecting the telescope flange to the detector chamber. Multiple baffles can also be added to reduce internal stray light further.

During this experiment, we built a temporary metallic EMI shield to tackle the intense EMI noise from the telescope motors. In the future, we will enclose our system in a permanent, sealed metal box to ensure the system works well in harsh environments with EMI and moisture.

To further characterize the performance of the SPINA system, we have built a light injection setup in the laboratory. This consists of a broad-spectrum lamp that provides optical power through a monochromator and an integrating sphere that provides a high neutral density (ND) ratio with real-time optical power monitoring. We plan to calibrate the absolute quantum efficiency from 300 to 1100nm. We will also use a picosecond pulse laser to examine the time-stamping accuracy of the system.

With the characterization data, we will optimize the operating parameters (bias voltage, filter bands, etc.) of the SPINA system to obtain an optimal balance between P.E. gain, spatial resolution, dark counts and crosstalk.

In Sec.V, we assumed some timescales (e.g. $10ms$ and $1\mu s$ bins) to calculate threshold levels of detection. Despite lacking prior knowledge regarding the expected timescales of astronomical transients, it is crucial to develop a multi-timescale model to investigate the potential presence of significant transient signals within the measured photon stream. To achieve this, we can employ a binning strategy with increasing time intervals, such as $8ns,\ 16ns,\ 32ns$, and so on, while establishing a trigger threshold for each timescale. Moreover, the SPINA system generates a considerable volume of data (approximately $100Mbps$, with 64 bits per event, under a typical 1.5 million events per second flux on the detector). Implementing a real-time event differentiation algorithm is essential for selecting potential transient data, thus effectively reducing data storage and internet bandwidth demands on our system.