About the Pedestal Variance

Variance calculations of the digitized Cherenkov light signals are known as the pedestal variance. The pedestal variance is proportional to light level, making it a great tool to continuously observe the light level sensed by the IACTs’ pixels. Better monitoring of the pedestal variance can improve VERITAS monitoring at the trigger level, which isolates the Cherenkov random events and also stores data onto a disk.

Data Acquisition in VERITAS

Each telescope in VERITAS is equipped with a 499-pixel camera where each pixel is a photomultiplier tube (PMT) combined with a preamplifier. A PMT is a device that takes advantage of the photoelectric effect, allowing a photon to be converted into a measurable electric signal. The preamplifier then serves to increase the signal-to-noise ratio by amplifying the signal before it traverses 45 m of signal cable from the camera to nearby electronics for processing.

The nearby electronics include flash analog-to-digital converters (FADCs), which digitize the electric signals from the camera pixels.The FADCs convert the raw light level data at each pixel to 8-bit digitized samples at a rate of 500 MHz. These samples are temporarily stored in a 65 us buffer on a Field-Programmable Gate Array (FPGA). But how to distinguish between Cherenkov light pulses and random Night Sky Background (NSB) events (which are due to things like starlight or scattered diffuse galactic light)? VERITAS implements a three-level trigger system in order to isolate Cherenkov light pulses in real time. Once the three-level trigger system’s criteria is met, the FPGAs stop buffering the new Cherenkov light pulse samples to store the data onto a disk. Simply put, Cherenkov light monitoring is not continuous and storing the Cherenkov light pulse data incurs some amount of deadtime for the system. Furthermore, the three-level trigger system only allows for VERITAS to take short Cherenkov light pulse samples, causing a low duty cycle of less than 20%.

Pedestal Variance

Each pixel described previously is capacitively coupled to its respective FADC, meaning that the DC level of the pixel’s raw input signal, known as the pedestal, is blocked; only the AC component of the raw input signals (from photon contributions from the night sky background as well as electronic noise) propagate to the FADC and aforementioned three-level trigger logic.

However, these fluctuations of the AC component may dip below zero, while the FADCs can only measure positive values. To circumvent this issue, VERITAS engineers add an artificial pedestal (DC voltage) to the AC component so that the resultant signal is entirely positive. The total light level (including the NSB) is proportional to the average number of photons detected per sample and the average number of photons detected is small (photon arrival probability distribution resembles a Poisson distribution), so we know that the variance of the digitized signal, known as the pedestal variance, is ultimately proportional to the light level sensed by each pixel. (It is important to note here that the variance of this artificial pedestal is directly proportional to the variance of the input pedestal which is itself proportional to the light level. When we say pedestal variance, we will be referring to the variance of the artificial pedestal, which is included in our digitized signals.)

Thus, since pedestal variance is proportional to light level, continuously calculating the pixel pedestal variance is to effectively continuously monitor the light level being sensed by that pixel. A bonus to this is that VERITAS would really be able to detect all the light hitting its cameras, not just Cherenkov pulses, as in the existing system.

Calculating Pedestal Variance

In order to calculate the pedestal variance, we will compute the sum of all samples and the sum of all squared samples. Statistically, we are calculating and storing E[X]*N and E[X2]*N where N is the fixed number of samples in a variance calculation window, so we can calculate 𝝈^2 = E[X^2] – (E[X])^2 after the fact from what we store.