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→Detailed Characterization
=== Detailed Characterization ===
=== Detailed Characterization ===
Since the SiPM performance is sensitive to the bias voltage applied and the ambient temperature, a measurement SiPM properties as functions of bias voltage (V<sub>b</sub>) and temperature (T) was performed on the SSPM-06~. (By this point, the SSPM-06~ was judged to a better sensor for the tagger microscope, owing to higher sensitivity in the blue-green range and better active area match to the fiber cross-section. Aside from gains in efficiency and dynamic range of the resulting readout, higher photon detection implies higher time resolution because of the scintillation decay time of 2.7ns in the fiber.)
Since the SiPM performance is sensitive to the bias voltage applied and the ambient temperature, a measurement SiPM properties as functions of bias voltage (V<sub>b</sub>) and temperature (T) was performed on the SSPM-06~. (By this point, the SSPM-06~ was judged to be a better sensor for the tagger microscope, owing to [[:Image:Image:BCF20,LED,SiPMs comp.png|higher sensitivity in the blue-green range]] and better active area match to the fiber cross-section. Aside from gains in efficiency and dynamic range of the resulting readout, higher photon detection implies better time resolution because of the scintillation decay time of 2.7ns in the fiber.)
The range of interest for these operating variables were:
The range of interest for these operating variables were:
* V<sub>b</sub>: from 0.5V below to 0.5V above the operating range: 19V-21V
* V<sub>b</sub>: from 0.5V below to 0.5V above the operating range, yielding a ranger of interest: 19V-21V
* T: 0-above room temp., in practice 3°C (to avoid growing snow) to 25°C
* T: 0-above room temp., in practice 3°C (to avoid growing snow) to 35°C
However, it was found that the peaks were very indistinct by at bias voltages below 20V and temperatures above 20°C. This was probably due to the narrowing of the peaks due to smaller gain or convolution of the additional dark counts detected.
However, it was found that the peaks were very indistinct at bias voltages below 20V and temperatures above 20°C. This was probably due to the narrowing of the peaks due to smaller gain or convolution of the additional dark counts detected.
==== Histogram Fitting Method ====
==== Histogram Fitting Method ====
{| border="0" cellpadding="0"
{| border="0" cellpadding="0"
|-
|-
|<math>q \equiv \frac{x-x_0}{g}\quad</math> ||width="50px"| || a unit normalized to pixel counts (and zeroed accordingly)
|<math>q \equiv \frac{x-x_0}{g}\quad</math> ||width="50px"| || where <math>g</math> is a gain factor equaling the distance between peaks in Vs. <math>q</math> is therefore a unit normalized to pixel counts and zeroed accordingly.
|-
|-
|<math>x\quad</math> || || is the real integral value (in Vs) and <math>x_0</math> is the pedestal offset (location of first peak).
|<math>x\quad</math> || || is the real integral value (in Vs) and <math>x_0</math> is the pedestal offset (location of first peak).
<math>\lambda_{(p)}, \lambda_{(s)}, \sigma_0, \sigma_1, g, x_0 \quad</math> are the fit parameters. Note the absence of a vertical scale parameter. The vertical scale depends on the number of samples collected, whereas the equation in this model is normalized. Rescaling works as follows:
<math>\lambda_{(p)}, \lambda_{(s)}, \sigma_0, \sigma_1, g, x_0 \quad</math> are the fit parameters. Note the absence of a vertical scale parameter. The vertical scale depends on the number of samples collected, whereas the equation in this model is normalized. Rescaling works as follows:
If <math>f(x)=T\,f(q)</math>, where <math>T</math> is a vertical scaling parameter and since <math>dq=dx/g</math>,
If <math>f(x)=T\,f(q)</math>, where <math>T</math> is a vertical scaling parameter and since <math>dq = dx/g</math>,
<math>\int_{-\infty}^{\infty} f(x)\, dx = Tg \int_{-\infty}^{\infty} f(q)\, dq = Tg </math> implies that Tg is the number of events collected times the bin width (in Vs).
<math>\int_{-\infty}^{\infty} f(x)\, dx = Tg \int_{-\infty}^{\infty} f(q)\, dq = Tg </math> implies that Tg is the number of events collected times the bin width (in Vs).