def ENF(p_crosstalk: float) -> float:
"""
Calculate excess noise factor (ENF) of the detector
See formulas 2.16, 2.17 and 2.27 in [1]
Parameters
----------
p_crosstalk : float
The probability of a single crosstalk event.
Returns
-------
ENF : float
Excess noise factor.
References
----------
.. [1]
Gallego, L., et al. "Modeling crosstalk in silicon photomultipliers."
Journal of instrumentation 8.05 (2013): P05010.
https://iopscience.iop.org/article/10.1088/1748-0221/8/05/P05010/pdf
"""
d = d_crosstalk_4n(p_crosstalk)
r = d[5] / (1 - sum(d[1:5]))
e1 = moment(d[:5], 1) + d[5] * (1 + 4 * r) / r**2
var1 = moment(d[:5], 2) + d[5] * (2 + 7 * r + 16 * r**2) / r**3 - e1**2
return 1 + var1 / e1**2
def c_moments(model, k):
"""
Constraint rule for difference QEST initial moment of order k
and the same moment of Q.
This difference must be less than 1%
Parameters
----------
model : InvPBaseModel
k : int
Order of moment.
"""
return (1 - 1e-2, moment(model.QEST, k) / moment(model.Q, k), 1 + 1e-2)
def c_sum_qest(model):
"""
Parameters
----------
model : InvPBaseModel
Returns
-------
Constraint rule for equality of sum(QEST) and 1
"""
return moment(model.QEST, 0) == 1
def c_noisesum(model):
return moment(model.p_noise, 0) == 1
def e_noisemean(model):
return moment(model.p_noise, 1)
def e_ppoisson(model, n):
pmean = moment(model.P, 1) - moment(model.p_noise, 1)
return exp(-pmean) * pmean ** n / fact(n)