probability_measurement

optika.sensors.probability_measurement(iqy=<Quantity 1. electron / ph>, cce=1)

The probability that a photon absorbed in the epitaxial silicon layer results in at least one photoelectron measured by the sensor.

For most of the electromagnetic spectrum, this quantity is nearly unity, but in the ultraviolet, there is a significant chance that all the photoelectrons associated with a photon recombine before being measured.

Parameters:

• iqy (Quantity | AbstractScalar) – The ideal quantum yield of the sensor in electrons per photon, calculated by quantum_yield_ideal().

• cce (float | AbstractScalar) – The charge collection efficiency of the detector computed using charge_collection_efficiency().

Return type:

AbstractScalar

Examples

Plot the probability of measuring an absorbed photon vs the charge collection efficiency

import matplotlib.pyplot as plt
import astropy.units as u
import astropy.visualization
import named_arrays as na
import optika

# Define a grid of wavelengths
wavelength = na.geomspace(10, 10000, axis="wavelength", num=1001) * u.AA

# Compute the ideal quantum yield of silicon for these wavelengths
iqy = optika.sensors.quantum_yield_ideal(wavelength)

# Compute the charge collection efficiency for each wavelength
cce = optika.sensors.charge_collection_efficiency(
    absorption=optika.chemicals.Chemical("Si").absorption(wavelength),
)

# Compute the probability of measuring an absorbed photon
# vs the charge collection efficiency
p_m = optika.sensors.probability_measurement(iqy, cce)

# Plot the results
with astropy.visualization.quantity_support():
    fig, ax = plt.subplots(constrained_layout=True)
    na.plt.plot(
        wavelength,
        cce,
        ax=ax,
        label="charge collection efficiency",
    )
    na.plt.plot(
        wavelength,
        p_m,
        ax=ax,
        label="probability of measurement",
    )
    ax.set_xscale("log");
    ax.set_xlabel(f"wavelength ({ax.get_xlabel()})");
    ax.set_ylabel("probability");
    ax.legend();

Notes

The probability that all the electrons recombine before being measured is

\[P_r = (1 - \text{CCE})^\text{IQY}\]

Where \(\text{CCE}\) is the charge collection efficiency, and \(\text{IQY}\) is the ideal quantum yield of the sensor. So then the probability of a photon being measured is just the compliment of \(P_r\),

\[P_m = 1 - P_r.\]

References to optika.sensors.probability_measurement
probability_measurement