"""
detector.py
------------
Handles detector signal and noise calculations.
This module includes functions to compute the expected signal and noise
levels for a detector based on the hardware specifications.
Constants:
- ELEMENTARY_CHARGE: Electron charge (C)
- ANODE_RADIANT_SENSITIVITY: Anode radiant sensitivity (A/W)
- DARK_CURRENT: Dark current noise (A)
- BANDWIDTH: Bandwidth (Hz)
- INPUT_CURRENT_NOISE: Preamplifier input current noise (A/√Hz)
Functions:
- laser_power_density(laser_power, beam_major, beam_minor): Computes
the laser power density at the aerosol stream.
- estimate_signal_noise(truncated_csca, laser_power): Estimates signal
and noise levels for a given truncated scattering cross section and
laser power.
Citations:
- Gao, R.S., et al. 2016. A light-weight, high-sensitivity particle
spectrometer for PM2.5 aerosol measurements. Aerosol Science and
Technology 50, 88-99. https://doi.org/10.1080/02786826.2015.1131809
- Thor Labs. TIA60 Transimpedance Amplifier Datasheet. https://www.thorlabs.com/drawings/c627bb63fbc792f9-BE0A1D53-FE71-D4E9-369F32E2683F2FB6/TIA60-SpecSheet.pdf
- Hamamatsu Photonics. H10720 Series Photomultiplier Tube Datasheet. https://www.hamamatsu.com/content/dam/hamamatsu-photonics/sites/documents/99_SALES_LIBRARY/etd/H10720_H10721_TPMO1062E.pdf
"""
from __future__ import annotations
from typing import TYPE_CHECKING
from warnings import warn
import math
import numpy as np
from numpy.typing import NDArray
if TYPE_CHECKING:
from .OPS import OpticalParticleSpectrometer
# Physical constants
[docs]
ELEMENTARY_CHARGE = 1.602176634e-19 # C
# Detector specifications - Hamamatsu H10720-110 PMT
[docs]
H10720_110_CATHODE_RADIANT_SENSITIVITY = 110 # mA/W
[docs]
H10720_110_GAIN_SLOPE = 8.645 # slope of gain curve (log-log scale)
[docs]
H10720_110_GAIN_INTERCEPT = 6.299 # intercept of gain curve (log-log scale)
[docs]
H10720_110_DARK_CURRENT = 1e-9 # typical dark current (A)
# Specifications from Gao et al. 2016
[docs]
BANDWIDTH = 4e6 # bandwidth (Hz)
# Preamplifier specifications - Thor TIA60 PMT amplifier
[docs]
def anode_radiant_sensitivity(PMT_control_voltage: float) -> float:
"""Return the anode radiant sensitivity of the PMT in A/W.
Parameters
----------
PMT_control_voltage : float
Control voltage of the PMT in volts.
Returns
-------
float
Anode radiant sensitivity in A/W.
"""
if PMT_control_voltage <= 0:
raise ValueError("PMT control voltage must be a positive value.")
if PMT_control_voltage > 1.1 or PMT_control_voltage < 0.5:
warn(
"H10720_110 PMT control voltage should be between 0.5 and "
"1.1 V. Please verify the input value unless you are using "
"a different PMT."
)
gain = 10 ** (
H10720_110_GAIN_SLOPE * np.log10(PMT_control_voltage)
+ H10720_110_GAIN_INTERCEPT
)
return H10720_110_CATHODE_RADIANT_SENSITIVITY * gain / 1000
[docs]
def laser_peak_power_density(
laser_power: float,
beam_major: float = 6,
beam_minor: float = 0.054,
) -> float:
"""Return the laser peak power density at the aerosol stream.
Assumes a Gaussian beam profile and that the beam is focused at the
aerosol stream. Also assumes that the aerosol passes through the
center of the beam where the power density is highest.
The initial beam dimensions are taken from Gao et al. 2016 and the
beam waist at the aerosol stream is estimated below assuming a
Gaussian beam profile. The laser power density is then calculated as
the laser power divided by the beam area at the aerosol stream.
Horizontal beam waist at aerosol stream:
spot_diameter = 4M² * λ * L / (π * w_initial) = 0.054 mm
where λ = 405 nm, L = 75 mm, w_initial_horizontal = 1 mm, M² = 1.4
(assumed).
Vertical beam waist at aerosol stream:
spot_diameter = 2M² * λ * L / (π * w_initial)
where L = 25 mm, w_initial_vertical = 3 mm.
DOF = 2 * π * (spot_diameter / 2)² / (M² * λ)
beam_diameter = spot_diameter
* sqrt(1 + (distance_from_lens - L)² / (DOF/2)²) = 6 mm
Parameters
----------
laser_power : float
Laser power in mW.
beam_major : float, optional
Length of major axis of the oval laser beam at the aerosol
stream in millimeters. Default is 6.
beam_minor : float, optional
Length of minor axis of the oval laser beam at the aerosol
stream in millimeters. Default is 0.054.
Returns
-------
power_density : float
Optical power density (W/µm^2).
References
----------
Gao, R.S., et al. 2016. A light-weight, high-sensitivity particle
spectrometer for PM2.5 aerosol measurements. Aerosol Science and
Technology 50, 88-99. https://doi.org/10.1080/02786826.2015.1131809
Laser spot size and beam waist calculator and formulas. Gentec.
(n.d.).
https://www.gentec-eo.com/laser-calculators/beam-waist-spot-size
"""
if beam_major <= 0 or beam_minor <= 0:
raise ValueError("Beam major and minor axes must be positive values.")
if beam_major > 10 or beam_minor > 10 or beam_major < 1e-4 or beam_minor < 1e-4:
warn(
"Beam dimensions in millimeters seem unrealistic. "
"Please verify the input values."
)
if laser_power < 0:
raise ValueError("Laser power must be non-negative.")
if laser_power > 1e3 or laser_power < 1e-3:
warn(
"Laser power in milliwatts seems unrealistic. "
"Please verify the input value."
)
beam_area = math.pi * (beam_major / 2 * 1e3) * (beam_minor / 2 * 1e3) # µm^2
return 2 * laser_power * 1e-3 / beam_area # W/µm^2
[docs]
def estimate_signal_noise(
ops: OpticalParticleSpectrometer,
truncated_csca: float | NDArray[np.float64],
) -> tuple[float | NDArray[np.float64], float | NDArray[np.float64]]:
"""Return signal and noise estimates.
Computes signal and noise estimates for a given truncated single
scattering cross section and laser power. This function uses the
maximum gain settings for the PMT and preamplifier. This is expected
to be larger than the actual signal and noise levels in typical
operation, but provides a useful upper bound.
Parameters
----------
ops : OpticalParticleSpectrometer
Instance of the OpticalParticleSpectrometer class.
truncated_csca : float or np.ndarray
Truncated scattering cross section in units of µm².
Returns
-------
signal : float or ndarray
Estimated signal current (A).
noise : float or ndarray
Estimated noise (A).
"""
signal_current = (
truncated_csca # µm²
* laser_peak_power_density(ops.laser_power) # W/µm²
* ops.anode_radiant_sensitivity # A/W
* ops.mirror_reflectivity # unitless
) # A
signal_noise = 2 * ELEMENTARY_CHARGE * signal_current # C^2 s^-1
dark_noise = 2 * ELEMENTARY_CHARGE * ops.dark_current # C^2 s^-1
preamp_noise = ops.input_current_noise**2 # C^2 s^-1
total_noise = np.sqrt(
(signal_noise + dark_noise + preamp_noise) * ops.bandwidth
) # A
return signal_current, total_noise