Joshua Follansbee, Derek Burrell, Orges Furxhi, C. Kyle Renshaw, and Ronald G. Driggers, "Radiometry and contrast-to-noise ratio for continuous-wave and laser range-gated active imaging systems," Appl. Opt. 62, 9317-9325 (2023)
Resolution and sensitivity must be considered in the design of an active imaging system. System sensitivity is characterized by the signal-to-noise or contrast-to-noise ratio and is derived through radiometry. We present a tutorial for the radiometry associated with the contrast-to-noise ratio for active continuous-wave and laser range-gated imaging systems, giving a useful metric for determining reflective-band sensor performance against a target and background. A calculation of the full power and contrast-to-noise ratio terms is shown for an example case, and all relevant radiometric signal terms are covered while describing the assumptions made. Coherent effects on signal-to-noise ratio are excluded from this analysis.
Data underlying the example modeling in this paper are provided in
Section 6.
Cited By
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Spectral solar path radiance, sensor-to-background
[]
Aperture diameter
[cm]
Aperture solid angle
[sr]
Fractional optics transmission
[unitless]
Focal length
[mm]
Detector size
[µm]
Integration time
[s]
Spectral detector quantum efficiency
[e-/photon]
Dark current
[e-/s]
The path radiance terms ${L_{\text{tgt}}}$, ${L_{\text{sky}}}$, and ${L_{\text{bkg}}}$ represent the band-integrated solar path radiance along the sensor path, acquired from the moderate resolution atmospheric transmission model (MODTRAN) [12].
Table 2.
Expressions for Received Power at the Detector Using the Radiometric Expressions Derived in Section 3
Expanded expressions for each standard deviation are shown in Column 3. Camera data sheets generally specify the read noise standard deviation ${\sigma _{\text{read}}}$, whose square is the read noise variance. Different formulations of SNR and CNR may require counting different signal terms as photon noise contributors.
The sensor parameters are based on an Attollo Phoenix SWIR camera [24]. The target spatial variance is set to zero for a flat reflectivity target with no spatially varying characteristics.
Table 5.
MODTRAN-Generated Values for Fractional Atmospheric Transmission over a 1 km Path Length and Solar Irradiancea
[µm]
Fractional Transmission, 1 km [unitless]
Solar Irradiance []
1.00
0.913112
0.055583
1.05
0.929628
0.055703
1.10
0.93203
0.053785
1.15
0.930855
0.051189
1.20
0.910736
0.046858
1.25
0.797721
0.036331
1.30
0.623141
0.0226
1.35
0.589637
0.018826
1.40
0.719093
0.026048
1.45
0.842382
0.033143
1.50
0.895656
0.035829
1.55
0.920736
0.036898
1.60
0.935399
0.036703
1.65
0.936194
0.034819
1.70
0.9276
0.033036
Wavelengths are sampled coarsely in order to fit all data required to reproduce the example.
Table 6.
MODTRAN-Generated Solar Path Radiance [] for Three Range Values (1 km, 2 km, 3 km)
Spectral solar path radiance, sensor-to-background
[]
Aperture diameter
[cm]
Aperture solid angle
[sr]
Fractional optics transmission
[unitless]
Focal length
[mm]
Detector size
[µm]
Integration time
[s]
Spectral detector quantum efficiency
[e-/photon]
Dark current
[e-/s]
The path radiance terms ${L_{\text{tgt}}}$, ${L_{\text{sky}}}$, and ${L_{\text{bkg}}}$ represent the band-integrated solar path radiance along the sensor path, acquired from the moderate resolution atmospheric transmission model (MODTRAN) [12].
Table 2.
Expressions for Received Power at the Detector Using the Radiometric Expressions Derived in Section 3
Expanded expressions for each standard deviation are shown in Column 3. Camera data sheets generally specify the read noise standard deviation ${\sigma _{\text{read}}}$, whose square is the read noise variance. Different formulations of SNR and CNR may require counting different signal terms as photon noise contributors.
The sensor parameters are based on an Attollo Phoenix SWIR camera [24]. The target spatial variance is set to zero for a flat reflectivity target with no spatially varying characteristics.
Table 5.
MODTRAN-Generated Values for Fractional Atmospheric Transmission over a 1 km Path Length and Solar Irradiancea
[µm]
Fractional Transmission, 1 km [unitless]
Solar Irradiance []
1.00
0.913112
0.055583
1.05
0.929628
0.055703
1.10
0.93203
0.053785
1.15
0.930855
0.051189
1.20
0.910736
0.046858
1.25
0.797721
0.036331
1.30
0.623141
0.0226
1.35
0.589637
0.018826
1.40
0.719093
0.026048
1.45
0.842382
0.033143
1.50
0.895656
0.035829
1.55
0.920736
0.036898
1.60
0.935399
0.036703
1.65
0.936194
0.034819
1.70
0.9276
0.033036
Wavelengths are sampled coarsely in order to fit all data required to reproduce the example.
Table 6.
MODTRAN-Generated Solar Path Radiance [] for Three Range Values (1 km, 2 km, 3 km)
Add to BibSonomy