SpecTIR Signal-to-Noise Ratio Modeling
O.Weatherbee, W. Procino- March 2010
Abstract. Presented here is a description of signal-to-noise (SNR) characterization of the
ProSpecTIR hyperspectral imagers. Results will be similar to any imager of this general
type which incorporate Specim based spectrometers from the AISA Eagle and Hawk
product lines. The SNR information pertain to any of the data products delivered by
SpecTIR LLC to clients and the extensive information presented here is essential for
endusers to understand this important tool for judging the potential effectiveness in a
specific application.
SNR for Imaging Spectroradiometers: The inadequacies of the “Average SNR” term
It is common practice in presenting estimated signal-to-noise ratios (SNR) of hyperspectral
imagers to assign a single number, e.g., 300:1, for the entire spectral range, and at some
"standard" level of irradiance at the sensor. This fails to communicate to potential users,
sufficient information to understand the capability or limitations of an imager at
wavelengths and radiance levels of interest to a given application or target. As a start, the
user is better served by estimates of SNR as a function of wavelength over the entire
spectral region covered by the imager of interest.
All the components of an imaging hyperspectral sensor have an impact on the final SNR
performance of a system. For example the specific responsivity of the focal plane array
(FPA) and the transmission behavior of the optical components will impact the system’s
sensitivity at different wavelengths. Two systems with the same spectral range sensitivity
could have maximum SNR performance at different areas within the spectrum.
Understanding the wavelength dependence of a system’s SNR performance is critical in
evaluating and/or modeling its suitability for a given application or target. For example, a
VNIR system with poor SNR in the 400-500nm range but high SNR from 700-1000nm
would not be as suitable for aquatic applications as one with reverse behavior. However
they could both report the same average SNR value which is why it is important to provide
SNR values by wavelength, not just by averages.
Further compounding the inadequacies of a simple statement of SNR is that systems such
as those available from SpecTIR and Specim, have complete flexibility of VNIR and SWIR
integration times as well as spectral and spatial binning all of which have a substantial
impact on the resultant SNR performance. The same instrument, depending on
configuration at the time of image acquisition will have different SNR performance.
Additionally, inherent to the entire concept of SNR is the fact that if the “signal” varies, so
does the calculated ratio with what is typically a relatively stable noise floor. So when
reporting SNR values it must be done with relation to the amount of signal used in the
calculation. Often a statement of a target albedo is offered such as a 50% reflectance target
but without additional information relating to the actual irradiance level being reflected,
this again does not allow any meaningful conclusions to be drawn and should prompt the
interested party to request additional information.
SpecTIR SNR Modeling
The calculation of the SNR performance of an imaging hyperspectral instrument is an
engineering, laboratory based measurement that can be used to model a sensors’
performance against theoretical reflectance targets under some illumination criteria.
Empirical estimation of SNR from actual survey data is not really feasible or reliable as it is
subject to high errors due to the natural variability of the imaged target background and
subsequent mixed pixel effects which creates an artificially high standard deviation and
therefore a low SNR calculation. Even an apparently uniform sandy beach will have
substantial signal variation across an area large enough to be considered a relevant
statistical sample.
Whereas a researcher can try and identify areas of uniform features within an image to
estimate or generate a scene based SNR value, this is not generally feasible for contractual
SNR standards because of the underlying mixed pixel variance as well as the fact that most
SNR standards used for contracts are based on a theoretical reflectance target not found in
real world scenes, e.g. a 50% reflectance across the entire spectrum. .
To address these issues, SpecTIR has worked to build an accurate SNR model for their
imaging spectrometers grounded in component level characterizations such as CCD/CMOS
Quantum Efficiencies (QEs), pixel full well capacities, binned well capacities, detector shot
noise, readout noise, spectrometer transmission, lens transmission, etc. All of these factors
and more were utilized in the creation of a sensor performance model.
Model Testing, and Validation
As a means to test and verify the model, direct SNR calculations were generated using
measurements taken from a Labsphere USS2000 uniform radiance source. This sphere
carries a NIST-traceable spectral radiance calibration from 400 nm to 2500 nm at a
sampling interval of 5 nm. The resultant spectral response curve of this sphere is typical
for halogen light sources (Figure 1).
The exit port uniformity of this sphere is certified to 98% and so even in this best case
scenario, there could be a 2% variance which could impact estimated SNR values from
imagery acquired.
Figure 1. Spectral Radiance Response Curve of SpecTIR's Calibration Sphere
The direct estimation of the imaged SNR was performed as per the methodology outlined in
the whitepaper Signal, Uncertainty, Error, and Noise from Analytical Spectral Devices
Incorporated (2001). The data was processed to radiance, removing all systematic errors
related to dark current and flat fielding response, at which point only the sum of all random
errors remains. This quantity is characterized by the standard deviation of the mean. The
SNR value is simply the ratio of the mean signal and this standard deviation value.
Based on the known sphere spectral radiance response and inputting the VNIR and SWIR
integration times and imaging array binnings used at the time of the measurements, the
modeled estimated SNR was calculated and compared to the results generated from the
image itself. This comparison was used as validation and shows that the SpecTIR sensor
performance model accurately characterizes the system SNR performance (Figure 2).
This validation was performed for different integration times and sensor configurations to
ensure the robustness of the model.
As previously described, SpecTIR’s systems can be operated with different binnings, an
example of which is the spectral binning between ~5nm and ~10nm spectral band centers.
As expected and demonstrated in Figure 2, the doubling of the binning or integration of
channels results in an increase in the measured and modeled SNR by approximately a
square root of 2, essentially a 40% improvement.
In comparing the relatively smooth input signal (Figure 1) to the resultant SNR plots, some
observations can be quickly made. The relatively low SNR in the blue region is not
surprising as the halogen lamp is outputting a low signal at those wavelengths. However,
the curved shape of the SNR curve in the 400-960 nm region does not match well with the
ramping up of the halogen light signal. This is primarily related to the VNIR array’s Silicon
sensitivity fall off at this range. Similarly, the 940-1010nm spectral range is just at the
beginning of the SWIR Mercury Cadmium Telluride (MCT) detector response range and so
it too has a lower SNR performance in this range.
Figure 2. Sensor performance model validation
In remote sensing applications, however, this area of low SNR occurs in an atmospheric
window centered on 940nm which is rarely used for any diagnostic analysis. For this
reason, the crossover between the two sensor systems is centered on this atmospheric
region.
The plots shown in Figure 2 are the validation of the model to predict the SNR that is
actually measured from a halogen light source on a sphere with no atmosphere related
absorption features. To build upon the utility of this model, a modeled solar irradiance
curve was incorporated as a means to convolve input reflectance spectra and generate
expected SNR curves of the system for real world imaged targets at varying sun angle
conditions (Figure 3).
Airborne imagers receive upwelling irradiance in response to illumination by the sun
modulated by atmospheric constituents as depicted by the absorption windows shown in
Figure 3. As the SNR model is radiance based, not reflectance based, it is necessary to
convolve target reflectance data into theoretical on-chip radiance levels. A simple
approach to doing this is to take the theoretical Solar irradiance curve (Figure 3) and
multiply it by an input reflectance curve. Sun angle variation and illumination changes are
modeled by simply multiplying this input theoretical irradiance by the cosine of the solar
angle.
Figure 3. Solar Irradiance Model with Atmospheric Absorption Windows Highlighted in Gray.
To test the efficacy of this approach, calculated reflectance curves taken from actual
airborne hyperspectral data products were processed and compared against the original
input radiance values.
SpecTIR’s standard processing converts radiance to reflectance using ATCOR4, a
MODTRAN-based software package. Figure 4 shows reflectance spectra derived from the
SpecTIR-VS1 instrument and ATCOR4 processing: bare ground spectra from Cuprite,
Nevada (with a clear signature of the mineral alunite), and grass spectra from a collection
in Beltsville, Maryland.
Figure 4. Sample ATCOR Reflectance Curves
The solar irradiance curve of Figure 3 was multiplied by the reflectance spectra in Figure
4, modulated by the cosine of the different sun angles at the time of acquisition. The two
estimated radiance of these reflectance curves and the true measured radiance plots are
shown in Figure 5 and Figure 6.
Figure 5. Comparison of modeled grass radiance to measured radiance
Figure 6. Comparison of Modeled Bare Ground Radiance and Measured Radiance
The agreement shown in Figures 5 and 6 between the ProSpecTIR-VS1 measured radiance
and simply conversion of ATCOR4 based reflectance curves is remarkable considering the
model does no complex calculations such as variable water vapor corrections and only
modifies the single input solar irradiance term based on sun angle. Again, it should be
emphasized that these data were acquired months apart, under different atmospheric
conditions, sun angles, and in the case of the VNIR sensor, different integration times.
SNR Model Application
With confidence in the radiance calculation aspect of the model, it is now possible to input
a reflectance curve, sensor configuration settings, and sun angle and calculate and accurate
estimation the system’s SNR performance.
A common standard SNR performance reference in the literature is for a 50% reflectance
target at a 30 degree solar zenith angle. That would mean a target that reflects exactly 50%
of the downwelling solar irradiance across the entire sampled spectrum. While this type of
theoretical target is interesting, it is not realistic in terms of the variation in reflectance
spectra that is found in actual imagery. For the included comparison, two additional
reflectance spectra were selected from the standard spectral libraries included with every
ENVI software distribution, Buddingtonite from the mineral library, and “Lawn_Grass”
from the USGS vegetation libraries. These spectra are shown in Figure 7 and are provided
in order to allow researchers in possession of this whitepaper to extrapolate the presented
results to their possible targets of interest.
Figure 7. Selected Reflectance Spectra for SNR Calculations
These target spectra were entered into the model with a simulated framerate of 60 Hz (60
frames per second), 30 deg solar zenith angle, and VNIR/SWIR integration times of 5 and
8ms, respectively. These are approximate settings which would be used operationally for
acquiring 1 meter GSD imagery from a platform traveling at 120 knots. The results for both
the ~5nm and ~10nm band sets are shown in Figure 8.
Figure 8. SNR Curves for Different Reflectance Targets; 1 m GSD, 5ms VNIR/8ms SWIR Integration Times; 30 deg SZA
As previously discussed, presenting a single SNR value has little meaning without
accompanying SNR spectral curves. However, for the purpose of illustrating the impact of
different targets on calculated SNR performance, overall numbers are provided below. For
the data as presented in Figure 8, the SNR statistics are shown in Table 1. The “NonAtmospheric Window Mean SNR” calculation is based on simply omitting those spectral
channels which fall within the atmospheric windows shown in gray in Figure 8 (and
Figure 3).
Target
50% Reflectance
Target
Lawn_Grass
Buddingtonite
Total Mean SNR:
Non-Atmospheric
Window Mean SNR
Total Mean SNR:
Non-Atmospheric
Window Mean SNR
Total Mean SNR:
Non-Atmospheric
Window Mean SNR
~5nm Band Set
365:1
~10nm Band Set
516:1
417:1
589:1
228:1
323:1
259:1
356:1
386:1
546:1
439:1
620:1
Table 1. Mean SNR Values For Figure 6 Targets
Quoting ProSpecTIR-VS SNR Values for Proposals
At this point, it should be abundantly clear that the true answer to the question, “What is your
system’s SNR performance” is: “it depends.” However, certain proposals and or clients may not
allow an opportunity to provide a correct, nuanced discussion of these technical points when
responding to a query or RFP. In this case, the standard SpecTIR response should be along the
following guidelines.
For a 50% reflectance target, 1 m GSD collection, 30 degree solar zenith angle, the SNR of the
ProSpecTIR-VS is provided below:
Total Mean SNR:
Non-Atmospheric
Window Mean SNR
~5nm Band Set
365:1
~10nm Band Set
516:1
417:1
589:1