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A new radiometric unit of measure to
characterize SWIR illumination
A. Richards, M. Hübner
A. Richards, M. Hübner, "A new radiometric unit of measure to characterize
SWIR illumination," Proc. SPIE 10178, Infrared Imaging Systems: Design,
Analysis, Modeling, and Testing XXVIII, 101780C (3 May 2017); doi:
10.1117/12.2261459
Event: SPIE Defense + Security, 2017, Anaheim, California, United States
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A new radiometric unit of measure to
characterize SWIR illumination
A. Richards*, FLIR Systems, Inc. Goleta, CA USA
M. Hübner, Hensoldt, Oberkochen, Germany
We propose a new radiometric unit of measure we call the ‘swux’ to unambiguously characterize scene illumination in the
SWIR spectral band between 0.8µm-1.8µm, where most of the ever-increasing numbers of deployed SWIR cameras (based
on standard InGaAs focal plane arrays) are sensitive. Both military and surveillance applications in the SWIR currently
suffer from a lack of a standardized SWIR radiometric unit of measure that can be used to definitively compare or predict
SWIR camera performance with respect to SNR and range metrics. We propose a unit comparable to the photometric
illuminance lux unit; see Ref. [1]. The lack of a SWIR radiometric unit becomes even more critical if one uses lux levels to
describe SWIR sensor performance at twilight or even low light condition, since in clear, no-moon conditions in rural areas,
the naturally-occurring SWIR radiation from nightglow produces a much higher irradiance than visible starlight. Thus, even
well-intentioned efforts to characterize a test site’s ambient illumination levels in the SWIR band may fail based on
photometric instruments that only measure visible light. A study of this by one of the authors in Ref. [2] showed that the
correspondence between lux values and total SWIR irradiance in typical illumination conditions can vary by more than two
orders of magnitude, depending on the spectrum of the ambient background. In analogy to the photometric lux definition, we
propose the SWIR irradiance equivalent ‘swux’ level, derived by integration over the scene SWIR spectral irradiance
weighted by a spectral sensitivity function S(λ), a SWIR analog of the V(λ) photopic response function.
1. INTRODUCTION
Imaging in the SWIR band is becoming more and more commonplace as the cost of InGaAs sensor technology falls and
interest in the unique advantages of this waveband increases. One of the most compelling imaging applications is imaging
in low-light conditions, where visible cameras can sometimes be at a distinct disadvantage compared to SWIR cameras
because the ambient illumination spectrum is skewed heavily towards the SWIR band. This is particularly true in clear, nomoon conditions in rural areas where naturally-occurring SWIR radiation from nightglow dominates over visible starlight.
The SWIR spectrum can also dominate over the visible spectrum in urban areas with relatively high levels of light pollution.
An airport parking lot in Los Angeles, for example, may have more ambient SWIR irradiance than the unaided eye would
suggest, due to the very red and near-infrared dominated spectrum of older urban lighting equipment. Another advantage of
SWIR cameras is their superior ability to image through haze and smog relative to color visible cameras. This is because
SWIR radiation passes much more freely through typical haze and smog aerosol distributions compared to visible light,
because of the reduced scattering cross section at the longer wavelengths.
The SWIR imaging world has been at somewhat of a loss in terms of predicting camera performance in different lighting
conditions, because there has not been an extensive effort to measure SWIR ambient backgrounds, particularly for
commercial applications. Yet fair comparisons of visible or infrared cameras from different manufacturers depend on
accurate radiometry in the correct band. For example, a camera vendor “shootout” might be held at a dark-skies test site,
and several competing InGaAs products might be tested simultaneously on a given night at that site. Without some kind of
SWIR radiometry to measure ambient background, it is impossible to quantitatively compare the test results on that night to
a similar set of tests run on a different night (with possibly different SWIR lighting conditions). Photometric instruments
that measure lux levels will give some indication of visible-light levels, but that metric turns out to be a very poor predictor
of SWIR light levels. Thus, even well-intentioned efforts to characterize a test site’s ambient illumination levels in the
SWIR band may fail miserably based on photometric instruments that only measure visible light. A study of this by one of
the authors showed that the correspondence between lux values and SWIR backgrounds in typical illumination conditions
can vary by more than two orders of magnitude, depending on the spectrum of the ambient background2.
* austin.richards@flir.com, +1-805-284-5757
Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXVIII, edited by Gerald C. Holst,
Keith A. Krapels, Proc. of SPIE Vol. 10178, 101780C · © 2017 SPIE
CCC code: 0277-786X/17/$18 · doi: 10.1117/12.2261459
Proc. of SPIE Vol. 10178 101780C-1
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This paper is a proposal to define a new unit of measure for SWIR irradiance, something like a lux unit but for the SWIR
waveband. The unit is based on the spectral response of “typical” InGaAs camera detectors, rather than the spectral
response of the human eye. We also propose a method of measuring this particular in-band SWIR irradiance in the
laboratory or in the field with a calibrated single-element InGaAs detector connected to a high-performance current meter.
The authors note that many papers and articles published about SWIR imaging show images taken with InGaAs cameras
where the ambient illumination is either described only qualitatively, as in “no-moon rural conditions”, or else is described
in lux units which relate only to visible light. We propose to quantify SWIR ambient backgrounds so that fair comparisons
between different cameras and different ambient lighting conditions can be made.
The characterization of SWIR illumination conditions is generally done in two ways, neither of which is particularly
convenient or intuitive in judging camera performance. The first and more rigorous way is to start with an irradiance
spectrum plot, such as Figure 1 below, that data for which was taken from 0.4-2.0 micron input datasets for the NVESD
modeling software SSCamIP 2009. It shows the night spectrum in clear starlight conditions; the illumination of a scene in
the SWIR band. It is not immediately intuitive what either SWIR camera or visible camera absolute performance would be
in these conditions, though it is obvious that there is a lot more SWIR radiation than visible radiation, due to nightglow.
SSCamIP software takes this spectrum along with user inputs that describe the camera system (optics and sensor), and
computes some parameters of the camera system performance with it. Systems engineers can build their own simple
radiometric models using tools such as Excel to predict camera performance and use the spectrum shown below and other
like it as the input irradiance. The problem is that the actual irradiance spectrum at a test site may vary from this “typical”
spectrum for many reasons, including cloud cover, light pollution and atmospheric aerosols.
Clear Starlight Spectral Power Irradiance Curve
from NVESD SSCamIP 2009 model
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1
1.2
1.9
1.6
1.8
2
Wavelength (microns)
Figure 1. Clear Starlight spectral power irradiance curve in 10nm intervals from the NVESD SSCamIP 2009 model. Note the
much higher irradiance in the InGaAs band (0.95 to 1.68 microns) compared to the visible band (0.4 to 0.75 microns)
Measuring the spectrum of nightglow and producing a plot like Figure 1 is no easy task, since the amount of radiation in
narrow spectral channels is quite small. A spectroradiometer that can measure starlight levels of irradiance in 10-20nm
channels in the 0.8-1.8 microns waveband requires a high-performance grating monochromator, extremely low-noise TE
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cooled detectors connected to phase-lock amplifier circuits, and both a filter wheel and a chopper wheel. A much simpler,
easier to use and less expensive measurement method is to use a current-measuring radiometer with a single-element
detector and some simple optics to measure the ambient SWIR irradiance in a much broader band. The detector is simply
oriented towards the sky, giving a cosine-weighed measurement of irradiance as an object in the scene would receive it.
This method is very convenient as it reduces a spectral irradiance curve to a single-number figure of merit that is linearly
proportional to InGaAs camera response. For tests of conventional night vision equipment such as image intensifiers or
low-light color sCMOS cameras, the unit of measure is the lux, and the detector used for a lux meter is a single-element
silicon device with a filter to shape the spectral response of the silicon to be photopic, which is the standardized spectral
response of the cone receptors of the human eye’s retina. The lux is a measure of visible-light illumination in units of
lumens per square meter. The lumen is a power unit that is spectrally weighted by the photopic response of the human eye.
Typical lux values are given in Table 1, which is excerpted from the Wikipedia entry on lux units:
Table 1. Lux values for common ambient lighting conditions
Illuminance (lux)
Surfaces illuminated by:
0.0001
Moonless, overcast night sky
0.002
0.05 -0.36
3.4
Moonless clear night sky
with airglow
Full moon on a clear night
Dark limit of civil twilight under a
clear sky
20-50
Public areas with dark
surroundings
50
Family living room lights
80
Office building hallway lighting
100
Very dark overcast day
320 -500
Office lighting
400
Sunrise or sunset on a clear day
1000
Overcast day; typical TV
studio lighting
10,000 -25,000
Full daylight (not direct sun)
32,000 -100,000
Direct sunlight
Figure 2 shows the photopic response curve superimposed on the data from Figure 1. Note the very minimal overlap
between the photopic response curve and the majority of the clear starlight irradiance. Neither an unaided eye nor a lowlight color video camera receives much useful radiation in these conditions, so lux units are a poor way to characterize the
spectrum for a SWIR camera. One can calculate the lux value of this SSCamIP starlight irradiance in Figure 1 by
multiplying the photopic response curve by the starlight spectral irradiance curve at each wavelength, and then summing all
the photopic-weighted irradiance values in each channel. The lux value that one obtains is 1.2 millilux, consistent to first
order with the stated value for a moonless clear night sky given in Figure 1.
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Photopic Response Curve and Clear Starlight Spectral Power Irradiance Curve
from NVESD SSCamIP 2009 model
1.2
8.00E -08
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0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Wavelength (microns)
+Ckar Starlight
--Photopic Response
Figure 2. Clear starlight spectrum from NVESD SSCamIP 2009 model, with photopic V(λ) function superimposed
A similar analysis using the SSCamIP spectral irradiance model input dataset can also be performed for a full moon
spectrum, as shown in Figure 3. The full moon lux value is 110 millilux, which again is consistent to first order with the
value in Table 1. One can then say that there is 92 times more photopic illumination in full moon conditions than in clear
starlight conditions. This will give a system engineer some idea of the relative performance of the unaided eye in these two
lighting conditions. However, the lux values convey a very misleading characterization of InGaAs camera performance in
those same two lighting conditions. Using the SSCamIP data, we find that the total InGaAs-weighted irradiance in the 0.951.68 micron band is 6.48e-4 W/m2 in full moon conditions. The InGaAs-weighted irradiance in clear starlight conditions is
2.15e-4 W/ m2, which is only a factor of ~3 lower. The moon does not add much irradiance in the SWIR band to the sky,
since the whole sky is glowing and the moon only subtends a very small solid angle as seen from the ground relative to the
solid angle subtended by the whole sky.
To summarize, the amount of ambient InGaAs-band radiation in full moon conditions only increases by a factor of 3 over
clear, no-moon conditions, not a factor of 92 as in the case of the human eye. An InGaAs camera can utilize much more
ambient light than the eye in clear, no-moon conditions, and the addition of the full moon only increases the InGaAs-band
irradiance by a factor of three, or about 1.5 stops. Clearly, the lux unit is a poor way to describe SWIR irradiance
conditions!
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Photopic Response Curve and Full Moon Spectral Power Irradiance Curve
from NVESD SSCamIP 2009 model
2.00E-07
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£ 1.40E-07
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1.2
1.4
1.6
1.8
2
Wavelength (microns)
+Full Moon
-e- Photopic Response
Figure 3. Photopic response curve and full moon spectral power irradiance from NVESD SSCamIP 2009 model. There are several orders
of magnitude more irradiance usable by the human eye in these conditions relative to clear starlight.
2. THE NEW SWIR RADIOMETRIC QUANTITIES
We propose a new unit of illumination measurement that is spectrally weighted to the standard lattice-matched InGaAs
band. This unit is dubbed the swux, short for SWIR lux. The swux unit would be a good choice for characterization of
ambient lighting conditions that exist during test trials of InGaAs camera systems, particularly at night where human
observers tend to severely underestimate ambient SWIR backgrounds based on their subjective visual perception of lighting
conditions. We also propose a method for measurement of ambient SWIR levels, a so-called “swux-meter” that can be
constructed from COTS light measurement components and a COTS absorbing glass filter to shape the InGaAs detector’s
spectral response on the shortwave end of the band, to compensate for variations in InGaAs backside processing.
2.1 Swux Derivation
In the following we describe the definition of the new SWIR-specific radiometric units by analogy to their corresponding
counterparts of photometric quantities. Photometric quantities are all based on the photometric candela definition. The
candela, an SI-based unit that describes the luminous intensity corresponding to the more general radiant intensity, was
redefined by CGPM in 1979 in a manner that makes it independent from the definition and realization of a specific radiant
source:
“The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency
540x1012 hertz and that has a radiant intensity in that direction of (1/683) watts per steradian”.
All photometric quantities like e.g. luminous flux (‘lumen’) or illuminance (‘lux’) are defined by the integral over the
corresponding wavelength-dependent radiometric quantity from 360nm-830nm, weighted by V(λ), the spectral luminous
efficiency function for photopic vision as published by CGPM in 1982 to supplement the definition of the candela.
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2.2 SWIR-Specific Radiometric Units: Basis
The intention of the new SWIR-specific spectroradiometric units (based on the idea of an analogous source-independent
SWIR-candela definition) is to provide a practical integral measure for a unified quantification of SWIR scene illumination
conditions that can improve the performance prediction and comparison of SWIR cameras, most of which have a spectral
sensitivity curve in the spectral band between 0.9µm and 1.68µm. We start with the proposal of a source independent SWIRcandela definition:
The SWIR-candela is proposed to be the radiant intensity, in a given direction, of a source that emits
monochromatic radiation of frequency 193.413x1012 Hz (λ =1.55µm in vacuum),
with a radiant intensity in that direction of sc watt per steradian, where sc = (1/210,000)
The choice of the λ =1.55µm wavelength within this definition was driven by the large amount of available standard LED
light sources at this wavelength that can be used for calibration of a swux meter if the relative spectral shape of the meter’s
detector is known. In the next section, we will show our derivation of the (1/210,000) SWIR-candela scaling factor. A
SWIR-candela is 4.7619x10-6 watts/steradian at 1.55 microns.
The scaling for the following proposed SWIR-specific spectroradiometric units swir-lumen (for SWIR-specific radiant flux),
swux (for SWIR-specific irradiance) and swux/steradian (for SWIR-specific radiance) is determined by the choice of the
scaling factor sc. This choice is an important one, as it leads to the resulting scale of values that describe the typical SWIRspecific radiance levels of certain natural or artificial scene illumination conditions ranging from e.g. clear starlight over
full-moon conditions to direct sunlight at noon. Put simply, we had to decide whether a clear starlight irradiance condition is
on the order of 1 swux in magnitude, or 10 swux or 100 or some other value. We propose two possible methods to define
scaling factors for these new units. Both of these methods are an attempt to make a connection to existing standards and
practices in the field of radiometry and photometry. The first is based on proposed methods for night vision goggle (NVG)
gain calibration3, while the second method provides a direct relationship to the well-understood and accepted photometric
units in the visual (VIS) spectral band.
Method 1: In many cases, particularly in tactical applications, system engineers want to characterize their SWIR camera
performance in low-light scene conditions. We propose to build up a reasonable link to the currently-used NVG gain
definition, typically used to describe image intensifier-based NVG performance under low-light conditions. NVG gain
measurements are typically calibrated by an industry-standard test set at a fixed-level input radiance of 2.48x10-6W m-2 sr-1
with one of two types of standardized illumination sources. One is an integrating sphere illuminated by near-infrared LEDs
peaking at 820nm. The other is an integrating sphere configured as a CIE standard Illuminant A.3
A precise relationship between spectral bands centered around wavelengths of 820nm and 1.55µm that is based on a CIE
standard Illuminant A is not yet possible, since the official definition of the spectral radiance of a CIE standard illuminant A
is only given up to 820nm3. Nevertheless, for a representative 2856K Illuminant A integrating sphere spectral radiance (as
shown in Figure 4), we propose below a procedure for setting the scale factor sc, and thus scaling all the proposed SWIRspecific radiometric units. This is done by relating the radiance level of a representative 2856K illuminant A integrating
sphere used for NVG calibration, to the unity SWIR-specific radiance quantity.
Method 2: The second possible scaling scenario to define the sc factor is based on the technique of equalizing the ratio of
both quantities of the VIS photometric radiance and the SWIR-specific radiance to unity in case of a 2856K Illuminant A
source.
2.3 SWIR-specific radiometric units: S-lambda curve
For the definition of all SWIR-specific radiometric quantities, we must first define a SWIR spectral radiant efficiency
function for SWIR sensing called S(λ), as shown in the following set of curves. This function is a SWIR analog to the
photometric V(λ) curve. A precise definition of S(λ) is given later.
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-
2856K integrating sphere PTFE
Starlight spectral radiance NVESD 2009
lambda curve
lambda curve
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IF
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A
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Figure 4. The four curves shown here are a) Normalized irradiance spectrum for a typical as-built 2856K integrating sphere which gives a
good match to the standard CIE illuminant A source spectrum within the defined spectral range up to 820nm. b) NVESD SSCamIP 2009
starlight spectral irradiance data. c) V(λ) curve for photopic human eye vision. d) A proposed ‘S-lambda’ curve S(λ), representing a new
spectral radiant efficiency function used for the definition and calculation of SWIR-specific spectroradiometric units like swir-lumen,
swux, and swux/steradian.
There are different ways to generate this S(λ) curve, since a unique spectral response like the standard human eye spectral
sensitivity does not exist in the manifold of currently available photovoltaic detectors for the SWIR spectral range, even if
we take only standard lattice-matched InGaAs photodiodes and photodiode arrays into consideration. Quantum efficiency or
spectral sensitivity curves in [Aphotocurrent/watt] of InGaAs single-element photodiodes and corresponding focal plane arrays
(FPA) show variations in slope and shape within their common spectral range typically between 0.9µm-1.68µm, and these
variations cannot be neglected. In particular, the low wavelength side around 900nm shows processing-dependent variations
in the slope of the sensitivity curves. Based on practical considerations, we therefore propose a combination of a
representative sample average of as-built lattice-matched InGaAs photodiode sensitivity curves5 at 288K lattice temperature.
This “industry-average” detector is then combined with a standard Schott RG1000 (3mm thickness) filter glass placed in
front.6
The addition of the RG1000 curve does an excellent job of equalizing the corresponding slope variations within the low
wavelength end of the considered spectral range around 0.9µm, while on the high wavelength end the unique bandgap
response at a given lattice temperature of lattice-matched InGaAs is common to all high-quality diode material available.5
We thus propose to define the SWIR spectral radiant efficiency function for SWIR sensing by S(λ) as given in the following
formula (1):
S (l ) = RG1000d = 3mm (l ) ⋅ sInGaAs (l ) for 0.80µm ≤ l ≤ 1.80µm , normalized to 1 at l = 1.55µm
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(1)
with the spectral response of the standard NIR color filter glass RG1000d=3mm and the average photocurrent sensitivity
s InGaAs (λ ) of an industry-representative set5 of lattice-matched InGaAs at a 288K lattice temperature. The curve is shown
in Figure 5 below.
1
S(X): SWIR spectral efficiency
0.4
0.
Smx(X=1.55µm) =1
1000
1200
1400
1600
1
Wavelength [nmj
S(2) = RG1000d =3,m,,(2) Slntâa,u( %)
for 0.80pm <_2 <_ 1.80pm
Figure 5. The black curve shows the proposed SWIR sensing specific spectral radiant efficiency curve. The S(l) curves is generated by
multiplication of an average spectral responsivity curve for lattice-matched InGaAs photodiodes, and the curve for a 3mm thick filter of
Schott RG1000 filter glass. The RG1000 filter equalizes spectral responsivity variations in the low wavelength range (<1.4µm) caused by
different processing methods of the substrate material upon which the InGaAs is grown (typically Indium Phosphide).
We remind the reader that the spectral sensitivity curves differ generally from quantum efficiency (QE) curves due to the
different scales they use; i.e. radiant power in the case of the spectral responsivity in amps/watt, and photons/second in the
case of the QE, respectively. Achieving a good match to the S(λ) curve is easily implemented using commercially-available
materials by anyone who wants to build a swux meter device, based on the definitions in the following subchapters. For this
purpose, we list the values of S(λ) in Table 2:
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Table 2. Values of the SWIR-specific spectral radiant efficiency curve S(l ).
Wavelength
(microns)
0.80
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
I
I
S(Lambda)
Standard Values
Wavelength
(microns)
S(Lambda)
Standard \'aloes
Wavelength
(microns)
S(Lambda)
Standard Values
0.0000
0.0000
0.0001
0.0003
0.0007
0.0015
0.0027
0.0048
0.0079
0.0129
0.0198
0.0289
.0406
0.0556
0.0740
0.0959
0.1210
0.1483
0.1772
0.2059
0.2343
0.2623
0.2900
0.3174
0.3437
0.3688
0.3925
1.07
1.08
1.09
1.10
0.4154
0A376
0.4590
0.4795
0.4995
0.5183
0.5359
0.5534
0.5707
0.5880
0.6051
0.6219
0.6385
0.6549
0.6705
0.6853
0.6996
0.7134
0.7266
0.7400
0.7537
0.7673
0.7805
0.7931
0.8053
0.8168
0.8277
1.34
0.8386
0.8495
0.8603
0.8707
0.8808
0.8904
0.8996
0.9084
0.9172
0.9258
0.9344
0.9430
0.9517
0.9598
0.9675
0.9749
0.9812
0.9864
0.9910
0.9949
0.9974
1.0000
0.9999
0.9995
0.9993
0.9983
0.9966
1.11
t
1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
1.26
1.27
1.28
1.29
1.30
1.31
1.32
1.33
135
1.36
137
1.38
139
1.40
1.41
1.42
1.43
1.44
1.45
1.46
1.47
1.48
1.49
1.50
1.51
1.52
1.53
1.54
1.55
1.56
1.57
1.58
1.59
1.60
Wavelength
(microns)
161
1.62
1.63
1.64
1.65
1.66
1.67
1.68
1.69
1.70
1.71
1.72
1.73
1.74
1.75
1.76
1.77
1.78
1.79
1.80
S(Lambda)
Standard Values
0.9931
0.9869
0.9747
0.9419
0.8680
03494
0.6107
0.4594
03143
0.2045
0.1356
0.0848
0.0491
0.0279
0.0132
0.0044
0.0004
0.0002
0.0001
0.0000
The definition of the S(λ) function is a reasonably good match to the normalized power spectral response of most standard
lattice-matched InGaAs focal plane arrays in commonly-deployed commercial SWIR cameras. Figure 6 is a plot of S(λ) and
the power spectral response of an as-built commercial InGaAs camera.
S(X) Spectral Efficiency Function
and FI.IRA6261sc Camera FPA Normalized
Power Spectral Response
1.00
0.90
L 0.80
v
w
0.70
5
0.60
eW
0.50
'
ii
i
LI 0.40
u
/
C. 0.30
0.20
0.10
e
0.00
0.80
i
0.90
s.
1.00
1.10
1.20
1.30
1.40
130
1.60
1.70
1.80
Wavelength (microns)
- - S(lambda)
-A6261 Power Response
Figure 6. Plots of S(λ),and the power spectral response of an as-built commercial InGaAs camera.
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2.4 SWIR-specific radiometric units: Definitions
Based on the proposed SWIR candela definition in section 1.2 and the SWIR-specific S-lambda curve in section 1.3 we
define in analogy to the photometric quantities a new set of SWIR specific radiometric units. We derive the relevant
calibration and correction factors for a detector-based implementation of the new SWIR-specific radiometric scale and
follow herein the framework published in Ref. [7].
We define the SWIR-specific flux quantity
Φ S (swir - lumen) = AS ⋅ ∫
1.80 µm
0.80 µm
Φ S with the new proposed unit ‘swir-lumen’:
Φ e ( l ) ⋅ S ( l ) ⋅ dl
(2)
with AS = (1 / sc ) swir - lumen/watt
and Φ e (l ) = incident spectral power distribution of the radiation [watts/micron]
The definition of the SWIR-specific irradiance quantity with the new proposed unit ‘swux’ (which is a swir-lumen/square
meter), is as follows:
1.80 µm
E S (swux ) = AE ⋅ ∫
0.80 µm
E e ( l ) ⋅ S ( l ) ⋅ dl
(3)
with AE = (1 / sc ) swux/(watt ⋅ m -2 )
and Ee (l ) = incident spectral irradiance distribution of the radiation [watts/m2 /micron]
The definition of the SWIR-specific radiance quantity with the new proposed unit ‘swux/steradian’, is as follows:
1.80 µm
LS (swux/steradian) = AL ⋅ ∫
0.80 µm
Le (l ) ⋅ S (l ) ⋅ dl
with AL = (1 / sc ) swux ⋅ sr -1/(watt ⋅ m -2 ⋅ sr -1 )
(4)
and Le (l ) = spectral radiance distribution of the radiation
2.5 Method 1: Scaling of the SWIR-specific radiometric unit level relating to NVG gain calibration
As already introduced earlier, we propose to scale the sc value and thus the AL , AS and AE factors in equations (2), (3) and
(4), respectively, based on the objective to set the SWIR-specific radiance quantity that is emitted from typically-used
broadband NVG calibration equipment to unity.
The procedure is described based on the data plotted in the following Figures 7a and 7b. Scaling of the SWIR-specific
radiometric quantities is done by defining the effective SWIR-specific radiance quantity to be unity for the case of
integration over wavelength of the product of the scaled 2856K Illuminant A spectral radiance curve in Fig. 7b and the S(l)
curve for SWIR sensing that we have earlier defined:
LLED
( l ) = spectral radiance of the 820nm LED illuminated integrating sphere with
e
∫l L
LED
e
( l ) ⋅ dl = 2.48 ⋅ 10 -6 W ⋅ m -2 ⋅ sr -1 integral radiance.
K
L2856
(l ) = spectral radiance of the 2856K Illuminant A integrating sphere
e
with NVG Type B - weighted radiance equivalent to the NVG Type B - weighted 820nm LED radiance :
∫l L
LED
e
K
(l ) ⋅ sTypeB (l ) ⋅ dl =∫ L2856
(l ) ⋅ sTypeB (l ) ⋅ dl = 2.35 ⋅ 10 -6 W ⋅ m -2 ⋅ sr -1
e
l
For the data shown in Fig. 7a and 7b we get:
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(5)
1 swux / sr ≡ AL
1800 nm
2856 K
e
800 nm
∫L
(λ ) ⋅ S SWIR (λ ) ⋅ dλ = AL ⋅ 4.825 ⋅ 10 -6 W ⋅ m -2 ⋅ sr -1 = AL ⋅
1
W ⋅ m -2 ⋅ sr -1 (6)
2.0726 ⋅ 105
⇒ AL = 2.0726 ⋅ 105 (swux ⋅ sr -1 ) / (W ⋅ m -2 ⋅ sr -1 )
We declare the resulting effective SWIR radiance in equation (6) to be one swux/steradian, and for convenience the relevant
scaling factor AL can be rounded up to a value of:
AL ≡ 210,000 (swux ⋅ sr -1 ) / (W ⋅ m -2 ⋅ sr -1 )
The absolute value of 210,000 of this scaling factor is analogous to the factor 683 for photometric lux units, and it is now the
basis for the initial definition of the factor (1/sc) = 210,000 we defined earlier, and all A-factors in equations (2)-(4).
At this point it becomes obvious that an international standard illumination source based on a 2856K blackbody spectral
radiance that covers the spectral range from the visual to the full SWIR spectral range is required for any attempt to
standardize integral radiometric units in the SWIR, or even NIR spectral range. This standard illuminant does not currently
exist.
820nm LED
- Typical 2856K Illuminant A
NVG type B
-,-S- lambda for SWIR sensing
820nm LED
-Typical 285 6K Illuminant A
-- NVG type B
Figure 7a,b. The plot in Figure 7a (upper) shows the normalized relevant spectral radiance curves of a typical integrating sphere
implementation with PTFE coating of a 2856K Illuminant A source, as well as a test set’s 820nm LED emission spectrum. Both types of
sources are used for NVG gain calibration [Reference 3,8]. The spectral sensitivity of standardized Type-B NVG tubes and the hereindefined SWIR-specific spectral radiant efficiency curve for definition of the new SWIR-specific spectroradiometric quantities are also
shown.
The lower Figure 7b shows two spectral radiance curves. One is the 820nm LED spectral radiance normalized to 2.48x10-6 W/m2/sr total
integrated radiance, the other is a 2856K Illuminant A spectral radiance curve which has been normalized to emit the equivalent Type B
NVG-weighted radiance, just as in the case of irradiation with the 820nm LED radiance level shown. Scaling of the SWIR-specific
radiometric quantities is done by setting the effective SWIR-specific spectral radiance to unity. This radiance results from integration over
the product of the 2856K Illuminant A spectral radiance curve in Fig. 7b and the S(l) curve for SWIR sensing.
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2.6 Method 2: Scaling of the SWIR-specific radiometric unit level to the photometric unit level
As already mentioned earlier, the second possible scaling scenario of the SWIR-specific radiometric units is based on the
idea to equalize the corresponding photometric quantity level and the SWIR-specific quantity level in the case of a 2856K
Illuminant A source set up for NVG Type B gain calibration. In this case, the lux is then equal to the swux. The advantage
of this scaling method would be a relatively good direct comparison of the relative content of either spectral radiance
contribution within the measured scene radiation. As we will see in Table 3, the ratios of the swux/lux levels of the listed
NVESD standard scene illuminations closely resemble the ratios of underlying spectral radiance contributions between
SWIR and VIS. Also, the absolute levels of the SWIR-specific quantities would vary by the same orders of magnitude as the
well-known typical photometric scene levels.
Assuming
aE ⋅
1800 nm
2856 K
e
800 nm
∫L
(λ ) ⋅ S SWIR (λ ) ⋅ dλ ≡ 683 ⋅
830 nm
∫L
2856 K
e
(λ ) ⋅ V Photopic (λ ) ⋅ dλ
360 nm
(7)
⇒ a E = 79.25
⇒ AE = a E swux/(watt ⋅ m -2 )
2.7 SWIR-specific radiometric units: Examples
Following the definitions in equation (3), we present the corresponding calculated swux levels for certain scene illumination
conditions given by NVESD spectral irradiance data used in SSCamIP 2009. Additionally, we list the swux level for the
2856K Illuminant A integrating sphere from Figure 7b. For comparison, we also provide the calculated photometric quantity
levels based on photopic vision.
Table 3. Calculated swux and lux levels for the same scene irradiance conditions for comparison. The resulting swux/lux ratio for same
scene condition can vary by more than 5 orders of magnitude. We chose to work with Method 1 where (1/sc) = 210,000 for the
experimental validation.
Overcast starlight
Clear starlight
Quarter Moon
Full Moon
Overcast daylight
Direct sunlight
Swux level
Swux/Lux
Swux level
Swux/Lux
Lux level
1 /sc= 2.1E +5
Ratio
1 /sc = 79.25
Ratio
Photo s ie
3.8
38.3
44.1
96.5
4.62E +04
2.82E +07
319796
31979.6
3992.6
968.0
1.43E -3
1.20E-4
1.44E -2
1.66E -2
3.64E -2
1.74E +2
1.06E +4
1.20E -3
1.1E -02
51.7
319.2
9.97E -2
8.93E +2
8.84E +4
For further consideration and experimental implementation, we decided to use the first scaling method with reference to the
industry-standard NVG gain calibration source, and thus we are using a corresponding calibration value for the swux meter
of (1/sc) = 210,000.
2.8 SWIR-specific radiometric units: Detector specific calibration and correction factors
A swir-lumen meter detector measuring the SWIR-specific flux in (2) has an output current given by
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I ( A) = ∫ Φ e (l ) ⋅ s(l ) ⋅ dl
(8)
l
where s(l ) is the detector spectral responsivity in [A/watt]
It is advantageous to factor
s(l ) [A/watt ] = s(1.55µm) ⋅ sn (l )
where s(1.55µm) is the value of s(l ) at 1.55µm in [A/watt ]
and sn (l ) is the dimensionless normalized spectral responsivity
(9)
The SWIR-specific radiant flux of the swir-lumen meter results in:
Φ e (λ ) ⋅ sn (λ ) ⋅ dλ
I
s (1.55µm) ∫λ
sS (A/swir - λumen) =
=
⋅
AS
ΦS
∫ Φ e ( λ ) ⋅ S ( λ ) ⋅ dλ
(10)
λ
To account for a mismatch between the as-built detector spectral responsivity s(λ) and the SWIR spectral radiant efficiency
function S(λ), a spectral mismatch correction factor F can be calculated:
F=
∫λ Φ
e
(λ ) ⋅ S (λ ) ⋅ dλ
∫ Φ e ( λ ) ⋅ s n ( λ ) ⋅ dλ
(11)
λ
This correction factor F is only independent of the incident spectral power distribution of the radiation if the spectral
responsivity curve of the detector exactly matches the (S(l) function. The design goal for a swux meter is to make F close
to unity for a variety of spectral irradiance conditions, from clear starlight where the spectral irradiance is heavily biased to
the longer wavelengths of SWIR, to overcast daylight conditions where the irradiance above 1.2 microns is heavily absorbed
by the water in the clouds.
Calibration of a swir-lumen meter means that the swir-lumen meter sensor captures all the flux of a known calibration beam
within its active area. This is done by scaling the measured photocurrent I in the following way:
F S (swir - lumen) = I ⋅
AS ⋅ F
where As is (1/sc) swir-lumen/watt
s(1.55µm )
(12)
Calibration of a swux-meter with a sensor aperture of precisely known area Asensor begins with detector illumination with
SWIR radiation at 1.55 microns, where the SWIR radiation overfills the aperture reasonably uniformly. The swux-meter
would have an output current I that is proportional to the SWIR-specific irradiance quantity measured in swux given by the
following expression:
E S ( swux ) = I ⋅
AS ⋅ F
where As is (1/sc) swir-lumen/watt
s(1.55µm) ⋅ Asensor
(13)
3. SWUX METER PROTOTYPES
We experimented with two different InGaAs detectors to learn from experience how to make a calibrated swux meter and to
understand the requirements for such devices. A summary of the requirements is as follows:
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1) The whole sky dome is radiating down-welling SWIR nightglow, and to properly capture that radiation, the swux
meter detector should have a compound parabolic concentrator optic or cosine theta diffuser to help detect light
rays striking the aperture of the collection aperture at very oblique angles.
2) The swux meter detector should be TE cooled to reduce dark current to a level that is no greater than 10 picoamps
for a 3mm diameter device. The predicted photocurrents from clear starlight will be on the order of 1000
picoamps, depending on the optics placed in front of the detector. A typical TE cooler setpoint will be around 233K
and the detector will be in a metal housing with adequate heatsinking.
3) The swux meter detector should have an active area of at least 0.07 square cm, which is the area of the fairly
common 3mm diameter single-element InGaAs detectors used throughout the industry. Smaller area devices (1mm
diameter) will tend to be too insensitive to nighttime swux levels, though they would work for daytime
measurements.
4) The current meter that records the photocurrent should be able to measure from a few milliamps (for direct sunlight
conditions) down to less than 10 picoamps for starlight conditions.
3.1 Uncooled Swux meter prototype
A prototype swux meter was constructed using a 3mm diameter InGaAs detector made by Oriel Corp. (P/N 71585, no longer
in production) and a Gooch and Housego OL 730E radiometer to measure the current from the device. The InGaAs detector
had a front-mounted 3mm thick filter made of Schott RG1000 absorbing glass with no AR coating on it and is shown in
Figure 8 making a measurement of the swux level for mid-morning direct sunlight with a sun elevation angle of 25 degrees.
The direct sunlight spectral irradiance gives a predicted swux level of 28.2x106 swux, as shown in the last row of Table 3.
The measurement made with a sun angle of 25 degrees was 26.5x106 swux.
Figure 8. Oriel InGaAs swux meter detector head pointing at mid-morning sun.
The spectral responsivity curve of this detector by itself was measured by Gooch and Housego using a spectroradiometer
calibration station, and the RG1000 spectral transmission curve was multiplied in after the calibration. The normalized
spectral responsivity curve is shown in Figure 9 below, plotted with the S(l) function for comparison. This InGaAs detector
was operated at a temperature of approximately 295K – it is not TE cooled. It has a dark current of 50nA, which corresponds
to a swux level of about 1300 swux. This is a factor of ~30 higher than the swux level of clear starlight, so this embodiment
of a swux meter is not suitable for most nighttime illumination conditions, except perhaps in areas with high levels of manmade SWIR irradiance.
There is a ratio of ~1 million between direct sunlight and clear starlight in the InGaAs spectral band. A swux meter used to
characterize the full range of naturally-occurring swux levels must have a dynamic range of at least 1 million and a dark
current that is at least several orders of magnitude lower than 1nA for a 3mm diameter InGaAs detector collection area. The
OL 730E radiometer meets the requirement for current measurement. It has automatically-selected ranges that go from a 2e3 amp maximum value down to a 2e-10 amps maximum value, with a resolution at the most sensitive range of 1e-14 amps.
This range of ranges encompasses the expected photocurrent from a typical 3mm circular InGaAs detector with RG1000
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filter from direct sunlight conditions down to clear starlight. The radiometer can be programmed for different scene
irradiance spectra, and it can be programmed to display the output in swux units, as shown in Figure 10 below. The lighted
display can be disabled for computer logging, and the unit connects to control and logging software through a USB
connection. The radiometer weighs 1.1 kg and is approximately 20x20x10cm, so it is portable, though it does not have an
internal battery power option.
SQ.) Spectral Efficiency Function
and Oriel Detector with RG1000 Filter s(lambda)
1.00
0.90
0 0.80
0.70
(
it a
g
0.60
^,r 0.50
W
0.40
/
ao
= 0.30
i
j 0.20
/
0.10
0.00
0.80
0.90
LOO
1.20
1.10
130
1.40
1.50
L60
L70
L80
'Wavelength (microns)
- - S(lambda)
-Oriel and RG1000 s(lambda)
Figure 9. S(l) spectral efficiency function and Oriel detector with RG1000 filter S(l)
f
0l 730E
RADIOIAFTfIt
111
Man
OOOp
60W.6Nq..pp
OffEprow
lOsvr
OOOO
Figure 10. Gooch and Housego OL 730E radiometer
The Oriel detector and RG1000 filter combination is a reasonably good approximation to an ideal detector that perfectly
matches the S(l) function. Table 4 shows the calculated F spectral mismatch values for the Oriel detector and RG1000 filter
glass for the two brightest SSCamIP 2009 irradiance conditions.
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Table 4. Calculated F correction factors for various scene illumination conditions for the Oriel 71585 and RG1000 filter combination
Irradiance Condition: (NVESD 2009 SSCamIP)
F Correction Factor
Predicted Photocurrent [A]
Overcast Daylight
1.22
1.47E-06
Direct Sunlight
1.01
1.08E-03
As mentioned earlier, this uncooled detector has too high of a level of dark current for measurements of nighttime conditions
at typical operating temperatures, but it is usable starting where swux levels are at least 5X higher than the dark current
equivalent swux level, or about 6000 swux. The overcast daylight condition gives a much larger variation in the F
correction factor from unity, because of the mismatch between S(l) and the Oriel/RG1000 s(l) between 1 and 1.1 microns
and the greatly reduced SWIR illumination above 1.2 microns due to water absorption of the SWIR component.
Figure 11a,b shows color visible and SWIR images of the same interior laboratory scene illuminated with two different
spectral distributions of light. The swux meter detector is to the left of the lab equipment (a non-operating cavity
blackbody). The upper pair of images (a) was taken with fluorescent lighting and some daylight. The swux level is 40,000
swux and the SWIR image is noticeably dim. The lux level is 303lx. In the bottom pair of images (b), two incandescent
lamps have been turned on which increased the swux level to 320,000 swux, or a factor of ~10 increase. The SWIR image
is much brighter and more of the room behind the blackbody can be seen. But the lux level has only been increased by the
incandescent lamps to 645lx. The human eye would not interpret the incandescent scene as being that much brighter to a
SWIR camera.
Figure 11a,b. Visible – left, SWIR InGaAs - right. The upper pair of images (a) was taken with fluorescent lighting
and some daylight. In the bottom pair of images (b), incandescent lamps have been turned on
3.2 Cooled Swux meter prototype
We evaluated the Labsphere PH3-In-1.7T-INT-D0 detector head, which is connected to Labsphere’s Heliosense software
through two USB interfaces, enabling logging of swux levels at a 1Hz rate. This device is TE cooled to -40C, and has an
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observed dark current value of ~10pA. Figure 12 shows the detector mounted on a tripod plate with the cabling and TE
cooler controller for the device, which itself draws 1 amp at 12 volts DC.
Figure 12. Labsphere detector and TE cooler controller
The device was equipped with a cos theta diffuser that was in place when it was calibrated with a spectroradiometer. We
covered the diffuser with an RG1000 filter to get the correct spectral shaping. Direct sunlight photocurrent was measured to
be 0.5 mA (20% lower than expected), and clear starlight at zenith measured to be 0.5 nA, a factor of at least two lower than
the predicted value which is probably due to Fresnel reflection off the RG1000 filter of oblique starlight rays and sky
obscuration by nearby trees. The observed photocurrent levels show a variation of 6 orders of magnitude which was
predicted by modeling the detector with the diffuser and RG1000 filter using the SSCamIP model data. Figure 13 shows the
normalized spectral responsivity curve, plotted with the S(l) function for comparison.
Table 5. Calculated F correction factors for various scene illumination conditions for the Labsphere PH3-In-1.7T-INT-D0 detector and
RG1000 filter combination
Irradiance Condition: (NVESD 2009 SSCamIP)
F Correction Factor
Predicted Photocurrent [A]
Clear Starlight
Quarter Moon
Full Moon
Overcast Daylight
Direct Sunlight
1.05
1.06
1.10
1.25
1.13
1.01E-09
1.16E-09
2.44E-09
1.03E-06
6.93E-04
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S(A) Spectral Efficiency Function
and Labsphere Detector with RG1000 Filter s( lambda)
1.00
0.90
0.80
I
0.70
C 0.60
V
4 030
¿0.40
V
0.30
X020
0.10
0.00
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
Wavelength (microns)
- - S(lambda)
-Oriel and RG1000 s(lambda)
Figure 13. S(l) spectral efficiency function and Labsphere detector with RG1000 filter s(l)
We also logged swux levels in a suburban neighborhood in Santa Barbara over a period of several days to observe the
diurnal variations in swux levels. The detector head was pointed due north and looks out at a scene with a mixture of manmade surfaces, trees, shrubbery and sky. The sky was overcast during some of the logging. The results are shown in Figure
14.
Swux Diurnal Cycle
(l.absphere detector with RGI000 looking out from north facing office building wall in suburban Goleta, CA)
10,000,000
1,000,000
7,
100,000
ry
7
10,000
1.000
100
10:48 AM
4:48 PM
10:48 PM
4:48 A.\1
10:48 AM
4:48 PM
10:48 PM
4:48 AM
10:48 AM
Date and Time
Figure 14. Multi-day plot of Labsphere PH3-In-1.7T-INT-D0 swux detector with RG1000 shaping filter looking out from the north-facing
side of a building in suburban Goleta, California. The very low swux levels measured several hours after the start of the log were caused
by a dark current measurement where the sensor was covered to find the dark current. This is 10 picoamps, which is 0.4 swux, or about
1% of clear starlight swux. The first day of the logging was overcast with a marine layer, which dropped the swux level down about a
factor of 10 from a clear sunny day. Note the gradual reduction in man-made light sources as the night progresses, with occasional
sporadic artificial light sources turning on and off. The measured swux floor is 250 swux or about 6 times clear starlight.
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3.3 Alternative cooled swux meter detector
As mentioned earlier, the Gooch and Housego OL 730E radiometer is well suited to being incorporated into a highsensitivity swux meter because of its very high dynamic range with automatic gain selection and extremely low noise
preamplifier. A cooled swux meter with comparable specifications to the Labsphere device can be assembled by combining
the G&H OL 730-InGaAs and OL 730-TE cooler controller with the OL 730E radiometer. The OL 730-InGaAs is TEcooled to -40C and has a noise floor of 0.15 pA, ~4 orders of magnitude below the photocurrent predicted for the detector
exposed to clear starlight lighting conditions. We did not have access to this detector during the writing of this paper, but
we modeled its performance using the spectral responsivity curve for an as-built OL 730-InGaAs detector, the spectral
irradiance curve for clear starlight used by SSCamIP, and the detector active area. The predicted photocurrent when the
detector is pointed at zenith in a clear dark sky environment is 1.1 nA. The same calculations were performed for SSCamIP
full moon and direct sunlight spectral irradiance data, and yielded results of 3.0 nA and 0.99 milliamps respectively. As
with the Labsphere detector head, there is a spectral mismatch between this cooled detector and the S(l) function caused by
the shift in bandgap energy when the detector is cooled to -40C. Figure 15 shows the two curves plotted together, and Table
6 shows the predicted spectral mismatch coefficient values.
S()) Spectral Efficiency Function
and G&H Detector with RG1000 Filter s(lambda)
1.00
0.00
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
Wavelength (microns)
- - S(lambda) -G &H and RG1000 s(lambda)
Figure 15. S(l) spectral efficiency function and G&H detector with RG1000 filter s(l)
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Table 6. Calculated F correction factors for various scene illumination conditions for the Gooch and Housego OL 730-InGaAs detector
and RG1000 filter combination.
Irradiance Condition: (NVESD 2009 SSCamIP)
F Correction Factor
Predicted Photocurrent[A]
Clear Starlight
Quarter Moon
Full Moon
Overcast Daylight
Direct Sunlight
1.03
1.01
0.93
0.68
0.84
1.1E-09
1.3E-09
3.0E-09
2.0E-06
9.9E-04
CONCLUSION
The swux unit of measure promises to be a very useful concept for prediction of InGaAs camera performance in different
lighting conditions, and a swux meter offers a simple and relatively inexpensive way to continuously monitor SWIR
irradiance levels during field trials or camera “shoot-outs”, determine the SWIR output of an arbitrary light source, or
characterize urban SWIR irradiance levels. A technician installing InGaAs security cameras can use a swux meter to ensure
that adequate SWIR irradiance is provided by lighting in a parking lot. The swux unit is a direct analog to the very widely
used lux unit of photometry, but it is specific to the spectral response of the vast majority of SWIR cameras currently
fielded. The measured swux level of irradiance in a scene will correlate much more tightly with InGaAs camera
performance in those conditions than the lux unit. The radiometry instrument industry would be well advised to consider
testing the market for commercial swux meters, but in any event, InGaAs camera users can make their own swux meters
using COTS components. As the cost per camera continues to fall, the installed base of InGaAs cameras will grow rapidly,
and there will be more and more opportunities to make use of the swux unit and its associated radiometric units, the swir
lumen and the swir candela. Finally, we recommend the CIE Illuminant A to be defined beyond 820nm, e.g. up to 2000nm.
Special thanks to Alex Fong, Austin Dowd and Tarek Nagaty from Gooch and Housego, Chris Durell and Joe Jablonski
from Labsphere, and Howard Yoon and George Eppeldauer from NIST.
REFERENCES
[1] Ross McCluney, ‘Introduction to Radiometry and Photometry’, 1994 ARTECH HOUSE, INC.
[2] M. Hübner et al., ‘Verification of sensitivity enhancement of SWIR imager technology in advanced multispectral
SWIR/VIS zoom cameras with constant and variable F-number’, Proc. SPIE 9819, Infrared Technology and
Applications XLII, 981905 (May 20, 2016)
[3] Vyacheslav B. Podobedov; George P. Eppeldauer; Thomas C. Larason, New night vision goggle gain definition,
SPIE 9452, Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXVI, 945214 (12 May 2015).
[4] ISO 11664-2:2007(en) Colorimetry — Part 2: CIE standard illuminants
[5] Report on the Key Comparison CCPR-K2.a-2003 Spectral Responsivity in the Range of 900 nm to 1600 nm Final
Report November 30, 2009 Prepared by Steven W. Brown et al., NIST (USA)
[6] See e.g. http://www.us.schott.com/advanced_optics/english/filter/us/pdf/SCHOTT_rg1000_e.pdf
[7] C.L. Cromer, G. Eppeldauer, J.E. Hardis, T. C. Larason, and A. C. Parr, National Institute of Standards and
Technology detector-based photometric scale, APPLIED OPTICS, Vol. 32. No.18, June 1993
[8] Department of Defense Interface Standard MIL-STD-3009, Lighting, Aircraft, Night Vision Imaging System
(NVIS) Compatible, Feb2, 2001
Proc. of SPIE Vol. 10178 101780C-20
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