Implementation of Vicarious
Calibration for High Spatial
Resolution Sensors
Stephen J. Schiller
Raytheon Space and Airborne Systems El Segundo, CA
Collaborators:
Dennis Helder- South Dakota State University
Mary Pagnutti and Robert Ryan - Lockheed Martin Space Operations, Stennis Space
Center
Vicki Zanoni – NASA Earth Scinece Applications Directorate, Stennis Space Center
Overview
• Calibration Considerations for Absolute Radiometry
• Vicarious Calibration and its application to High Spatial
Resolution Sensors
• Design of Ground Targets and Ground Truth
Measurements
• Top-of-Atmosphere Radiance Estimates Using
MODTRAN and Considering:
– BRDF Effects
– Adjacency Effect
– Aerosol Modeling
– Evaluating Model Radiance Accuracy
• Error Propagation Model
Sensor Absolute Calibration
• Absolute Calibration establishes the link to physical
parameters and processes recorded in the remote
sensing image.
• Multiple paths to SI units are necessary to evaluate
systematic errors in calibration coefficients.
• Vicarious calibration provides a known at-sensor
radiance independent of on-board calibration sources
• Goal of this presentation is to outline the process for not
just obtaining a gain estimate at a single radiance level
but to generate a Vicarious Calibration Curve over the
operational dynamic range of the sensor
Reflectance Based Vicarious
Calibration Methodology
• Measure surface/atmospheric optical properties at the
site containing one or more uniform targets
• Constrain input parameters in a radiative transfer model
(MODTRAN 4) to match surface and atmospheric
conditions at the time of the sensor overpass
• Predict the top-of-atmosphere spectral radiance for the
ground target (hyperspectral resolution)
• Extract target signal from sensor data for each band
• Integrate the at-sensor radiance spectrum with the
sensor’s relative spectral response for each band
• Calculate the gain and bias for each band
• Method provides an absolute calibration established
relative to the solar spectral constant
Ground-Based Vicarious Calibration of Sensor Gain
and Bias
Measure
Target
Reflectance
Solar Spectral Constant
0.5
Average Surface Reflectance Spectrum of Grass Target
Recorded between 11:49 and 12:10, June 30, 2000
0.3
0.2
0.0
0.1
Reflectance
0.4
Average of 108 Spectra
1 Std. Dev. Limits of Reflectance Variability
500
1000
1500
2000
2500
Wavelength (nm)
10.6
June 30, 2000 Evening Langley Plot at 521 nm
Linear Fit is Between 2 and 4 Air Mass
10.4
10.2
10.0
ln Irradiance (Detector DN)
Extinction Equation
ln I = 10.8376 - 0.2115(Air mass)
1
2
3
4
Air mass
Monitor Atmospheric
Transmittance,
Diffuse/Global Ratio
Radiative Transfer Calculation of
Sensor Signal (S) of Ground Targets
At-Sensor Radiance (L)
S = (dS/dL) L +B
Gain and Bias
Sensor
Traditional Approach to Vicarious
Calibration of Remote Sensing Systems
(Developed for Large Footprint Sensors Requiring Natural Targets)
Typical approach has been
to characterize a large bright
uniform target at a desert
site to provide a known topof-atmosphere radiance
level.
June 10,
2000 Blue
Band
IKONOS Image of Lunar Lake, Nevada
Provides a gain value based
on a single radiance level
Uncertainty is estimated to
be ~ +/- 3% (RSS estimate of
measurement and modeling errors)
Improvement is to Generate a Calibration Curve Over the Sensor’s
Dynamic Range using Multiple Sites – IKONOS
Six Deployments
Lunar
Lake Playa
Railroad
Valley Playa
Vegetation Cover (Brookings)
Deep Dense Vegetation or Water Bodies (~zero reflectance)
White Sands
Calibration Curve Generation From A Single Field Campaign
(Using Man-made Targets)
Does the tight
linear fit imply a
better gain
estimate?
Does the data
resolve detector
non-linearity?
No! Not Yet.
More Data shows There are Systematic Variations in Gain Estimates
Between Sites and Dates
However, we now
be seeing
differences due
to:
• Stray light,
•Out of band
leakage,
•Temperature
variations of focal
plane and readout
electronics,
•Limitations of
ground truth data
and atmospheric
modeling.
Enhanced application applied to
high spatial resolution sensors
• Generate a Vicarious Calibration Curve
covering the sensor dynamic range in a single
image
• Same atmospheric effects, scattered light levels,
adjacency effect, sensor responsivity conditions
• Evaluates both gain and bias.
• Potential to evaluate non-linear responsivity.
• Potential to reduce cost compared to multiple
campaigns
Enhanced Ground Target Design
•
Lay out six to eight targets covering ~
0% to 85% reflectance
•
Targets include
-
Spectrally flat (gray toned targets for
calibration curve generation)
-
Strong spectral contrast (evaluate effects of
spectral banding)
-
Sample of surround spectrum (location
where image DN for each band is near the
average of the entire image)
•
Reflectance of each target is
measured at the site close to the time
of the sensor overpass
•
Use a site that is similar to image
sites collected in operational use.
(reproduce scattered light and out-ofband leakage effects)
-
Ocean/coastal, vegetation, desert
Vicarious Calibration Curve
Generation for Push Broom Sensors 1
• Assumes a flat field image has been acquired
for relative calibration of all detector channels
on the focal plane (i.e. cloud, ice or desert
scenes , side slither image)
• Relative gain for each channel is derived from
its response in terms of the average response
of all the channels
rel
g chan,
band 
Detector Array
Uniform cloud
or ground scene
flat
DN chan,
band
DN
flat
chan,band focal plane
Side slither image
Vicarious Calibration Curve Generation
for Push Broom Sensors 2
•Next, apply the relative gain to the vicarious
calibration image
•Raw signal (DNraw ) of calibration targets are
converted to relative signal (DNrel) and average
over the target area
TOA Radiance (Watts/m2-ster)
DN
rel
chan,band

raw
DN Chan,
band  Bias
rel
g chan,
band
•Weighted least-squares regression of
TOA Radiance, L
, vs relative
signal DN
gives absolute gain,G
with respect to average responsivity of
focal plane,
TOA
band tar
abs
band focal plane
rel
chan,band tar
LTOA
band
tar
abs
 Gband
focal plane
rel
DN chan,
band
This relation defines the vicarious
calibration curve
Slope =
abs
band focal plane
G
•Absolute gain of each channel,
abs
Gchan,band,
,is given by
abs
abs
Gchan,
band  Gband
rel
DN chan,
band
tar
focal plane
rel
/ g chan,
band
tar
Achieving Accurate Top of
Atmosphere Radiance Estimates 1
• Radiative transfer model (MODTRAN) must account for
all major atmospheric effects
Target Reflectance (BRDF)
Surround Reflectance
Achieving Accurate Top Of
Atmosphere Radiance Estimates 2
• Requires extensive set of field data obtained
with well calibrated radiometers and reference
panels.
– BRDF (Bi-directional Reflectance Distribution
Function) of calibration panels and targets
– Atmospheric transmittance, upwelling radiance,
diffuse/global ratio, almucantor scans of sky path
radiance (if possible - hyperspectral resolution)
– Verticle profiles of water vapor and aerosols (altitude
of boundary layer)
– radiosonde / lidar / aircraft based measurements
Achieving Accurate Top Of
Atmosphere Radiance Estimates 3
• Requires MODTRAN parameters to be
established via user supplied inputs (using a
default atmosphere or surface reflectance is not
adequate)
– Target and surround reflectance spectrum
(hyperspectral resolution, user supplied BRDF)
– Wavelength characterized aerosol extinction known
below and above the boundary layer (user supplied
from sun photometry)
– Surface Range in the boundary layer (adjusted to
reproduce observed transmittance)
– Aerosol scattering phase function ( adjust H-G
asymmetry factor or input user-supplied)
Comments on MODTRAN Model
Characterization
• BRDF Considerations
• Adjacency Effect
• Aerosol Vertical Profile
BRDF Knowledge of calibration panel
and ground targets is essential
0.5
Changes In Average Surface Reflectance Spectrum of Grass Target
Between 11:12 and 12:00, June 30, 2000
0.3
0.2
0.0
0.1
Reflectance
0.4
Average Reflectance Spectrum Recorded Between 11:00 and 11:25
Average Reflectance Spectrum Recorded Betwen 11:49 and 12:10
500
1000
1500
Wavelength (nm)
BRDF effects are reduced with higher diffuse-to-global ratio
2000
2500
Multi-angle images should be collected to verify
atmospheric and BRDF model
Θz=7o
Θz=19o
Comments on MODTRAN Model
Characterization
• BRDF Considerations
• Adjacency Effect
• Aerosol Vertical Profile
Measuring Atmospheric Parameters To
Characterize The Adjacency Effect Is Critical
Radiance for Spectralon Panel
0.05
Radiance
0.045
0.04
0.035
ASD Radiance
MODTRAN
Average ASD Radiance
MODTRAN Radiance
0.03
0.025
0.02
0.015
Surround
0.01
0.005
Target
0
0.4
0.5
0.6
Target spectrum= surround spectrum
0.05
Grass spectrum used for surround
0.8
0.9
1
1.1
1.2
Radiance of Spectralon Panel
0.045
0.04
0.035
Radiance
Modeling adjacency effect
is required to reproduce
measured upwelling
radiance off ground targets
0.7
Wavelengthmm)
(
0.03
0.025
0.02
0.015
Surround
0.01
0.0
05
Target
0
0.4
0.5
0.6
0.6
70.
0.8
0.9
Wavelength (mm)
1
1.1
1.2
Surround Spectrum’s Influence On
Sky Path Radiance
0.15
PGAMS Sky Path Radiance Spectra
Recorded at ARM/CART Site Sept. 26, 1997
Solar Position: Alt = 51 Deg. Az = 166 Deg.
0.10
Red edge of vegetation observed in
the downwelling sky path radiance
0.05
Cirrus Cloud Spectrum
Clear Sky Spectrum
0.0
Radiance (Watts/m2/nm/str)
Alt=30.0 Deg. Az=11.6 Deg
Alt=20.0 Deg. Az=10.6 Deg.
400
600
800
Wavelength
1000
Comments on MODTRAN Model
Characterization
• BRDF Considerations
• Adjacency Effect
• Aerosol Vertical Profile
Aircraft Measurements Of Extinction At The
Boundary Layer Improve Aerosol Model
Solar radiometer observations at the top of the boundary
layer (altitude defined in the MODTRAN model) revealed
a significantly higher transmittance than available with
MODTRAN model atmospheres. The 1976 standard
atmosphere was scaled to fit the observations.
Aerosol vertical profile plays a significant role in
modeling the adjacency effect and extinction as a function
of wavelength (composition varies with height).
Vertical Transmittance Above the Boundary Layer Sept. 14, 2000
Fit of Adjusted Modtran to Reagan Measurements
0.8
0.7
Transmittance
0.6
0.7
0.6
Vertical Transmittance Measured Using
Reagan Sunphotometer From An Aircraft at 3200 m
Modtran Model Vertical Transmittance Using a Scaled 1976
Standard Atmosphere Aerosol Profile From 3200 m
0.5
0.5
Vertical Transmittance Measured Using
Reagan Sunphotometer From An Aircraft at 3200 m
Modtran Model Vertical Transmittance Using Default 1976
Standard Atmosphere Aerosol Profile From 3200 m
0.4
0.4
Transmittance
0.8
0.9
0.9
1.0
1.0
Vertical Transmittance Above the Boundary Layer Sept. 14, 2000
Comparison Between Reagan Measurements and Modtran Model
400
600
800
Wavelength (nm))
1000
400
600
800
Wavelength (nm))
1000
Analysis Designed To Uses Multiple Paths to
SI Units for Accuracy Assessment
• MODTRAN parameterization achieved with input of
unitless quantities ties TOA radiance only to solar
spectral constant
–
–
–
–
Transmittance
Reflectance
Diffuse/global ration
Assymetry factor
• Ground truth validation data from calibrated radiometers
is traceable to NIST standards
– Upwelling radiance at surface
– Sky path radiance
• Direct comparison of MODTRAN predicted and
measured upwelling radiance and sky path radiance
evaluates systematic errors
Comparison of MODTRAN and Measured
Upwelling Radiance: Grass Target
Comparison of MODTRAN and
Measured Sky Path Radiance
TOA Error Propagation Model
• Apply error propation analysis to the following
radiative transfer equation from ground to sensor.
•
•
•
Lup
t
up
TOA
LTOA

L
T

L
s
t
sen
p
is the upwelling target radiance at ground level
Tsen is the transmittance along the path between the target
and the sensor
TOA
Lp
is the sky path radiance contribution as seen from the sensor
when viewing the target (the signal produced if looking at a surface
of zero reflectance)
• Each component is directly related to calibrated
ground measurements of which their uncertainty is
known based on the measurement errors of the
spectroradiometer and sunphotometer
Error Propagation Equation: Deriving the
Uncertainty in the TOA Radiance

msen
LTOA
s
msun
2
2



T


 msen
 sen, Mod  
 TSens, Mod up    Lup


t , Mod 


m
L
sun


T
t , meas 

sun. Mod  



2



2
2
TOA


(
A

T
)



B

L




sun, Mod
ground
p , Mod
 Tsun,meas
  Lp ,meas 






2


1/ 2

• Ratio of air mass from ground to sun and sensor
Tsun.Mod Tsen, Mod •MODTRAN calculated transmittance to sun and sensor
•MODTRAN calculated upwelling radiance at the ground
Lup
t , Mod
T


sun, meas
•Measurement uncertainty in transmittance from ground to sun
Ltup, meas •Measurement uncertainty in upwelling radiance from target
Lground
•Measurement uncertainty in in sky path radiance from ground observation
p , meas
A  Tsun, Mod
•Uncertainty in estimating aerosol extinction at the MODTRAN input wavelengths from solar
radiometry. A is a fraction of the total transmittance.
B  LTOA
p , Mod
• uncertainty in TOA sky path radiance using the H-G scattering phase function
characterized with ground measurements. B is a fraction of the TOA path radiance,
Described in “Technique for estimating uncertainties in top-of-Atmosphere
radiances derived by vicarious calibration”, S.J. Schiller, SPIE vol. 5151, 2003
Conclusion
• Progress made in vicarious claibration techniques for high spatial
resolution sensors.
– Natural targets to grey-toned deployed targets
– Single radiance levels at different sites & dates to multiple levels evaluated
in a single campaign event.
• Goal is to generate a vicarious calibration curve over the operational
dynamic range of EO sensors (Vis to SWIR)
• Atmospheric model (i.e. MODTRAN) must be characterized using “user
supplied” parameters
Ground truth must address:
– BRDF properties of targets
– Adjacency effect (knowledge of surround spectrum)
– Aerosol vertical profile
– Radiometric accuracy knowledge of ground truth data for TOA radiance
uncertainty estimates
• Working toward <3% absolute accuracy from environments consistent
with operational use