Transcript Image Restoration and Enhancement

Radiometric and Atmospheric
Correction
Lecture 3
Prepared by R. Lathrop 10/99
With slide by Z. Miao
Revised 1/09
Where in the World?
RS Applications to Disaster Response: Haiti
Matterhorn by apanotous
Statement of problem
Data collection
Signal (W m-2)
At-satellite
radiance
signal
0
Dt (Time)
Data-to-Information
Conversion
Remote
sensing
process
Julian day
Image presentation
0
Julian day
Dt (Time)
Target surface
reflectance
signal
# of pixels
Analog-to-DN
conversion
Spectral or histogram
enhancement (e.g.,
LUT stretch)
# of pixels
Signal (W m-2)
Radiometric
correction
0
DN (Brightness value)
255
0 DN (Brightness value)
etc.
255
Learning objectives
• Remote sensing science concepts
– Basic interactions between EMR & earth surface and atmosphere
– The differences between DN values, radiance and reflectance, at-satellite and
surface radiance Principle of conservation of energy
– Radiometric Correction
– Atmospheric correction: need for and basic overview of techniques
– Terrain correction: need for and basic overview of techniques
• Math Concepts
– Analog-to-DN and DN-to-radiance conversion response function
– Linear regression analysis for scene-to-scene normalization
• Skills
– Applying radiometric response functions
– Determining best-fit relationships using linear regression for simple
atmospheric correction
Radiometric correction
• Radiometric correction: to correct for
varying factors such as scene illumination,
azimuth, elevation, atmospheric conditions
(fog or aerosol), viewing geometry and
instrument response.
• Objective is to recover the “true” radiance
and/or reflectance of the target of interest
Analog-to-digital conversion process
A-to-D conversion transforms continuous
analog signal to discrete numerical (digital)
representation by sampling that signal at a
specified frequency
Continuous analog signal
Discrete
sampled value
Radiance, L
dt
Adapted from Lillesand & Kiefer
Units of EMR(electro-magnetic
radiation) measurement
• Irradiance - radiant flux incident on a
receiving surface from all directions,
Energy per unit surface area, W m-2
• Radiance - radiant flux emitted or
scattered by a unit area of surface as
measured through a solid angle, W m-2 sr1 µm-1(energy (Watt) per unit area (square
meter) per solid angle per unit wavelength
(µm-1))
• Reflectance - fraction of the incident flux
that is reflected by a medium
For today’s lecture, we’ll use Landsat
imagery for our examples
For more info, go to:
http://ltpwww.gsfc.nasa.gov/IAS/han
dbook/handbook_toc.html
Radiometric response function
• Conversion from radiance (analog signal) to
DN follows a calibrated radiometric
response function that is unique for channel
• Inverse relationship permits user to convert
from DN back to radiance. Useful in many
quantitative applications where you want to
know absolute rather than just relative
amounts of signal radiance
• Calibration parameters available from
published sources and image header
Radiometric response function
• Radiance to DN conversion
DN = G x L + B
where
G = slope of response function (channel gain)
L = spectral radiance
B = intercept of response function (channel
offset)
• DN to Radiance Conversion
L = [(LMAX - LMIN)/255] x DN + LMIN
where
LMAX = radiance at which channel saturates
LMIN = minimum recordable radiance
Radiometric response function
Spectral Radiance to DN
DN to Spectral Radiance
255
DN
Lmax
Slope =
channel
gain, G
L
Slope =
(Lmax – Lmin) / 255
Lmin
0
Lmin
L
Bias = Y intercept
Lmax
0
DN
255
High vs. Low Gain Dynamic Ranges
Some sensors such
as Landsat ETM
can operate under
high gain settings
when image
brightness is low
or low gain when
image brightness
is high
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter6/chapter6.html
Radiometric response function
Example: Landsat 5 Band 1
• From sensor header, get Lmax & Lmin
• Lmax = 15.21 mW cm-2 sr-1 um-1
• Lmin = -0.15200000 mW cm-2 sr-1 um-1
• L = -0.15200000 + ((15.21 - 0.152)/255) DN
• L = -0.15200000 + (0.06024314) DN
• If DN = 125,
L = -0.15200000 + (0.06024314) 125
L = -0.15200000 + 7.53039
L = 7.37839 mW cm-2 sr-1 um-1
Radiometric response function
Example: Landsat 7 Band 1
• Note that Landsat Header Record refers to gain
and bias, but with different units (i.e., W m-2 sr-1
µm-1, rather than mW m-2 sr-1 µm-1)
• 1 W m-2 sr-1 µm-1= 0.1 mW cm-2 sr-1 µm-1
• L = Bias + (Gain* DN)
If DN = 125, L = ?
Landsat Science Data User’s Handbook
ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter1
DN-to-Radiance conversion
Example: Landsat ETM
Band
1
Gain
0.7756863
Bias
-6.1999969
2
0.7956862
-6.3999939
3
0.6192157
-5.0000000
4
0.6372549
-5.1000061
5
0.1257255
-0.9999981
6
0.0437255
-0.3500004
•Note that Landsat Header Record refers to gain and bias, but
with different units (W m-2 sr-1 um-1)
Radiometric response function
Example: Landsat 7 Band 1
• Note that Landsat Header Record refers to gain and
bias, but with different units (W m-2 sr-1 µm-1)
• Gain = 0.7756863 W cm-2 sr-1 µm-1
• Bias = -6.1999969 W cm-2 sr-1 µm-1
• L = -6.1999969 + (0.7756863) DN
If DN = 125, L = 90.76079 W m-2 sr-1 µm-1
Same 9.076079 mW cm-2 sr-1 µm-1
Landsat Science Data User’s Handbook
ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11
Radiometric response function
Example: Landsat 5 Thermal IR
• Gain = 0.005632 mW cm-2 sr-1 um-1
• Bias = 0.1238 mW cm-2 sr-1 um-1
• L = 0.1238 + (0.005632) DN
To convert to at-satellite temperature (o K):
T = 1260.56 / loge [(60.776/L) + 1]
Remember 0oC = 273.1K
For more details see Markham & Barker. 1986. EOSAT Landsat Technical Notes v.1, pp.3-8.
Radiometric response function
Example: Landsat 7 Thermal IR
•
•
•
•
For High Gain Band 6: MIN = 3.2; LMAX = 12.65
Gain = 0.037059 W m-2 sr-1 mm-1
Bias = 3.2W m-2 sr-1 mm-1
L = 3.2 + (0.03706) DN
To convert to at-satellite temperature (o K):
T = 1282.71 / loge [(666.09/L) + 1]
Remember 0oC = 273.1K
For more details see Markham & Barker. 1986. EOSAT Landsat Technical Notes v.1, pp.3-8.
Oyster Creek Nuclear Plant, NJ Thermal plume
• Landsat ETM Dec 1, 2001
• What’s the temperature difference between the plume
and ambient Barnegat Bay waters?
High gain B6
Plume DN = 133
Bay DN = 118
What’s the Temperature difference
between plume and ambient bay?
• L = 3.2 + (0.03706) DN
• Plume DN = 133
L = 8.13
• Bay DN = 118
L = 7.57
T (oC)= {1282.71 / loge [(666.09/L) + 1]} – 273.1
•Plume Temperature = 17.2 oC
•Ambient Bay temperature = 12.7 oC
Remember this is the uncorrected at-satellite temperature, but the
relative temperature difference of approx 4.5 oC should be valid
For more details see.
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11/chapter11.html
At-Satellite Reflectance
To further correct for scene-to-scene differences in solar
illumination, it is useful to convert to at-satellite reflectance. The
term “at-satellite” refers to the fact that this conversion does not
account for atmospheric influences.
At-Satellite Reflectance, pl = (p Ll d2 ) / (ESUNl cosq)
Where
Ll = spectral radiance measured for the specific waveband
q = solar zenith angle
ESUN = mean solar exoatmospheric irradiance (W m-2 um-1), specific to the
particular wavelength interval for each waveband, consult the sensor
documentation.
d = Earth-sun distance in astronomical units, ranges from approx. 0.9832 to
1.0167, consult an astronomical handbook for the earth-sun distance for the
imagery acquisition date
At-satellite
reflectance
Ground
reflectance
Solar zenith vs.
elevation angle
Tangent plane
Zenith angle
Solar elevation angle
= 90 - zenith angle
http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter6/chapter6.html
Solar Zenith angle
qo = 60
qo = 0
qo = solar zenith angle
zenith angle
qo = 0
cosqo = 1
As qo
cosqo
Tangent line
Solar elevation angle
= 90 - zenith angle
=30
N
Azimuth
angle
At-Satellite Reflectance
Example: Landsat 7 Band 1
• If Acquisition Date = Dec. 1, 2001
• At-Satellite Reflectance = ?
http://aa.usno.navy.mil/data/docs/AltAz.html
Table 11.4 Earth-Sun Distance in Astronomical Units
Julian
Day
Dista
nce
Julian
Day
Dista
nce
Julian
Day
Dista
nce
Julian
Day
Dista
nce
Julian
Day
Distanc
e
1
.9832
74
.9945
152
1.014
0
227
1.012
8
305
.9925
15
.9836
91
.9993
166
1.015
8
242
1.009
2
319
.9892
32
.9853
106
1.003
3
182
1.016
7
258
1.005
7
335
.9860
46
.9878
121
1.007
6
196
1.016
5
274
1.001
1
349
.9843
60
.9909
135
1.010
9
213
1.014
9
288
.9972
365
.9833
Landsat Science Data User’s Handbook
ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11
Solar Spectral Exoatmospheric
Irradiances(ESUN): Landsat ETM
Band 1
Band 2
Band 3
Band 4
Band 5
Band 7
Band 6
Watts m-2 um-1
1969.0
1840.0
1551.0
1044.0
225.70
82.07
1368.0
Landsat Science Data User’s Handbook
ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11
At-Satellite Reflectance
Example: Landsat 7 Band 1
The equation for converting radiance to reflectance:
pl = (p Ll d2 ) / (ESUNl cosq)
•
•
•
•
•
•
•
Dec. 1, 2001  Julian Day = 335
Earth-Sun d = 0.986
ESUNl = 1969.0
Cosq = Cos(63.54) = 0.44558
Ll = 90.76079 W m-2 sr-1 um-1
pl = (3.14159*90.76079*0.9862)/(1969.0*0.44558)
pl = 277.20558/877.34702 = 0.31596. pl=surface target
reflectance at a specific wavelength.
Landsat Reflectance Conversion:
ERDAS Imagine module
Atmospheric Correction
Path radiance and target radiance
Target Reflectance (BRDF)
Surround Reflectance
Basic interactions between EMR and
the atmosphere
• Scattering, S
• Absorption, A
• Transmission, T
• Incident E = S + A + T
• Within atmosphere, determined by
molecular constituents, aerosol particles,
water vapor
Atmospheric windows
Transmittance (%)
•Specific wavelengths where a majority of the EMR is absorbed by the atmosphere
•Wavelength regions of little absorption known as atmospheric windows
Graphic from http://earthobservatory.nasa.gov/Library/RemoteSensingAtmosphere/
From Shaw, G.A. and H.K. Burke. Spectral Imaging for Remote Sensing.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.69.1178&rep=rep1&type=pdf.
Atmospheric interference with EMR
• Shorter wavelengths strongly scattered,
adding to the received signal
• Longer wavelengths absorbed, subtracting
from the received signal
Signal
decreased by
absorption
Signal increased
by scattering
Ref
0.4
0.5
0.6
0.7
0.8
1.1 um
Adapted from Jensen, 1996, Introductory Digital Image Processing
Atmospheric Interference
• Interaction of the atmosphere with
reflected/emitted ENMR can add noise to the
signal. Noise: extraneous unwanted signal
response
• Want high signal-to-noise ratio
• Over low reflectance targets (i.e. dark pixels
such as clear water) the noise may swamp the
actual signal
Observed
Signal
True
Signal
Noise
+
Atmospheric correction
• Atmospheric correction procedures are
designed to minimize scattering & absorption
effect due to the atmosphere
• Scattering increases brightness. Shorter
wavelength visible region strongly influenced
by scattering due to Rayleigh, Mie and
nonselective scattering
• Absorption decreases brightness. Longer
wavelength infrared region strongly
influenced by water vapor absorption.
Satellite Received Radiance
Total radiance, Ls = path radiance Lp + target radiance Lt
Ideally, we want to get target radiance as more as possible.
Target radiance, Lt = 1/p RTqu (E0 deltalTqo cosqo deltal+ Ed)
Where R = average target reflectance
qo = solar zenith angle
u = nadir view angle
Tqo = atmospheric transmittance at angle q to zenith
E0l = spectral solar irradiance at top of atmosphere
Ed = diffuse sky irradiance (W m-2)
Delta l = band width, l2 – l1
Atmospheric correction techniques
• Absolute vs. relative correction
• Absolute removal of all atmospheric
influences is difficult and requires a number
of assumptions, additional ground and/or
meteorological reference data and
sophisticated software (beyond the scope of
this introductory course)
• Relative correction takes one band and/or
image as a baseline and transforms the other
bands and/or images to match
Atmospheric correction techniques:
Histogram adjustment
• Histogram adjustment: visible bands, esp.
blue have a higher MIN brightness value.
Band histograms are adjusted by
subtracting the bias for each histogram, so
that each histogram starts at zero.
• This method assumes that the darkest pixels
should have zero reflectance and a BV = 0.
Atmospheric correction techniques:
Dark pixel regression
adjustment
• Select dark pixels, either deep clear water or
shadowed areas where it is assumed that
there is zero reflectance. Thus the observed
BV in the VIS bands is assumed to be due
to atmospheric scattering (skylight).
• Regress the NIR vs. the VIS.
• X-intercept represents the bias to be
scattered from the VIS band (visible band).
Atmospheric correction techniques:
Scene-to-scene normalization
• Technique useful for multi-temporal data sets
by normalizing (correcting) for scene-to-scene
differences in solar illumination and
atmospheric effects
• Select one date as a baseline. Select dark,
medium and bright features that are relatively
time-invariant (i.e., not vegetation). Measure
DN for each date and regress.
DB b1, t2 = a + b DN b1, t1
Scene-to-Scene Normalization
Example: Landsat 5 vs Landsat 7
Landsat 7: Sept 01
Landsat 5: Sept 95
Scene-to-Scene Normalization
Example: Landsat 5 vs Landsat 7
Landsat 5: Sept 95
Landsat 7: Sept 99 & 01
250
250
200
150
sept99-B4
sept01-B4
100
Sept 99-01 B5
Sept 99-01 B4
200
150
sept99-B5
sept04-B5
100
50
50
0
0
0
20
40
60
80
100
120
Sept 95 B4
99 R2 = 0.932
01 R2 = 0.963
140
160
0
50
100
Sept 95 B5
99 R2 = 0.971
01 R2 = 0.968
150
200
Scene-to-scene normalization: work flow
Set baseline image
From the baseline image and target image, select
DARK, MEDIUM AND BRIGHT features
that do NOT change with time.
Input DN values of selected features of the two
images into two columns of spreadsheet, and
generate linear regression equation.
Input the linear equations into
your ERDAS model and run
NOTE: the selected
features of the two
images must
correspondingly come
from SAME locations.
Hyperspectral
Image Cube
From Shaw, G.A. and H.K. Burke. Spectral Imaging for Remote Sensing.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.69.1178&rep=rep1&type=pdf.
Atmospheric correction: absolute
• MODTRAN (Moderate resolution TRANsmission model)
predicts the atmospheric emission, thermal scatter, and solar
scatter for arbitrary, refracted paths above the curved earth,
incorporating the effects of molecular absorbers and scatterers,
aerosols and clouds.
• FLAASH (Fast Line-of-sight Atmospheric Analysis of Spectral
Hypercubes) handles data from a variety of hyper- and multispectral imaging sensors, supports off-nadir as well as nadir
viewing, and incorporates algorithms for water vapor and aerosol
retrieval and adjacency effect correction. Based on MODTRAN.
• Marketed by Spectral Sciences Inc. http://www.spectral.com/remotesense.shtml
AVIRIS
before
AVIRIS
after
FLAASH
• Fast Line-of-Sight Atmospheric Analysis of
Spectral Hypercubes (FLAASH) approach
From Shaw, G.A. and H.K. Burke. Spectral Imaging for Remote Sensing.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.69.1178&rep=rep1&type=pdf.
FLAASH
• Fast Line-of-Sight Atmospheric Analysis of Spectral
Hypercubes (FLAASH) approach
• Employs a band ratio technique to quantify the effect of
water vapor on hyperspectral measurements. Involves
comparing ratios of radiance measurements made near
edges of known atmospheric water-vapor absorption bands
in order to estimate the column water vapor in the
atmosphere on a pixel-by-pixel basis.
• Look-up tables, indexed by measured quantities in the
scene, combined with other information such as the solar
zenith angle, are used to estimate reflectance across the
scene, without resorting to reference objects within the
scene.
.
From Shaw, G.A. and H.K. Burke. Spectral Imaging for Remote Sensing
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.69.1178&rep=rep1&type=pdf.
Terrain Shadowing
USGS DEM
Landsat ETM Dec 01
Solar elevation = 26.46
Sun Azimuth = 158.78
Terrain correction
• To account for the seasonal position of the sun
relative to the pixel’s position on the earth (i.e., slope
and aspect)
• Normalizes to zenith (sun directly overhead)
• Lc = Lo cos (o) / cos(i)
where Lc = slope-aspect corrected radiance
Lo = original uncorrected radiance
cos (o) = sun’s zenith angle
cos(i) = sun’s incidence angle in relation to the
normal on a pixel (i = o-slope)
Cosine Terrain correction
Sensor
Sun
o
i
Lc = Lo cos (o) / cos(i)
90o
Terrain: assumed to
be a Lambertian
surface
Adapted from Jensen
Terrain correction
• Terrain Correction
algorithms aren’t just a
black box as they don’t
always work well, may
introduce artifacts to the
image
• Example: see results on
right from ERDAS
IMAGINE terrain
correction function
appears to “overcorrect”
shadowed area
Summary
• The differences between DN values, radiance and
reflectance, at-satellite and surface radiance;
• Analog-to-DN and DN-to-radiance conversion
response function;
• Radiometric Correction;
• Atmospheric correction, e.g., scene-to-scene
normalization.
Statement of problem
Data collection
Signal (W m-2)
At-satellite
radiance
signal
0
Dt (Time)
Data-to-Information
Conversion
Remote
sensing
process
Julian day
Image presentation
0
Julian day
Dt (Time)
Target surface
reflectance
signal
# of pixels
Analog-to-DN
conversion
Spectral or histogram
enhancement (e.g.,
LUT stretch)
# of pixels
Signal (W m-2)
Radiometric
correction
0
DN (Brightness value)
255
0 DN (Brightness value)
etc.
255
Homework
• Landsat TM Thermal IR calibration;
• Reading Ch. 6; ERDAS Field Guide Ch. 5:
132-135.