Download Electromagnetic Radiation Principles and Radiometric

Electromagnetic Radiation Principles
and Radiometric Correction
Geography
KHU
Jinmu Choi
1.
2.
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4.
5.
Electromagnetic Radiation Model
Atmospheric Energy-Matter Interaction
Correcting RS System Detector Error
Atmospheric Correction
Correcting for Slope
Electromagnetic Radiation Principles
and Radiometric Correction
• Radiometric correction attempts to improve the
accuracy of spectral reflectance, emittance, or backscattered measurements obtained using a remote
sensing system.
• Geometric correction is concerned with placing the
reflected, emitted, or back-scattered measurements or
derivative products in their proper planimetric (map)
location so they can be associated with other spatial
information in a geographic information system (GIS)
or spatial decision support system (SDSS).
How is Energy Transferred?
(source: Jensen, 2011)
Remote Sensing
3
Wave Model of Electromagnetic Radiation
In the 1860s, James Clerk Maxwell (1831–1879) conceptualized
electromagnetic radiation (EMR) as an electromagnetic wave that travels
through space at the speed of light, c, which is 3 x 108 meters per second
(hereafter referred to as m s-1) or 186,282.03 miles s-1. A useful relation for
quick calculations is that light travels about 1 ft. per nanosecond (10-9 s). The
electromagnetic wave consists of two fluctuating fields — one electric and
the other magnetic. The two vectors are at right angles (orthogonal) to one
another, and both are perpendicular to the direction of travel.
(source: Jensen, 2011)
Radiometric Quantities
The relationship between the wavelength (l) and
frequency (n) of electromagnetic radiation is based on
the following formula, where c is the speed of light:
c  l 
c

l
and

c
l

(source: Jensen, 2011)
How is Electromagnetic Radiation Created?
(source: Jensen, 2011)
Electromagnetic radiation is generated
whenever an electrical charge is
accelerated. The wavelength (l) of the
electromagnetic radiation depends upon the
length of time that the charged particle is
accelerated. Its frequency (n) depends on
the number of accelerations per second.
Wavelength is formally defined as the mean
distance between maximums (or
minimums) of a roughly periodic pattern
and is normally measured in micrometers
(mm) or nanometers (nm). Frequency is the
number of wavelengths that pass a point per
unit time. A wave that sends one crest by
every second (completing one cycle) is said
to have a frequency of one cycle per
second, or one hertz, abbreviated 1 Hz.
Sources of Electromagnetic Energy
(source: Jensen, 2011)
Thermonuclear fusion taking place on the surface of the Sun yields
a continuous spectrum of electromagnetic energy. The 5770 – 6000
kelvin (K) temperature of this process produces a large amount of
relatively short wavelength energy that travels through the vacuum
of space at the speed of light.
Radiometric
Quantities
All objects above absolute zero (–273°C or 0 K)
emit electromagnetic energy, including water, soil,
rock, vegetation, and the surface of the Sun. The
Sun represents the initial source of most of the
electromagnetic energy recorded by remote
sensing systems (except RADAR, LIDAR, and
SONAR). We may think of the Sun as a 5770 –
6000 K
(a theoretical construct that
absorbs and radiates energy at the maximum
possible rate per unit area at each wavelength (l)
for a given temperature). The total emitted
radiation from a blackbody (Ml) measured in
watts per m2 is proportional to the fourth power of
its absolute temperature (T) measured in kelvin
(K). This is known as the Stefan-Boltzmann law
and is expressed as:
Solar and Heliospheric
M l  sT 4
Observatory (SOHO)
Image of the Sun Obtained where s is the Stefan-Boltzmann constant,
on September 14, 1999
5.66697 x 10-8 W m-2 K-4.
Wein’s Displacement Law
In addition to computing the total amount of energy exiting a
theoretical blackbody such as the Sun, we can determine its
dominant wavelength (lmax) based on Wien’s displacement law:
lmax
k

T
where k is a constant equaling 2898 mm K, and T is the absolute
temperature in kelvin. Therefore, as the Sun approximates a 6000
K blackbody, its dominant wavelength (lmax ) is 0.48 mm:

2898mmK
0.483 mm 
6000 K
Blackbody Radiation Curves
(source: Jensen, 2011)
Blackbody radiation curves for several objects including the Sun and the
Earth which approximate 6,000 K and 300 K blackbodies, respectively.
Electromagnetic Spectrum
(source: Jensen, 2011)
• The Sun: a
spectrum of
energy from
gamma rays to
radio waves
that continually
bathe the Earth
in energy.
• The visible
portion of the
spectrum
measured using
wavelength
(mm or nm) or
electron volts
(eV)
Atmospheric
Refraction
Refraction in three
nonturbulent atmospheric
layers. The incident energy is
bent from its normal
trajectory as it travels from
one atmospheric layer to
another. Snell’s law can be
used to predict how much
bending will take place, based
on a knowledge of the angle
of incidence (q) and the index
of refraction of each
atmospheric level, n1, n2, n3.
(source: Jensen, 2011)
Refraction
The index of refraction (n) is a measure of the optical density of a substance.
This index is the ratio of the speed of light in a vacuum, c, to the speed of light
in a substance such as the atmosphere or water, cn:
c
n
cn
Refraction can be described by Snell’s law, which states that for a given
frequency of light (we must use frequency since, unlike wavelength, it does not
change when the speed of light changes), the product of the index of refraction
and the sine of the angle between the ray
 and a line normal to the interface is
constant:
n1 sin q1  n2 sin q2
n1 sin q1
sin q2 
n2
Atmospheric Layers
and Constituents
Subdivisions of the atmosphere
and the types of molecules and
aerosols found in each layer.
Clear Sky-> Blue
scatter: Blue sky
Pollution, dust ->
Orange, Red: scatter
blue , violet; beautiful
Sunset, Sunrise
Cloud-> White: scatter
all visible light well
Type of scattering is a function of:
(source: Jensen, 2011)
1) the wavelength of the incident radiant energy,
2) the size of the gas molecule, dust particle, and/or water vapor droplet encountered.
Rayleigh Scattering
The intensity of Rayleigh scattering varies
inversely with the fourth power of the
wavelength (l-4).
The approximate amount of Rayleigh
scattering in the atmosphere in optical
wavelengths (0.4 – 0.7 mm) may be
computed using the Rayleigh scattering
cross-section (tm) algorithm:
8 n 1
3
tm 
(source: Jensen, 2011)
2
2
2 4
3N
 l
where n = refractive index, N = number of air
molecules per unit volume, and l = wavelength.
The amount of scattering is inversely related to the
 power of the radiation’s wavelength.
fourth
Absorption
window
(source: Jensen, 2011)
Reflectance
(source: Jensen, 2011)
Terrain Energy-Matter Interactions
Total amount of radiant flux (F) measured in watts (W):
Fil  Freflected l  Fabsorbedl  Ftransmittedl
(source: Jensen, 2011)
Freflected
Hemispherical reflectance (rl) rl  F
il
tl 
Hemispherical transmittance (tl)
Ftransmitted
F il

Fabsorbed
Hemispherical absorptance (al) a l  Fil

Percent reflectance :
rl 
%

Freflected l
Fil
100
% Reflectance:
This quantity is
used in remote
sensing research
to describe the
general spectral
reflectance
characteristics
of various
phenomena.
Radiance
Radiance (Ll) is the
radiant flux per unit
solid angle leaving an
extended source in a
given direction per
unit projected source
area in that direction
and is measured in
watts per meter
squared per steradian
(W m-2 sr -1 ).
(source: Jensen, 2011)
Correcting Remote Sensing
System Detector Error
Several of the more common remote sensing system–induced
radiometric errors are:
• random bad pixels (shot noise),
• line-start/stop problems,
• line or column drop-outs,
• partial line or column drop-outs, and
• line or column striping.
Shot Noise Removal
BVi , j ,k
 8

BV
 n 
 int  n1

 8 


(source: Jensen, 2011)
Line or Column
Drop-outs
Line-start Problems
N-line Striping
BVi , j ,k
 BVi 1, j ,k  BVi 1, j ,k 
 int 

2


It is difficult to restore the data
without extensive human
interaction on a line-by-line basis
Every line and pixel in the scene
recorded by the maladjusted
detector may require a bias
(additive or subtractive)
correction or a more severe gain
(multiplicative) correction after
histogram comparison.
Types of Atmospheric Correction
• Absolute atmospheric correction
- to turn the digital brightness values recorded by a RS system
into scaled surface reflectance values
- with in situ atmospheric measurements
- Atmospheric correction based on radiative transfer modeling
-Algorithm: ACORN, ATERM, FLAASH, ATCOR
- Empirical Line Calibration
• Relative atmospheric correction
- to normalize the intensities among the different bands or
from multiple dates of imagery
- with multi bands to cancel out the atmospheric effects
- Single-image Normalization Using Histogram Adjustment
- Multiple-date Image Normalization Using Regression
Atmospheric Correction Based on
Radiative Transfer Modeling
Radiative transfer-based atmospheric correction algorithms require
that the user provide:
• latitude and longitude of the remotely sensed image scene,
• date and exact time of remote sensing
2 data collection,
2


RMS error
 (e.g.,
x  x20
y  yorig
origkmAGL)
• image acquisition
altitude
• mean elevation of the scene (e.g., 200 m ASL),
• an atmospheric model (e.g., mid-latitude summer, mid-latitude
winter, tropical),
• radiometrically calibrated image radiance data (i.e., data must be
in the form W m2 mm-1 sr-1),
• data about each specific band (i.e., its mean and full-width at halfmaximum (FWHM), and
• local atmospheric visibility at the time of remote sensing data
collection (e.g., 10 km, obtained from a nearby airport if possible).

 

Atmospheric Correction Based on
Radiative Transfer Modeling Algorithm
• ACORN: Atmospheric CORrection Now
- used for hyperspectral image
• ATERM: Atmospheric REMoval program
2
2


RMS error  x  xorig  y  yorig
- water vapor
• FLAASH: Fast Line of sight Atmospheric Analysis of
Spectral Hypercubes
- water vapor, oxygen, carbon dioxide, and so on.
• ATCOR: Atmospheric CORrection program
- Various terrain types.
- ATCOR 2 for flat, ATCOR 3 for rugged for 3D

 

Empirical Line Calibration
Empirical line calibration (ELC) to force the remote
sensing image data to match in situ spectral reflectance
measurements (at approximately the same time and on
the same date as the remote sensing overflight)
Empirical line calibration is based on the equation:
BVk  rl Ak  Bk
where BVk is the digital output value for a pixel in band k, pl equals the
scaled surface reflectance of the materials within the remote sensor
IFOV at a specific wavelength (l), Ak is a multiplicative term affecting
the BV, and Bk is an additive term. The multiplicative term is associated
primarily with atmospheric transmittance and instrumental factors, and
the additive term deals primarily with atmospheric path radiance and
instrumental offset (i.e., dark current).

Radiance
Paired Relationship:
Bright
Target
Band 1
Fieldspectra
48
One
Remote
47
measurement Bright Target48
Dark
Target
49
Band 2
48
55 54
Band 3
50
54 57
40 40
Remote Measurement m = 49
55 56
40 39
m = 55
F = 59
42 41
Fieldspectra= 55
Band 1 Band 2 Band 3
Wavelength, nm
m= 41
F = 48
Band 1
Fieldspectra
Bright
Target
Dark
Target
Y  aX  b
One
Dark Target
9 10
10 11
5
4
Band 3
12 10
6
5
0
0
4
6
0
4
2
1
Remote Measurement m = 11
Fieldspectra= 13
Field spectra  gain  radiance image  offset
Radiance

image (e.g., Band 1)
Band 2
m=5
F=7
m=3
F=4
(source: Jensen, 2011)
Cosine Correction for Terrain Slope
cosqo
LH  LT
cosqi
where:

(source: Jensen, 2011)
LH = radiance observed for a horizontal
surface (i.e., slope-aspect
corrected
remote sensor data).
LT = radiance observed over sloped
terrain
(i.e., the raw remote sensor data)
q0 = sun’s zenith angle
i = sun’s incidence angle in relation to
the normal on a pixel
Next



Lab: Exercise: Radiometric Correction
Using Empirical Line Calibration
Lecture: Geometric Correction of Remote
Sensor Data
Source:

Jensen and Jensen, 2011, Introductory Digital
Image Processing, 4th ed, Prentice Hall.