Hyperspectral Remote Sensing

1

HyperspectralRemote Sensing

Keck Center, National Academies, Washington, DC10 December 2013

Workshop Instructor:Dr. Ronald G. Resmini

rresmini@mitre.org and rresmini@gmu.edu

ASPRS/Potomac Region’sGeoTech 2013

2

Dr. Ronald G. ResminiThe MITRE Corporation and

George Mason UniversityPlease call me Ron

v: 703-470-3022rresmini@mitre.org and rresmini@gmu.edu

http://mason.gmu.edu/~rresmini/

3

What sort of remote sensing system acquired this image?Is it a panchromatic visible? multispectral? hyperspectral? panchromatic infrared?

polarimetric? SAR? How can you tell?

4

Introduction toHyperspectral Imagery (HSI)

Remote Sensing

and to ENVI®

5

writ large...the phenomenology of spectra;remote material detection, identification, characterization

and quantification

Introduction to Hyperspectral Imagery (HSI)Remote Sensing

HSI is, fundamentally:

6

HSI Remote Sensing:Frame of Reference...•Remote sensing of the earth

airbornespaceborneground (portables)

• But bear in mind other apps:medicalindustrialmany, many others

7

Applications of HSI RS

• Geology• Forestry• Agriculture• Mapping/land use, land cover analysis• Atmospheric analysis• Environmental monitoring• Littoral zone RS• Many, many others

8

• Where/how do we do HSI remote sensing?

• What is the nature of what is measured?

• What is there to measure?

• How is it done?

• Are there distinguishing observables?

• etc...

9

Electromagnetic EnergyElectromagnetic Spectrum

Electromagnetic Spectrum

Wavelength (nm)

Cosmic Rays

Gamma Rays

X Rays

Microwaves (Radar)

Radio & Television WavesUV

105 106 107 108 109 1010 1011 10121011010-110-210-310-410-5

Shorter WavelengthsHigh Energy

Longer WavelengthsLow Energy

V / NIR / SWIR / MWIR / LWIR

Optical Region

400 14000

4000.4

1400014.0

15001.5

30003.0

50005.0

7000.7

NIR MWIRSWIRRG LWIR B LWIRWavelength (nm)(m)

Emitted Energy

Reflected Energy

10

HSI Sensors Measure Radiance

)microflick(f1msrm

W0.100msrcm

W22

Check-out the fancylingo used in the field

11

Reflected vs. Emitted Energy

1

104

1000

100

10

0.1 1 1053 7

Irrad

ianc

e (W

-m-2-u

m-1)

Wavelength (µm)

Earth Emission

(100%)

EarthReflectance

(100%)

radiant exitance (W-m

-2-um-1)

MWIR

Assumes no atmosphere

.4 .7

12

NIR SWIR MWIR LWIRRB G

0.4 m 1.5 3.0 5.0 14.0 m0.7

Panchromatic or single b&w image

0.4 m 1.5 3.0 5.0 14.0 m0.7

A normal color-composite image

0.4 m 1.5 3.0 5.0 14.0 m0.7

Hyperspectral: hundreds of narrow bands – hundreds of images

0.4 m 1.5 3.0 5.0 14.0 m0.7

Multispectral: tens of broad bands – tens of images

0.4 m 1.5 3.0 5.0 14.0 m0.7

Sam

plin

g Fu

nctio

n

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So...what sort of remote sensing system acquired this image?

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BTW, This is Dispersion:

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Interaction of energy and objects

Transmitted Energy

Absorbed Energy

Reflected EnergyV-MWIR

Emitted EnergyMW-LWIR

Energy Balance Equation: EI () = ER() + EA() + ET()

Incident Energy

16

NASA AVIRIS Cuprite, NV, HSI Data, (1995)

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An AVIRIS (NASA) HSI Image Cube

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The Spectrum is the Fundamental Datum of HSI RS

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Levels of Spectral Information

Quantification: Determines the abundance of materials.

Characterization: Determines variability of identified material (e.g. wet/dry sand, soil particle

size effects).

Identification: Determines the unique identity of the foregoing generic categories (i.e. material

identification).

Discrimination: Determines generic categories of the foregoing classes.

Classification: Separates materials into spectrally similar groups.

Detection: Determines the presence of materials, objects, activities, or events. Panchromatic

Low Spectral Resolution

High Spectral Resolution

Hyperspectral(100’s of bands)

Multispectral(10’s of bands)

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Image from the NASA Langley Research Center, Atmospheric Sciences Division.http://asd-www.larc.nasa.gov/erbe/ASDerbe.html

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Electromagnetic EnergyAtmospheric Absorption

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Reflectance: Is the ratio of reflected energy to incident energy. Varies with wavelength Function of the molecular properties of the material.

Reflectance Signature: A plot of the reflectance of a material as a function of wavelength.

Reflected Energy

Red brick KaoliniteSandy loamConcreteGrass

All solids and liquids have reflectance signatures that

potentially can be used to identify

them.

23

Emissive EnergyBasic Concepts

• Blackbody – A theoretical material that absorbs and radiates 100% of the energy incident upon it. BB curve is a function of temperature and wavelength.

• Planck’s Law – gives shape of blackbody curve at a specific temperature.• Wien’s Displacement Law – determines wavelength of peak emittance.

Wavelength (µm) 0.2 0.4 0.7 1 2 3 5 8 10 30

Spec

tral

Rad

iant

Em

ittan

ce

PeakEmittance

300KAmbient

250K500K

800K

373KBoilingWater

6000KSun

3000KLight Bulb

1500KHot Coals

24

1

52 12

kT

hc

BB ehcM

The Planck or Blackbody Radiation Equation:

mm

W2Units:

TMTM

BB

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Emissive Energy• Emissivity - is a measure of how efficiently an object radiates

energy compared to a blackbody at the same temperature. Varies with wavelength Function of the molecular properties of the material.

• Emissivity Signature - A plot of emissivity as a function of wavelength. All materials have emissivity signatures that potentially can be used to identify them.

Blackbody

GraybodySelective emitter(emissivity signature)

Em

issi

vity

0

0.5

1.0

Wavelength

Red brick KaoliniteGrass Water

Black paint Concrete

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Spectral Signature Libraries

• Spectral signatures of thousands of materials (solid, liquid, gas) have been measured in the laboratory and gathered into “libraries”.

• Library signatures are used as the basis for identification of materials in HSI data.

27

Understanding Spectral Data: Signature Variability Factors

Brightness BRDF Target morphology • shape• orientation

Particle size Moisture Spectral mixing

Composition • original • change over time

Surface quality • roughness• weathering

Shade & Shadow Temperature

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Reflected Energy• The manner in which a material reflects energy is primarily a

function of the optical properties and surface roughness of the feature.

• Most objects are diffuse reflectors

Specular Reflectance

Diffuse Reflectance

Angle of Incidence = Angle of Reflectance

Smooth Surface

Rough Surface

(Microscopic)

Energy Scattered in

All Directions

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Emissive EnergyIdentification of Gases

DetectedSignature

Plume

Wavelength

Emission

Background (Cool)

Gas (Warm)

Gases appear in either emission or absorption depending on the temperature contrast between the gas and the background.

Same Temperature

Wavelength

No Detection

Background

Gas

Wavelength

Absorption

Background (Warm)

Gas (Cool)

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• Spatial Resolution

• Radiometric Resolution

• Temporal Resolution

Resolutions

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HSI Fundamentals Summary• Hyperspectral remote sensing involves measuring

energy in the Visible – LWIR portions of the electromagnetic spectrum.

• Some of the measured energy is reflected from objects while some energy is emitted from objects.

• Every material has a unique spectral signature.• Spectral image data are collected such that signatures

can be extracted for material detection, classification, identification, characterization, and quantification.

• Spectral, spatial, radiometric, and temporal resolution determine the capabilities of the remote sensing sensor/system.

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Properties of the Data Cube

• # of samples, lines, bands• Headers, preline, postline, footers, etc.• Data type• Interleaving (BIP, BIL, BSQ)• Byte order• Wavelengths, FWHM• Bad bands list• Band names (very optional)• The logical and physical data cube• The ENVI “.hdr” file• History file (it doesn’t exist) – keep notes!

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An AVIRIS (NASA) HSI Image Cube

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• What you need to know about your data; a check-list:• Date, time, location, ground elevation, platform elevation,

heading, GSD, be able to calculate where the sun is;i.e., all RS angles (geometry)

• On-going sensor characterization; know what it is; ask for it!• Spatial sampling; spatial resolution• Spectral sampling; SRF; spectral resolution• NESR, NEDr, NED, NEDT• Issues: smile, keystone, FPA misregistration, vibration,

parallax, scattered light, self-emission, platformmotion/imaging distortions, etc.

There’s More to Know...

35

Reconstituted Reflectance High SNR spectra

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

400.0 700.0 1000.0 1300.0 1600.0 1900.0 2200.0 2500.0

Wavelength (nm)

Ref

lect

ance

Conifer Grass

Broad Leaf Sage_Brush

NPV

A couple of slides on SNR, NESR

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0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

400.0 700.0 1000.0 1300.0 1600.0 1900.0 2200.0 2500.0

Wavelength (nm)

Ref

lect

ance

Conifer Grass

Broad Leaf Sage_Brush

NPV

Reconstituted Reflectance Low SNR spectra

37

Information Content and Extraction

• HSI RS is based on the measurement of a physical quantityas a function of wavelength: its spectroscopy

• HSI is based on discerning/measuring the interaction oflight (photons, waves) with matter

• The sun is the source; or active systems; or very hot objects• Earth RS scenarios involve the atmosphere• There are complex interactions in the atmosphere• There are complex interactions between light and targets

of interest in a scene• There are complex interactions between light, targets of

interest, and the atmosphere• There’s a lot (lots!) of information in the spectra

The

Gen

eral

Dat

a A

naly

sis/

Exp

loita

tion

Flow

DN

Calibration

Fixes/Corrections

Data Ingest

Look At/Inspect the Data!!

Atmospheric Compensation

Algorithms for Information Extraction

Information Fusion

Geometric/Geospatial

Product/Report Generation

Distribution

Archive/Dissemination

Planning for Additional Collections

Spectral Library Access

Iteration

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HSI Remote Sensing:Frame of Reference...

• A Scientist’s Approach to the Data: look at the data(!)observables have a physical,

chemical, biological, etc. basismust understand nature of observablesbumps and wiggles have real,

physical (spectroscopic) significanceapplication of tools comes last!

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NASA Hyperion:http://edcsns17.cr.usgs.gov/eo1/sensors/hyperion

NASA AVIRIS:http://aviris.jpl.nasa.gov/

NASA AIRS:http://www-airs.jpl.nasa.gov/

ProSpecTIR and SEBASS:http://www.spectir.com/airbornesurveys.html

Probe-1:http://www.earthsearch.com/index.php?sp=10

AHI:http://www.higp.hawaii.edu/~lucey/hyperspectralpaul.html

AISA:http://www.channelsystems.ca/SpectralImaging-AISA.cfm

NRL HICO:http://www.nrl.navy.mil/pao/pressRelease.php?Y=2009&R=90-09r

Some HSI Systems

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Defining HSI Dimensionality• Hundreds of bands of data in an HSI data cube• An HSI pixel (a spectrum) is an n-D vector

n = number of bandsa spectrum is a point in an n-D space

• “Redundancy” of information• Embedding or spanning dimension• Intrinsic dimension/virtual dimension• A distinction

large volume of datadimensionality

42

HSI or MSI• 100’s of bands vs. 10’s of bands• Maybe all you need is 6 bands but...

you need six; and you need six; and so on• Atmospheric compensation...• HSI is spectroscopy writ large

its about resolving spectral informationfine spectral featuresbroad spectral features

• Today’s FPAs make HSI a breeze anyway...

43

Multispectral - Hyperspectral Signature Comparison

Multispectral Hyperspectral

Resampled to Landsat TM7 Bands

44

4000.40

15001.50

30003.00

7000.70

NIR SWIRRGB

Wavelength (nm)(m)

Minerals/Geology

SoilsBathymetry

Vegetation

FuelsAerosols

Atmos. Comp.

PlasticsFabrics

Paints

O2 CO2

Chlorophyll

DOM/CDOM Cirrus

Iron oxides

Similar figures may be constructed for M/LWIR regions.

45

Thinking About Spectra;Thinking about HSI

46

• Spectral parameterization• Albedo/brightness• Band depth• Band width• Band shape/superimposed features• Spectral slope• Spectral indices• Derivative spectroscopy• Wavelet transform• Combinations

• Pre-processing transforms; e.g., SSA• All must have a physical basis!

• Tie all observations to physical reality!!

47

48

HSI Algorithms:An Introduction

(Don’t Panic!!)

49

•Algorithm types, classes, categories:an overview•Angular Metrics

•SAM•Distance Metrics

•w/, w/o statistics•Data transformations

•PCA, MNF, ICA•SMA/OSP/CEM/SMF/ACE•Derivative Spectroscopy/other Parameterization Methods

~Pro

porti

onal

to In

crea

sing

Deg

ree

of C

ompl

exity

Overview

50

An Algorithm Progression

SAM, MD (whole pixel matchers)

SMA (subpixel mixtures)

Orthogonal SubspaceProjection

Spectral Matched Filter

Variations of theSpectral Matched Filter

JM Distance

B Distance

Traditional MSIClassification Methods

Spectral

Parameterizations

Spectral

ParameterizationsSpectral

Parameterizations

51

The n-D Space — Where Many Algorithms Operate

Each HSI spectrum (or pixel) is an n-D vector that

can be represented as a single point in n-D space.

n-D space is actually where many of our algorithms

operate.

Tn7654321 ,...,,,,,,,)pixelor(Spectrum rrrrrrrr

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.4 0.8 1.2 1.6 2.0 2.4

Wavelength (m)

Ref

lect

ivity

, r

52

Four (A-D) Equivalent Notations/Representations

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50

Wavelength (micrometers)

Ref

lect

ance

, r

(0.11, 0.23, 0.30, 0.25, 0.16, 0.27, 0.31, 0.37,...,)

...p.o.n.m.l.k.j.i. 370310270160250300230110

r, Band a

r, B

and

b

Spectrum s1

...imagine an n-Dhyperspace...

A B

C

D

53

Some HSI Scatter Plots; Spectra as Points in ‘Hyperspace’

54

SAM: n-D Geometry

A 2D scatterplot with 2 spectra:

Band a

Ban

d b

Spectrum s1

Spectrum s2

Angular Distance Metric (Spectral Angle Mapper or SAM)

Assume a two band spectral remote sensing system. Each two point‘spectrum’ is a point in Band b vs. Band a space.

The angle, , between the twolines connecting each spectrum

(point) to the origin is the angularseparation of the two spectra. Smaller angular separations in-

dicate more similar spectra.

55

SAM: The Math

• Chang (2003), ch. 2, pp. 20-21; and...• Assume two 5-band spectra as shown:

21

2T

11

sssscos T1s

2s

56

e2e1d2d1c2c1b2b1a2a12T

1 ssssssssssss

• Let the 5 bands have band names a, b, c, d, and e:

1T

1e1e1d1d1c1c1b1b1a1a11 sssssssssssss

2T

2e2e2d2d2c2c2b2b2a2a22 sssssssssssss

2T

222

22

22

22

222 ssssssss

• The output units are radians• ENVI does all this for you

57

• Invariant to albedo...why:

A 2D scatterplot with 2 spectra:

Band a

Ban

d b

Spectrum s1

Spectrum s2

Move s1 towards origin...angle does not change

58

• Application strategiesRadiance, reflectanceScaled values

• A few comments on SAM andmixed pixels

59

Euclidean Distance: n-D Geometry

A 2D scatterplot with 2 spectra:

Band a

Ban

d b

Spectrum s1

Spectrum s2

Whole-Pixel Distance Metric in n-D Hyperspace

Assume a two band spectral remote sensing system. Each two point‘spectrum’ is a point in Band b vs. Band a space.

Euclidean Distance

60

Euclidean Distance: n-D Geometry

A 2D scatterplot with 2 spectra:

Band a

Ban

d b

Spectrum s1

Spectrum s2

Whole-Pixel Distance Metric in n-D HyperspaceAssume a two band spectral remote sensing system. Each two point

‘spectrum’ is a point in Band b vs. Band a space.

Euclidean Distance

61

Euclidean Distance: The Math

It’s the Pythagorean Theorem

A 2D scatterplot with 2 spectra:

Band a

Ban

d b

Spectrum s1

Spectrum s2

a

b

cc = Euclidean Distance

c2 = a2 + b2

62

T1s

2s

Euclidean Distance: More Math

As with SAM, assume two five-band spectra.

63

212

e2e12

d2d12

c2c12

b2b12

a2a1 ssssssssssc

• Let the 5 bands have band names a, b, c, d, and e:

• The output units are reflectance• ENVI does all this for you

64

• Application strategiesRadiance, reflectanceScaled values

• A few comments on Euclidean distanceand mixed pixels

65

Linear Spectral UnmixingThe reflectance of an image pixel is a linear combination ofreflectances from (typically) several “pure” substances (orendmembers) contained within the ground-spot sampled by theremote sensing system:

n

jii,jji rMfR

1

where: Ri is the reflectance of a pixel in band i,

fj is the fractional abundance of endmember j in the pixel,

Mj,i is the reflectance of endmember substance j in band i,

ri is the unmodeled reflectance for the pixel in band i, and

n is the number of endmembers.

66

Spectral Mixture Analysis (SMA)

• An area of ground of, say 1.5 m by 1.5 m may contain 3 materials: A, B, and C.• An HSI sensor with a GSD of 1.5 m would measure the ‘Mixture’ spectrum• SMA is an inversion technique to determine the quantities of A, B, and C

in the ‘Mixture’ spectrum• SMA is physically-based on the spectral interaction of photons of light and matter• SMA is in widespread use today in all sectors utilizing spectral remote sensing• Variations include different constraints on the inversion; linear SMA; nonlinear SMA

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40

Wavelength (micrometers)

Ref

lect

ance

A

B

C

Mixture

‘Mixture’ = 25%A + 35%B + 40%C

67

A linear equation...

7 x 5 5 x

1

7 x

1

5 endmembers in a 7-band spectral data set

Ax

b

bAAAx TT 1bAx

68

Linear Spectral Unmixing TheorySpectral unmixing theory states that the reflectance of an image pixel is alinear combination of reflectances from the (typically) several “pure”substances (or endmembers) contained within the ground-spot sampled bythe remote sensing system. This is indicated below:

n

jii,jji rMfR

1

where: Ri is the reflectance of a pixel in band i, f j is the fractional abundance of substance (or

endmember) j in the pixel, and Mj,i is the reflectance of endmember substance j in band i. r i is

the band-residual or unmodeled reflectance for the pixel in band i, and n is the number of endmembers. A spectral unmixing analysis results in n fraction-plane images showing the quantitative areal distribution of each of the endmember substances and one root mean squared (RMS) image showing an overall or global goodness of fit of the suite of endmembers for each pixel. The RMS image is formed, on a pixel-by-pixel basis, by:

n

j

in

rRMS1

2Objects may also be detected asanomalies in the RMS image.

69

y,xny,xMy,xr

d,uuuM 1pi1

1pi1 uuuU

nUdr p

OSP/LPD/DSR: Scene-Derived Endmembers

(Harsanyi et al., 1994; see also ch. 3 of Chang, 2003)

70

This is equivalent to Unconstrained SMA

Some math happens to generate a vector called q...

PddPxd

T

T

p

scalary,xrqT

71

Statistical Characterization of the Background(LPD/DSR)

0

nUr

q

1i

Tiir rr

q1

(Harsanyi et al., 1994)

72

VV rT

r

#VVIP~

P~dw TT

scalary,xrwT

73

Constrained Energy Minimization (CEM)• The description of CEM is similar to that of OSP/DSR (previous slides)• Like OSP and DSR, CEM is an Orthogonal Subspace Projection (OSP)

family algorithm• CEM differs from OSP/DSR in the following, important ways:

CEM does not simply project away the first n eigenvectors The CEM operator is built using a weighted combination of the

eigenvectors (all or a subset)• Though an OSP algorithm, the structure of CEM is equally readily observed by

a formal derivation using a Lagrange multiplier

• CEM is a commonly used statistical spectral matched filter• CEM for spectral remote sensing has been published on for over 10 years• CEM has a much longer history in the multi-dimensional/array signal

processing literature• Just about all HSI tools today contain CEM or a variant of CEM• If an algorithm is using M-1d as the heart of its filter kernel (where M is the

data covariance matrix and d is the spectrum of the target of interest), thenthat algorithm is simply a CEM variant

74

Hº: pº(x)= )xMxexp(M TJ 1212

212

J = # of Bands

H1: p1(x)= )bxMbxexp(M TJ 1212

212

Form the log-likelihood ratio test of Hº and H1:

Xpxpln)x(l

0

1

Stocker, A.D., Reed, I.S., and Yu, X., (1990). Multi-dimensional signal processing for electro-Optical target detection. In: Signal and Data Processing of Small Targets 1990, Proceedingsof the SPIE, v. 1305, pp. 218-231.

Derivation taken from:

75

)xMxexp(M

)bxMbxexp(Mln)x(l

TJ

TJ

1212

1212

212

212

)xMxexp(

)bxMbxexp(ln

T

T

1

1

21

21

xMx

bxMbx1T

1T

Some algebra...

76

A trick...recast as a univariable problem:

2

2

2

2

1

1

21

21

21

xbxexp)xMxexp(

)bxMbxexp(

T

T

After lots of simple algebra applied to the r.h.s:

2

2

2 2bbxexp

Now, go back to matrix-vector notation:

0

1T1T

2bMbxMbexp

a scalar threshold

77

Take the natural log:

sxMb 1T ...a scalar for each pixel{ {

FilterKernel Pixel

0

1T1T ln

2bMbxMb

Threshold, T

{ >T for H1; <T for H0

78

xQQbxMb TTT 11

“The vector: QTx is a projection of the original spectraldata onto the eigenvectors of the covariance matrix, M,which corresponds to the principal axes of clutterdistribution.” Stocker et al., 1990.

79

“Further SCR gain is obtained by forming the optimumweighted combination of principal components usingthe weight vector:”

1QbT

From Stocker et al., 1990.

80

Today’s HSI algorithms can also benefit from1) spatial and spectral subsetting; 2) hierarchicalapplication of techniques; 3) other...

Its Important to Note That...

81

A Day at the Office with HSI and ENVI•Given:See/have thoroughly completed actions (most) on next 3 slidesChecklists (data and sensor)

•You’re given an HSI cube; the fun begins!•Open it/import it in ENVI•Look at the data; spectra, animation, interactive stretching, statistics•Apply a PCA and/or MNF; inspect results, link, mouse about•What are you to do with the data? Devise a strategy.•Gather ancillary information; build/acquire spectral library(ies)•Apply atmospheric compensation; this may be (is!) iterative•Look at the data; spectra, animation, interactive stretching, statistics•Apply algorithms: SAM, MF, SMA, other; this is iterative; link; mouse aboutIn-scene spectra, library spectra

•Apply fusion with ancillary data and information•Problem not solved? May have to resort to other techniques...•Build products/reports

82

• The entire remote sensing problem:• Problem analysis• Reason(s) for RS measurements• Planning (inc. costs/budget)• Tasking• Ground-truth• Logistics/persmissions/trespassing/etc...• Shipping to/from Field• Collection platform(s)• Ancillary data (e.g., DEM)• HSI data (now the fun begins!)• Archiving/Including metadata• Distribution

• A good RS report:• RS products

83

Properties of the Data Cube

• # of samples, lines, bands• Headers, preline, postline, footers, etc.• Data type• Interleaving• Byte order• Wavelengths, FWHM• Bad bands list• Band names (very optional)• The logical and physical data cube• History file (it doesn’t exist) – keep notes!

84

• What you need to know about your data; a check-list:• Date, time, location, ground elevation, platform elevation,

heading, GSD, be able to calculate where the sun is;i.e., all RS angles (geometry)

• On-going sensor characterization; know what it is; ask for it!• Spatial sampling; spatial resolution• Spectral sampling; SRF; spectral resolution• NESR, NEDr, NED, NEDT• Issues: smile, keystone, FPA misregistration, vibration,

parallax, scattered light, self-emission, platformmotion/imaging distortions, etc.

There’s More to Know...

85

Introduction to RadiativeTransfer Theory

86

Introduction to Radiative Transfer (RT) Theory

• The RT equation• Simplified expressions get you >90% of what

you need to know…• Radiometry and radiation propagation; this

discussion is largely from Schott (1997), ch. 4• Coordinates; frames of reference; principal plane, etc.

• Illumination angle, direction• View angle, direction• Phase angle• Azimuth, relative/absolute

87

The Geometry of Remote Sensing

http://rst.gsfc.nasa.gov/Front/tofc.html

88

The Radiative Transfer Equation

cos( , )

( , )( )

( , ) ( , , )' ' '

II

wI p d

4 4

Jw

p i T

( )( , , ) exp( cos ) ( , )

4 0

Eq. 7.21 on pg. 156 of Hapke (1993).

89

Some Simplified RT Expressions

Schott, J.R., (1997). Remote Sensing: The Image Chain Approach. Oxford University Press, New York, 394 p.

This discussion is largely taken from:

• RT can be (and in practice is) viewed as an accountingof terms based on radiance interactions in the RS scenario

• Bear in mind, however, that there is a link between theterms in the accounting and solutions to the RT equation

• The accountings can be as simple or as complicated asnecessary to address the RS question(s)/scenario(s)• i.e., add terms, delete/ignore terms

90

,LLm.sr.m/WL u2r2

s

u2davgbd

d1''

s LrLF1rFErcosE

u2d

d1''

ss LrErcosEL

For a horizontal surface:

u2T2d

d1''

ss LLrErcosEL

Now, add a thermal emission term:

Solar/Reflective RS:

91

uus2dbbsd

ddsT1''

s LLrLLF1rEEFLrcosEL

The “Big Equation”

FCHGEBDA LLLLLLLLL

92

FCHGEBDA LLLLLLLLL

2d

ds2T21''

srFELrcosEL

LA LD LB

uus2db2dbs2d

d LLrLF1rLF1rFE

LE LG LH LC LF

The “Big Equation” (continued)

There’s an LI, too; it’s the adjacency effect—and it’s sometimesincluded in the LC term.

93

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Massachusetts, 676 p. Jensen, J.R., (2007). Remote Sensing of the Environment: An Earth Resource

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Interscience, John Wiley and Sons, New Jersey, 508 p. Richards, J.A., and Jia, X., (1999). Remote Sensing Digital Image Analysis, An Introduction,

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Pr. Inc., 512 p. Schott, J.R., (1997). Remote Sensing: The Image Chain Approach. Oxford University Press,

New York, 394 p. Solé, J.G., Bausá, L.E., and Jaque, D., (2005). An Introduction to the Optical Spectroscopy of

Inorganic Solids. John Wiley & Sons, Ltd., 283 p.