GEOG4110/5100AdvancedRemoteSensing

Lecture2

DataQualityRadiometricDistortionRadiometricErrorCorrection

Relevantreading:Richards,sections2.1– 2.8;2.10.1– 2.10.3

DataQuality/Resolution

• Spatialè IFOVè GIFOV

• Spectralè l Range,Bandwidth,Dl

• Temporalè Dt

• Radiometricè SNR,DynamicRange

Resolution,PixelSize

Quality,Resolution

• IFOV:Theangularextentofthesensorindependentofthealtitude.

• GIFOV:Ameasureofthespatialresolutionofaremotesensingsystem,theprojectionoftheIFOVontotheground(pixelsize),altitudedep.

GIFOV(Nadir)=2*Altitude*tan(IFOV/2)

SpatialResolution

IFOV

GIFOV

Altitude

SignaltoNoiseRatio(SNR)

• Signalstrengthdependsonradiancefluxreflectedoremittedfromthesurface,pixelsize,altitude,spectralbandwidth.

• ratioofasignalpowertothenoisepowercorruptingthesignal.Aratiohigherthan1:1indicatesmoresignalthannoise.

• comparesthelevelofadesiredsignal(suchasmusic)tothelevelofbackgroundnoise.Thehighertheratio,thelessobtrusivethebackgroundnoiseis.

Signal-to-NoiseRatio

Time

L,R

SNR=Signal/RMSnoise

Noise=0.01è SNR=1001.0

0.1 Noise=0.01è SNR=10

0.01 Noise=0.01è SNR=1

e.g.Data=185197204205200220210190180199Mean=199RMS=~12SNR=~17

2

DynamicRangeBits:Eachdigitalvalueisrecordedasaseriesofbinarydigitsknownasbits.

BrightnessorIntensityLevel:Thenumberofdiscretelevelsfordescribingtheradiancelevelofapixel,scaledfromzerobrightnesstothehighestbrightnessthatwouldbeexpected.Themorediscretelevels(orbitsofinformation),themorepreciselytheradianceofthescenecanbemeasured.Wetypicallydealwith8-bitbrightnessmeasurementsor256levels,alsoreferredtoasdynamicrange.

DynamicRangedeterminesthenumberofdistinctcolorsorrepresentationsthatimagerycanberesolvedinto

PossibleCombinationswith:1bit: 0or1 =2or212bits: 0,0,0,11,01,1 =4or223bits: 0,0,00,0,10,1,0,0,1,1 =8or23

1,0,01,0,11,1,01,1,1

Nbits: =2N

GainandOffset(Bias)

GroundSceneBrightness(Input)

ImageBrightness(O

utpu

t)

IdealSensorResponse

ActualSensorResponse

Bias,Offset,DarkCurrent

ContributionstoInstrumentSignal

DistortionDistortion:achange,twist,orexaggerationthatmakessomethingappeardifferentfromthewayitreallyis.

• RadiometricDistortion:Errorsinpixelbrightnessvalues– Instrumentation– Wavelengthdependenceofsolarradiation– Effectofatmosphere

• GeometricDistortion:Errorsinimagegeometry,(location,dimensions,etc.)– Platformandinstrumentrelativemotions– Scananglesandscanpatterns– RotationoftheEarth– Attitudeandaltitudevariability

RadiometricDistortion

• Relativebrightnessdiffersfromwhatexistsontheground

• Relativebrightnessofasinglepixelfrombandtobandcanbedifferentfromthetruespectralreflectancecharacteristicsontheground

• Primarilyeffectfromatmosphere

• Irradiance:Theamountofenergyincidentonagivenareaofasurfaceinagivenamountoftime(W/m2).

• Radiance:Theamountofenergyscatteredinaparticulardirection(W/m2/sr).

• Solidangle:Theratiooftheareaofasphericalsurfacetothesquareoftheradius.

Ω=A/r2

Ω

BasicRadiometricTerms

A

r

• SpectralIrradiance:Theamountofenergyavailableacrosswavelengthrange(W/m2/µm).

• Hemisphericalreflectance:Theratiooftheradiantfluxfromasurfacetotheradiantfluxincidenttoit.

• Hemisphericaltransmittance:Theratiooftheradiantfluxtransmittedthroughasurfacetotheradiantfluxincidenttoit.

• Hemisphericalabsorptance:Theratiooftheradiantfluxabsorbedbyasurfacetotheradiantfluxincidenttoit.

BasicRadiometricTerms

EffectsoftheAtmosphere

AbsenceofanAtmosphereInAbsenceofanatmospheresurfaceirradiancebetweenwavelengthsis

Where:Eλ =solarspectralirradianceattheearth.θ =solarzenithangle.

Formostremotesensingdevicesthewavelengthsaresmallenoughthat:

Wm-2

Wm-2

AbsenceofanAtmosphere

• IfthesurfacehasareflectanceofR,theradiancereflectedbacktotheatmosphereis

• KnowingL,wecandeterminetheIrradianceattheSensorfromadigitalnumberC(e.g.0-255)

L = EΔλcosθ.ΔλRπ

L S=Ck + Lmin

Where: k=(Lmax – Lmin)/Cmax andLmax andLmin arethemaximumandminimummeasureableradiancesasindicatedbytheinstrumentmanufacturer

Wm-2sr-1

Wm-2sr-1

WiththeAtmosphere• Someirradianceisattenuatedbytheatmosphere(functionof

wavelength)asdefinedbyatmospherictransmissivity alonganangularpath(Tθ)

• Someirradianceisincidentuponthepixelfromthesky(ED)

Wm-2

€

EG = Tθ EΔλ cosθ Δλ[ ] + ED

WiththeAtmosphere• Totalradianceduetotheglobalirradianceofthepixelbecomes

• Abovetheatmosphere,wehavetoaddinscatteringfromotherpixelsintotheobservingpathalongthepathattheanglef betweenthepixelandthesensor,andscatteringfromtheatmosphereitself(Lp),andwehavetoremovewhatisattenuatedbytheatmosphereinthedirectionofthesensor (Tf)

Thesearethecomponentsoftheequationusedtorelatethedigitalnumbertomeasuredradiance

Wm-2sr-1

Wm-2sr-1

€

LT =RTφπ

Tθ EΔλ cosθ Δλ[ ] + ED{ } + Lp

€

EG = Tθ EΔλ cosθ Δλ[ ] + ED

WiththeAtmosphere• Someirradianceisattenuatedbytheatmosphere(functionof

wavelength)asdefinedbyatmospherictransmissivity alonganangularpath(Tθ)

• Someirradianceisincidentuponthepixelfromthesky(ED)

• Totalradianceduetotheglobalirradianceofthepixelbecomes

• Abovetheatmosphere,wehavetoaddinscatteringfromotherpixelsintotheobservingpathalongthepathattheanglef betweenthepixelandthesensor,andscatteringfromtheatmosphereitself(Lp)

€

EG = Tθ EΔλ cosθ Δλ[ ] + ED

€

LT =Rπ

Tθ EΔλ cosθ Δλ[ ] + ED{ }

€

LT =RTφπ

Tθ EΔλ cosθ Δλ[ ] + ED{ } + Lp

Thisiswhatshouldbepluggedintoequationatbottomofpreviouspage

CorrectingforAtmosphericEffects• Factorsthatinfluenceatmosphericdistortioneffects

– Humidity– Temperature– Pressure– Aerosols,clouds,particulatematter,etc.

• Thesecharacteristicsdetermineopticalthickness(t)oftheatmosphere

• Opticalthicknessandscatteringmechanism(mie,rayleigh andnon-selective)inturndeterminetheradianceavailabletoreachthesensor

• Correctionsaretypicallytheoreticallyderivedwithradiative transfermodels

€

II0

= e−τcosθ

€

Tθ = e−τcosθ

€

Tφ = e−τcosθf

BulkAtmosphericCorrection• Oftenitissufficienttoassume

therearepixelvaluesclosetozerointheimagery(e.g.water)

• Inthiscase,anybrightnessobservedwillbearesultofatmosphericcontributions(PrimarilyLP butalsoED)

• Histogramsofeachchannelwillshowanoffsetfromzeroasaresult• Wavelength dependent

• Subtracting thisoffsetfromtheentireimagewillremovethevastmajorityofatmosphericeffects

AbsorptionandAtmosphericWindows

AIRSmeasuresupwellingradiancesin2378spectralchannelscoveringtheIRspectralband,3.74to15.4µm.AsetoffourchannelsintheVisible/Near-IR(VIS)observeswavelengthsfrom0.4to1.0µmtoprovidecloudcoverandspatial-variabilitycharacterization.

StripinginImagery

SouthernMaruitania neartheSenegalborder,October10,1980,LANDSAT4Multi-SpectralScanner(MSS). Themajorityoftheland-coverconsistsofriparianvegetation,poorgrassland,andbarrenground

Band1 NDVI