Image Restoration and Atmospheric Correction

Lecture 3

Prepared by R. Lathrop 10/99

Revised 2/04

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

Discrete sampled value

Continuous analog signal

Radiance, L

dt Adapted from Lillesand & Kiefer

Analog-to-digital conversion process

• Sampling rate - must be twice as high as the highest frequency in the signal if that highest frequency is to be resolved (Nyquist frequency)

• Example: if highest frequency = 4 cycles/sec then the sampling rate should be at least 8/sec

dt = 1secSweep across 4 line pairs in one second, need to take signal measurement on both line and spacing in between, thus 8 measures pr sec

Signal-to-Noise Ratio (SNR)• SNR measures the radiometric accuracy of

the data

• Want high SNR

• Over low reflectance targets (I.e. dark pixels such as clear water) the noise may swamp the actual signal

True Signal NoiseObserved

Signal

+

Noise Removal• Noise: extraneous unwanted signal response• Noise removal techniques to restore image to as

close an approximation of the original scene as possible

• Destriping: correct defective sensor• Line drop: average lines above and below• Bit errors: random pixel to pixel variations, average

neighborhood (e.g., 3x3) using a moving window (convolution kernel)

Radiometric correction

• Radiometric correction: to correct for varying factors such as scene illumination, atmospheric conditions, viewing geometry and instrument response

• Objective is to recover the “true” radiance and/or reflectance of the target of interest

Units of EMR measurement

• Irradiance - radiant flux incident on a receiving surface from all directions, 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 sr-1

• Reflectance - fraction of the incident flux that is reflected by a medium

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 saturatesLMIN = minimum recordable radiance

Radiometric response function

L

DN

DN

L

Lmin

Lmin

Lmax

Lmax

0

255

0 255

Slope = channel gain, G

Slope =

(Lmax – Lmin) / 255

Spectral Radiance to DN DN to Spectral Radiance

Bias = Y intercept

Radiometric response functionExample: 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 = 7.37839 mW cm-2 sr-1 um-1

Radiometric response functionExample: Landsat 7 Band 1

• Note that Landsat Header Record refers to gain and bias, but with different units (W m-2 sr-1 um-1)

• L = Bias + (Gain* DN)

If DN = 125, L = ?

Landsat Science Data User’s Handbookltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11

DN-to-Radiance conversionExample: Landsat ETM

Band Gain Bias

1 0.7756863 -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 functionExample: Landsat 7 Band 1

• Note that Landsat Header Record refers to gain and bias, but with different units (W m-2 sr-1 um-1)

• Gain = 0.7756863 mW cm-2 sr-1 um-1

• Bias = -6.1999969 mW cm-2 sr-1 um-1

• L = -6.1999969 + (0.7756863) DN

If DN = 125, L = 90.76079 W m-2 sr-1 um-1Same 9.076079 mW cm-2 sr-1 um-1

Landsat Science Data User’s Handbookltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11

Radiometric response functionExample: 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 = 273.1KFor more details see Markham & Barker. 1986. EOSAT Landsat Technical Notes v.1, pp.3-8.

At-Satellite ReflectanceTo 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, p = ( Ld2 ) /(ESUNcos)

Where

L= spectral radiance measured for the specific waveband

= 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

Solar Zenith angle

= solar zenith angle

coso = 1

As o coso

o = 0o = 60

Solar elevation angle = 90 - zenith 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

Distance

Julian Day

Distance

Julian Day

Distance

Julian Day

Distance

Julian Day

Distance

1 .9832 74 .9945 1521.014

0227

1.0128

305 .9925

15 .9836 91 .9993 1661.015

8242

1.0092

319 .9892

32 .9853 1061.003

3182

1.0167

2581.005

7335 .9860

46 .9878 1211.007

6196

1.0165

2741.001

1349 .9843

60 .9909 1351.010

9213

1.0149

288 .9972 365 .9833

Landsat Science Data User’s Handbookltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11

Solar Spectral Irradiances: Landsat ETM

Watts m-2 um-1

Band 1 1969.0

Band 2 1840.0

Band 3 1551.0

Band 4 1044.0

Band 5 225.70

Band 7 82.07

Band 8 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

p = ( L d2 ) / (ESUN cos) • Dec. 1, 2001 Julian Day = 335

• Earth-Sun d = 0.986

• ESUN = 1969.0

• CosCos(63.54) = 0.44558

• L90.76079 W m-2 sr-1 um-1• p = (3.14159*90.76079*0.9862)/(1969.0*0.44558)

• p = 277.20558/877.34702 = 0.31596

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

Satellite Received RadianceTotal radiance, Ls = path radiance Lp + target radiance Lt

Target radiance, Lt = 1/ RT (E0 deltaTo coso delta+ Ed)

Where R = average target reflectance

o = solar zenith angle

= nadir view angle

To = atmospheric transmittance at angle to zenith

E0 = spectral solar irradiance at top of atmosphere

Ed = diffuse sky irradiance (W m-2)

Delta band width, –

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.

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.

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 NormalizationExample: Landsat 5 vs Landsat 7

Landsat 5: Sept 95 Landsat 7: Sept 99 & 01

0

50

100

150

200

250

0 50 100 150 200

Sept 95 B5

Sep

t 99

-01

B5

sept99-B5

sept04-B5

0

50

100

150

200

250

0 20 40 60 80 100 120 140 160

Sept 95 B4

Sep

t 99

-01

B4

sept99-B4

sept01-B4

99 R2 = 0.971 01 R2 = 0.968

99 R2 = 0.93201 R2 = 0.963

Terrain ShadowingUSGS 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 = Oo - slope)

Cosine Terrain correction

Lc = Lo cos (o) / cos(i)

o

i

Terrain: assumed to be a Lambertian surface

Sun

Sensor

90o

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