1. Radiometric and Atmospheric Correction
Lecture 3
Prepared by R. Lathrop 10/99
With slide by Z. Miao
Revised 1/09

2. Where in the World?

3. RS Applications to Disaster Response: Haiti
Matterhorn by apanotous

5. Data-to-Information Conversion
Statement of problem
Signal (W m-2)
Dt (Time)
Julian day
Data collection
At-satellite radiance signal
Remote sensing process
Data-to-Information Conversion
Image presentation
Radiometric correction
Spectral or histogram enhancement (e.g., LUT stretch)
Signal (W m-2)
Dt (Time)
Julian day
As for remote sensing data processing, there are four major steps: Statement and definition of your problem; data collection; Data-to-information conversion which is one of the most important processes; and information presentation.
For data-to-information, we already studied image display and spectral enhancement (Lookup-stretch ) in last lecture and lab. Today we will go through radiometric and atmospheric correction of image.
Analog-to-DN conversion
DN (Brightness value)
255
# of pixels
# of pixels
DN (Brightness value)
255
etc.
Target surface reflectance signal

6. Learning objectives Remote sensing science concepts Math 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

7. 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
When the emitted or reflected electro-magnetic energy is observed by a sensor on board an aircraft or spacecraft, the observed energy does not coincide with energy emitted or reflected from the same object observed from a short distance. This is due to sun’s azimuth and elevation, atmospheric conditions (fog or aerosols), sensor’s response.

8. 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
As we know, remote sensor record in analog format or directly in digital number (with digital camera). For analogy sensor, we should converse analog signal to DN(i.e., brightness value).
Discrete sampled value
Radiance, L dt
Adapted from Lillesand & Kiefer

9. 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 sr-1 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
Here we want to clear three definitions: irradiance, radiance and reflectance. Irradiance is radiant flue incident on an object of interest. Radiance is radiant flux emitted or scattered by a unit area of surface. Unit of radiance and reflectance is w m-2 sr-1 um-1.
The difference between radiance and reflectance are that reflectance is part of incident radiant flux.
Solid angle: an angle formed by three or more planes intersecting at a common point.

10. For today’s lecture, we’ll use Landsat imagery for our examples
For more info, go to:

11. 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
We use a calibrated radiometric response function to convert radiance to DN. Of course, we are able to use inverse relationship to convert DN back to radiance.

12. 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
We use the linear to convert radiometric response function to DN or from DN to L.

13. Radiometric response function
Spectral Radiance to DN
DN to Spectral Radiance
255
Lmax
Slope = channel gain, G DN L
Slope =
(Lmax – Lmin) / 255
DN to spectral radiance: slope=(Lmax-Lmin)/255.
Lmin
Lmin L
Lmax DN
255
Bias = Y intercept

14. 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
Some sensor can change gain (slope of radiance to DN) values based on image brightness.

15. Radiometric response function Example: Landsat 5 Band 1
From sensor header, get Lmax & Lmin
Lmax = mW cm-2 sr-1 um-1
Lmin = mW cm-2 sr-1 um-1
L = (( )/255) DN
L = ( ) DN
If DN = 125,
L = ( ) 125
L =
L = mW cm-2 sr-1 um-1

16. 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)
Unit conversion: 1 W m-2 sr-1 µm-1 = 1000 mW/10000cm2 sr-1 µm-1= 0.1 mW cm-2 sr-1 µm-1
If DN = 125, L = ?
Landsat Science Data User’s Handbook
ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter1

17. DN-to-Radiance conversion Example: Landsat ETM
Band
Gain
Bias 1 2 3 4 5 6
Note that Landsat Header Record refers to gain and bias, but with different units (W m-2 sr-1 um-1)

18. 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 = W cm-2 sr-1 µm-1
Bias = W cm-2 sr-1 µm-1
L = ( ) DN
If DN = 125, L = W m-2 sr-1 µm-1
Same mW cm-2 sr-1 µm-1
Landsat Science Data User’s Handbook
ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11

19. Radiometric response function Example: Landsat 5 Thermal IR
Gain = mW cm-2 sr-1 um-1
Bias = mW cm-2 sr-1 um-1
L = ( ) DN
To convert to at-satellite temperature (o K):
T = / loge [(60.776/L) + 1]
Remember 0oC = 273.1K
For more details see Markham & Barker EOSAT Landsat Technical Notes v.1, pp.3-8.

20. Radiometric response function Example: Landsat 7 Thermal IR
For High Gain Band 6: MIN = 3.2; LMAX = 12.65
Gain = W m-2 sr-1 mm-1
Bias = 3.2W m-2 sr-1 mm-1
L = ( ) DN
To convert to at-satellite temperature (o K):
T = / loge [(666.09/L) + 1]
Remember 0oC = 273.1K
Next slides we will show the results.
For more details see Markham & Barker EOSAT Landsat Technical Notes v.1, pp.3-8.

21. 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

22. What’s the Temperature difference between plume and ambient bay?
L = ( ) DN
Plume DN = 133 L = 8.13
Bay DN = 118 L = 7.57
T (oC)= { / 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
Radiance signal of an object of interest on the ground should be higher than at-satellite signal.
For more details see.

23. 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 to , consult an astronomical handbook for the earth-sun distance for the imagery acquisition date

24. Solar zenith vs. elevation angle
At-satellite reflectance
Tangent plane
Ground reflectance
Zenith angle
Solar elevation angle = 90 - zenith angle
Zenith: the point on the celestial sphere that is directly above the observer.

25. Solar Zenith angle qo = 0 qo = 60 qo = solar zenith angle
qo = 0 cosqo = 1
As qo cosqo
zenith angle
Tangent line
Solar elevation angle = 90 - zenith angle =30
If zenith angle=60, solar elevation angle=30. Note that the sum of zenith and solar elevation angle is always equal to 90.
Note zenith angle is different from azimuth angle. N
Azimuth angle

26. At-Satellite Reflectance Example: Landsat 7 Band 1
If Acquisition Date = Dec. 1, 2001
At-Satellite Reflectance = ?

27. We can use the website to get altitude/azimuth table.

28. Table 11.4 Earth-Sun Distance in Astronomical Units
Julian Day
Distance 1
.9832 74
.9945
152
1.0140
227
1.0128
305
.9925 15
.9836 91
.9993
166
1.0158
242
1.0092
319
.9892 32
.9853
106
1.0033
182
1.0167
258
1.0057
335
.9860 46
.9878
121
1.0076
196
1.0165
274
1.0011
349
.9843 60
.9909
135
1.0109
213
1.0149
288
.9972
365
.9833
This is the earth-sun distance in Astronomical Unit.
Landsat Science Data User’s Handbook
ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11

29. Solar Spectral Exoatmospheric Irradiances(ESUN): 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 6
1368.0
Landsat Science Data User’s Handbook
ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_htmls/chapter11

30. At-Satellite Reflectance Example: Landsat 7 Band 1 The equation for converting radiance to reflectance: pl = (p Ll d2 ) / (ESUNl cosq)
Dec. 1,  Julian Day = 335
Earth-Sun d = 0.986
ESUNl =
Cosq = Cos(63.54) =
Ll = W m-2 sr-1 um-1
pl = ( * *0.9862)/(1969.0* )
pl = / = pl=surface target reflectance at a specific wavelength.
The equation may be used to convert radiance to reflectance.

31. Landsat Reflectance Conversion: ERDAS Imagine module
Erdas Imaging offers a tool to caclulate landsat reflectance conversion.

32. Atmospheric Correction

33. Path radiance and target radiance
Target Reflectance (BRDF)
Surround Reflectance
Multiple Scattering
Direct Solar Irradiance
Adjacency Effect
Sky Path Radiance (Single scattering)
Path Radiance
Path radiance is radiance imposed by atmosphere.

34. 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
Atmosphere composite, aerosol particule and water vapor affect radiation reflectance.

35. Atmospheric windows
Specific wavelengths where a majority of the EMR is absorbed by the atmosphere
Wavelength regions of little absorption known as atmospheric windows
Transmittance (%)
Some specific wavelength is of little absorption known as atmospheric windows. The atmospheric window lies approximately at wavelength of infrared radiation between 8 and 15 micrometers.
Graphic from

36. From Shaw, G. A. and H. K. Burke. Spectral Imaging for Remote Sensing

37. 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 um
Ref
Longer wavelengths is absorbed more by atmosphere. So at-satellite signal is decreased comparing ground signal. Short wavelength strongly scattered, at-satellite signal is increased. All of these interference are noise. We better remove it.
Adapted from Jensen, 1996, Introductory Digital Image Processing

38. 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
Atmospheric interference on reflectance is noise. So, we want signal-to-noise ratio as high as possible.
True Signal
Observed Signal
Noise +

39. 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 is designed for minimizing scattering and absorption effect due to atmosphere. Generally, shortwave band is increased by scattering, and longer wave band is reduced by absorption.

40. 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
Qu = 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

41. 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

42. 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.

43. 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).
For, histogram adjustment, we should select dark pixels, e.g., deep clear water or shadowed areas. Then the BV at dark pixels will be set to 0

44. 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
Another correction method is scene-to-scene normalization. As for scene-to-scene normalization, we should select one date as a baseline. Then select dark, medium and bright features that are relatively time-invariant and make regression for those features. We talk more detail in the lab class.

45. Scene-to-Scene Normalization Example: Landsat 5 vs Landsat 7 Landsat 7: Sept 01 Landsat 5: Sept 95

46. Scene-to-Scene Normalization Example: Landsat 5 vs Landsat 7 Landsat 5: Sept 95 Landsat 7: Sept 99 & 01
99 R2 = R2 = 0.968
99 R2 = 0.932
01 R2 = 0.963

47. Scene-to-scene normalization: work flow
NOTE: the selected features of the two images must correspondingly come from SAME locations.

48. Hyperspectral Image Cube
From Shaw, G.A. and H.K. Burke. Spectral Imaging for Remote Sensing.

49. 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 multi-spectral 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.
AVIRIS after
AVIRIS before

50. 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.

51. 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.

52. Terrain Shadowing USGS DEM Landsat ETM Dec 01
Since terrain shadow can affect target reflectance, we should do terrain shadow correction sometimes.
Solar elevation = 26.46
Sun Azimuth =

53. 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 (Qo) / cos(i) where Lc = slope-aspect corrected radiance Lo = original uncorrected radiance cos (Qo) = sun’s zenith angle cos(i) = sun’s incidence angle in relation to the normal on a pixel (i = Qo-slope)
By accounting for the seasonal position of the sun relative to the pixels’s position on the earth, we normalize sun position zenith.

54. Cosine Terrain correction
Sensor Qo
Sun
Lc = Lo cos (Qo) / cos(i) i
90o
Terrain: assumed to be a Lambertian surface
Adapted from Jensen

55. 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

56. 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.

57. Data-to-Information Conversion
Statement of problem
Signal (W m-2)
Dt (Time)
Julian day
Data collection
At-satellite radiance signal
Remote sensing process
Data-to-Information Conversion
Image presentation
Radiometric correction
Spectral or histogram enhancement (e.g., LUT stretch)
Signal (W m-2)
Dt (Time)
Julian day
As for remote sensing data processing, there are four major steps: Statement and definition of your problem; data collection; Data-to-information conversion which is one of the most important processes; and information presentation.
For data-to-information, we already studied image display and spectral enhancement (Lookup-stretch ) in last lecture and lab. Today we will go through radiometric and atmospheric correction of image.
Analog-to-DN conversion
DN (Brightness value)
255
# of pixels
# of pixels
DN (Brightness value)
255
etc.
Target surface reflectance signal

58. Homework Landsat TM Thermal IR calibration;
Reading Ch. 6; ERDAS Field Guide Ch. 5: