1. Sensor Effects
Calibration: correction of observed data into physically meaningful data by using a reference.
DN  Radiance (sensor)  Radiance (surface)  Reflectance
Ground and on-board calibration…

3. Radiance = (gain x DN) + bias
Sensor Effects
Sensor calibration: electro-optical sensors are calibrated so that the radiance at the sensor can be derived from the output signal (voltage).
This correction is done by applying a set of linear equations to the raw image data.
Radiance = (gain x DN) + bias
The DNs of a raw image (e.g. ASTER Level 1A) are in unitless “counts”. The sensor calibration equations convert the counts to radiance units (W m-2 str-1).

5. Atmospheric Effects
Electromagnetic radiation from a source is modified on its way through the atmosphere to the target being illuminated.
Reflected/emitted radiation from a target is modified on its way through the atmosphere back to the sensor.

6. Atmospheric Effects

11. Atmospheric Attenuation
Reduction of electromagnetic radiation intensity through the atmosphere is extinction or attenuation. Includes scattering and absorption…
Scattering produces illumination (adds brightness) but reduces contrast.
Absorption decreases illumination and contrast.

12. Optical Thickness
Distance over which extinction reduces the intensity by a factor of 1/e.
Dependent on…
Aerosols – dust, smoke, etc.  Mie and nonselective scattering. Quite variable effect.
Molecules – CO2, H2O, etc.  Rayleigh scattering and absorption. Approximately constant effect spatially and temporally.
Wavelength of the radiation.

13. Atmospheric Attenuation
Ideally, radiant energy recorded by detectors is absolute function of only the radiant flux directly leaving the target under investigation…
…but other radiant energy can enter the IFOV from other paths (path radiance)…

16. Radiance Paths
Electromagnetic radiation (EMR) from illumination source that was attenuated very little before reaching target (direct path).
EMR scattered before reaching target.
EMR scattered/absorbed/re-emitted before illuminating target (different spectra/polarization than direct path).
EMR reflected/scattered by nearby surfaces into IFOV (non-illumination).
EMR reflected/scattered by nearby surfaces & atmosphere to illuminate target.

17. Atmospheric Attenuation
Total solar irradiance reaching surface:
Total irradiance reflected back by surface:
Not all that is reflected back makes it to the sensor. Some is lost and some is added (path radiance):

18. Atmospheric Transmittance
With no atmosphere, transmittance (Tq) of electromagnetic radiation is 100%. Scattering and absorption decrease it.
Tq depends on the optical thickness (t) and the angle of incidence (q):
Optical thickness (at a given l) is the sum of all the attenuating coefficients:

19. Atmospheric Attenuation
Diffuse-sky irradiance: (Ed) secondary illumination of the scene due to scattered irradiance from the atmosphere (sky light) or the ground (Paths 3 and 5).
Path radiance: (Lp) radiance that entered the IFOV of the sensor by scattering in the atmosphere.
Some never reached the surface (Path 2).
Some reflected from the surface but was (multiply) scattered (Path 4).
Attenuation is the sum of effects of transmittance, diffuse sky irradiance, path radiance, etc.

21. Atmospheric Correction
Ways to do it…
Ignore atmosphere if S/N great enough.
Using in situ ground truth
Measure ground targets in the field at the time the imagery is obtained. Compare the field measurements with the remote sensing. Not always practical.
Using a radiative transfer equation (absolute correction)
Quantitative models for the interaction of radiation with atmosphere, including aerosols and water vapor. Difficult to do. (Lab 3)
Other
Measure the target and the atmosphere simultaneously.
Multiple bands (relative correction).
Repeat look (relative correction).
Normalization functions (relative correction). (Lab 2)

22. Radiative Transfer Equations
Absolute atmospheric correction requires knowledge of atmospheric parameters, time of year, latitude, longitude, and altitude.
Radiative transfer: the process of transmission of electromagnetic radiation through the atmosphere (model atmosphere).
Multiplicative effects…
Additive effects…

23. Atmospheric Effects Multiplicative effects… Additive effects…
Solar illumination
Lighting effects (sun angle and topography)
Atmospheric transmittance
Sensor gain
Additive effects…
Path radiance
Sensor offset (bias)

26. Atmospheric Effects
Atmosphere adds a component of brightness to each cell in an image band (offset or bias). Effect diminishes with increasing wavelength.
Offset is not uniform across the image (atmosphere is not homogenous over large areas).
Inhomogeneity contributes a multiplicative effect to the DN of each pixel (gain).

27. Absolute Correction

28. Absolute Correction for Attenuation
Band averaged total irradiance at surface:
Total band-averaged radiance reflected back to sensor:
Total band-averaged radiance that makes it to sensor:

29. Absolute Correction for Attenuation
Brightness values in imagery can therefore be used to obtain radiance:
K is the sensor coefficient used to calibrate DNs to radiance at sensor.

30. Absolute Atmospheric Correction
This business can get quite sophisticated and include specific meteorologic data including aerosol content, humidity, barometric pressure, etc. and more complex radiative transfer equations e.g. ATREM.
Best is when those models are combined with ground truth field data.

32. Relative Correction of Attenuation
Can use to…
Normalize intensities among different bands
Normalize the intensities of bands in an image from one time to some standard
Done without explicit knowledge of atmospheric parameters or even a mathematical model of atmospheric interactions.

33. Single-Image Normalization
Uses histogram adjustment (bias shift) to remove effects of atmospheric scattering.
Infrared data (l > 0.7 mm) are free of most scattering.
Shorter wavelengths (visible) are scattered preferentially (Rayleigh scattering)  produces haze and reduces contrast of images.

34. Single-Image Normalization
Example: Landsat TM Band 7 is essentially free of scattering…
…intercept of linear plot of Band 7 vs. Band n should be 0. Scattering in Band n produces a shift of the intercept away from the origin (bias). Use bias to correct Band n DNs.

36. Single-Image Normalization
Example: Histogram of shadowed areas in an image should have some pixels with 0 DN…
…path radiance effects (scattering) instead produce an abrupt step in the histogram at DN > 0. Use location of step as bias to correct Band n DNs.

39. Multiple-Date Image Normalization
Uses linear regression of the DNs from two bands (images) to normalize scenes taken at different times.
Possible strategies:
Empirical – use spectrally constant target.
Deterministic – use a constant, near-zero reflectance target.

40. Empirical
Problem: Historical data are usually taken on non-anniversary dates with varying environmental conditions.
Objective: Normalize multiple data sets to a standard scene so variations are eliminated.
How: Choose pseudo-invariant ground targets present in each image for normalization…

41. Empirical
Apply regression equations that predict what a given DN would be if it had been acquired under the same conditions as the standard scene.
Equations developed based on the normalization targets.
Normalization targets assumed to be constant reflectors s.t. changes in their reflectance between images is due to atmospheric attenuation, etc.

43. Empirical
Coefficients (gain) and intercepts (bias) of linear regressions between normalization scene “A” and uncorrected scene “B”…
…used to compute normalized scene “B” with same spectral characteristics as “A”.

44. Empirical Target choice criteria
At mean elevation of rest of the scene
Minimal vegetation
Topographically flat and smooth
No pattern/structural changes

45. Deterministic: Dark Subtraction
Approach:
Obtain path radiance correction (bias) from a constant, near-zero reflectance target in the standard image (dark normalization target).
Calculate multiplicative term (gain or offset) from detector calibration, solar zenith angle, Earth-sun distance, etc.

46. Dark Subtraction

48. ENVI: Flat Field Correction
Single-image, deterministic normalization method.
Image DNs are normalized to an area in the image with known “flat” reflectance across all bands.
Normalization region of interest spectrum is divided into the spectrum of all other pixels.
Reduces data to “relative reflectance” which assumes atmospheric effects have been “cancelled out”.

49. ENVI: IAR Reflectance
Single-image, deterministic normalization method.
Internal Average Relative Reflectance
Consider all image pixels and calculate an “average spectrum” for the image.
Normalize (divide) the spectrum of all image pixels by the “average spectrum”.

50. field spectra = ( (gain) * (DN) ) + (bias)
ENVI: Empirical Line
Single-image, empirical normalization method.
Calibration technique that forces image pixel spectra to match field spectra/laboratory spectra/spectral library (assumes ground truth knowledge).
Linear regression for each band is used to equate image DN to reflectance:
field spectra = ( (gain) * (DN) ) + (bias)
If n field spectra selected, an n-dimensional regression is done for each band.

51. ENVI: Empirical Line Single-image, deterministic normalization method.
Calibration technique that can remove solar irradiance, atmospheric transmittance, instrument gain, topographic effects, albedo effects, etc.
Similar to IARR in that only image statistics are needed.
Uses the geometric mean calculated in both a spatial and spectral sense. Normalizes the image by both means.

52. Relative Atmospheric Corrections
Flat field conversion and Internal Average Reflectance only account for multiplicative effects (you are dividing spectra by a reference).
Used in studies focusing on mapping in the SWIR ( mm) where the additive effects of the atmosphere are minimal.
Spectral analysis of the VNIR needs to take into account additive effects due to path radiance
Empirical Line takes this into account (bias and gain).
Dark subtraction also takes this into account (subtract minimum spectra)

54. Illumination, Perspective, & Terrain Effects
Topographic attenuation: effects of slope, aspect, and illumination geometry also affect radiance  shadowing.
Very significant in terrain with lots of relief.
Need to remove topographically-induced illumination variation so two objects with same reflectance properties are equally bright regardless of topographic disposition...

55. Illumination
Defined as the cosine of the incident solar angle e.g. the proportion of direct solar radiation hitting a pixel (Lambertian assumption).
Dependent on the relative orientation of the pixel (slope and aspect) toward the sun.
Each topographic correction depends on the illumination parameter and requires a DEM (registered to the image and with the same pixel size)…

58. The Cosine Correction
Assume: Lambertian surface, constant Earth-Sun distance, constant solar illumination.
Correction:
Limitations: treats surface as a mirror; weakly illuminated areas may be overcorrected; assumes reflection is wavelength independent.

59. Minnaert Correction Correction:
k is the Minnaert constant which varies between 0 and 1. Lamertian surface has k = 1 (typical cosine correction).
k is computed empirically.

60. Minnaert Correction With optional terrain slope correction
Qn = terrain slope angle
With optional terrain slope correction

61. c Correction Adjustment to the cosine correction…
c is like the Minnaert constant and compensates for overcorrection of weakly illuminated pixels.
c is obtained from regression of LT = m cos(i) + b wherer c = b/m.

62. Statistical-Empirical Correction
Correlate expected illumination from the DEM with the actual DNs in the image.
Apply regression equation (m and b computed as before):

63. Topographic Corrections
Require a DEM of the same resolution as the image to be corrected
Lambertian surface assumption overcorrects (slopes away from the sun turn out to be brighter than sun facing ones).
Path irradiance often ignored (it shouldn’t be).
Geometry dependences of apparent reflectance need to be considered (anisotropy).
Wavelength dependences need to be considered (IR bands are severely affected by topography).
Severe shadowing is hard to get rid of no matter what.