RADIOMETRIC CORRECTION

 

Radiometric correction is the process of removing sensor and environmental errors from satellite images so that the measured brightness values (Digital Numbers or DNs) truly represent the Earth's surface reflectance or radiance.

In other words, it corrects for sensor defects, illumination differences, and atmospheric effects.

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1. Detector Response Calibration

Satellite sensors use multiple detectors to scan the Earth's surface. Sometimes, each detector responds slightly differently, causing distortions in the image. Calibration adjusts all detectors to respond uniformly.

This includes:

(a) De-Striping

• Problem: Sometimes images show light and dark vertical or horizontal stripes (banding).

  • Caused by one or more detectors drifting away from their normal calibration — they record higher or lower values than others.

  • Common in early Landsat MSS data.

• Effect: Every few lines (e.g., every 6th line) appear consistently brighter or darker.

• Solution (De-Striping):

  • Compare histograms of scan lines (e.g., 1,7,13 or 2,8,14) for mean and standard deviation.

  • Adjust the detector's response to match neighboring detectors.

  • Methods:

    • Histogram equalization and normalization

    • Fourier transformation (removes periodic striping patterns)

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(b) Missing Scan Line Removal

• Problem: Sometimes a detector stops working or becomes temporarily saturated, creating blank lines or missing data in the image.

• Solution:

  • Replace missing lines with estimated pixel values based on the lines above and below using interpolation techniques.

  • Example: Affected Landsat 7 ETM+ (Scan Line Corrector failure).

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(c) Random Noise Removal

• Problem: Some pixels show random bright or dark spots known as "salt-and-pepper noise" or "snowy noise."

  • Caused by random electronic interference or transmission errors.

• Solution:

  • Spatial filtering: Replace noisy pixels with average values from neighboring pixels.

  • Convolution filtering: Smooths image by using a moving filter (kernel) to reduce random pixel variation.

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(d) Vignetting Removal

• Problem: In images taken with lenses, the corners often appear darker than the center — this is vignetting.

• Cause: Uneven illumination across the sensor array or lens curvature.

• Solution:

  • Use sensor calibration data that describes how brightness varies from center to edges.

  • Apply Fourier Transform or other normalization methods to equalize brightness.

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2. Sun Angle and Topographic Correction

(a) Sun Angle Correction

• The sun's position changes with time of day and season, affecting image brightness.

• Higher solar angle (summer) → more direct sunlight → brighter image.

• Lower solar angle (winter) → less sunlight → darker image.

• Correction Method:

  • Adjust each pixel's brightness (DN) by dividing it with the sine of the solar elevation angle:
    [
    DN_{corrected} = \frac{DN_{original}}{\sin(\text{solar elevation angle})}
    ]

  • Solar elevation data is given in the image metadata or header file.

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(b) Topographic Correction

• Problem: In hilly or mountainous areas, slopes facing the sun appear brighter, while those facing away appear darker due to uneven solar illumination.

• Cause:

  • Slope and aspect of terrain

  • Shadowing effects

  • Bidirectional Reflectance Distribution Function (BRDF) differences

• Solution: Adjust radiance based on slope orientation and sun angle using models such as:

  Minnaert Correction:
  [
  L_n = L \cdot (\cos e)^{k-1} \cdot \cos i
  ]
  Where:

  • (L_n): normalized radiance

  • (L): measured radiance

  • (e): slope angle (from DEM)

  • (i): solar incidence angle

  • (k): Minnaert constant (depends on land cover and illumination conditions)

  This correction helps produce uniform brightness across slopes.

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3. Atmospheric Correction

• Problem: Before reaching the sensor, sunlight interacts with the atmosphere, where gases, dust, and water vapor scatter and absorb radiation.

  • Causes haze, color distortion, and lower contrast in the image.

• Goal: Remove the effects of atmosphere to obtain true surface reflectance.

• Methods:

  • Dark Object Subtraction (DOS): Assumes that dark pixels (like water) should have near-zero reflectance; subtracts atmospheric haze values.

  • Radiative Transfer Models: e.g., 6S, MODTRAN, FLAASH, or QUAC to simulate atmospheric scattering and absorption effects accurately.

Type of Correction	Problem Fixed	Example of Error	Common Methods
Detector Calibration	Uneven sensor response	Striping, noise	Histogram matching, Fourier transform
Missing Line	Lost data lines	Landsat 7 SLC failure	Interpolation
Random Noise	Salt-and-pepper noise	Bright/dark spots	Spatial/convolution filtering
Vignetting	Dark corners	Lens-based images	Fourier normalization
Sun Angle	Seasonal/diurnal illumination	Winter images darker	Divide by sin(solar angle)
Topographic	Slope illumination difference	Bright/dark slopes	Minnaert correction
Atmospheric	Scattering, absorption	Hazy images	DOS, FLAASH, MODTRAN