1. Electromagnetic Radiation Principles and Radiometric Correction
Geography KHU Jinmu Choi
Electromagnetic Radiation Model
Atmospheric Energy-Matter Interaction
Correcting RS System Detector Error
Atmospheric Correction
Correcting for Slope

2. Electromagnetic Radiation Principles and Radiometric Correction
Radiometric correction attempts to improve the accuracy of spectral reflectance, emittance, or back- scattered measurements obtained using a remote sensing system.
Geometric correction is concerned with placing the reflected, emitted, or back-scattered measurements or derivative products in their proper planimetric (map) location so they can be associated with other spatial information in a geographic information system (GIS) or spatial decision support system (SDSS).

3. How is Energy Transferred?
(source: Jensen, 2011)
Remote Sensing

4. Wave Model of Electromagnetic Radiation
In the 1860s, James Clerk Maxwell (1831–1879) conceptualized electromagnetic radiation (EMR) as an electromagnetic wave that travels through space at the speed of light, c, which is 3 x 108 meters per second (hereafter referred to as m s-1) or 186, miles s-1. A useful relation for quick calculations is that light travels about 1 ft. per nanosecond (10-9 s). The electromagnetic wave consists of two fluctuating fields — one electric and the other magnetic. The two vectors are at right angles (orthogonal) to one another, and both are perpendicular to the direction of travel.
(source: Jensen, 2011)

5. Radiometric Quantities
The relationship between the wavelength (l) and frequency (n) of electromagnetic radiation is based on the following formula, where c is the speed of light:
and
(source: Jensen, 2011)

6. How is Electromagnetic Radiation Created?
Electromagnetic radiation is generated whenever an electrical charge is accelerated. The wavelength (l) of the electromagnetic radiation depends upon the length of time that the charged particle is accelerated. Its frequency (n) depends on the number of accelerations per second. Wavelength is formally defined as the mean distance between maximums (or minimums) of a roughly periodic pattern and is normally measured in micrometers (mm) or nanometers (nm). Frequency is the number of wavelengths that pass a point per unit time. A wave that sends one crest by every second (completing one cycle) is said to have a frequency of one cycle per second, or one hertz, abbreviated 1 Hz.
(source: Jensen, 2011)

7. Sources of Electromagnetic Energy
(source: Jensen, 2011)
Thermonuclear fusion taking place on the surface of the Sun yields a continuous spectrum of electromagnetic energy. The 5770 – 6000 kelvin (K) temperature of this process produces a large amount of relatively short wavelength energy that travels through the vacuum of space at the speed of light.

8. Radiometric Quantities
All objects above absolute zero (–273°C or 0 K) emit electromagnetic energy, including water, soil, rock, vegetation, and the surface of the Sun. The Sun represents the initial source of most of the electromagnetic energy recorded by remote sensing systems (except RADAR, LIDAR, and SONAR). We may think of the Sun as a 5770 – K blackbody (a theoretical construct that absorbs and radiates energy at the maximum possible rate per unit area at each wavelength (l) for a given temperature). The total emitted radiation from a blackbody (Ml) measured in watts per m2 is proportional to the fourth power of its absolute temperature (T) measured in kelvin (K). This is known as the Stefan-Boltzmann law and is expressed as:
where s is the Stefan-Boltzmann constant, x 10-8 W m-2 K-4.
Solar and Heliospheric Observatory (SOHO)
Image of the Sun Obtained on September 14, 1999

9. Wein’s Displacement Law
In addition to computing the total amount of energy exiting a theoretical blackbody such as the Sun, we can determine its dominant wavelength (lmax) based on Wien’s displacement law:
where k is a constant equaling 2898 mm K, and T is the absolute temperature in kelvin. Therefore, as the Sun approximates a K blackbody, its dominant wavelength (lmax ) is 0.48 mm:

10. Blackbody Radiation Curves
(source: Jensen, 2011)
Blackbody radiation curves for several objects including the Sun and the Earth which approximate 6,000 K and 300 K blackbodies, respectively.

11. Electromagnetic Spectrum
The Sun: a spectrum of energy from gamma rays to radio waves that continually bathe the Earth in energy.
The visible portion of the spectrum measured using wavelength (mm or nm) or electron volts (eV)
(source: Jensen, 2011)

12. Atmospheric Refraction
Refraction in three nonturbulent atmospheric layers. The incident energy is bent from its normal trajectory as it travels from one atmospheric layer to another. Snell’s law can be used to predict how much bending will take place, based on a knowledge of the angle of incidence (q) and the index of refraction of each atmospheric level, n1, n2, n3.
(source: Jensen, 2011)

13. Refraction
The index of refraction (n) is a measure of the optical density of a substance. This index is the ratio of the speed of light in a vacuum, c, to the speed of light in a substance such as the atmosphere or water, cn:
Refraction can be described by Snell’s law, which states that for a given frequency of light (we must use frequency since, unlike wavelength, it does not change when the speed of light changes), the product of the index of refraction and the sine of the angle between the ray and a line normal to the interface is constant:

14. Atmospheric Layers and Constituents
Clear Sky-> Blue scatter: Blue sky
Pollution, dust -> Orange, Red: scatter blue , violet; beautiful Sunset, Sunrise
Subdivisions of the atmosphere and the types of molecules and aerosols found in each layer.
Cloud-> White: scatter all visible light well
Type of scattering is a function of:
the wavelength of the incident radiant energy,
the size of the gas molecule, dust particle, and/or water vapor droplet encountered.
(source: Jensen, 2011)

15. Rayleigh Scattering
The intensity of Rayleigh scattering varies inversely with the fourth power of the wavelength (-4).
The approximate amount of Rayleigh scattering in the atmosphere in optical wavelengths (0.4 – 0.7 mm) may be computed using the Rayleigh scattering cross-section (tm) algorithm:
where n = refractive index, N = number of air molecules per unit volume, and l = wavelength. The amount of scattering is inversely related to the fourth power of the radiation’s wavelength.
(source: Jensen, 2011)

16. Absorption
window
(source: Jensen, 2011)

17. Reflectance
(source: Jensen, 2011)

18. Terrain Energy-Matter Interactions
Total amount of radiant flux (F) measured in watts (W):
Hemispherical reflectance (rl)
Hemispherical transmittance (tl)
Hemispherical absorptance (al)
Percent reflectance :
(source: Jensen, 2011)
% Reflectance:
This quantity is used in remote sensing research to describe the general spectral reflectance characteristics of various phenomena.

19. Radiance
Radiance (L) is the radiant flux per unit solid angle leaving an extended source in a given direction per unit projected source area in that direction and is measured in watts per meter squared per steradian (W m-2 sr -1 ).
(source: Jensen, 2011)

20. Correcting Remote Sensing System Detector Error
Several of the more common remote sensing system–induced radiometric errors are:
random bad pixels (shot noise),
line-start/stop problems,
line or column drop-outs,
partial line or column drop-outs, and
line or column striping.
Shot Noise Removal
(source: Jensen, 2011)

21. Line or Column Drop-outs
It is difficult to restore the data without extensive human interaction on a line-by-line basis
Line-start Problems
Every line and pixel in the scene recorded by the maladjusted detector may require a bias (additive or subtractive) correction or a more severe gain (multiplicative) correction after histogram comparison.
N-line Striping

22. Types of Atmospheric Correction
Absolute atmospheric correction
- to turn the digital brightness values recorded by a RS system into scaled surface reflectance values
- with in situ atmospheric measurements
- Atmospheric correction based on radiative transfer modeling
Algorithm: ACORN, ATERM, FLAASH, ATCOR
Empirical Line Calibration
Relative atmospheric correction
- to normalize the intensities among the different bands or from multiple dates of imagery
- with multi bands to cancel out the atmospheric effects
- Single-image Normalization Using Histogram Adjustment
- Multiple-date Image Normalization Using Regression

23. Atmospheric Correction Based on Radiative Transfer Modeling
Radiative transfer-based atmospheric correction algorithms require that the user provide:
latitude and longitude of the remotely sensed image scene,
date and exact time of remote sensing data collection,
image acquisition altitude (e.g., 20 km AGL)
mean elevation of the scene (e.g., 200 m ASL),
an atmospheric model (e.g., mid-latitude summer, mid-latitude winter, tropical),
radiometrically calibrated image radiance data (i.e., data must be in the form W m2 mm-1 sr-1),
data about each specific band (i.e., its mean and full-width at half-maximum (FWHM), and
local atmospheric visibility at the time of remote sensing data collection (e.g., 10 km, obtained from a nearby airport if possible).

24. Atmospheric Correction Based on Radiative Transfer Modeling Algorithm
ACORN: Atmospheric CORrection Now
- used for hyperspectral image
ATERM: Atmospheric REMoval program
- water vapor
FLAASH: Fast Line of sight Atmospheric Analysis of Spectral Hypercubes
water vapor, oxygen, carbon dioxide, and so on.
ATCOR: Atmospheric CORrection program
Various terrain types.
ATCOR 2 for flat, ATCOR 3 for rugged for 3D

25. Empirical Line Calibration
Empirical line calibration (ELC) to force the remote sensing image data to match in situ spectral reflectance measurements (at approximately the same time and on the same date as the remote sensing overflight) Empirical line calibration is based on the equation:
where BVk is the digital output value for a pixel in band k, pl equals the scaled surface reflectance of the materials within the remote sensor IFOV at a specific wavelength (l), Ak is a multiplicative term affecting the BV, and Bk is an additive term. The multiplicative term is associated primarily with atmospheric transmittance and instrumental factors, and the additive term deals primarily with atmospheric path radiance and instrumental offset (i.e., dark current).

26. Radianceimage (e.g., Band 1)
Paired Relationship:
Bright
Target
Band 1
Fieldspectra 48 49
Band 2
One
Bright Target
Remote
measurement 47 48
Radiance 55 54
Band 3
Dark
Target 48 50 54 57 40 40
Remote Measurement m = 49 55 56 40 39
Fieldspectra= 55
m = 55
F = 59
Band 1
Band 2
Band 3 42 41
Wavelength, nm
= 41
F = 48
Band 1
Bright
Target 9 10
Band 2
One
Dark Target 10 11 5 4
Band 3
Dark
Target 12 10 6 5
Fieldspectra
Remote Measurement m = 11 4 6 4
Fieldspectra= 13
m = 5
F = 7 2 1
m = 3
F = 4
Radianceimage (e.g., Band 1)
(source: Jensen, 2011)

27. Cosine Correction for Terrain Slope
where:
LH = radiance observed for a horizontal
surface (i.e., slope-aspect corrected
remote sensor data).
LT = radiance observed over sloped terrain
(i.e., the raw remote sensor data)
q0 = sun’s zenith angle
i = sun’s incidence angle in relation to the normal on a pixel
(source: Jensen, 2011)

28. Next
Lab: Exercise: Radiometric Correction Using Empirical Line Calibration
Lecture: Geometric Correction of Remote Sensor Data
Source:
Jensen and Jensen, 2011, Introductory Digital Image Processing, 4th ed, Prentice Hall.