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The radiometric domain: facts without (too many) formulae

 
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PostPosted: 10/25/2014, 05:29 pm    Post subject: The radiometric domain: facts without (too many) formulae Reply with quote

Electromagnetic Radiation


In all known matter the constituent molecular and/or atomic structure is in an energy state of vibration or “excitement”. These phenomena cause the release of energy. Some of this energy is released when individual electrons drop to lower energy levels around their nuclei, emitting a small packet or quantum of energy (N.B.  To retain its original energy level the atom would need to absorb exactly the same quantum: emission and absorption therefore being complementary).  
  
 
 
However the main source of energy emission is thermal , or kinetic, agitation.  The level of this internal kinetic energy (Kinetic meaning “derived from motion”) is manifest as the temperature of the matter and is proportional to it.      
 
 
 
 
 
An object having no internal kinetic energy would therefore also have zero temperature.  This level cannot be achieved in reality, but by extrapolation it is at around -273 degrees centigrade (°C) or Zero degrees Kelvin (°K).    
 
 
 
 
 
At any temperature above 0 °K all matter in the known universe emits or “radiates” energy. This energy is known as Electromagnetic Radiation (EMR) and the measurement of it is termed Radiometry.  
 
 
 
 
 
 
 
 
Some features of EMR 
 
 
 
EMR travels across a vacuum at the velocity of light which is around 300,000 Kilometers (or 186,000 miles) a second.  
 
 
 
 
 
It can be thought of in two ways, either as a waveform or as a stream of particles of energy (known as quanta or photons). We use both concepts in Imagery Analysis and Remote Sensing applications.   
 
 
 
 
 
In dealing with EMR as a waveform some basic relationships become evident.













Fig1. Electromagnetic Waveform






Note that: 


a.    There are two waveforms (Electric and magnetic) in synchrony but at 90 degrees to each other.   
b.    The velocity of light “c” (on the “distance” axis above) is fixed and determined as around 300,000 km/s .This is often alternatively expressed as 3X108m/s.   
 
 
c.    The wavelength “λ” (lambda) covers a complete cycle of the wave, i.e. from peak to through peak.    
 
 
d.    The frequency v (nu) is the number of wave cycles passing a given point in time (usually 1 second).



Thus as the wavelength gets longer, so the frequency gets lower and vice versa,  since when multiplied together they must come to the fixed velocity constant “c”.  
 
 
 
 
 
In other words, when treating EMR as a waveform:  
 
 
 
 
 
Velocity(v) x wavelength (λ) is a constant value, this being  the velocity of light (c)   
 
 
 
Vλ= c   
 
 
 
One consequence of this relationship is that there is continuous family of wavelengths and frequencies all adding up to “c”. We categorize these in rough groups according to wavelength along what is termed the electromagnetic spectrum.  
 
 
 
Common measurements for wavelength include Millimeters (mm= 1/1000m), Microns (μm = 1/1000mm) and Nanometers (1nm =1/1000μm) 


 
 
 
 
 
 
  
 Fig. 2 EM Spectrum 
 
 
 
 
 
It will be seen that the radiation spectrum is, fairly arbitrarily, divided into several sections, typically seven or eight.  
 
 
 
For example NASA typically uses gamma-ray Radiation, X-Rays, Ultraviolet, Visible, Infrared, microwave and radio.  
 
 
 
The portion of the spectrum visible to the human eye is small, ranging only from about 400nm to 700nm. Within this “blue” is very approximately from 400-500nm, “green” 500-600nm and “red” from 600 to around 700nm.


Going on from red the spectrum goes in to the infrared (IR) and this is typically sub-divided in to three categories: near IR (from 0.7 to 1.3μm), mid IR (from 1.3 to 3μm) and thermal IR (beyond 3μm).


N.B. within the IR bands only thermal IR energy is directly related to the sensation of “heat”. Near IR and mid IR energy is not.  
 
 
 
 
 
Adjoining the Blue end of the visible spectrum, the Ultraviolet is also invisible to us (but not to bees incidentally), however our bodies can react to overexposure to UV in the form of sunburn.   
 
 
 
 
 
Radiometry is often defined as the measurement of optical radiation, which is electromagnetic radiation within wavelengths between 0.01 and 1000 micrometers (μm), and includes the ultraviolet, the visible and the near infrared. Alternatively sometimes it is used to embrace the entire Solar Spectrum i.e. that put out by our nearest star and this range goes from X-Rays right through to radio waves.  
 
 
 
 
 
Photometry, on the other hand, is restricted to the measurement of light which is defined as EMR as detected by the human eye and thus restricted to the wavelength range from about 400 to 700 nanometers.  Also photometry, being based upon the non-linear spectral stimulus response (identified qualitatively by the human visual system in psychophysical experiments) invokes a few different concepts and definitions to radiometry, but to which it can still be mathematically related. 
 
 
  
 
 
 
 
 
Reflection, Refraction, Absorption etc.  
 
 
 
 
 
When rays of EMR encounter a physical interface (e.g. a solid object), one or, more normally, a combination of several, phenomena will occur.  
 
 
 
 
 
a.    The waves can pass through the object (Transmission)  
 
 
b.    The waves can bounce back off the object as in a mirror  (Reflection)  
 
 
c.    The waves can bounce off the object in different directions (Scattering)  
 
 
d.    The waves can dissipate within the object (Absorption)  
 
 
e.    The waves  can alter the angle of their path through the object (Refraction) 
  
 
 
 
  
 
 
 
 
 
 

 
  
 
 
 
 
 

 Fig. 3 EMR interaction with materials. 
 
 
 
 
 
The coefficient of transmission varies with wavelength from 0-1 and is usually considered along with that of absorption for the same wavelength and thus may not usually be 1 since, for transparency, both coefficients have to sum to 1, the object thus having a degree of transparency. 
 
 
 
 
 
With reflection some or all of the EMR bounces back off of the encountered surface in a manner dictated basically by that surface’s roughness in comparison to the wavelength(s) of the incident EMR.  With a comparatively smooth surface this is termed specular reflection (from speculum, a type of mirror) in this case the incident and reflected angles of the EMR at the surface are the same. Polished surfaces, such as with many metals and alloys, show this characteristic. The coefficient of reflection for a specific wavelength is also in the range 0-1 inclusive.  
 
 
 
 
 
If the surface is rough compared to the incoming EMR then it may bounce off and around the surface as it is scattered. Rough surfaces such as oxidized metals and tarmac may exhibit this non-specular reflecting. In addition small particles in the atmosphere scatter EMR in various ways according to their size. Raleigh (when the particles are small compared to the incoming EMR wavelengths) and Mie (when the particles size approximates the EMR wavelengths) are examples. Blue skies during the day are due to Raleigh scattering the blue wavelengths around and Red sunsets are due to Mie scattering filtering out the shorter wavelengths, thus leaving the longer Red to predominate to the ground observer.   
 
 
 
 
 
If the EMR velocity slows (or speeds up) across the interface then bending or refraction occurs. This bending is for any angle of incidence wavelength variable. Hence the opening up of the visible spectrum “rainbow” in a glass prism.  
 
 
 
 
 
A surface’s Albedo is another term for its reflection coefficient, derived from Latin albedo "whiteness" (or reflected sunlight) in turn from albus "white," and is the diffuse reflectivity or reflecting power of a surface. It is the ratio of reflected EMR from a surface to that of the incident radiation upon it. Surfaces such as snow have a high albedo, whilst loose damp earth tends to have a much lower level due to the high percentage of EMR absorption in the latter. Note that albedo can vary considerably with the wavelength of incident EMR.  
 
 
 
 
 
The concepts of reflection, transmittance and absorption of EMR come together when ideal surfaces in thermodynamic equilibrium with their environment are considered.  The theoretical ideal surface that fully absorbs all received EMR and emits maximum EMR along all wavelengths is termed a blackbody.  
 
 
 
  
 
 
 
 
 
Black-body Radiation  
 
 
 
 
 
There are three important laws of physics which describe the characteristics of EMR generated by any body above absolute zero.  
 
 
 
 
 
Firstly the Stefan Boltzmann Law describes the total amount of EMR emitted for a body at a stated temperature. Basically this determines that the total EMR emittance (M) goes up enormously as temperature increases, by the Stefan Boltzmann constant (σ) multiplied by the fourth power of the absolute temperature (T)  
 
 
 
 
 
M = σT4  
 
 
 
 
 
This dramatic variation in EMR across the spectrum is very useful, for example in thermal imaging applications where very minute differences in surface temperature of ambient everyday objects can be identified.  
 
 
 
 
 
Next, Wein’s Displacement Law determines the temperature (T) in deg K at which the maximum EMR wavelength (λm) is emitted. 
 
 
 
λm  = A/T  
 
 
 
 
 
“A” is a constant (2898μm K)   
 
 
 
 
 
In word this means that as the temperature increases, the wavelength at which EMR is at a maximum decreases. 

Next Plank's Formula, which is a quite intimidating construction, wraps up how much EMR emittance occurs at each wavelength for a body of known temperature. The formula provides a model for the behavior of an idealized material that emits in a perfect fashion at all wavelengths. This is a blackbody.  
 
 
 
 
 
The Planck formulation is best considered by a visualization of the amount of EMR produced with respect to wavelength.
 
 
 
 
 
 
 
 
 
   
Fig. 4 Spectral profile of blackbody radiance versus absolute temperature. 
 
 
  
 
 
The Sun can be considered to be a blackbody with a surface temperature of around 6000 deg K .Referring to Fig 4 above, it can be seen that this equates to a maximum emission wavelength of around .5 microns (μm) or 500nm. This approximates to the maximum sensitivity of the human visual system. The Sun being by far the biggest source of EMR reaching the Earth it is consequential that the human being has well adapted to “seeing” solar radiation.  
 
 
 
 
 
It can also be seen in Fig. 4 that the surface temperature of the Earth (around 300 deg K or 27deg C) would, if it was a black-body, radiate EMR at this ambient temperature at around a wavelength of 9.6μm. In reality, this is not the case and there is a slight shift, nevertheless this maximum emission takes place at wavelengths far beyond those perceivable by the human eye.  
 
 
 
 
 
In reality natural bodies are considered as gray-bodies. Unlike theoretical blackbodies, graybodies do not absorb all received radiation but reflect or transmit a part of it. Likewise a gray-body does not emit as much EMR as a black-body at the same temperature. When in thermodynamic (kinetic) equilibrium with its environment, its emissivity is in balance with its absorption, this being dependent on its temperature.  It will be noted that this partial reflectivity of solar radiation is what allows us to see objects and colors.  
 
 
 
 
 
A relationship can now be deduced, the Radiation budget. Since that part of radiation which is not absorbed must be reflected or transmitted. For a given wavelength: 
 
 
 
 
 
The coefficients of absorption + reflection + transmission = 1  
 
 
 
 
 
Each of these individual coefficients are between 0 and 1 inclusive.  
 
 
 
 
 
So: for a blackbody, both reflection and transmission (by definition) are 0, so absorption = 1 (all)  
 
 
 
 
 
For an opaque body, transmission = 0, so reflection and absorption sum to 1.  
 
 
 
 
 
For a transparent body, reflection = 0, so absorption and transmission sum to 1.  
 
 
 
 
 
Some real world examples:  
 
 
 
 
 
An apparent “red” balloon is at ambient temperature (i.e. on a typical day on Earth). Therefore its specific natural EMR according to Fig 4 above, is in the IR range and not visible to us. It looks “red” because it reflects the visible red waves that it receives from the Sun and partially or fully absorbs the shorter (blue) visible wavelengths.  
 
 
 
 
 
A “white” balloon reflects visible EMR across the visible spectrum from” red” to “blue”.  
 
 
 
 
 
In contrast, a black balloon absorbs all wavelengths of visible EMR and thus we see it in contrast to other neighboring graybodies. (Black is the absence of color)  
 
 
 
 
 
Hence the justification of the term tending to “Blackbody” i.e. total absorption, no reflection.  
 
 
 
 
 
  
 
 
 
 
 
Radiometric resolution  
 
 
 
 
 
IPACO software works upon imagery that is input in computer digital format.  
 
 
 
 
 
Such an image is composed of a matrix of rows and columns of pixels (picture elements). Each pixel has a brightness value determined by the EMR recorded at that point in the image. 
  
 
 
 
 

  
 
 


Radiometric resolution determines how finely such an image can represent or distinguish differences of EMR intensity, and is usually expressed as a number of levels or a number of bits, for example 8 bits or 256 levels (0-255) that is typical of computer image files. The higher the radiometric resolution, the better subtle differences of intensity can be represented, at least in theory. In practice, the effective radiometric resolution is typically limited by the noise level, rather than by the number of bits of representation.  
 
 
 
 
 
 
 
References



Rather than provide references from text books that will not be easily accessible to the reader it is recommended that the text in bold highlighted above be used in internet searching.  
 
 
 
 
 
For example “googling” Radiometry brings up several excellent references including this one: 
 
 
 
 
 
http://fp.optics.arizona.edu/Palmer/rpfaq/rpfaq.htm


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