Radiometry

Radiomentry is the science of measuring light in any portion of the electromagnetic spectrum. In practice, the term is usually limited to the measurement of infrared, visible, and ultraviolet light using optical instruments.

There are two aspects of radiometry - theory and practice. The practice involves the scientific instruments and materials used in measuring light, including radiation thermocouples, bolometers, photodiodes, photosensitive dyes and emulsions, vacuum phototubes, charge-coupled devices, and a plethora of others. What we are interested in, however, is the theory.

Radiometric theory is such a simple topic that most texts on physics and optics discuss it in a few paragraphs. Unfortunately, they rarely discuss the topic in enough detail to be useful. Shorn of convoluted mathematics and obtuse definitions, radiometric theory is simple and easily understood.

Radiant Energy

Light is radiant energy. Electromagnetic radiation (which can be considered both a wave and a particle, depending on how you measure it) transports energy through space. When light is absorbed by a physical object, its energy is converted into some other form. A microwave oven, for example, heats a glass of water when its microwave radiation is absorbed by the water molecules. The radiant energy of the microwaves is converted into thermal energy (heat).

Similarly, visible light causes an electric current to flow in a photographic light meter when its radiant energy is transferred to the electrons as kinetic energy.

Radiant energy (denoted as Q) is measured in joules.

Spectral Radiant Energy

A broadband source such as the Sun emits electromagnetic radiation throughout most of the electromagnetic spectrum, from radio waves to gamma rays. However, most of its radiant energyis concentrated within the visible portion of the spectrum. A single-wavelength laser, on the other hand, is a monochromatic source; all of its radiant energy is emitted at one specific wavelength.

From this, we can define spectral radiant energy, which is the amount of radiant energy per unit wavelength interval at wavelength λ. Spectral radiant energy is measured in joules per nanometer.

Radiant Flux (Radiant Power)

Energy per unit time is power, which we measure in joules per second, or watts. A laser beam, for example, has so many milliwatts or watts of radiant power. Light “flows” through space, and so radiant power is more commonly referred to as the “time rate of flow of radiant energy,” or radiant flux.

In terms of a photographic light meter measuring visible light, the instantaneous magnitude of the electric current is directly proportional to the radiant flux. The total amount of current measured over a period of time is directly proportional to the radiant energy absorbed by the light meter during that time. This is how a hotographic flash meter works -- it measures the total amount of radiant energy received from a camera flash.

The flow of light through space is often represented by geometrical rays of light such as those used in computer graphics ray tracing. They can be thought of as infinitesimally thin lines drawn through space that indicate the direction of flow of radiant energy (light). They are also mathematical abstractions -- even the thinnest laser beam has a finite cross section. Nevertheless, they provide a useful aid to understanding radiometric theory. Radiant flux is measured in watts.

Spectral Radiant Flux (Spectral Radiant Power)

Spectral radiant flux is radiant flux per unit wavelength interval at wavelength λ. It is measured in watts per nanometer.

Radiometers

 The spectro-radiometer is used to analyse all the details of an electromagnetic spectrum. This instrument can analyse all of the frequencies of the spectrum. Other instruments measure the intensity of radiation in just a few frequency ‘windows’.

These instruments normally work by means of a sensitive element or detector that modulates the current passing through it in line with the electromagnetic energy that it receives. Different types of detector are used for the different wavelengths. Each machine is usually equipped with a single detector and thus takes readings on a certain wavelength interval. The result is a graph of the type shown before.

Several sensitive elements can be placed side by side to create a matrix of sensors. Each individual sensor acts like a spectro-radiometer, but if the (numerical) readings of each sensor are considered to be so many numerical values associate with a pixel in an image, the result is an imaging spectro-radiometer. For example, a spectro-radiometer composed of cells that are sensitive to thermal infrared waves will record higher values in hotter areas. If the pixel coding convention is ‘0 = black, 255 = white’, these hot spots will correspond to the palest areas in the image.

 

 Radiometric adjustments

 An ideal Earth observation system should be equipped with a perfect spectro-radiometer that can measure accurately and uniformly the amount of energy that is reflected by objects located on the Earth’s surface.

Unfortunately, the sunlight that illuminates objects is perturbed by its passage through the atmosphere and does not hit all objects at the same angle.

What is more, the light that is reflected by the objects must also cross the atmosphere before being analysed by the satellite’s sensors, and this journey also perturbs the signal. These perturbations are due to the presence of gases and dust that can absorb and/or reflect specific wavelengths, thereby changing the radiation’s spectral properties. What is more, the electronic processing of the rays that reach the sensors is also accompanied by some perturbations. Consequently, it is actually rather difficult to get accurate radiometric values from the data recorded by Earth-observing satellites.

Now, it is sometimes very useful to be able to calibrate these data precisely, for example to compare the data recorded by different satellites or recorded by the same satellite at different times, and several solutions do exist to try to overcome these flaws. Some of them are based on complex mathematical models that describe the main interactions involved. These models are effective.

However, to apply them the values of certain parameters (i.e. the atmospheric composition) when and where the pictures are taken must be known, and this is seldom possible.

Other radiometric correction methods are based on the observation of reference targets whose radiometry is known. The surfaces of bodies of water, glacial ice caps, and expanses of desert sand are often used, but here too you can understand that actually making the corrections often is not that easy. In fact, the overwhelming majority of remote sensing research uses radiometrically uncorrected data.

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