Electromagnetic Spectrum: The Photon and Radiometric Quantities¶
Contents
The concepts of the electromagnetic spectrum and the role of the photon in transmitting energy are introduced; the variations in sine wave form in terms of frequency, and the basic equations relating EM energy to frequency are covered. Some commonly used radiometric terms and quantities are defined and cursorily explained. The technique of expressing powers of ten is explained in the footnote at the bottom of this page.
Electromagnetic Spectrum: The Photon and Radiometric Quantities¶
Hereafter in this Introduction and in the Sections that follow, we limit the discussion and scenes examined to remote sensing products obtained exclusively by measurements within the electromagnetic spectrum. Our emphasis is on pictures (photos) and images (either TV-like displays on screens or “photos” made from data initially acquired as electronic signals, rather than recorded directly on film). We concentrate mainly on images produced by sensors operating in the visible and near-IR segments of the electromagnetic spectrum (see the spectrum on the following page), but also inspect a fair number of images obtained by radar and thermal sensors. We begin with a survey of some fundamentals of the physics of remote sensing.
Synoptic Statement: The underlying basis for most remote sensing methods and systems is simply that of measuring the varying energy levels of a single entity, the fundamental unit in the electromagnetic (which may be abbreviated “EM”) force field known as the photon. As you will see later on this page, variations in photon energies (expressed in Joules or ergs) are tied to the parameter wavelength or its inverse, frequency. EM radiation that varies from high to low energy levels comprises the electromagnetic spectrum. Radiation from specific parts of the EM spectrum contain photons of different wavelengths whose energy levels fall within a discrete range of values. When any target material is excited by internal processes or by interaction with incoming EM radiation, it will emit photons of varying wavelengths whose radiometric quantities differ at different wavelengths in a way diagnostic of the material. Photon energy received at detectors is commonly stated in power units such as Watts per square meter per wavelength unit. The plot of variation of power with wavelength gives rise to a specific pattern or curve that is the spectral signature for the substance or feature being sensed.
Now, in more detail: The photon is the physical form of a quantum, the basic particle studied in quantum mechanics (which deals with the physics of the very small, at atomic and subatomic levels). It is also described as the messenger particle for EM force or as the smallest bundle of light. This subatomic massless particle comprises radiation emitted by matter when it is excited thermally, or by nuclear processes (fusion, fission), or by bombardment with other radiation. It also can become involved as reflected or absorbed radiation. Photons move at the speed of light: 299,792.46 km/sec (commonly rounded off to 300,000 km/sec or ~186,000 miles/sec). These particles also move as waves and hence, have a “dual” nature. These waves follow a pattern that we described in terms of a sine (trigonometric) function, as shown in two dimensions in the figure below.
The distance between two adjacent peaks on a wave is its wavelength. The total number of peaks that pass by a reference in a second is that wave’s frequency (in cycles per second and hertz).
A photon travels as an EM wave having two components, oscillating as sine waves mutually at right angles, one consisting of the varying electric field, the other the varying magnetic field. Both have the same amplitudes (strengths) which reach their maxima-minima at the same time. Unlike other wave types which require a carrier (e.g., water waves), photon waves can transmit through a vacuum (such as in space). When photons pass from one medium to another, e.g., air to glass, their wave pathways are bent (follow new directions) and thus experience refraction.
A photon is said to be quantized, in that any given one possesses a certain quantity of energy. Some other photon can have a different energy value. Photons as quanta thus show a wide range of discrete energies. The amount of energy characterizing a photon is determined using Planck’s general equation:
where v has some discrete value determined by (v2 - v1). In other words, a particular energy change is characterized by producing emitted radiation (photons) at a specific frequency v and a corresponding wavelength at a value dependent on the magnitude of the change.λ.
` <>`__I-4 ** Is there something wrong with the equation just above? **ANSWER**
Wavelength is the inverse of frequency (higher frequencies associate with shorter wavelengths; lower with longer), as given by the relationship:
where c is the constant that expresses the speed of light, so that we can also write the Planck equation as
` <>`__I-5 Come up with a very simple mnemonic phrase (one that helps your memory) for associating the energy level (amount of energy) with wavelength. `ANSWER <answer.html#I-5>`__
` <>`__I-6: Calculate the wavelength of a quantum of radiation whose photon energy is 2.10 x 10:sup:`-19` Joules; use 3 x 10:sup:`8` m/sec as the speed of light c. `ANSWER <answer.html#I-6>`__
` <>`__I-7: ** A radio station broadcasts at 120 MHz (megahertz or a million cycles/sec); what is the corresponding frequency in meters (hint: convert MHz to units of Hertz). `ANSWER <answer.html>`__
The distribution of all photon energies over the range of observed frequencies is embodied in the term spectrum (a concept developed on the next page). A photon with some specific energy level occupies a position somewhere within this range, i.e., lies at some specific point in the spectrum
There is much more to the above than the brief summary given. Consult a physics text for more information. Or, for those with some physics background, read the Chapter on The Nature of Electromagnetic Radiation in the Manual of Remote Sensing, 2nd Ed., published by the American Society of Photogrammetry and Remote Sensing (ASPRS). From that chapter the writer has extracted the following useful information that explains some of the terminology and the concepts they represent as used by specialists in the remote sensing field:
Radiant energy (Q), transferred as photons, is said to emanate in short bursts (wave train) from a source in an excited state. This stream of photons moves along lines of flow (also called rays) as a flux (φ) which is defined as the time rate at which the energy Q passes a spatial reference (in calculus terms: dQ/dt). The units are either joules (or ergs) per second (1 J/sec = 1 Watt). The flux concept is related to power, defined as the time rate of doing work or expending energy. The nature of the work can be one, or a combination, of these: changes in motion of particles acted upon by force fields; heating; physical or chemical change of state. Depending on circumstances, the energy spreading from a point source may be limited to a specific direction (a beam) or can disperse in all directions.
Radiant flux density is just the energy per unit volume (cubic meters or cubic centimeters). The flux density is proportional to the squares of the amplitudes of the component waves. Flux density as applied to radiation coming from an external source to the surface of a body is referred to as irradiance (E); if the flux comes out of that body, it’s nomenclature is exitance (M) (see below for a further description).
The notion of radiant intensity is given by the radiant flux per unit of solid angle ω (in steradians - a cone angle in which the unit is a radian or 57 degrees, 17 minutes, 44 seconds); this diagram may help to visualize this:
Thus, for a surface at a distance R from a point source, the radiant intensity I is the flux φ flowing through a cone of solid angle ω on to the circular area A at that distance, and is given by I = φ/(A/R2). Note that the radiation is moving in some direction or pathway relative to a reference line as defined by the angle θ.
From this is derived a fundamental EM radiation entity known as radiance (commonly noted as “L”). In the Manual of Remote Sensing, “radiance is defined as the radiant flux per unit solid angle leaving an extended source (of area A) in a given direction per unit projected surface area in that direction.” As stated mathematically, L = φ/ω times 1/cos θ. Or, restated with intensity specified, L = I/cosθ. Radiance is closely related to the concept of brightness as associated with luminous bodies. What really is measured by remote sensing detectors is radiances at different wavelengths leaving extended areas (which can “shrink” to point sources under certain conditions).
Radiant fluxes that come out of sources (internal origin) are referred to as radiant exitance (M) or sometimes as “emittance” (now obsolete). Radiant fluxes that reach or “shine upon” any surface (external origin) are called irradiance. Thus, the Sun, a source, irradiates the Earth’s atmosphere and surface.
The above radiometric quantities Q, φ, I, E, L, and M, apply to the entire EM spectrum. Most wave trains are polychromatic, meaning that they consist of numerous sinusoidal components waves of different frequencies. The bundle of varying frequencies (either continuous within the spectral range involved or a mix of discrete but discontinuous monochromatic frequencies [wavelengths]) constitutes a complex or composite wave. Any complex wave can be broken into its components by Fourier Analysis which extracts a series of simple harmonic sinusoidal waves each with a characteristic frequency, amplitude, and phase. The radiometric parameters listed in the first sentence can be specified for any given wavelength; this spectral radiometric quantity (which has a value different from those of any total flux of which they are a part [unless the flux is monochromatic] is recognized by the addition to the term of a subscript λ, as in Lλ.
EM radiation can be incoherent or coherent. Waves whose amplitudes are irregular or randomly related are incoherent; polychromatic light fits this state. If two waves of different wavelengths can be combined so as to develop a regular, systematic relationship between their amplitudes, they are said to be coherent; monochromatic light generated in lasers meet this condition.
The above, rather abstract, sets of ideas and terminology is important to the theorist. We include this synopsis mainly to familiarize you with these radiometric quantities in the event you encounter them in other reading.
* The Powers of 10 Method of Handling Numbers: The numbers 10-34 (incredibly small) or 1012 (very large - a trillion), as examples, are a shorthand notation that conveniently expresses very large and very small numbers without writing all of the zeros involved. Using this notation allows one to simplify any number other than 10 or its multiples by breaking the number into two parts: the first part denotes the number in terms of the digits that are specified, as a decimal value, e.g., 5.396033 (through the range 1 to 10); the second part of the number consists of the base 10 raised to some power and tells the number of places to shift the decimal point to the right or the left. One multiplies the first part of the number by the power of ten in the second part of the number to get its value. Thus, if the second part is 107, then its stretched out value is 10,000,000 (7 zeros) and when 5.396033 is multiplied by that value, it becomes 53,960,330. Considering the second part of the number, values are assigned to the number 10n where n can be any positive or negative whole integer . A +n indicates the number of zeros that follow the number 10, thus for n = 3, the value of 103 is 1 followed by three zeros, or 1000 (this is the same as the cube of 10). The number 106 is 1000000, i.e., a 1 followed by six zeros to its right (note: 100 = 1). Thus, 1060 represents 1,000,000,000,000,000… out to 60 such zeros. Likewise, for the -n case, 10-3 (where n = -3) is equal to 0.001, equivalent to the fraction 1/1000, in which there are two zeros (three places) to the left of 1 (or the right of the decimal point). Here the rule is that there is always one less zero than the power number, as located between the decimal point and 1. Thus, 10-6 is evaluated as 0.000001 and the number of zeros is 5 (10:sup:-1 is 0.1 and has no zero between the . and 1). Any number can be represented as the product of its decimal expression between 1 and 10 (e.g., 3.479) and the appropriate power of 10, (10:sup:n). Thus, we restate 8345 as 8.345 x 103; the number 0.00469 is given as 4.69 x 10-3.