Principles of Remote Sensing: The Photon and Radiometric Quantities

Most remote sensing texts begin by giving a survey of the main principles, to build a theoretical background, mainly in the physics of radiation. While it is important to have such a framework to pursue many aspects of remote sensing, we do not delve into this complex subject in much detail at this point. Instead, we offer on this and the next several pages an outline survey of the basics of relevant electromagnetic concepts. On this page, the nature of the photon is the prime topic. Photons of different energy values are distributed through what is called the **Electromagnetic Spectrum**. A full discussion of the electromagnetic spectrum (EMS) is deferred to page I-4.

Hereafter in this Introduction and in the Sections that follow, we limit the discussion and scenes examined to remote sensing products obtained almost exclusively by measurements within the Electromagnetic Spectrum (force field and acoustic remote sensing are briefly covered elsewhere in the Tutorial). 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 map on page I-4), but also inspect a fair number of images obtained by radar and thermal sensors.

The next several pages strive to summarize much of the underlying theory - mainly in terms of Physics - appropriate to Remote Sensing. The reader can gain most of the essential knowledge by working through those pages. In addition, optionally you can choose to read a reproduction of extracts from the Landsat Tutorial Workbook that deal with the theory by clicking onto page I-2a. Or, if you choose not to, read this next inserted paragraph which synopsizes key ideas from both the present and the I-2a pages:

**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* (EMS). 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 or reflect 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 (discussed on page I-5).

Now, in more detail: The photon is the physical form of a quantum, the basic particle of energy studied in quantum mechanics (which deals with the physics of the very small, that is, particles and their behavior at atomic and subatomic levels). The photon is also described as the messenger particle for EM force or as the smallest bundle of light. This subatomic massless particle, which also does not carry an electric charge, comprises radiation *emitted* by matter when it is excited thermally, or by nuclear processes (fusion, fission), or by bombardment with other radiation (as well as by particle collisions). 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).

Various aspects of the nature and behavior of photons are considered on this page but for a fuller treatment consult this Wikipedia website that deals with the nature of photons and the history of their discovery by Einstein as he first described them in a famous 1905 paper.

Photon particles also move as waves and hence, have a "dual" nature. These waves follow a pattern that can be 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 (top of the individual up-down curve) that pass by a reference lookpoint in a second is that wave's frequency (in units of cycles per second, whose SI version [SI stands for System International] is known as a Hertz [1 Hertz = 1/s-1]).

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 *h* is Planck's constant (6.6260... x 10-34 Joules-sec)* and *v* is the Greek letter, nu, representing frequency (the letter "*f*" is sometimes used instead of *v*). Photons traveling at higher frequencies are therefore more energetic. If a material under excitation experiences a change in energy level from a higher level E2 to a lower level E1, we restate the above formula as:

where *v* has some discrete value determined by (*v*2 - *v*1). 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..

**I-4Is 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 **

**I-6: Calculate the wavelength of a quantum of radiation whose photon energy is 2.10 x 10-19 Joules; use 3 x 108 m/sec as the speed of light c. ANSWER**

**I-7**:**A radio station broadcasts at 120 MHz (megahertz or a million cycles/sec); what is the corresponding wavelength in meters (hint: convert MHz to units of Hertz). ANSWER**

A beam of radiation (such as from the Sun) is usually polychromatic (has photons of different energies); if only photons of one wavelength are involved the beam is monochromatic. 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

How are the photon energy levels in EM radiation quantified and measured? The answer lies in the discovery of the *photoelectric effect* made by Albert Einstein in 1905. Consider this diagram:

Einstein found that when light strikes a metal plate C, photoelectrons (negative charges) are ejected from its surface. In the vacuum those electrons will flow to a positively charged wire (unlike charges attract) that acts as a cathode. Their accumulation there produces an electric current which can be measured by an ammeter or voltmeter. The photoelectrons have kinetic energy whose maximum is determined by making the wire potential ever more negative (less positive) until at some value the current ceases. The magnitude of the current depends on the radiation frequencies involved and on the intensity of each frequency. From a quantum standpoint (Einstein's discovery helped to verify Planck's quantum hypothesis), the maximum kinetic energy is given by:

K.E. = hf + φ (the energy needed to free the electron)

This equation indicates that the energy associated with the freed electron depends on the frequency (multiplied by the Planck constant h) of the photon that strikes the plate plus a threshold amount of energy required to release the electron (φ, the work function). By measuring the current, and if that work energy is known and other adjustments are made, the frequency of the photon can be determined. His experiments also revealed that regardless of the radiation intensity, photoelectrons are emitted only after a threshold frequency is exceeded. For frequencies below the threshold, no electron emission takes place; for those higher than the threshold value (exceeding the work function) the numbers of photoelectrons released re proportional to the number of incident photons (this number is given by the intensities involved.

When energies involved in processes from the molecular to subatomic level are involved (as in the photoelectric effect), these energies are measured in __electron volt__ units (1 eV = 1.602 x 10-19; this number relates to the charge on a single electron, as a fraction of the SI unit for charge quantity, the Coulomb [there are about 6.24 x 1018 electrons in one Coulomb).

Astute readers may have recognized the photoelectric effect as being involved in the operation of vacuum tubes in early radio sets. In remote sensing, the sensors used contain detectors that produce currents (and voltages, remember V = IR) whose quantities for any given frequency depend on the photoelectric effect.

From what's been covered so far on this page, let's modify the definition of remote sensing (previous page) to make it "quantum phenomenological". In this approach, *electromagnetic* remote sensing involves the detection of photons of varying energies coming from the target (after the photons are generated by selective reflectance or by internal emittance from the target material(s)) by passing them through frequency (wavelength)- dependent dispersing devices (filters; prisms) onto metals or metallic compounds/alloys which undergo photoelectric responses to produce currents that become signals that can be analyzed in terms of energy-dependent parameters (frequency, intensity, etc.) whose variations are controlled by the atomic level composition of the targets. The spectral (wavelength) dependency of each material is diagnostic of its unique nature. When these photon variations are plotted in X-Y space, the shapes of the varied distributions of photon levels produce patterns that further aid in identifying each material (with likely regrouping into a *class* or *physical feature*.

There is much more to the above than the brief exposition and summary given. Read the next page for more elaboration. 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). This last source contains a summary table that lists and defines what can be called basic __radiometric quantities__ but the print is too small to reproduce on this page. The following is an alternate table which should be legible on most computer screens.

*Radiant energy* (Q), transferred as photons moving in a radiation stream, is said to emanate in minutely short bursts (comprising a 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:φ = dQ/dt). The energy involved is capable of doing work. The SI units of work are Joules per second (alternately expressed in ergs, which equal 10-7 Joules). The flux concept is related to *power*, defined as the time rate of doing work or expending energy (1 J/sec = 1 Watt, the unit of power). 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 *intensity of radiation* is defined as the power P that flows through unit area A (I = P/A); power itself is given by P = ΔE/Δt (the rate at which radiant energy is generated or is received). The energy of an EM wave (sine wave) depends on the square of its amplitude (height of wave in the x direction; see wave illustration above); thus, doubling the amplitude increases the power by 4. Another formulation 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 ASPRS 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." This diagram, from that Manual, visualizes the terms and angles involved:

As stated mathematically, L = Watt � m-2 � sr-1; where the Watt term is the radiant flux (power, or energy flowing through the reference surface area of the source [square meters] per unit time), and "sr" is a solid angle Ω given as 1 steradian. From this can be derived L = Φ/Ω times 1/Acos θ, where θ is the angle formed by a line normal to the surface A and the direction of radiant flow. Or, restated with intensity specified, L = I/Acosθ. Radiance is loosely related to the concept of *brightness* as associated with luminous bodies. What really is measured by remote sensing detectors are radiances at different wavelengths leaving extended areas (which can "shrink" to point sources under certain conditions). When a specific wavelength, or continuum of wavelengths (range) is being considered, then the radiance term becomes Lλ.

In practical use, the radiance measured by a sensor operating above the ground is given by:

Ltot = ρET/π + Lp

where Ltot is the total spectral radiance (all wavelength) received by the sensor; ρ is the reflectance from the ground object being sensed; E is the irradiance (incoming radiant energy acting on the object); T is an atmospheric transmission function; and Lp is radiance from the atmospheric path itself.

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 or wavelength interval (range); 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 and Qλ. This subscript denotes the specificity of the radiation as at a particular wavelength. When the wavelengths being considered are confined to the visual range of human eyes (0.4 to 0.7 µm), the term "luminous" precedes the quantities and their symbols are presented with the subscript "v", as Φv for a luminous flux.

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... (a total of 20 "000"s) 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 to the left of 1 (or three places to the right of 1 to encounter 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; (10-1 is 0.1 and has no zero between the . and 1). In this special case, 100 is reserved for the number 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, (10n). Thus, we restate 8345 as 8.345 x 103; the number 0.00469 is given as 4.69 x 10-3.

Source: http://rst.gsfc.nasa.gov