“Optical Signals”
3 God said, "Let Newton be! " and all waslight. --Alexander Pope.*
In order to understand the optical design of animal signals one must study how they are generated, transmitted and received. This chapter is the first of three providing relevant background. It deals with physical properties of light, to be followed by chapters dealing with generation and reception of optical signals.
The choice of what constitutes the channel between sender and receiver (fig 2-1) is somewhat arbitrary. One might consider the entire informational processing line between the central nervous system of the sender and that of the receiver as the channel. In fact, Shannon (Shannon and Weaver, 1949) and others conceive of a communication system as consisting of an informational source connected to a transmitter that generates signals on one end of the channel and a receiver per se connected to a destination at the other end. For present purposes, boundaries are conveniently set at the physical limits of the communicating organisms; one is a sender, the other a receiver in the broad sense, and everything in between is the channel.
In animal communication, the optical channel consists of electromagnetic energy propagated through air or water. In order to understand this channel it is necessary to review some relevant facts about the physics of light, ambient radiation from the chief source of light (the sun) and the propagation of light through media that may contain suspended materials (e.g., water vapor in air) and macro-objects (e.g., plants). All these topics are used in later chapters in attempting to uncover the design of optical signals used in animal communication.
In order to transfer information, signals must have variety (ch 2). Therefore, understanding of the optical channel begins with sources of variety in signals : the physical variables of light.
Light is electromagnetic radiation that causes visual sensation. Electromagnetic radiation is emitted and absorbed in indivisible units called quanta, a quantum of light also being known as a photon. The photon may be visualized as a moving wave having electric and magnetic vectors (fig 3-1). Each quantum has a measurable wavelength (λ) and speed of movement (c),related by the general wave equation
where ν is the frequency.Quanta having frequencies in the range of 750 ≥ ν ≥ 400 THz are absorbed by the human photoreceptors and hence define the visible spectrum. The energy of a photon is proportional to its frequency:
where the proportionality constant h is Planck's constant (6.624 x 10-27 erg-s).* The speed of light in a vacuum (c) is about 3 x 108m/s, so by eq (3.1) the wavelengths of visible light are 400 ≤ λ ≤ 750 nm. Other media slow light tosome value c, and the ratio
Fig 3-1. Representation of a photon moving from lower left to upper right with its electric vector (e)shown in the vertical plane and its magnetic vector(h) at right angle and in phase. The wavelength (λ) is shown as the distance between peaks, and the number of peaks that pass a point in space in a given time is the frequency (v), related by the photon's speed (eq 3.1).
is the index of refraction,When a photon is slowed its frequency is invariant, but its wavelength changes according to eq (3.1).
A few photons absorbed by the eye in quick succession are sufficient for the minimum visual excitation, but ordinarily the temporal flux is very high before weare aware of light. The flux is expressed by the number of quanta per unit time or the amount of energy per unit time (related by the frequency according to eq 3.2). The latter is called radiant power (measured in watts, where 1 W = 1 Joule/s and 1 J =107 erg). Radiance is the power emitted from a radiant area such as the sun’s disk and irradiance is the power falling upon an irradiated area such as an animal’s body; both are expressed in units such as W/m2 and denoted I, but context usually distinguishes them.
Light has emergent properties due to its composition of different kinds of photons. When all are of the same frequency (wavelength), the light is monochromatic,and if their waves are exactly in phase the light is coherent, as from lasers (fig 3-2). Spectrally complex (i.e., not monochromatic) light may be characterized by a density-distribution of irradiance per spectral increment through the spectrum (e.g., W m-2 THz-1 as a function of THz). When the electric (and hence alsomagnetic) vectors of the photons are aligned the light is plane-polarized (fig 3-3, p. 60), and there also exist more complicated kinds of polarization.
One may imagine a spatial arrayof photons traveling toward an observer in which the component parts of the array may differ in spectral-power distribution and degree of polarization. The possible compositions of such an array are effectively without bound, and the rapidity with which the composition canchange in time is likewise nearly limitless. Therefore, the capacity of the optical channel to carry information (ch 2) is virtually infinite: a given array has an indefinitely large number of alternative states, and these states can change very rapidly.
Fig 3-2. Complex , monochromatic and coherent light shown by electric vectors of photons moving from left to right. At top (a) the three photons differ in frequency, hence their wave lengths (eq 3.1) also differ. The group constitutes spectrally complex light. At middle (b) the three photons are of the same frequency (wavelength), but out of phase, andhence constitute monochromatic light. At bottom (c) they are in phase, so the light is also coherent.
If there are bounds to the capacity with which information is transferred by light, these bounds relate to the sender's ability to promulgate signals or the receiver's ability to accept them, or both. As necessary background to these limitations, to be considered in the following two chapters, one must understand how light interacts with matter.
Fig 3-3. Plane-polarization of light diagramed as electric vectors seen from in front of on-coming photons (upper diagrams) and as oommonly represented (lower diagrams). In ordinary unpolarized light (left) theplanes are not aligned, whereas in plane-polarized light (right) all electric vectors arein parallel planes.
Energy and mass are convertible according to Einstein's famous equation, but in ordinary physical interactions on earth energy is conserved during transitions from one form to another. An atom or molecule of matter absorbs a photon by converting its electromagnetic energy to electronic energy,which raises the molecule from a ground state to an excited state. Spontaneous return to the ground state emits a photon, and in both, absorption and emission the difference in energy between ground and excited states is exactly the energy of the photon (eq 3.2). Induced emission occurs when one quantum absorbed by an excited molecule causes it to emit multiple quanta in the return to the ground state.
Single atoms and simple molecules have only a few possible ground and excited states,whereas complex molecules have many possible states. Hence the former can undergo limited electronic transitions, which absorb or emit specific frequencies according to eq (3.2). These simple molecules exhibit line Spectra of emission or absorption such as those used by astronomers to identify the chemical composition of stars from their light. Complex molecules, on the other hand, have ever-changing states described by density-distributions of probability as a function of transition-energy. Therefore, they show continuous Spectra: probability of absorption or emission as a function of frequency, or (over some finite time-increment) power absorbed or emitted as a function of frequency. For this reason, absorption spectra of the complex visual-pigment molecules in the eye resemble Gaussian, bell-shaped probability density-distributions (ch 5, below).
Energetic relations in molecules concern heat and other forms of energy apart from photons. Adding energy to substances, such as electric current passed through a tungsten wire, heats the molecules to incandescence so that they emit energy in the form of photons (thermoluminescence). An ideal incandescent radiator (the black body) emits a spectrum that depends upon its absolute temperature according to an equation known as Planck's law. Conversely, absorbed photons may be converted to heat and other internal energy, causing degeneration of the excited state without emission of light.
A particular kind of emission occurs when a quantum is absorbed and the molecule exchanges energy internally while in the excited state (relaxation). The molecule thus degenerates to a lower excited state and then emits a quantum of energy less than that absorbed. The emitted quantum must therefore have a lower frequency than the absorbed quantum (eq 3.2), the familiar example being visible fluorescence of light from a substance irradiated by higher frequency ultraviolet radiation. When fluorescence is delayed because of certain electronic structure of the molecules involved, the phenomenon is phosphorescence.
Other forms of light-emission always involve adding energy by some mechanism, which may be quite complex in some cases. Fusion and fission processes, such as those in military bombs and in the interiors of stars, may provide the energy. Modern technology uses electric current applied to thin conducting panels to create electroluminescence, and chemical reactions may provide chemiluminescence. Certain animals, such as fireflies, use chemical reactions to create bioluminescent signals (ch 4).
Most animal signals are created by reflecting ambient light form some surface as the animal’s body, which becomes a secondary source of radiation. In a gross sense, light striking a non-fluorescing substance has three fates:
where I0 is the incident radiation, Ir the radiation reflected, Ia the radiation absorbed and It the radiation transmitted (fig 3-4). When It = I0, the substance is transparent and when It = 0, it is opaque. All substances absorb at least some of the incident radiation (often turning it to heat), and most either reflect or transmit the rest, although some substances do all three. Equation (3.4) may have different values at different frequencies, so it becomes useful to define coefficients as r = Ir/I0, a = Ia/I0 and t = It/I0, and rewrite eq (3.4) as
Fig 3-4. The fate of incident light (I0) striking a substance. Some light may be reflected (Ir), other absorbed (Ia) and the remaining transmitted (It) through the substance.
where 1 = r + a + t. (A coefficient multiplied by 100 is the percent absorption, reflection or transmission; A = 100a, R = 100r and Τ = 100t.) The coefficients may vary with frequency, and hence a plot of r vs ν (or λ ) is the reflectance spectrum and of t vs ν the transmittance spectrumof the substance. Most substancesthat both reflect and transmit have similar reflectance and transmittance spectra, but these two spectra may differ (e.g., in gold leaf), a phenomenon known as selective reflectance.
When the value of a is independent of frequency, the substance is spectrally neutral,as with neutral density filters. In this case it is convenient to define density as
where OD is also known as optical density (see next section, below). Densities conveniently add, so that a filter transmitting 0.1 I0 (density 1) in series with a similar filter has a combined density of 1+1 = 2 and a combined transmission of 0.1 X 0.1 = 0.01 or 10-2.
absorption, extinction and optical density
The transmission of light through a substance depends upon the spectrally dependent extinction coefficient (α) of the substance and the distance (d) that light travels through it:
where ε is the base of the natural logarithm. (For chemical solutions, d includes a factor for the concentration of solute as well as the length of light-path.) Because t = It/I0, it follows with rearrangement and passing to logarithms that
When common logarithms are used instead of natural logs, the quantity is optical density (eq 3.5). Normalized optical densities are independent of the thickness or concentration of the substance because distance cancels from ratios such as αd/αmaxd. Therefore, each substance has one relative extinction spectrum,but an indefinitely large number of absorption spectra, depending upon the thickness (or concentration).
Absorption (a) and extinction (α) coefficients are related by optical density. By eq (3.5), OD = -log t, so that t = 10-OD. Furthermore, assuming negligible refle ctance, t = 1-a by eq (3.4a), so that
This equation may be expanded to an infinite series (Dartnall, 1957), the first term of which is about 2.3OD, succeeding terms being fractions whose numerators are increasing powers of 2.3OD. If the light-path is very short (or the solution is very dilute), so that optical densities are small (OD < 0.05), the numerators of the series are fractions themselves, yielding very small second and subsequent terms, which may be disregarded. Therefore,
,
and since the light-path or concentration is also negligible, absorption is nearly proportional to extinction. For this reason, absorption spectra of very dilute solutions are treated as if they were extinction (optical density) spectra, a fact utilized in characterizing of visual-pigment absorption (ch 5).
reflection, refraction and polarizatton
On a microscopic level the angle of incident light equals the angle of reflected light. Therefore, on a micro-smooth surface, most of the incident light reflects at one angle (specular reflectance) that is equal to the incident angle (fig 3-5a) . Fish scales, for example, refleet specularly (ch 4) . On a micro-rough surface, light is multiply reflected at the surface before being propagated into space, and hence emerges in various directions (diffuse reflectance,fig 3-5b). Most bird feathers, for example, reflect diffusely. An ideal diffusing surface obeys Lambert's law:
where Ιφ is the magnitude of Ir angle φ in fig 3-5c.
When passing from one medium to another having a different refractive index, as in going from air to water, light partially reflects and partially penetrates at an angle that depends upon the refractive indices (eq 3.3) of the two media, the change in direction being called refraction.Wavefront theory accurately predicts that
Fig 3-5. Types of reflectance. On a microsmooth surface (a,left),the angle of reflection equals the angle of incidence on a gross level,but on a micro-rough surface (b,right)the equality of angles causes multiple small reflections resulting in gross diffusion of the reflected light.Ideal diffusion (c,bottom)follows Lambert’s law (eq 3.6).
where θ1 is the angle of incidence, θ2 the angle of refraction and n the index of refraction, as shown in fig 3-6 (p. 66). Because n air= 1, the ratio of sines in eq (3. 7) provides the refractive index of denser materials such as water (nwater = 1.3, depending upon temperature and dissolved materials, i.e., depending upon density). Refraction is important to fish in detecting predatory seabirds in the air above the surface, and is also the basis of lenses, such, as those in light-emitting organs (ch 4) and eyes (ch 5).
A peculiar thing happens when light passes from one medium into a less dense one, as in passing from water into air. The refracted light is bent away from the normal, and at a certain critical angle of incidence numerical solutions of eq (3.7) for the angle of refraction yield impossible values. At this critical angle, no refracted light emerges into the less dense medium; instead, there is total internal reflection within the denser medium. For water, the critical angle is about 49°, and for the glass-air interface it is about 42°--a fact utilized in the design of 45-90-45° prisms used as perfect mirrors to change the direction of light. Because of reflection at the air-water interface, fish face a potential problem of confusing real images of objects above or below the surface with reflected images of objects in the water. Moody (1975) has shown that rosy barbs, however, can make the discrimination with ease.
Fig 3-6. Refraction of light as it leaves a less dense medium (1) and passes into a more dense medium (2). The angles of reflection (θ1) and refraction (θ2) are related by the refractive indices of the media by eq (3.7).
The reflected light (fig 3-6) is partially polarized in the plane parallel to the surface between the media, and when θ1 + θ2 = 90°, the reflected light is completely polarized. Some materials also polarize light by transmitting vectors in one plane but absorbing those in others. Since environmental glare from water and wet roads is horizontally polarized reflectance, sunglasses that transmit only vertically polarized light cut glare without reducing other light substantially.
Most transparent substances such as glass refract light differentially throughout the visible spectrum, such that
Newton capitalized on this fact when he used a glass prism to spread white light into its component frequencies [refractive dispersion). However, this same property is an important hindrance in the manufacture of lenses because it causes chromatic aberration: focusing of different frequencies to different places in space. Chromatic aberration of the eye produces a depth-illusion based on color (ch 5).
Equation (3.4) is not a complete statement of the fate of incident light because some light may be scattered within the substance through which it passes. Scattering may be thought of as multiple reflection by small particles. When the particles are very small (<_ λ/10) they scatter light nearly independently of one another according to
where sRay is the coefficient of Rayleigh Scattering. Equation (3.9) means that short wavelengths (high frequencies) from the "blue" end of the visible spectrum will be scattered strongly, whereas long wavelengths (low frequencies) from the "red" end will penetrate strongly. For this reason, we see penetrating light from the rising sun as very orange and the back-scattered light to the west as deep blue. Scattering is not precisely proportional to the inverse of the fourth power of the wavelength (eq 3.9) --as sometimes stated--because the n is spectrally dependent (e.g.,eq 3.7). Electric vibrations in the particles polarize light scattered normally to incident radiation, as may be appreciated by looking at the sky 90° from the sun and rotating Polaroid sunglasses.
When scattering particles are large (> 25λ) ordinary geometrical optics applies, but when the range is between this and Rayleigh scattering the effect is Mie Scattering, which has complicated mathematical properties. Mie scattering is due to the interaction among light waves that have been reflected, refracted and otherwise affected. At small particle sizes (relative to the wavelength of light), Mie scattering occurs in all directions relative to the incident light-path, although the scattering is never uniform as in Rayleigh scattering. As the particle size increases, Mie scattering is directed forward to an increasing degree until nearly all scattered light is directed forward when the radius of the particle is about the size of the wavelength. The Mie scattering coefficient may be summarized as
where γ is the radius of the scattering particle and Μ is a dimensionless oscillatory function. If the particle size and index of refraction are held constant, the effect of wavelength on Mie scattering may be appreciated. At very short wavelengths (large γ/λ values), Μ has a limiting dimensionless value of about 2. As the wavelength becomes longer, Μ rises to higher values and falls to about 2 in oscillations that increase until a final peak near λ = γ. After this final peak, Mie scattering falls monotonically to zero, as shown in fig 3-7 for the refractive index of water. The refractive index changes the oscillatory function only quantitatively, and a given maximum value of Μ occurs at increasingly longer wavelengths as n increases.
Fig 3-7. Wavelength-dependency of Mie scattering depends upon the function Μ (eq 3.10). Wavelengths are expressed in terms of the radius (γ) of the scattering spherical particles which have the refractive index (n) of water in this exemplary function.
The spectral effects of Mie scattering are very complex and depend on the size of the particle in relation to the wavelength of light, as may be appreciated with some quantitative examples in reference to fig 3-7. Suppose γ = 400 nm; then sMie ↥ l/λ (for 400 ≤ λ ≤_ 750 nm) , and the effect is somewhat similar to that of Rayleigh scattering (eq 3.9) , in that scattering decreases monotonically with wavelength. However, in Mie scattering, light of wavelength near the particle-size diameter is scattered forward, and hence does not cause the strong filtering-like effect of Rayleigh scattering.
Continuing with examples, at γ = 550 nm, γ/2 = 225 nm so that by reference to fig 3-7 Mie scattering increases with wavelength from 400 to 550 nm in the visible, then decreases from 550 to 750 nm. Or, with γ = 750 nm, γ/2 = 375 nm and the entire visible spectrum is contained between γ/2 and γ, meaning that Mie scattering increases monotonically with wavelength. At the upper limits of particle size causing Mie scattering, γ = 18 μm, so that γ/6 = 3 ym and the entire visible spectrum is off the graph to the left of fig 3-7; Mie scattering is therefore almost constant with wavelength. Finally, as a last example, consider γ = 900 nm. Then the visible spectrum lies between γ/2.25 and γ/1.2, meaning that Mie scattering from short to long wavelengths in the visible first decreases to a minimum, then increases again.
Therefore, even though the general trend of peaks in fig 3-7 is to increase with wavelength (the broken line labelled M’) , the spectral effects of Mie scattering within the visible spectrum can be extremely varied. Furthermore, most scattering aerosols contain a variety of particle sizes, often of mixed materials with differing refractive indices, so that virtually any kind of spectral effects are possible. This means that effects of air polution in the atmosphere (mentioned again later in this chapter), and transmission of light between sender and receiver in a scattering medium such as fog, must be investigated empirically in given cases.
Light spreads out in space after passing through a small hole, and at the edge of every obstacle the light-path is bent. Such diffraction can be seen by looking at a distant streetlamp through a window screen: light is bent at the four edges of the square holes of the screen, and hence spreads out vertically and horizontally to form a cross.
Light rays from the same source that reach the same locus in space by different routes have waves that may be in or out of phase. These waves interact, and if they are in phase they add (constructive interference), whereas if they are out of phase they cancel (destructive interference) . The result of diffraction from two slits or pinholes is patterned light due to such diffractive interference (fig 3-8). Rayleigh was the first to realize that diffraction and subsequent interference of light on the shadowed side of an object should create a light spot in the shadow. He demonstrated this counter-intuitive principle with a penny placed in a shaft of sunlight, although the phenomenon is a subtle one and difficult to see convincingly without a controlled laboratory setup. Rayleigh’s penny is analogous to the opaque portion between the double slits in fig 3-8: there is a bright spot centered behind the portion. The slits in fig 3-8 could also be spacings between small rods aligned in a row, causing interference of light waves analogous to the way in which rows of pilings cause interference of surface waves on water. Light waves from different sources do not ordinarily show interference because of constantly changing phase relationships.
Fig 3-8. Diffraction and interference. Light from a single source spreads out after passing through a slit (diffraction). The wavefronts propagated from two slits interfere, reinforcing along some 1oci (dashed lines) and partically cancelling elsewhere. At right is the banded pattern of light and darkas seen on the screen.
Interference also occurs without diffraction when two partially reflecting surfaces are arranged parallel (thinlayer interference) , as in the inner and outer surfaces of a soapbubble. Some of the light that penetrates the first surface is reflected back by the second. If the spacing between surfaces is exactly one-half the wavelength, the interference of incoming and reflected light is completely destructive (fig 3-9). Destructive interference occurs at a series of spacings (λ/2, 3λ/2, 5λ/2,etc.). Thin-layer interference is the basis of highreflectivity in fish scales (see ch 4, below).
Fig 3-9, Interference in thin films such as soapbubbles. The parallel vertical lines represent the inner and outer surfaces of the film and two wavefronts are shown approaching from the left. The film is one-half wavelength in thickness. The first wavefront (a) to reach the fim is partially reflected from the first surface (not shown) and partially penetrates to strike the second surface (b),where it is partially reflected back. By the time the second wavefront reaches the first surface (c) , the reflected first wavefront reaches the same point and the second cancels the first moving in the leftward direction. Light owavelength λ is therefore eliminated from the reflection in the leftward direction. However , the first wave front is re-reflected toward the right where it combines with the second wavefront constructively to e-merge in the rightward direction. Thin films therefore selectively remove wavelengths from reflection.
Diffractive and thin-layer interference are both used as principles for creating dispersion by means other than a prism (refractive dispersion). A plate ruled in precisely spaced lines (diffraction grating) or two metal films spaced by increasing distance along one dimension (interference Wedge) are both used in monochromators : devices that disperse white light and isolate the component wavelengths for experimental use.
The foregoing optical principles explain the variation of surface colors under different viewing conditions. Some surfaces appear multicolored, or appear differently colored at different viewing angles. These phenomena are almost always due to interference (e.g., figs 3-8 and 3-9) and the resultant coloration is iridescence. Repetitive elements of microstrueture of a substance give rise, often in complex geometries, to diffractive iridescence, as in the feathers of some birds (ch 4), whereas spaced reflecting layers give rise to thin-layer iridescence, as in the scales of fishes. The latter structure shows different colors either (1) because the spacing varies, reinforcing some wavelengths here and others there, or (2) because light strikes the substance at different angles and hence has different lengths of light-path between the layers, so that one wavelength is reinforced at one angle and another wavelength at another angle. The iridescent sheen of mother-of-pearl in molluscs is probably due to both phenomena acting simultaneously.
Perhaps commonly occurring but not commonly noted are substances that appear two different colors, or vary continuously between two colors. Such coloration is due to a variety of causes variously called dichromatism or dichroism. The molecular structure of some materials differentially absorbs photons of different vector-orientations; therefore, the materials transmit polarized light of different colors depending upon the plane of polarization. Any substance that polarizes light by selective absorption of vectors is often referred to as dichroic , even if the absorption is spectrally neutral so that the substance appears the same color(but of different intensities) when irradiated with light of different planes of polarization. Because of this usage of dichroism, the generic term dichromatism is preferred for materials that appear in two colors.
Dichromatism may be due to causes other than dichroism. Commonly a substance will have two spectral bands absorption. Suppose a given thickness (or concentration of solution) absorbs 30% of the light (a = 0.3, eq 3.4a) in one spectral band and 65% in the other, so that the transmissions are t1= 0.7 and t2 = 0.35. If the thickness is doubled, these values become t1= 0.72 = 0.5 and t2= 0.352 = 0.12.Therefore, in the first case of single thickness, t1/t2 = 2, whereas doubling the thickness yields t1/t2 = 4. That is, the relative contribution of the two spectral bands to the transmitted light varies with the thickness or concentration, hence so does the apparent color. One expects such absorptive, dichromatism to occur with substances that appear green because green is the color sensation evoked by energy in the middle of the visible spectrum; therefore, green is absorptively created by absorption at spectral extremes (two absorption bands).
Absorptive dichromatism also occurs with reflected light viewed from different angles. This possibility seems counter-intuitive because we think of reflection as a simple bouncing of light from a surface (as in figs 3-5 and 3-6). Actually, some of the reflected light is absorbed and immediately re-radiated by molecules and other of it may be scattered back within a substance. Therefore, incident light penetrates substances and is partially absorbed before being propagated back as gross reflection. Whenever incident light penetrates materials to different degrees, absorptive dichromatism may occur. For example, if light penetrates on the average to a particular microdepth beneath the surface, it has a shorter path within the surface when incident at high angles than low ones. Similarly, absorptive dichromatism is responsible for differences between the reflectance and transmittance spectra of some substances.
The foregoing principles of the interactions of light with matter lay foundations for discussing the promulgation of optical signals (ch 4) and their reception (ch 5), but are also of immediate interest in describing more closely the real optical environment for signaling. Bioluminescent organisms excepted, almost all light used in animal communication originates with the sun, which must therefore be the starting place for discussing environmental light. Sunlight is altered in the atmosphere, and then again in terrestrial and aquatic habitats, where the media of transmission differ importantly in properties relevant to the design of optical signals.
The spectrum of sunlight measured from a rocket high above the earth’s surface resembles that of an ideal black-body radiator (fig 3-10a) . The peak irradiancedensity is near 0.5 nm (500 nm), which is near the peak sensitivity of the human eye (ch 5) , but sunlight also contains appreciable ultraviolet radiation (λ < 400 nm) and infrared radiation (λ > 750 nm). Many animals (particularly arthropods) are known to see into the near-UV, but only pitvipers and a few other animals can sense the near-IR (ch 5).
The irradiance at the surface of the earth differs from pure sunlight because of atmospheric effects (fig 3-l0b) . The spectrum shows bands of low irradiance in the IR due to absorption by water vapor in the atmosphere. Rayleigh scattering shifts sunlight toward longer wavelengths, hut also causes the entire sky to become luminous with a pronounced bluish coloration. (Space as seen from the moon is black because the moon has no atmosphere.) An irradiance spectrum measured just above the surface of the earth on a large, flat plane results from the combination of direct solar and sky-scattered radiation. When the sun is low in the sky, around the time of sunset and sunrise, its light has a longer path through the atmosphere so that scattering and absorption are more pronounced. Similar seasonal differences in irradiance spectra also occur with the sun at the same position in the sky because of differences in the atmosphericlight-path (Ch 7). Finally, changes in the atmospheric conditions cause shifts in the light reaching the earth. Clouds composed of large water molecules cause Mie scattering and absorb considerable radiation, and more complex effects may be due to air poilution such as from industrial smoke or eruption of volcanoes. A fire raging in Albert, Canada in September 1950 turned the sky in Edinburgh, Scotland deep indigo, where R. Wilson studied the light in great detail, calculating the diameter of polluting particles at about 1 μm based on equations for Mie scattering. Similar phenomena occurred world-wide after the great eruption of Krakatoa in 1883(Ruechardt, 1958).
Fig 3-10. Irradiance-density of sunlight measured from a rocket (above) and at theearth1s surface (below). (a) The upper curve is a proposed standard average (Thekaekara, 1972). (b)The lower curves are measurements made by the author in Panama (dots) and the spectrum simulated (Une segments,) by the model of McCullough and Porter (1971) for the same location and time (Barro Colorado Island, April 1973, noon, clear day).
McCullough and Porter (1971) published a computer algorithm, based on a detailed model of atmospheric conditions, that simulates spectral irradiance on the earth's surface. This ambitious tool delivers simulations at any geographic coordinates, any elevation, any time of year and any time of day, with added provisions for relative humidity and amount of cloud cover. The simulation is remarkably good (fig 3-10b , p. 75), and has subsequently been improved (Porter,pers. comm.).
The sun's disk subtends an angle of about a half-degree as viewed from the earth (31' 28" in January when the earth is farthest from the sun and 32' 30" in June when it is nearest). This subtended angle expressed in radians averages about θ = 1/107.5 rad. Any circular object smaller than the sun but subtending the same angle exactly blocks the sun's image, and hence casts a converging umbral shadow (fig 3-11). It follows from the definition of a radian that an object of diameter δ0 casts an umbra that converges at a distance about
because the diameter is very nearly an arc of a circle with radius D, as shownin fig 3-12a,Therefore, the length of the umbra is about 108 diameters of the object,and every animal within 100 body-lengths of the earth casts a shadow upon its surface.
Fig 3-11. Types of shadows oast by an object in sunlight (not to scale).
Fig 3-12. Umbral shadows, of objects. The length of an umbra (a) is about 107.5 timesthe diameter (δ0) of the object casting it, and the diameter of the shadow (δs) cast by an object closer to the substrate than 107, 5δ0 is linearly proportional to the distance (Ds).
Introduce a plane at distance D s from the object and distance D c from its umbra's convergence-point (fig 3-12b, previous page), such that the plane is normal to the umbra's axis. Let the plane represent the surface of the earth or other substrate upon which the shadow is cast. From the figure,
,
in parallel with eq (3.11). Rearrangement yields δS = DC θ and since D c =D – D s by fig 3-12, substitution gives
.
Finally, by eq (3.11) δ0= D θ, so that
This little exercise in algebra secures the conclusion that the size of the shadow is a linear function of the distance to the substrate. The shadow approaches the size of the object itself when the distance decreases to zero, and diminishes to zero when the distance increases to the length of the umbra (i.e., about 108 body-diameters). And, as the umbra decreases with distance from the substrate, the penumbra grows in size (fig 3-11), creating a hazy, indistinct shadow. The importance of shadows cast by animals is discussed in ch 6.
ambient irradiance in terrestrial habitats
Even a desert animal is not irradiated solely by sunlight and skylight because it is not a plane on the earth's surface. Rather, an animal is a three-dimensional object that receives reflected light from the ground and other objects in the environment. In vegetated habitats these objects are in part plants, which not only reflect light but also filter light through the leaves. Figure 3-13 shows the irradiance spectrum in a forest in Panama, with minima near 425 and 675 nm due primarily to absorption by chlorophyll.Although there is considerable transmission of long wavelengths, the eye is so insensitive to the far red part of the spectrum (ch 5)that forest light has a distinctively greenish hue due to the maximum irradiance near 550 nm. Moving upward within the forest increases the ambient light but does not appreciably alter its spectrum.
Fig 3-13. Spectral irradiance-density in a forestmeasured by the author in Panama at two different heights (Barrow Colorado Island, 18 April 1973). The maximum near 550 nm is due primarily to absorption by chlorophyll at shorter and longer wavelengths, giving ambient light a greenish hue. The high irradiance at very long wavelengths occurs where the human eye is almost insensitive to light. Irradiance-density is stronger high in the foresta but its spectral distribution is similar to that at ground level.
The ambient irradiance in terrestrial habitats is so complexly determined and so poorly studied that it cannot be modeled accurately at present and so must be determined empirically. Burtt (1977) made measurements in a variety of habitats in Minnesota and found that the primary spectrai differences were between broadleaved and coniferous forests. Light in coniferous forests is governed more by reflection from opaque materials such as branches and needle-leaves than by transmission through broad leaves as in hardwood forests. Consequently, the coniferous spectra tend to be flatter than those in fig 3-11, and the ambient light is more neutral than greenish. The absolute levels of irradiance, however, vary with the height and density of the trees.Figure 3-14 summarizes sources contributing to ambient irradiance in terrestrial habitats.
Fig 3-14. Principal sources of irradiance on an animal in a terrestrial habitat. Direct sunlight(Iq) or sunlight scattered in the sky (Is) may fall on the animal directly, befiltered by leaves and other objects (It) or reflected (Ir) from plants or other surfaces such as the ground. Diagramed is the male painted bunting, one of the most colorful birds in North America, having a blue head, red breast and rump, yellowish back and green wing-patches.
ambient Irriadlance In open ocean
The ambient irradiance in aquatic habitats is even more complexly determined than that of terrestrial habitats because of added factors. The irradiance falling on the surface of a woodland stream, for example, is subject to all the factors shown in fig 3-13, and then to additional factors within the new medium of the water itself.
It is useful to begin with the open tropical ocean where direct sunlight and skylight fall upon the surface of relatively clear water. Many factors in the irradiance of oceans are counter-intuitive so that it is useful to consider factors one by one. The ocean appears blue from above, and popular articles sometime ascribe this coloration to backlight from Rayleigh scattering. If that were true, long wavelengths should penetrate the ocean in the way that long wavelengths from the rising and setting sun penetrate the atmosphere. However, SCUBA divers know that long wavelengths disappear first in ocean depths: light becomes more bluish rather than reddish beneath the surface. Furthermore, inspection of spectral irradiance curves suggests that the bluish light above and beneath the surface of oceans does not have the expected Rayleigh scattering characteristics.
Spectral absorption measurements on water give conflicting results because of materials dissolved in it, but it does appear that absorption rises with increased wavelength:
Therefore, light in the ocean tends to lose energy from the long wavelengths ("red" end of the visible spectrum) toward the short wavelengths. The blue seen from above the surface is therefore probably due to backlight of Mie scattering or gross scattering, or both, and not primarily to Rayleigh scattering.
Until recently, available data have been spotty, but the study by McFarland and Munz (1975a) provides support for the foregoing reasoning as well as a useful bibliography to older data.Figure 3-15a shows their sample results of the spectra of irradiance falling upon a tropical sea, expressed in quantal rather than energy terms (see eq 3.2,p. 56). The observed quantal spectra are reiatively flat on both clear and overcast conditions, but 3 m below the surface the irradiance from above shows adramatically shifted spectrum (fig 3-15b , top curve). The bluish underwater light shows a similar spectrum when the detecting instrument is pointed downward (fig 3-15b , bottom curve), due to the back-scattering of the penetrating light that is not absorbed by the water.
Fig 3-15. Spectral irradiance-density in an ocean (after McFarland and Munz, 1975a).At left (a) is the downward quantal irradiance-density above the ocean under clear and overcast conditions, and at right (b) is the downward irradiance (top curve, left axis) and upward irradiance (bottom curve, right axis) at a point 3 m below the water’s surface. All vertical axes are in units of quanta cm-2 is-1nm-1 and must be multiplied by these factors for absolute values: 1014 (left axes of both diagrams) and 1012 (right axis of right diagram).
McFarland and Muntz (op. cit.) went on to measure the quantal irradiance spectraat many different directions from the same place beneath the surface. As expected, irradiance from the sun's direction is stronger and hence its long wavelengths are more pronounced, but for more than a hemisphere arounda point beneath the surface the irradiance spectra are highly similar to the lower curve in fig 3-15b. Asone descends in the water-column two predictable effects take place: (1) the ambient spectrum becomes increasingly narrow, shifting toward short wavelengths (bluish light), and (2) the ambient spectrum becomes similar inall directions. McFarland and Munz state that the minimum depth at which the directional similarity takes place varies with water conditions, and may be deeper than 1Q0 m in most clear tropical seas, Tyler (I960) made a detailed study of the total irradiance invarious directions from loci at increasing depths, in an inland lake, finding results generally similar to those of McFarland and Munz for the oceanic environment.
ambient Irradiance In complex aquatic habitats
Not all aquatic animals conduct pelagic lives in open oceans. Important ecosystems associated with coral reefs and shallow seas contain many of the fishes and other animals that use optical communication extensively. McFarland and Munz (1975a) found that in shallow waters the reflection of light from the bottom substrate played an important role in irradiance from below an animal. As expected, the shallower the water, the more intense the reflected contribution to irradiance, with corresponding shifts in spectrum away from short-wavelength-dominated light (fig 3-16a). Furthermore, the type of substrate affected the spectral distribution and absolute levels of reflected light (fig 3-16b , previous page). One is left, therefore, with the same situation resulting from considerations of ambient irradiance in terrestrial habitats: the factors are too many and complex to model accurately, and empirical measurements must be made for given cases.
Fig 3-16. Upward irradiance in shallow sea (after McFarland and Munz, 1975a). At left (a), the curve broadens as the bottom becomes closer to the surface, due to reflection from the bottom. At right (b), the reflectivity of the bottom surface influences the spectral distribution of upward irradiance. Axes are in units of quanta cm-2 s-1 nm-1 and must be multiplied by correction factors for absolute irradiance-density: 1013 (left diagram and top curve ofright diagram) and 0.33 χ 1013 (bottom curve of right diagram).
In estuarine and inland waters, the ambient light is further complicated by turbidity: absorption and scattering due to suspended materials such as mud particles. The spectral effects of turbidity probably vary greatly with the nature of the dissolved materials, but Luria and Kinney (1970), Jerlov (1968), Hutchinson (1957) and others find that
which is disconcertingly the opposite effect of absorption by water alone (eq 3.13 , p. 81). (In eq 3.14, may be due to scattering as well as true absorption, and Mie scattering of eq 3.10 could play an important role.) Furthermore, turbidity due to aquatic organisms such as phytoplankton may have quite different spectral effects on ambient irradiance, absorption by chlorophyll creating a greenish hue similar to that found in forests.
Finally, in inland waters, the important effects of vegetation and other factors of surrounding terrestrial habitats affect the spectral quality of light before it strikes the water. It seems a conservative conclusion to state that ambient irradiance in aquatic habitats (outside open ocean) is quite complexly determined, studies to date having yielded few trusty generalizations.
Most optical signals of animals consist of ambient light reflected from the sender's body or another object controlled by the sender.Chapter 4 concerns details of the reflection processes, and this section is devoted to generalities of how the reflected signal is affected during transmission fromsender to receiver.
signal radiance and irradiance
An optical signal is created when ambient light (Io) irradiates a surface of given spectral reflectivity (r) and is reflected as signal-radiance (Ir or simply I) according to eq (3.4a). Most animal surfaces used as signal-surfaces have diffuse reflectance, and hence approximate Lambert’s law (eq 3.6). Therefore, the radiance of a signal at a given angle of view is
The signal surface acts as a secondary source radiating light that falls on another surface (e.g.; a receiver's eye) as signal-irradiance (I’). The relative area of the signal-surface in the receiver's field of view decreases by the square of the distance from the surface. The surface continues to appear just as bright per unit area (in a perfectly transparent medium), but since its relative area decreases, the total irradiance arriving at the viewer decreases. Put simply, signal-radiance (I) remains constant and signal-irradiance (I’) decreases with distance.
Only for infinitely small surfaces (point-sources) will signal-irradiance follow the inverse-square law: I’ = I/d2, where d is the distance between source and irradiated surface. Irradiance from an infinite line source, approximated by a very long fluorescent tube viewed from afar, decreases linearly with the distance (I’ = I/d), and irradiance from an infinite plane is independent of distance (I’ = I). Finite radiant surfaces therefore fall somewhere between infinite planes and point-sources, approximately the former when they are large and the latter when they are small, so that one may state only that
which is none-the-less a possibly non-obvious phenomenon in a clear medium.
The transmission of the signal from sender to receiver encounters two kinds of distrubances in the channel: distrubances by the medium itself (air or water) and disturbances by objects in the medium, primarily opaque objects such as vegetation, coral heads and so on. All of the factors that influence the spectral quality of environmental light enumerated above can affect the light transmission from sender to receiver. In actuality, the communicative distance is usually so small that only some of the factors are really important. Air is ordinarily transparent, but fog can alter the spectral quality of light by Mie scattering (eq 3.10) and alter the image of the signal by diffuse Mie and gross scattering, thus seriously disrupting signals. Turbidity in water (eq 3.14) similarly disrupts the image-clarity and spectral distribution of light reaching the receiver. Whether these disruptions constitute mere distortion or important noise (see ch 2) becomes a consideration of the optical design of signals (ch 7). The point here is that many of the same factors that influence ambient light on the signal surface, discussed in foregoing sections, also influence the transmission of light from sender to receiver.
Disruption of the signal by opaque objects in the medium is a serious problem for communication, and one that has received little systematic attention. As an example of the genre of unstudied problems that exist, consider whether or not a receiver can see an entire signal object, such as a colored patch on an animal or a gesture with a appendage. For simplicity, consider the object to be circular with area A0. Then its apparent area is A0/d20, where d0 is the distance from object to viewer. If an environment such as a forest has circular "holes" in the vegetation mass through which one can see, the apparent area of a hole will be Ah/d2h, where Ah is the actual area and dh the distance from the observer. Only when
will the observer see the entire signal-object. Since Ah and A0are constant (for a given hole and object), eq (3.17) is encouraged toward the favorable inequality by minimizing dh and maximizing d 0.. Systematic investigation of such problems in the transmission of optical signals in real environments might greatly aid the understanding of the size and shape of optical signals (see ch 7).
A further problem arises in the transmission of signals in that they must be discriminable from other visual arrays. Therefore, signal-objects should be of different size, shape, color, etc., from other objects in the environment, which constitute an important source of noise. It seems likely, for example, that signals of terrestrial animals tend not to be green simply because there is so much green background against which the signals are seen by the receiver. The effects of these kinds of noise problems on the design of optical signals is the subject of ch 7.
In order to transmit information, optical signals must have variation. The relative intensities of different spectral frequencies in various spatial arrays provide a nearly boundless number of possible signals, which may be rapidly modulated, so that the informational capacity of the optical channel per se is effectively boundless. Limits, if they exist, must lie with senders and receivers, and hence it is necessary to review the physicai phenomena having to do with the interaction of light with matter: refractive index, radiance and irradiance, monochromaticity and spectral complexity, polarization, types of emission, absorption spectra, reflectance and transmittance, specular and diffuse reflectance, refraction and dispersion, types of scattering, shadows, diffraction and interference, iridescence and dichromatism, turbidity and geometric considerations of radiation. Because most optical signals of animals utilize reflected sunlight, it becomes relevant to know how ambient light is determined in different habitats. Differences in ambient light of terrestrial habitats are expected to correlate with time of day, time of year, geographic location, altitude, weather (e.g., fog), open areas vs woods, and within the latter, coniferous vs broadleaved woods, as well as height above ground. Ambient light in most aqua- tic habitats is possibly even more complexly determined, being affected by time of day, time of year, geographic location, weather, depth beneath the surface, water-depth itself, turbidity and so on. Once ambient light has been reflected from a signal-surface only a few of the foregoing factors, such as fog and turbidity, affect its transmission to the receiver. However, image-clarity becomes important, so opaque objects in the channel (e.g., plants) undoubtedly constitute noise. Finally, the similarity of signals with other optical arrays presents possible problems in the transfer of information from sender to receiver.
Recommended Reading and Reference
Most of the material in this chapter concerns straightforward physical optics that may be found in most college textbooks on physics; the reader without calculus at his command should choose a textthat explains physics with algebra only. The entire September 1968 issue of Scientific American is devoted to light and its interactions with physical and biological matter. Clayton (1970) is the first of two small volumes of introduction to Light and Living Matter presenting the physical basis of absorption and emission processes. An old, but useful and inexpensive reference to have at hand in the 1963 Dover (revised) edition of Monk's Light. A delightful book about natural phenomena of environmental light is Minnaert's (1954) Nature of Light and Colour in the Open Air. Many other volumes on physical optics are available. A treatise on scattering is provided by van de Hulst (1957), and there are good discussions of this and other topics in Robinson's (1966) Solar Radiation; Coulson (1975) includes much new data.
________________
* Peoe's "triple-entendre" comes from Epigram on Sir Isaac Newton: "Nature and Nature's laws lay hid in night: God said, 'Let Newton be!' and all was light." J.C. Squire (1884-1958) replied "It did not last: the Devil howling 'Ho! Let Einstein be!' restored the status quo." Relativistic considerations are omitted from this chapter.
* The magnetic vector is also denoted by h, but that symbol is used only in fig 3-1 above.
We use cookies to analyze our traffic. Please decide if you are willing to accept cookies from our website. You can change this setting anytime in Privacy Settings.