Making Free-Space Optics Work
- Transmission of IR Signals Through the Atmosphere
- The Impact of Weather
- Line of Sight (LOS)
- Other Factors Affecting FSO
- Selecting the Transmission Wavelength
At one time, connecting all of the people all of the time around all of the world was a nice idea but completely impractical. The Internet has changed all of that, and the possibility now exists.
How about all the bandwidth desired for all the high-bandwidth users in all the land? Can free-space optics deliver on this proposition? Well, if it weren't for fog (and other assorted atmospheric and installation-related issues) the light beams of FSO might just be that "silver bullet." As it is, FSO, although a bullet indeed, is perhaps a brass-jacketed one.
As with most technologies, knowledge is power. And armed with the knowledge of FSO's enemies, you will possess the power to properly deploy FSO where it is the right choice. You will also be capable of avoiding the chasm of "right tool, wrong application," and thus avoid incorrect selection when it is nonoptimal. This chapter discusses the factors that can affect the viability and success of FSO.
Transmission of IR Signals Through the Atmosphere
Even a clean, clear atmosphere is composed of oxygen and nitrogen molecules. The weather can contribute large amounts of water vapor. Other constituents can exist, as well, especially in polluted regions. These particles can scatter or absorb infrared photons propagating in the atmosphere.
Although it is not possible to change the physics of the atmosphere, it is possible to take advantage of optimal atmospheric windows by choosing the transmission wavelengths accordingly. To ensure a minimum amount of signal attenuation from scattering and absorption, FSO systems operate in atmospheric windows in the IR spectral range. As discussed in Chapter 2, "Fundamentals of FSO Technology," today's commercially available FSO systems operate in the near IR spectral windows located around 850 nm and 1550 nm. Other windows exist in the wavelength ranges between 35 μm and 814 μm. However, their commercial use is limited by the availability of devices and components and difficulties related to the practical implementation such as low-temperature cooling.
The impact of scattering and absorption on the transmission of light through the atmosphere is discussed in more detail in the following sections.
Beer's Law describes the attenuation of light traveling through the atmosphere due to both absorption and scattering. In general, the transmission, τ, of radiation in the atmosphere as a function of distance, x, is given by Beer's Law, as
where IR/I0 is the ratio between the detected intensity IR at the location x and the initially launched intensity I0, and γ is the attenuation coefficient.
The attenuation coefficient is a sum of four individual parametersmolecular and aerosol scattering coefficients α and molecular and aerosol absorption coefficients βeach of which is a function of the wavelength. You will see the application of this relationship among received intensity, scattering, and absorption a little later in this chapter.
The attenuation coefficient is given as
This formula shows that the total attenuation, represented by the attenuation coefficient γ, results from the superposition of various scattering and absorption processes. This will be discussed in more detail in the following sections.
Scattering refers to the "pinball machine" nature of light trying to pass through the atmosphere. Light scattering can drastically impact the performance of FSO systems. Scattering is not related to a loss of energy due to a light absorption process. Rather, it can be understood as a redirection or redistribution of light that can lead to a significant reduction of received light intensity at the receiver location. A nice overview of these processes can be found in the literature 1.
Several scattering regimes exist, depending on the characteristic size of the particles, (r), the light encounters on the trip to its destination. One description is given as x0 = 2þr/λ, where λ is the transmission wavelength and r is particle radius. For x0 << 1, the scattering is in the Rayleigh regime; for x0 &` 1, the scattering is in the Mie regime; and for x0 >> 1, the scattering can be handled using geometric optics. Compared to infrared wavelengths usually used in free-space optics, the average radius of fog particles is about the same size. This is the reason that fog is the primary enemy of the beam. Rain and snow particles, on the other hand, are larger, and thus present significantly less of an obstacle to the beam.
A radiation incident on the bound electrons of an atom or molecule induces a charge imbalance or dipole that oscillates at the frequency of the incident radiation. The oscillating electrons reradiate the light in the form of a scattered wave. Rayleigh's classical formula for the scattering cross section is as follows:
where f is the oscillator strength, e is the charge on an electron, λ0 is the wavelength corresponding to the natural frequency, ω0 = 2þc/λ0, ε0 is the dielectric constant, c is the speed of light, and m is the mass of the oscillating entity. The λ-4 dependence and the size of particles found in the atmosphere imply that shorter wavelengths are scattered much more than longer wavelengths. Rayleigh scattering is the reason why the sky appears blue under sunny weather conditions. However, for FSO systems operating in the longer wavelength near infrared wavelength range, the impact of Rayleigh scattering on the transmission signal can be neglected. The wavelength dependence of the Rayleigh scattering cross section in the infrared spectral range is shown in Figure 3.1.
Figure 3.1 Rayleigh scattering cross section versus infrared wavelength.
The Mie scattering regime occurs for particles about the size of the wavelength. Therefore, in the near infrared wavelength range, fog, haze, and pollution (aerosols) particles are the major contributors to the Mie scattering process. The theory is complicated, but well understood. The problem arises in comparing the theory to an experiment. Because absorption dominates most of the spectrum, data must be collected in wavelength ranges that occur in an atmospheric window, with the assumption that only scattering is taking place. In addition, the particle distributions must be known. For aerosols, this distribution depends on location, time, relative humidity, wind velocity, and so on. An empirical simplified formula that can be found in literature 1 and that is used in the FSO community for a long time to calculate the attenuation coefficient due to the Mie scattering is given by the following:
In this formula, V corresponds to the visibility, and λ is the transmission wavelength. However, this formula has been challenged recently by the FSO research community. The transmission wavelength dependency of the attenuation coefficient γ does not follow the predicted empirical formula. More precise numerical simulations of the exact Mie scattering formula suggest that the attenuation coefficient does not drastically depend on wavelength as far as the near infrared wavelength range typically used in FSO systems is concerned. The overall conclusion that can be derived from empirical observation is that Mie scattering caused by fog characterizes the primary source of beam attenuation, and that this effect is geometrically accentuated as distance is increased. For all practical purposes, the visibility conditions in the FSO deployment area must be studied. Visibility data collected over several decades is available from the National Weather Services and can be used to derive distance-dependent availability figures for a particular geographic region of deployment. However, a complication results from the fact that weather conditions are typically measured at airports that can be located away from the actual FSO installation location. Some FSO vendors have started to collect data directly from metropolitan areas and cross-correlate these findings with data collected at nearby airports to optimize the availability statistics. Environments with strong variations in microclimate are especially challenging. For most commercial FSO deployments, operation in heavy fog environments requires keeping the distances between FSO terminals short to maintain high levels of availability. The link power margins of most vendor equipment allow for availabilities that exceed 99.99% if distances are kept below 200 m.
Atoms and molecules are characterized by their index of refraction. The imaginary part of the index of refraction, k, is related to the absorption coefficient, α, by the following:
where σa is the absorption cross section and Na is the concentration of the absorbing particles. In other words, the absorption coefficient is a function of the absorption strength of a given species of particle, as well as a function of the particle density.
In the atmospheric window most commonly used for FSO, infrared range, the most common absorbing particles are water, carbon dioxide, and ozone. A typical absorption spectrum is shown in Figure 3.2. Vibrational and rotational energy states of these particles are capable of absorption in many bands. Well-known windows exist between 0.72 and 15.0 μm, some with narrow boundaries. The region from 0.72.0 μm is dominated by water vapor absorption, whereas the region from 2.04.0 μm is dominated by a combination of water and carbon dioxide absorption.
Figure 3.2 Atmospheric transmittance measured over a sea level 1820 m horizontal path 2.
The abundance of absorbing species determines how strongly the signal will be attenuated. These species can be broken up into two general classes: molecular and aerosol absorbers. Figure 3.3 shows the transmission spectrum for clear sky conditions with a standard urban aerosol concentration providing a visibility of 5.0 km. This graph was generated by using the Air Force's MODTRAN 3 program. Included in this calculation was absorption from water vapor, carbon dioxide, and so on.
In the near infrared, water vapor is the primary molecular absorber, with many absorption lines to attenuate the signal. Above 2.0 μm, both water vapor and carbon dioxide play a large role. The vibrational and rotational transitions determine which energies are easily absorbed, but the large number of permutations greatly increases the number of lines. Figure 3.4 shows the clear sky transmission for water vapor only. You can see that water vapor dominates the clear sky transmission in the near infrared. The large number of lines contributes to a complicated spectrum with occasional windows at popular FSO frequencies, such as 850 and 1,550 nm. Figure 3.4 shows the carbon dioxide transmission. Occasional sharp resonant peaks are superimposed on an overall relatively flat background.
Figure 3.3 Transmission as a function of wavelength under urban aerosol conditions (visibility = 5 km), as calculated by MODTRAN.
Aerosols occur naturally in the form of meteorite dust, sea-salt particles, desert dust, and volcanic debris. They can also be created as a result of man-made chemical conversion of trace gases to solid and liquid particles and as industrial waste. These particles can range in size from fine dust less than 0.1 μm to giant particles greater than 10.0 μm. One estimate determined that 80% of the aerosol mass is contained within the lowest kilometer of the atmosphere. Land produces more aerosols than ocean, and the Northern Hemisphere produces 61% of the total amount of aerosols in the world.4 Because the radii span the infrared, scattering from these particles can definitely be a problem for FSO systems. However, these particles also absorb in the infrared wavelengths. For example, carbon and iron have many absorption lines, but their abundance in the atmosphere is usually limited. Figure 3.5 shows the clear sky transmission including urban aerosols. A comparison of Figures 3.5 and 3.4 shows how the transmission of the atmosphere is affected by aerosol particles.
The desert might seem the perfect location for an FSO system. This is certainly true as far as the attenuation of the atmosphere is concerned. However, in hot, dry climates, turbulence might cause problems with the transmission. As the ground heats up in the sun, the air heats up as well. Some air cells or air pockets heat up more than others. This causes changes in the index of refraction, which in turn changes the path that the light takes while it propagates through the air. Because these air pockets are not stable in time or in space, the change of index of refraction appears to follow a random motion. To the outside observer, this appears as turbulent behavior.
Figure 3.4 Clear sky transmission as a function of wavelength for water (top) and carbon dioxide (bottom) as calculated by MODTRAN.
Laser beams experience three effects under turbulence. First, the beam can be deflected randomly through the changing refractive index cells. This is a phenomenon known as beam wander. Because refraction through a media such as air works similarly to light passing through any other kind of refractive media such as a glass lens, the light will be focused or defocused randomly, following the index changes of the transmission path. Second, the phase front of the beam can vary, producing intensity fluctuations or scintillation (heat shimmer). Third, the beam can spread more than diffraction theory predicts.1
A good measure of turbulence is the refractive index structure coefficient, Cn2. Because the air needs time to heat up, the turbulence is typically greatest in the middle of the afternoon (Cn2 = 10-13 m-2/3) and weakest an hour after sunrise or sunset (Cn2 = 10-17 m-2/3). Cn2 is usually largest near the ground, decreasing with altitude. To minimize the effects of scintillation on the transmission path, FSO systems should not be installed close to hot surfaces. Tar roofs, which can experience a high amount of scintillation on hot summer days, are not preferred installation spots. Because scintillation decreases with altitude, it is recommended that FSO systems be installed a little bit higher above the rooftop (>4 feet) and away from a side wall if the installation takes place in a desert-like environment.
Figure 3.5 Transmission as a function of wavelength for urban aerosol only as calculated by MODTRAN.
For a beam in the presence of large cells of turbulence compared to the beam diameter, geometrical optics can be used to describe the radial variance, σr, as a function of wavelength and distance, L, as follows:
This relationship implies that longer wavelengths will have less beam wander than shorter wavelengths, although the wavelength dependence is weak. Although keeping a narrow beam on track might be a problem, the rate of fluctuations is slow (under a kHz or two), such that a tracking system can be used.
When you have seen a mirage that appears as a lake in the middle of a hot asphalt parking lot, you have experienced the effects of atmospheric scintillation. Of the three turbulence effects, free-space optical systems might be most affected by scintillation. Random interference with the wave front can cause peaks and dips, resulting in receiver saturation or signal loss. "Hot spots" in the beam cross section can occur of the size , about 3 cm for an 850 nm beam 1 Km away. A great deal of work was done on this topic for applications like telescope signals and earth-satellite links, where a majority of the scintillation could be observed near the Earth's surface. FSO systems operate horizontally in the atmosphere near the surface, experiencing the maximum scintillation possible.
Scintillation effects for small fluctuations follow a log-normal distribution, characterized by the variance, σi, for a plane wave given by the following:
where k = 2þ/λ. This expression suggests that larger wavelengths would experience a smaller variance, all other factors being equal. For FSO systems with a narrow, slightly diverging beam, the plane wave expression is more appropriate than that for a spherical beam. Even if the wave front is curved when it reaches the detector, the transmitting beam is so much larger than the detector that the wave front would be effectively flat.
The expression for the variance for large fluctuations is as follows: 5
suggesting that shorter wavelengths would experience a smaller variance. In FSO deployment, the beam path must be more than 5 m above city streets or other potential sources of severe scintillation.
The beam size can be characterized by the effective radius, at, the distance from the center of the beam (z = 0) to where the relative mean intensity has decreased by 1/e. The effective radius is given by the following:
The wavelength dependency on beam spreading is not strong. The spot size can often be observed to be twice that of the diffraction-limited beam diameter. Many FSO systems incur approximately 1 m of beam spread per kilometer of distance. In a perfect world with no environmental attenuators present, beam spread would be the only distance-limiting variable.