In Part 1, we presented an introduction to optical communications over free space paths, in air as opposed to through fibers. It might be time to discuss the free space path.
The Free Space Path
There are many more effects that must be considered in transmission through the air: achieving line-of-sight; scattering by fog, haze, and rain; refraction by a turbulent atmosphere; etc. If we look at the fact that the receiving system is using a photodetector directly, a non-coherent detector, with no mixers or heterodyning, we see that the sensitivity of the system is not unlike that which we could get with a crystal set at radio frequencies. In fact designing for direct optical detection is not unlike designing for a crystal detector receiver. Selectivity and sensitivity, and even impedances and bandwidths, are similar. For that reason, most optical systems are designed for line of sight, and not for communication over obstructed paths. Atmospheric absorption, like that occuring at higher microwave frequencies, adds a certain number of dB loss per mile that becomes an almost insurmountable barrier. A loss of only 0.2 dB per mile may amount to only 2 dB over a 10-mile path, but 20 dB over a 100-mile path, and a very large 40 dB over a 200-mile path. That’s probably the main reason why terrestrial records are about 100 miles … and also that it’s very hard to find a line-of-sight, clear path, more than 100 miles long, even between two mountains.
The Obstructed Path
This is not to say that line-of-sight paths are the only ones that can be bridged. But most paths that require cloud bounce or forward tropo scattering or reflection carry a severe penalty in path loss. The transmitter power can be focused into a 1 mrad beam. The transmitted signal hits the scatterer or reflector and bounces off in a much wider beam, maybe 100 mrad wide. This amounts to an additional 40 dB or so in the path loss. This may be too much to absorb. Experimenters who have observed cloud bounce must deal with very weak receive signals and usually have to use computer software to “dig them out”.
Continuing on the mainstream discussion of optical free space communications, we observe that the most common transmitter today is the electrically modulated solid-state laser diode. The bare diodes have an optical beamwidth of maybe 5 or 10 degrees (100 to 200 mrad) not unlike their brothers, the light emitting diodes (LEDs). In fact much of what is said about laser diodes applies directly to LEDs, too. Most laser diodes are operated in a module containing a focusing lens to bring the beamwidth down to 1 or 2 mrad. To do so requires a lens that is only 1 or 2 mm in diameter. This module is the core of the now ubiquitous laser pointer. The laser diode has a maximum current that the diode can handle without its dissipation becoming so high that it burns out. The laser diode also has a minimum threshold current that it will “lase” at. Between these two current values lies the normal operating region where the optical power output is roughly proportional to the laser diode current.
This characteristic immediately suggests Intensity Modulation, similar to Amplitude Modulation, where the current is varied by the message around some quiescent bias level to vary the intensity of the optical output. Since most PDs produce an output current proportional to the light intensity falling on them, we should have a relatively linear transmission system.
This is not the only modulation scheme in use. Simple on-off keying of the laser diode from zero to some maximum current is often used, especially with a keyed subcarrier to avoid any 60 Hz or 120 Hz interference problems. The subcarrier can be at 800 Hz or so, producing a keyed tone at the receiver to handle CW, PSK, Hellschreiber, AFSK TTY, or any other modulation. In fact anything that could be handled over a voice grade phone line could easily be handled by this optical link. We could increase the bandwidth substantially to handle high-speed data communications, but here we will restrict ourselves to voice and 9600 baud or less.
A useful technique is the use of PWM in voice applications. The laser diode is turned on and off between zero and some max current at a sampling rate maybe four times the max audio frequency allowed. An example would be voice at up to 3 kHz sampled at 16 kHz. The voice is encoded into the duration of pulses at the sampling rate, their duty cycle varying from 0% to 100% and idling at 50% (a square wave). The transmitter laser’s linearity is no longer a factor. The receiver need only have a 3 kHz bandwidth too, and recovery should be excellent.
Now many laser diodes have an integral photodetector of their own to see if the diode is putting out any light. This detector is usually used in an optical power-leveling loop. The current into the laser diode is adjusted to produce its rated optical power output as seen by the integral PD. That’s fine until we try to modulate the laser diode. Then the feedback loop tries to fight us. This effect can be overcome in several ways. The simplest might be to always use on-off keying. The PD feedback could also be disconnected and the current modulated as above. Also the PD reference could be modulated by the message, and the optical output would be forced to track the modulated reference. Personally, I like to control my own current, thank you.
Many off these ideas are sketched in the figures on laser diode transmitters.
The receiving system uses a photodetector feeding its output signal into an audio amplifier. The amplifier need only have enough gain to “hear” the noise out of the PD, and enough bandwidth to handle the message. In practice, this means 60 dB gain or so and 3 kHz bandwidth for voice. It makes sense to remove noise at other unused frequencies by bandlimiting in the amplifier to just what is required by the message. The exact gain required depends on the detector circuit and the noise it produces. Let’s look at some typical detectors.
A simple but very effective PD is the photodiode. The photodiode is basically a regular diode with a junction exposed to incoming light such that a photon of light that is at or above a certain frequency has enough energy in it to knock an electron free from the valence band of the lattice to the conduction band of the lattice, where it can move through the junction to the terminals of the diode. One photon can be absorbed by one electron, which can now move and produce a photocurrent through the diode. The photodiode is usually operated in a reverse biased mode, where the “dark current” is fairly small and the charges created by photons in the junction are quickly attracted to the terminals. These detectors are very inexpensive.
A related device is the phototransistor. Here the junction area is usually smaller, but the photocurrent is “base” current for the transistor, so we observe current gain. These are usually not the best choice for communication systems since the current gain is not constant over optical power input, the active area is smaller, and the effective bandwidth is less. They are more suited to counters and positioners where parts count should be low and speed is not a requirement. They are usually noisier than photodiodes.
Another device is the avalanche photo diode or APD. Here the reverse bias is increased to the verge of breakdown. Then any photoelectrons produced are accelerated sufficiently so that as they collide with atoms in the lattice even more electrons are knocked free into conduction and the current “avalanches” into a larger value. These devices usually have fairly large active areas, good bandwidth, and current gain to improve the sensitivity. They are often slightly lower noise than photodiodes.
There are vacuum tube devices that operate as good PDs. Photocells have just a large coated detector
cathode and a collecting anode at a positive bias. Photons knock electrons off the cathode into the tube vacuum,
which are then pulled to the anode, producing a photocurrent. Photomultiplier tubes are similar, but
instead of a single anode, the device has a series of anodes at increasing
positive potentials. A photoelectron is
knocked free from the cathode and is accelerated toward the first anode. Its impact knocks other electrons free of
it, which are then accelerated toward the second anode. Their impact knocks even more free, and so
on, resulting in a large cascade of electrons from one photon. These devices appear to have the best
internal gain and lowest noise, but are also the most expensive. Their optical cutoff frequency is not all
that good of a match to red lasers or LEDs, tending to be better at yellow and
green. IR diodes may produce nothing at
all from a PMT. Note that silicon photodiodes
are a good match to red and near IR sources.
Let’s consider only silicon photodiodes here. We can estimate their responsivity and noise and therefore their sensitivity as detectors in a communications system. If a detector produces one photoelectron for one incident photon, we can say that it has a quantum efficiency of 100%. If the bandgap is 1 volt, the photon must have an energy of 1 electron-Volt (eV) to knock that electron free for conduction. The charge of the electron is 1.6e-19 coulomb, so the energy of that conduction electron is 1.6e-19 joules. If a current of electrons is produced by a beam of light, we need 0.6e+19 electrons per second to produce 1 ampere of current (1 coulomb/second). Such a light beam (or electron current) has a power of 1 watt (1 joule/second) too. So we can define the responsivity of the photodetector at a frequency or wavelength as the amount of current produced per watt of incident light. At their peak, in the near IR, silicon photodiodes have a responsivity of about 1 amp/watt. At red light wavelength (632 nm or about twice the frequency) the responsivity will have dropped to about 0.5 amp/watt, since each photon carries twice the energy, but still only produces one photoelectron.
Since no diode is perfect, but leak some current, we can measure the dark current of a photodiode (a diode in the dark) to be a few tens of nanoamperes typically. This small amount of dark current is really made up of a stream of discrete electrons therefore has a small ac noise in current superimposed on the dc current. In particular this shot noise is calculable as
In = sqrt(2*e*BW*Idc).
This is a noise that can’t be eliminated. Usually amplifier excess noise and resistor thermal noise are also present, but even if they are negligible, shot noise is still there. How big is the shot noise? Well, that depends on the dark current, but it also depends on the ambient light level … more ambient light, more Idc, yields more In, noise current. That noise current usually goes through a resistor, producing a noise voltage, etc. The limit of detectability occurs when there is no ambient light and the incident light produces maybe a few tens of electrons. Any ambient light should raise the idling current and therefore the shot noise. Avalanche photodiodes and photomultipliers have a different limit of detectability since the ratio of the signal current produced by light and the shot noise produced by their dark current is now different from regular photodiodes.
As an example, let’s consider a photodiode with 12 pa dark current, driving a 1 Meg load resistor. Let’s estimate the shot noise in a 2500 Hz bandwidth. By the equation,
In = sqrt(2*1.6e-19*2.5e3*12e-12) = 1e-12 amp
Putting it through a 1 Meg resistor produces 1 uV of noise voltage. Now the thermal noise voltage produced by a 1 Meg resistor by itself is about 6 uV, so we see that the shot noise voltage is a little smaller than the thermal noise voltage. Cooling the resistor would reduce the noise. By the way, low noise op-amps often have internal noise of 0.1 uV for 2500 Hz, so in this case, noise from a following stage should not dominate.
One might ask how does this stack up to an OPT101 for example. Well the OPT101 is specified to have a responsivity of 0.45 amp/watt using a transimpedance amplifier, with about 100 uV of noise voltage out in 2500 Hz bandwidth using its internal 1 Meg resistor. So as good as an OPT101 is, we are nowhere near theoretical limits. By the way, dark current is about 2.5 pA.
The OPT301 looks a bit better. Its responsivity is a little higher at 0.47 A/W; its dark current is a little lower at 0.5 pA; and it only has 30 uV of noise voltage in 2500 Hz using its internal 1 Megohm feedback resistor. Still the op-amp and resistor noises dominate.
The noise above is measured from 0.1 Hz up, so the 1/f noise of the op-amp is in there. 1/f noise appears to be appreciable only below 100 Hz. If we are concerned with 400 Hz to 2900 Hz, we should have negligible 1/f noise, and the noise power density should be closer to 0.75 uV on 2500 Hz for the OPT301. Also at room temperature, the dark current is closer to 0.5 pA, so the shot noise current should be 0.25 pA, producing 0.25 uV through a 1 Meg resistor. The OPT301 is getting close to theoretical limits
A useful concept is noise-equivalent-power (NEP). NEP is the input signal required to give a signal output equal to the noise output of the detector. For instance, the OPT301 has an NEP of 0.6e-10 watts or –72 dBm optical for a 2500 Hz bandwidth. The OPT101 is a little noisier at 1e-10 watts or –70 dBm NEP.
Many experimenters use higher values of resistance than 1 Meg shown here. That is because with constant responsivity, the signal voltage is higher linearly with R, while the noise voltage increases as sqrt(R). The problem is the bandwidth goes down linearly as resistance R. So until BW is a problem, or something else dominates, we should use higher R.
Well, for line of sight paths, the average solid-state laser pointer diode at 3 mW with a good receiver like an OPT101 over a voice bandwidth can muster about 70 dB of system gain to just have signal = noise. That means we have to pick up 1 millionth of the source with the receiver to have acceptable SNR. That means with a 20 mm diameter receiver lens, we need to keep the transmitter spot to 20 m diameter. With a 2 mrad laser pointer, that occurs at 10 km. For contest contacts, I think I’d like to broaden the transmitter beam to 10 mrad while keeping the field of view at the receiver to 10 mrad with a 20 mm lens. That should be fine for more than 1 km and much easier to align.