How to correctly calculate a fiber optic line.
No more difficult than calculating losses on ordinary copper wires.
Even easier.
You just need to get used to the terminology adopted by fiber optic engineers.
For example, manufacturers of receiving/transmitting equipment provide the so-called «optical budget» in their descriptions, i.e. the permissible losses of the optical signal along the entire path from the transmitter to the receiver.
Let's consider the TC4641 — TC4642 video signal transmission system.
An optical budget of 16 dB is specified for it. This means that the permissible transmission losses are 16 dB.
Let's estimate how many kilometers of transmission this will last.
1) Let's immediately provide a reserve for unexpected deterioration of the cable parameters over time (3 dB). The reserve is not a burden. Surely, someday someone will pull the connectors or step on the cable. They won't break it, but the losses will increase.
2) Since we are talking about kilometers, the main section of the cable laying is obviously on the street. Outdoor cables are inconvenient and even, as a rule, unsuitable for laying indoors (including due to fire safety requirements). Usually, immediately after entering the building, the external cable is connected to the internal one, which already goes to the equipment.
Losses at such joints are 2 times 0.5 dB. These losses can be reduced by welding the fibers very carefully (up to 0.05 dB), but in practice mechanical clamps are more often used than welding, and welding in the field by less experienced hands can give the same 0.5 dB. In principle, these losses can be avoided altogether, but then you will have to place the equipment near the point where the cable enters the building and very carefully separate the bare, unprotected fibers coming out of the sheath.
3) 12 dB left. Let's say we used a cable with a nominal loss level of 3 dB/km. If we take into account that on average the cable will have to be extended once per kilometer during installation (or subsequent repair), then the remaining 12 dB should be divided by 3.5. It turns out to be about 3.5 km.
4) However, that's not all. Now let's look at another parameter in the equipment datasheet — the signal bandwidth. The system mentioned implements high-quality, frequency-modulated transmission free from problems with attenuation instability. The required fiber bandwidth is 100 MHz. We look at the cable parameters and — oh horror! — the selected cable has only 250 MHz*km. So the permissible length is only 2.5 km.
We will have to choose another cable, this time we choose the one with the widest frequency band, which is — 600 MHz per kilometer.
Should be enough for 6 km! However: this cable has a fiber diameter of 50 µm. This is smaller than the standard 62.5 µm, so (according to the transmitter specifications) it will be possible to introduce significantly less optical signal power into this fiber (by 3 dB).
This time the length limitation arises due to the usual amplitude attenuation, so the permissible cable length will be (12-3)/3.5, i.e. again about 2500 meters.
Of course, and this is much more than can be achieved from a copper cable even with the use of amplifiers-correctors. And the calculations were made for the cheapest option, at a wavelength of 850 nm.
If 2.5 km is not enough for you, it is enough to take the version of receivers and transmitters at 1300 nm.
In this range, decent cables have an attenuation of 0.8-0.9 dB/km, and a frequency band of up to 1000 MHz/km, so 10 km is a completely realistic distance.
If this is not enough for you, then you will have to use the so-called single-mode systems.
The lasers used in them (don't be afraid of this word — these are semiconductor lasers, the same as in CD players) allow working with very thin (single-mode) fiber, only 9 µm in diameter, and provide such power that the permissible losses (optical budget) are 25-30 dB, and at an even longer wavelength — 1550 nm.
In that range, the losses in the cable are even less, the result is 100 km without problems.
If you do not remember minor problems like laying solid sections of cable 5 km long, welding all the connections and generally the need to avoid accidents — such as an excessively small bending radius or an excessively large angle from the horizontal (the parameters of the fibers deteriorate somewhat if they support at least their own weight).
However, such a system will work for 30 kilometers, even if you take «some» cable, throw it «somehow», and plug the ends on plasticine into the connectors of the transmitter and receiver.