The Free-Space Optical Link Budget

Scope

This article sets out the link budget for optical communication through air or vacuum rather than fiber: the terms that make up the received power, how each is estimated, and where free-space links behave unlike the fiber links the Datacenter Link Budget Explorer accounts. It covers geometric spreading loss, transmit and receive gain, pointing loss, atmospheric attenuation, and turbulence-induced scintillation, then works three budgets spanning eleven orders of magnitude in range: a terrestrial link, a low-Earth-orbit inter-satellite link, and a deep-space downlink. Background: free-space optics, Gaussian beam, beam quality.

Why free space is not fiber

A fiber link loses a fixed number of decibels per kilometer, so its budget is linear in length: double the distance, double the loss in dB. A free-space link obeys a different law. The dominant loss is geometric: the transmitted beam diverges, the far-field spot grows in proportion to range, and the receiver captures only the fraction of that spot its aperture subtends. Because the spot area grows with the square of range, the captured fraction falls with the square of range, and the loss in decibels grows by 20 dB for every tenfold increase in distance. A fiber link is billed by the kilometer; a free-space link is billed by the square of the distance, like any spreading wave.

That single difference organizes everything else. It is why free-space links live or die on how tightly the beam can be collimated and how accurately it can be pointed, and why the atmosphere, when there is one in the path, is the term that decides availability rather than reach.

Geometric loss

Take a beam with full divergence angle $\theta$ (radians). In the far field its spot diameter at range $d$ is approximately $\theta d$. A receive aperture of diameter $D_R$ captures the power fraction

$$\eta_\text{geo} \;\approx\; \left( \frac{D_R}{\theta d} \right)^2 \quad (\theta d > D_R),$$

which is the geometric loss when written in decibels. The divergence is set by the transmit aperture and beam quality: a diffraction-limited beam from an aperture of diameter $D_T$ has a divergence of order $\theta \approx 2\lambda / (\pi D_T)$, so a larger, cleaner transmit aperture spreads less. Real beams run several times the diffraction limit, and the beam quality factor $M^2$ multiplies the divergence directly.

A worked terrestrial case makes the scaling concrete. A beam with 1 mrad full divergence and a 0.10 m receiver, values typical of a modestly collimated terrestrial link:

The 20 dB per decade is the geometric law in the table: from 1 km to 10 km the loss rises by exactly 20 dB while nothing about the hardware changed. Tightening the beam is the only lever that moves the whole column, which is why serious links narrow the divergence to microradians and then face the pointing problem that narrowing creates.

The same physics is often written in the antenna form borrowed from radio, $\eta = G_T G_R (\lambda / 4\pi d)^2$, with transmit gain $G_T \approx 16/\theta^2$ and receive gain $G_R = (\pi D_R / \lambda)^2$. The two pictures agree exactly: for a 15 µrad beam and an 80 mm aperture at 1000 km, the antenna form gives a 108.5 dB transmit gain and a 104.2 dB receive gain against a 258.2 dB path loss, a net of 45.5 dB, which is precisely the geometric result for a 15 m spot captured by an 80 mm aperture. The geometric picture is the more useful one to reason with; the antenna form is convenient when the numbers are large.

Pointing

Narrowing the beam to recover the geometric budget creates the characteristic difficulty of free-space optics: the beam must be aimed to a fraction of its own divergence, continuously, against platform motion and vibration. A microradian is about the angle subtended by a one-millimeter object a kilometer away, and an inter-satellite beam holds that against orbital dynamics. Pointing error $\theta_p$ costs power as roughly $\exp[-(\theta_p/\theta)^2 \cdot \text{const}]$, so a pointing error equal to the beam divergence is not a small penalty but a lost link. This is why laser communication terminals are built around fast steering mirrors, beacon-based tracking, and closed-loop acquisition sequences, and why the acquisition-and-tracking subsystem, not the optics, is usually the hard engineering. It is the term that has no fiber analogue at all.

The atmosphere

A vacuum path has only geometry and pointing. An atmospheric path adds two terms that decide whether a terrestrial link is a carrier-grade service or a fair-weather one.

Attenuation is scattering and absorption by molecules and aerosols. In clear air at 1550 nm it runs a few tenths of a dB/km, negligible against the geometric term. Fog is the killer. The Kim model gives the attenuation from visibility $V$ as $\beta \approx (3.91/V)(\lambda/550\,\text{nm})^{-q}$, with $q$ falling as visibility shortens; evaluated at 1550 nm it gives about 0.35 dB/km in haze ($V = 4$ km), 2.3 dB/km in light fog ($V = 1$ km), and 7.8 dB/km in moderate fog ($V = 0.5$ km). Thick fog, with visibility under 50 m, reaches many tens to hundreds of dB/km, and at that point no reasonable power budget survives a kilometer. There is no wavelength that fixes this: fog droplets are comparable to or larger than the wavelength, so the scattering is nearly grey, and the near-infrared has no meaningful advantage over the visible. This is the reason terrestrial free-space links are sold with a fallback: the recently deployed Taara Lightbridge Pro, for instance, delivers 20 Gb/s full-duplex over kilometer-scale hops and switches to fiber or RF without a dropped packet when fog or heavy rain closes the optical path.

Scintillation is the second atmospheric term, and it degrades the link even in clear air. Turbulent eddies stir the refractive index, and the beam arrives with its intensity flickering and its wavefront distorted. The strength is set by the refractive-index structure parameter $C_n^2$, which ranges from about $10^{-17}\,\text{m}^{-2/3}$ in weak turbulence to $10^{-13}$ near a hot surface at midday, and enters through the Rytov variance $\sigma_R^2 = 1.23\, C_n^2\, k^{7/6} L^{11/6}$ for a plane wave over path $L$ at wavenumber $k$. When $\sigma_R^2$ approaches unity the fading is deep enough to demand several dB of margin held in reserve, spent by aperture averaging (a receiver larger than the intensity speckle integrates over the flicker), by multiple spaced apertures, or by coding and interleaving against the fade's slow timescale. Uplinks to space suffer more than downlinks, because the turbulence sits at the transmit end where it also steers the beam.

Three budgets

The budget itself is the familiar ledger: received power equals transmit power, plus transmit and receive optical efficiency, plus the gains, minus geometric loss, pointing loss, atmospheric attenuation, and a scintillation margin, and the result must clear the receiver sensitivity with margin to spare. What changes across applications is which term dominates.

Terrestrial, kilometer-scale. Geometry is modest (tens of dB over a few km) and the atmosphere is everything: clear-air attenuation is negligible, but the availability figure, the fraction of the year the link is up, is set entirely by the local fog and rain statistics. The design question is not reach but the failover strategy, which is why these links ship with an RF or fiber partner.

Inter-satellite, low Earth orbit. No atmosphere, so geometry and pointing are the whole budget. At 1000 to 5000 km the geometric loss is 45 to 60 dB for a diffraction-limited terminal, and with a watt of transmit power and a sensitive receiver this closes with margin; the engineering is entirely in holding microradian pointing between two platforms in independent orbits. Operational LEO constellations now fly these links in quantity, and the crosslink mesh they form is the reason a satellite network can route without a ground hop.

Deep space. Range dominates so completely that everything else is a rounding error. NASA's Deep Space Optical Communications terminal on the Psyche mission returned data at tens of Mb/s from roughly 0.4 astronomical units, about 60 million km, where the geometric loss exceeds 80 dB even with a large ground telescope and the received signal is counted in photons per bit rather than milliwatts. The link is made possible by photon-counting detectors and heavy coding, not by power, and it is the clearest demonstration that the free-space budget is, in the end, a statement about geometry.

Relation to the fiber budget

The Datacenter Link Budget Explorer accounts a fiber link, where loss is linear in length and dispersion is the second ledger. A free-space link shares the structure, transmit power down to receiver sensitivity with margin, but replaces the linear loss term with the quadratic geometric one and adds pointing and atmosphere. Reading the two budgets side by side is the fastest way to see why fiber won the ground and free-space won the vacuum: over a kilometer of clear ground the two are competitive and fiber is simply easier, while across a vacuum where no fiber can go, geometry is a cost every link pays and free-space optics is the only option that carries real bandwidth.

References: Andrews & Phillips, Laser Beam Propagation through Random Media (2nd ed., SPIE Press, 2005) for the turbulence and scintillation treatment; Kim, McArthur & Korevaar, "Comparison of laser beam propagation at 785 nm and 1550 nm in fog and haze," Proc. SPIE 4214 (2001) for the visibility-attenuation model; Kaushal & Kaddoum, "Optical communication in space," IEEE Access 5 (2017) for the space link budget; NASA Deep Space Optical Communications (DSOC) mission reports (2023-2026). The free-space optics entry summarizes the field and lists representative systems.