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NASA's Mission Page Deep Space Optical Communications (DSOC) includes the following:

Key DSOC technologies developed for the project include: a low-mass spacecraft disturbance isolation and pointing assembly; a high-efficiency flight laser transmitter; and a pair of high-efficiency photon counting detector arrays for the flight optical transceiver and the ground-based receiver. These technologies are integrated into the DSOC flight laser transmitter and ground-based receiver to enable photon-efficient communications with the capability to discern faint laser signals from background "noise" contributed by solar energy scattered by the Earth's atmosphere.

Two previous questions and their answer highlight that for conventional optical communications schemes based on photodiode conversion of modulated optical intensity to likewise-modulated electrical signals the achievable data rate scales as (surprisingly) $1/r^4$ rather than the familiar $1/r^2$ for conventional deep-space radio communications systems.

It is possible that an optical system based on photon counting will have a more favorable scaling of data rate versus distance than $1/r^4$ so I'd like to ask:

Question: How is the maximum data rate of the Psyche mission's Deep Space Optical Communications (DSOC) system expected to scale with distance?

Further reading:

From SPIE.org's news item Optical communications work best over relatively short distances in space (06 April 2006 Morio Toyoshima, Walter Leeb, Hiroo Kunimori, and Tadashi Takano)

From "Optical communications work best over relatively short distances in space" Figure 1. Maximum data rates for optical and RF communication systems versus link distance. GEO stands for geostationary earth orbit, and arrows show distances to GEO, Moon, and Mars.

Figure 1. Maximum data rates for optical and RF communication systems versus link distance. GEO stands for geostationary earth orbit, and arrows show distances to GEO, Moon, and Mars.

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The scaling with $1/r^4$ holds when receiving an optical signal in a way similar to a RF signal, i.e. by reading it as an amplitude signal.

Photons in the IR/visible/UV range however can be detected individually and their precise arrival time can be measured. That's what the mission page refers to as a "photon counting detector".

With such a detector we are indeed back at the traditional $1/r^2$ scaling - all that counts (no pun intended) is the number of photons received, which clearly scales with the size of the beam spot.

Slide 9 of the presentation (1) shows an analysis of the optical link planned to be used on the Psyche spacecraft. Looking at the linear part(*) of the plot between 0.6 and 2.4 AU gives us a reduction in datarate of about 40 - a scaling with $1/r^{2.3}$.

A more general analysis can be found in (2). Figure 19 shows the expected change in data throughput for different encoding schemes, and again the drop in data rate for reasonable encoding schemes (e.g. PPM=256) is around $1/r^{2}$.


(*) a linear curve in a logarithmic plot means that the relation between the two axes is a simple power law.

References

(1) Status of NASA’s Deep Space Optical Communications Technology Demonstration (JPL, Roberts, 2017)

(2) Deep space optical communications (DSOC) downlink simulation with varying PPM order (Aboagye, 2021)

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