Reference Systems
--

Reference systems for a spacecraft downlink to Earth will be *loosely based* on Voyager for X-band and NASA's DSOC (Deep Space Optical Communications) for optical.

    Type      Power(W)      f(GHz)     λ(cm)       TX diam(m)    RX diam(m)
    ------    --------    ---------    --------    ----------    ---------
    X-band       22             8.4    3.6            3.66          70
    Optical       4       193,500.     0.000155       0.5            5

Using the longer optical wavelength of 1550 nm instead of 850nm lets you have a nice optical fiber communications single-mode laser diode efficiently coupled to a single mode fiber, then use EDFAs (erbium-doped fiber amplifiers) to optically amplify the signal to several Watts while keeping it within a single mode fiber. This is necessary to take advantage of the diffraction limited optics of the telescope to produce a narrow transmit beam.

I used 0.5 meters for the spacecraft's optical "dish" because that's the diameter of an [actual telescope mirror that is on each of the voyagers now](https://space.stackexchange.com/a/17014/12102). 

Link Budget
--

From [this answer](https://space.stackexchange.com/a/24343/12102):

$$ P_{RX} = P_{TX} + G_{TX} - L_{FS} + G_{RX} $$

 - $P_{RX}$: received power on Earth
 - $P_{TX}$: transmitted power by Voyager
 - $G_{TX}$: Gain of Voyagers transmitting antenna (compared to isotropic)
 - $L_{FS}$: Free space Loss, what we usually call $1/r^2$
 - $G_{RX}$: Gain of Earth's receiving antenna (compared to isotropic)

$$G \sim \left( \frac{\pi d}{\lambda} \right)^2$$ 

$$L_{FS} = 20 \times \log_{10}\left( 4 \pi \frac{R}{\lambda} \right).$$

Currently Voyager 1 is about 2.1E+13 meters (yes, 21 *billion* kilometers!) away.

    Type      P_TX (dBW)    G_TX(dBi)    L_FS(dB)    G_RX(dBi)    P_RX(dBW)    photon/sec
    ------    ----------    ---------    --------    ---------    ---------    ----------
    X-band       13.4          50.0        317.3        75.7        -178.2       272,000
    Optical       6.0         120.1        404.6       140.1        -138.4       113,000

**That's an increase in received power of 10,000 times!**

So right off the bat we see that by shrinking the wavelength by 20,000 times more than offsets smaller diameters of the "dishes". 

A really surprising thing to me is that the number of photons ($E = h \nu$) is almost the same! At a handful of GHz we usually don't talk about photon rate because they are very difficult to count and even at liquid helium temperature the background photon rate is quite high.

But at optical frequencies we can certainly count individual photons! So instead of comparing the received power 1.5E-18 W to $k_B T$ (about 1.4E-22W at 10K) we can just go directly to photon counting statistics. Even at room temperature, the rate of thermally produced *optical photons* is very low. We are no longer in the Rayleigh-Jeans regime, [discussed further here](https://space.stackexchange.com/a/25744/12102).

I will leave further discussion of photon counting to a future question and answer session. Instead of photomultiplier tubes which work well for visible and just barely infrared (say 800 nm) what is in vogue now is superconducting nanowire position-sensitive photon detectors for the downlink receivers at least. See the images below for example (demonstrated by the Lunar XXX with LADEE)


Screenshots from [Overview and Status of the Lunar Laser Communications Demonstration](https://www.researchgate.net/publication/258711671_Overview_and_Status_of_the_Lunar_Laser_Communications_Demonstration):

[![enter image description here][1]][1]



----

REFERENCES:

 - [DESCANSO Voyager Telecommunications](https://descanso.jpl.nasa.gov/DPSummary/Descanso4--Voyager_new.pdf)
 - [Deep Space Optical Communications (DSOC)](https://www.lpi.usra.edu/opag/july2014/posters/9-DSOC_OPAG_Poster.pdf) poster
 - [Deep Space Optical
Communications](https://www.nasa.gov/sites/default/files/atoms/files/tglavich_dsoc.pdf) presentation
 - [Deep Space Optical Communications](https://en.wikipedia.org/wiki/Deep_Space_Optical_Communications) Wikipedia
 - [Overview and Status of the Lunar Laser Communications Demonstration](https://www.researchgate.net/publication/258711671_Overview_and_Status_of_the_Lunar_Laser_Communications_Demonstration) presentation in Researchgate
 - [Deep Space Communications via Faraway Photons](https://www.jpl.nasa.gov/news/news.php?feature=6967) NASA JPL News
 - [Psyche spacecraft](https://en.wikipedia.org/wiki/Psyche_(spacecraft)) Wikipedia


  [1]: https://i.sstatic.net/7QVL9.jpg