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Flight laser transmitter - for Psyche mission has Mass 29 kg (100 W).
It also requires pointing up to 3 degrees of the Sun (towards the receiver telescope).
My question is about really small probes (less than 1kg) that can carry only a small flashlight or a 1 W laser.
Deep Space Optical Communications (DSOC) - from what distance a flashlight1 can be detected2 by a space-based telescope3
tl;dr: At a million kilometers, with a thin, 2 cm diameter, f=10 cm Fresnel zone plate collimator and laser diode, into a 1 meter diameter receiving telescope, you should be able to pull of 1000 baud downlink with some very clever actuator engineering to keep the laser diode near the focus of the zone plate and doing micro-steering to compensate for your 1 kg spacecraft attitude errors.
We'll use a 1W laser diode because they are
Why is #5 important?
We want a narrow beam so that very far away a telescope will be cable to capture a useful amount of it.
The width of a beam in the far field (in radians) is basically the source diameter divided by the collimator focal length. A laser pointer will have a laser diode with a divergence of something like 3 to 10 degrees and a small collimating lens (molded plastic and therefore usually aspheric) as a single tiny module.
These can give final divergences close to the theoretical 1.22 $\lambda/d$ where the wavelength is of order 1 micron and the diameter is of order 1 mm so about 1 milliradian or about 0.06 degrees.
above: Composite image of two common laser diodes packaged with small collimating lenses, cropped and resized from Wikimedia Commons' Diode_laser.jpg and Metal_covered_Laser_diode_switched_on.jpg
That's good enough to be seen by eye from the ISS from Earth
but not good enough for us.
So your real challenge is to make the biggest aperture collimator for your 1 kg spacecraft.
That's not going to be a big old Newtonian or Cassegrain reflector telescope with a glass or silicon carbide mirror
or a thick bulk lens
it's going to be a planar diffractive device like a zone plate or Fresnel lens or optical counterpart of a Fresnel zone antenna. Basically, since you have essentially an almost single wavelength of light, you can collapse your thick lens or deep-dish mirror to a nearly flat device where only the fractional part of the phase surface is used.
Some excellent examples of this for radio waves can be found in
The simplest, easiest, lightest weight collimator lens I can think of is a thin glass disk (say a 300 um thick fused silica nearly-optically-flat wafer) with a Fresnel zone pattern either etched into it for a phase plate, or patterned as thin absorbing aluminum or gold (say 10 to 100nm thick) as an amplitude plate.
You need to be a clever engineer to find a way to make this thing pop up on deployment such that the laser diode is near the correct focal distance and somewhere near the optical axis (line drawn from the center of the zone plate perpendicular to it). Maybe a shape memory alloy or something even more clever.
This could be a few up to 10 cm. Let's be conservative and call it 2 cm diameter with a focal length of 10 cm. Such a zone plate will have about 1,000 zones with a 5 micron period at the edge - really quite easy to make in a modest university lab these days.
Your theoretical divergence (half-angle) from 1.22 $\lambda/d$ is now about 60 microradians or about 0.0035 degrees.
Sounds impossible to point now, doesn't it? With your 1 kg spacecraft? Well it's doable with a lot more clever engineering. You do have to get pretty good attitude control, but a tiny actuator using light-weight voice coil or other MEMS actuators moves the little laser diode around in 3D near the focal point of your zone plate, so you can do sub 1 degree pointing of the beam electronically to correct for spacecraft attitude imperfections.
At 1 million kilometers (109 meters) a 60 $\times 10^{-6}$ radian beam will be 60,000 meters in diameter.
Your reasonably sized 1 meter diameter receiving telescope will pick up (1/60,000)2 of that, or 3 $\times 10^{-7}$ milliwatts. In engineering terms that's -75 dBm which is not bad at all!
If we assume 1 eV per photon, that's 6 $\times 10^{18} \ \times 3 \times 10^{-10}$ or over a billion photons per second received. Expressed as a photocurrent that's a few tenths of a nanoampere.
If we assume that shot noise limits your bandwidth (rather than kBT thermal noise) then your bandwidth will be something like the square root of the photon rate, or of order 10 kHz.
So with your 1 Watt laser diode, a 2 cm diameter zone plate at 10 cm focal length and a distance of 1 million kilometers, you should be able to pull off something very roughly like 1000 baud.
I've used a nominal wavelength of 1 micron. You'll probably use something between 800 nm and 1.5 microns.
Several factors of 2, $\pi$, and 1/2 and $1/\pi$ have been swept under the rug here, I'm just trying to get an order of magnitude data point
Please note that you can't always scale data rate vs distance the same way that you can for radio because of the way photons are first converted to carriers and then the photocurrent is detected in conventional receivers. If you use a fancier direct conversion receiver it gets better.
