I was thinking about the silent-alarm problem: suppose a human is being robbed at gunpoint in their store or home, and they want to sound an alarm, but without getting shot. This requires some kind of alarm system and at least unidirectional communication from them to it; it’s very helpful if this connection is bidirectional, so the alarm system can notify them that you’re tripping it, and maybe avoid false alarms.
Anything the human can do voluntarily does can be interpreted as a signal by the alarm system, given appropriate sensors: blinking, head tilts, hand gestures, other eye gestures, other head gestures, tongue movements, shifting their weight, whistling, humming, breathing patterns, sucking in their stomach or pooching it out, wiggling their toes inside their shoes (as in The Eudaemonic Pie), swallowing, raising eyebrows, emitting brain waves, and so on. But since, by hypothesis, they are under close observation and possibly physical restraint from the robbers, the signals ought to inspire a minimum of suspicion.
Communication in the other direction is subject to similar constraints. The actuators used by the alarm system to communicate with its humans need to be inconspicuous so that the robbers do not deactivate them (for example, with a bullet or spray paint), and in particular should be much more difficult for the robbers to observe than for the defenders. So, for example, sounds on loudspeakers, visible flashing lights, pervasive floor vibrations, and the like, might draw suspicion.
An additional constraint in some circumstances is that the actuators themselves should not be tempting theft targets; conspicuous LCDs and luminaires may induce robberies where otherwise none would have occurred. Prevention is better than cure, because prevention doesn’t get you shot during a failed robbery and doesn’t provoke retribution.
In-ear and behind-ear hearing aids (see Hearing aids for disability compensation, protection, and augmentation) can receive a variety of signals (radio waves, infrared, near-field electromagnetic, ultrasound, etc.) and provide auditory cues to the wearer. They are only moderately likely to tempt theft or to be suspected of forming part of an alarm system, at least initially, and robbers will hesitate before removing them, since usually their objective requires that the defenders be able to hear their demands.
Also, hearing aids can be equipped with a variety of sensors for communication in the other direction: accelerometers to measure head tilt, galvanometers to measure subcutaneous nerve activity related to muscle movement, and of course microphones and cameras.
There’s a significant safety concern here, in that buggy hearing-aid firmware can easily produce sound at ear-damaging volumes.
The available communication bandwidth here is presumably close to that of human speech, some 39 bits per second.
Several ultrasound-pointcasting demonstration systems have been built that project ultrasound beams at people’s ears to produce private sound. These use nonlinear air–ear interactions to produce audible-range sounds inside people’s ears from much stronger ultrasound.
Presumably it is possible to do the same kind of thing with millimeter-wave radio beams if they are strong enough, but I’m not sure if there’s a mechanism for converting the millimeter-wave light to nerve impulses that isn’t destructive to the human, such as skin heating. I have similar safety concerns about ultrasound.
Again, this is probably around 39 bits per second.
A receiver cemented to a tooth with dental cement or implanted in a tongue piercing can produce bone-conduction sound that the human can detect even at very low energy levels. Electric shock (<1mA) is another possible communication channel. Implants in such places are also well situated to sense tongue movements, tooth clacking, and sotto voce vocal signals.
These have a great advantage over hearing aids: they are entirely invisible if the robbers do not know to look for them, and even then they are difficult to distinguish.
These, too, are probably around 39 bits per second, except that the electrical-shock channel is probably more like 5 bits per second.
Cellphones commonly alert the humans to events by vibrating, stimulating the skin. This approach can also be used as a communications channel of rather low bandwidth, perhaps around 5 bits per second.
An indicator light, such as a conventional 40mW green LED emitting its ≈4mW (2–3 lumens†) of light, can easily be visible at 1–10 meters distance, depending on lighting conditions; by flashing in different time-domain patterns, such as Morse code, it can convey messages, perhaps around 10 bits per second.
However, a normal LED suffers from equal visibility to the robbers. If a defender looks at the LED, the robbers may understand the LED’s significance and destroy or paint over it.
The 2–3 lumens of a conventional LED is spread over about π steradians, thus amounting to about one candela. At 2 meters radius, this 2–3 lumens is spread over about 13 m² of the 50-m²-area sphere of 2 meters radius centered on the LED, thus illuminating the defender at about 0.1–0.2 lux.
This situation can be improved by using a laser, steered by mirrors, to pointcast the information to the defender’s eye pupil. This will be minimally visible to the robbers, because it is only necessary to use the same 0.1–0.2 lux to achieve the same visibility to the defender that the conventional LED would have had. If the pupil is about 4 mm across, this amounts to about 1.3 × 10⁻⁵ m² out of the 13 m² mentioned above, so the laser can and indeed must be much dimmer than the LED: rather than 2–3 lumens, it should run at 2–3 microlumens, amounting to a few nanoamperes of drive current for a semiconductor diode.
A higher data rate, however, would be desirable.
† I’m guessing here; I haven’t checked datasheets.
This higher data rate is achievable by using spatial modulation as well as time-division multiplexing. If the defender has their eye focused on the laser, it will appear as merely a point of light; however, if they defocus their eye, like any other point source, the point of light expands to a blurry bokeh circle like those discussed in Real-time bokeh algorithms, and other convolution tricks and Debokehfication. The pattern of the bokeh reflects the spatial modulation of the light at the pupil; for example, if part of the pupil is obscured by eyelashes, the shadows of those eyelashes can be seen on the retina.
By scanning the laser in a raster pattern over the pupil, using either galvo-controlled mirrors or something subtler like piezo-controlled mirrors, while modulating a video signal onto it, could produce a readable message in the defocused bokeh. The defender will need to look at it so that the message is focused on their fovea, but robbers following their gaze will see nothing of interest.
The degree of defocus possible, and thus the maximum degree of expansion of the bokeh pattern on the retina, depends on the individual person and on the state of their eye, especially the degree of dilation of the pupil. Earlier today, indoors during the day, this body’s eyes had a defocus diameter equivalent to about 6 mm at a radius of 800 mm, or about 8 milliradians (26 minutes of arc, in ancient Babylonian units), but now that it’s night, it has a defocus diameter of about double that, about 16 milliradians. Presumably if I turned the light off and waited a while, I could beat 20 mrad†. All of this is for distant point-source lights, on the order of 8–20 m away, effectively ∞.
How much information could you display in an 8-milliradian-wide
circle? Well, that depends on the resolving power of the human visual
system. Right now, on this laptop, a 7×13 font is readable to this
body, but a 6×10 font is not. The screen is 1150 mm away from this
eye, 305 mm wide, and 1920 pixels wide. This means each (square)
pixel is 160 μm wide and subtends about 140 μrad (28 arcseconds, in
ancient Babylonian units.) Reading 7×13 (xterm -fn 7x13) requires,
roughly, distinguishing bright from dark areas that are separated by
about 1½ pixels.
However, a more direct measurement of the information-carrying capacity of a small area of the visual field is that the 7×13 characters are about a milliradian wide and 1.8 milliradians high, and carry about 6–7 bits of information each, for a textual information density of about 3–4 bits (or 0.56 letters) per square milliradian. Perhaps more advanced rendering methods like those described in Dercuano plotting could improve this bound, but it’s at least demonstrably feasible, with the eyes in this body.
So an 8-milliradian-wide circle, with its area of 50 mrad², could hold about 25–30 marginally readable letters, or 150–200 bits. The rapid serial visual presentation (“RSVP”) method associated with speed reading can display a series of phrases at around 1 Hz without losing readability, so this method has a bit rate of around 128–256 bits per second, probably dramatically higher than the others considered above.
The scanning action of the laser needs to be fairly precise. In pixels, we’re talking about something on the order of a 60-pixel-diameter circle. Considering a viewing distance of 2 m, these 60 pixels need to be mapped across the 4-mm pupil, so about 70 microns per pixel, which is 35 microradians; the laser beam thus needs to have a divergence of less than about 35 microradians, and the deflection-scanning apparatus needs to have a reproducibiity of 35 microradians or so to keep alignment of successive scan lines as we raster across the pupil.
However, there’s a huge problem! This small divergence requires a relatively large laser and mirrors; the Airy limit of sin θ = 1.220λ/D means 35 × 10⁻⁶ = 1.22 × 555 nm / D, which is to say D = 1.22 × 555 nm / 35 × 10⁻⁶ = 19 mm. This, in turn, means that the laser won’t look like a point source to the defender, since it subtends 10 milliradians, and the image of that aperture will be convolved with the desired bokeh pattern, blurring it all to shit!
This ratio between 10 mrad and 140 μrad is about 70, so by coarsening the intended resolution of the bokeh image by about √70, a factor of 8 or 9, to 1.2 mrad, we can use a laser aperture that also only subtends 1.2 mrad (2.4 mm for a viewing distance of 2 m), and achieve the desired effect. But instead of 25–30 readable letters, we have a 7-pixel-diameter circle, holding about 40 pixel — enough for one letter.
We can probably present more than one letter per second, but it suggests that the bokeh approach won’t beat the auditory approaches on bandwidth.
† milliradians, not millirads, of course.
Suppose that we give up on the whole bokeh idea. Can we use a similar laser-tracking approach to get a low-power video image that’s only visible to one person, without them defocusing their eyes? Something like Jeri Ellsworth’s CastAR retroreflective-surface VR projector, but without the conspicuous glasses.
Yes! Using point-source illumination from the opposite wall, which might or might not be a laser:
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In one variation of this scheme, we use a scannable laser on one wall which raster-scans across a deflectable mirror of some 20 mm diameter on the other wall (perhaps behind a color filter to filter out extraneous wavelengths), which is synchronously raster-scanning so that, wherever the beam falls on the mirror, that point gets reflected to the defender’s eye.
To get those same 60 pixels across the 20-mm mirror, you can tolerate a beam divergence of about 300 μm, which is achievable at a 2-meter distance with a laser output aperture of under 2 mm in diameter.
Of course, you don’t actually need the mirror to raster-scan for that. You could just use an ellipsoidal mirror (and probably just a parabolic one), so that you get the desired property even without scanning the mirror. However, you still need to move the mirror when the defender moves, in order to change the focal point; and, worse, you need focusing optics of some kind to adjust to different defender-eye focal distances. Deforming the mirror itself is a feasible solution, especially if it’s cheap metallized plastic; getting a radius of curvature of about 2 meters (ideal for redirecting all light between two foci each 2 meters from the mirror) only requires depressing the center of a 20-mm-wide mirror by about 25 μm, or depressing its center by 12.5 μm while raising its edges by that same 12.5 μm.
The above variations only need about 60 scan lines, but probably mechanically scanning a massive mirror at only 3.6 kHz would make a conspicuous noise, since that’s close to the humans’ peak auditory sensitivity frequency.
In another variation, the light source is just a point source, such as a small LED, perhaps shrouded like some keychain ultraviolet LEDs so that it illuminates the whole mirror and almost nothing else. The entire mirror is illuminated at once, rather than being scanned as in the above schemes, but this mirror is something like a DLP chip: it has pixels that can be individually turned on or off, either with actual DLP or with an LCD. You still need some kind of head tracking to point the result at the defender’s eyes. All of this can be hidden behind a color filter so it doesn’t draw attention.
With these approaches, you can get the 150–200 bits per second rates I was hoping for earlier from the bokeh approach, the ones ruined by the divergence problem.
These schemes encode the information not in the position of the laser spot on the viewer’s pupil, as the bokeh scheme does, but in the direction from which it enters. I don’t know if it’s possible to do better than either with some kind of combination scheme.
Normal laser communication like Ronja uses time-domain signaling, using optics only to get antenna gain, but perhaps you could use such a spatial-modulation approach for machine-to-machine communication as well, as CCD oscilloscope suggests doing for analog memory inside an oscilloscope. In that context you might not be limited by the considerations of clandestinity described here, so much larger optics might be feasible. By scanning your signaling beam across the lens of the receiver in a raster pattern, you can draw a bitmap in the bokeh on their “focal plane” sensor, which can be positioned at such a distance from the optical focal plane that the bokeh nearly covers it; or, by scanning it across your own output optics, you can paint a picture that they see when it’s entirely in focus.