Thinking a bit further on this ...

... amongst what I'll term displays, which is to say, an updatable presentation medium, there are generally illuminated and ambient variants. These date back to scratching on sand or dirt, erasable wax tablets (used by Greeks and Romans for education), slates (common amongst students in the 18th/19th centuries, roughly), and of course modern variants.

I use "illuminated" to describe any display in which the information content is expressed within the light incident or emitted from the display. This would capture all of, say, a traditional CRT video display, a projection screen (where the image is reflected off the display surface), rear-projection displays (see 1990s-styple projection televisions), Nixie tubes, neon (and related) signage, and discrete-element displays such as LCD or plasma screens. What this captures is the distinction between a CRT display in which an image is painted (using an electron gun and colour mask) and an LCD display in which individual pixel elements are activated. I was unhappy with how I'd considered both as equivalent in my initial comment. I would argue that both are screens, but what's really common is that the illumination carries the signal.

Ambient displays have a content encoding mechanism distinct from any illumination, thought that illumination might be integrated into the display itself such as with backlit liquid-crystal displays or "frontlit" e-ink (electrophoretic) displays. Here the surface itself is physically altered and ambient light is used to reveal that arrangement.

Again, your eyeball is a screen (incident light carries the image, see the camera obscura for a physical analogue), air ... is not.

If you wanted to consider how you might convey information via thin air, it seems that there are a few possible options:

- One could create a temporary screen surface within air and project onto it. The water screen display used in tunnel excess-height warning systems is one such example. Note that the prominent visuals for that system show it at night or under limited ambient light. The effect under direct daylight would be far less prominent. Other possibilities include some sort of mesh or hanging thread pattern onto which an image could be projected. This is actually used to an extent in some IMAX theatres, particularly domed screens, in which the "solid" dome is actually a mesh with many holes in it, which both reduce overall mass and permit greater ventilation of the theatre space itself. At viewing distance, the holes are undetectable. All of these still require low ambient light. Some of these options might be viable where a natural framing opportunity exists, e.g., a beaded door curtain or similar) exists. But that's not a generalisable method which an individual could carry with them.

- One could arrange for some particle swarm to organise within the message space to carry the image. Illuminated drone swarms are an example used now in entertainment and advertising (same low-ambient light requirement), though a reflective pigmented alternative might be conceived of. This ... would probably be difficult to maintain, and is effectively like spraying pigment into space. Either you're going to require a lot of ink, or the pigment elements would have to be both "smart" and movement-capable such that they could arrange themselves. In practice, static displays (print on paper or similar media) or dynamic ones (e-ink, transflective LCD, or similar) involving a very much non-thin-air medium is vastly more practicable.