Lol, no. Photon-photon scattering is very rare; you only expect it to happen in very high-energy situations. To scatter enough photons to create a visible image in the air you would need to pour so much energy into the air that it would turn into a plasma. A deadly radioactive plasma that explodes outward from your holographic display and kills everyone nearby. This would not be considered practical.
I think an important part of our humanity is our ability to laugh. I literally laughed when I read the question, because of the absurd impracticality of it. That's an important part of the answer.
On the other hand, it's true that a purely text-based medium like a comment doesn't have room for a lot of nuance. So for the sake of clarity, I will say that it was a good question. We should always look for ways to use new discoveries to our advantage. Let's just stick to things which are possible, like Dyson spheres, and leave the impossible for science fiction.
If you wanted to do this kind of holography, you’d be using multiple lasers (or masers) to stimulate different excitation states of atmospheric gases - you “just” have to have them sweep fast and accurately enough to intersect at each pixel. The engineering challenge is far from insignificant, but there is some progress being made in this general direction, coming from the 3d printing world (volumetric/tomographic printing).
Is the scattering probability a function of flux density or simply of photon energy?
If of photon energy, then the device is clearly impossible -- you would need to use invisible (and harmful) gamma-rays for scattering.
If of energy density, it still may not be theoretically feasible. For instance, you cannot make monochromatic pulses arbitrarily short -- eventually they will become spread in frequency (more and more energy in higher and potentially harmful frequencies), such that the total dosage necessary to get the desired visible flux is too large. (some calculations would need to be made...)
It's the flux. To scatter any photons takes a lot of flux, and to scatter enough to see would take quite a lot. Of course I haven't done the math either, so I'm just guessing what it would do to the atmosphere that got in the way.
Yes, this is much more practical. Short pulses to create a tiny ball of plasma that doesn't expand very much, but which can emit enough light to see. Still not what we want (which is Star Trek), but probably quite fun as long as the total volume of plasma stays small enough to be safe.
If you want Star Trek ( and so do I, of course :) ) then the simplest way I can imagine has to be with headsets as currently is.
Making them imperceptible, if that is even so important, has some challenges but not impossible (e.g. increasing resolution, lowering weight, or even adding devices to compensate its weight if the former is infeasible).
