In the world of Nerd Trek, TPTB decided to draft tedious scripts describing the holographic character of "the Doctor" on Star Trek Voyager.
The character was played by Robert Picardo, an excellent actor, but still a human being.
In watching the show, we are expected to suspend some disbelief and merely accept that the holographic program mimics a living person so well as to include all the subtle little movements that human beings do that you would think would never occur to a hologram to do.
But it raises some interesting questions... the writers didn't have to worry about really having A.I. on the show- they had an actor; fully capable of humanity in all its aspects.
In so doing, they opened a can of worms with the nature of the Doctors sentience and what this meant for a federation producing Slave Drones in the form of holographic characters.
Through all this... we can exclude "normal" holographic characters that are utilized on the holodeck, considering the Doc to be a Special Program like Vic Fontaine.
Because they dumbass writers also wrote scripts for "Fair Haven" and "Spirit Folk" in which characters demonstrated sentience above and beyond the usual depiction. You also have the episode, "Flesh and Blood."
Once the writers got their chops around smart, self aware holograms, they just couldn't help themselves. What they did was essentially show that ANY hologram program can have the potential to be sentient, as long as some ridiculous malfunction occurs, or someone gets a little unethical with a PADD.
The deeper question is; Are they Sentient at all, or merely mimicry?
I have my own thoughts on it...
--Inter Arma Enim Silent Leges--
“Science needs the light of free expression to flourish. It depends on the fearless questioning of authority, and the open exchange of ideas.” ― Neil deGrasse Tyson
"When photons interact with electrons, they are interacting with the charge around a "bare" mass, and thus the interaction is electromagnetic, hence light. This light slows the photon down." - BuleriaChk