A hologram, as it's scientifically defined, is a photographic recording of a light field, and it is an encoding of the light field as an interference pattern of seemingly random variations in the opacity, density, or surface profile of the photographic medium.
Disguised as Harrison Wells, Eobard Thawne sensed that the team was getting closer to discovering more about his super-villain alter-ego, "the Man in Yellow," and so created an elaborate plan, where he made holograms of the Reverse-Flash and configured it to say a set of predetermined lines, while he is in the room, throwing the team off the trail. Then Eobard would run to his vault, grab his suit and put it on, making it look like the Reverse Flash pulled Wells into the field, beating him up, until the Flash showed up, and then engaging with him outside while also maintaining a speed-mirage of Wells's body inside.
In the hopes of getting to the bottom of why the containment system failed the night that they captured the Reverse Flash, Cisco Ramon activated the Reverse Flash hologram and was soon confronted by Wells, who revealed himself to actually be Eobard Thawne, an individual from the future. Eobard then apologized to Cisco before killing him, trying to keep his secret. However, Barry's time travel ended up erasing this from ever happening.
In order to get Dr. Wells to confess to killing Barry's mother and therein freeing Henry, the team came up with a dangerous plan where Cisco tried to reenact what happened in the other timeline, and baited Wells to him by activating the Reverse-Flash hologram. However, the Wells that they saw was actually Hannibal Bates working for the real professor, who confirmed the team's fears regarding his true identity as Eobard Thawne.
A little bit after Barry Allen (Earth-1)Barry gave up his powers to Zoom in exchange for Wally's life, Cisco created a holographic image of the Flash which was controlled by him and in part Barry, using it to distract criminals until the police could get there and apprehend them. Zoom however didn't see it as a threat and openly divulged it to everyone. Team Flash later used a hologram of Caitlin Snow to take Zoom's attention, luring him into a false sense of security.
After Earth-2 Harrison Wells sent an equation which was meant as both an intelligence test and a message into Multiverse those who were able to decode it, almost exclusively being doppelgängers of Wells himself, sent the audition tapes/job interviews in the forms of full-scale holograms of themselves. A few days after that a giant monster roaming the streets of Central City was revealed to be a hologram.
Rip Hunter left a hologram message for the Legends on the Waverider before going missing. Additionally, both Rip Hunter and Eobard Thawne used a holographic projection to communicate with Gideon AI.
Depicted in holographic form
DC's Legends of Tomorrow
Freedom Fighters: The Ray
The Chronicles of Cisco
Behind the scenes
- Interestingly enough, both episodes of the Arrowverse shows titled "Out of Time" had characters use holograms in them.