This “sleight” — as commonly applied to a visual illusion created during a rear insertion of a card into a break — was developed by Dai Vernon. It circulated through the magic underground long before it was properly published under Vernon's name. This was due to photocopies of notebooks, compiled by Frank Csuri, being disseminated from the early 1960s onward. Karl Fulves wrote the first formally published description of the Depth Illusion, as executed by Vernon, long after it was common knowledge among card magicians. This occurred in The Pallbearers Review - Close-up Folio #10, 1977, p. 1026. The person who was most instrumental in making magicians aware of the Depth Illusion was Edward Marlo, who independently devised the sleight but conceded its previous invention to Vernon. Marlo developed a number of clever variations and applications for it, which he published in a booklet titled Tilt!, 1962. “Tilt” was a better name than The Depth Illusion and has been generally adopted by magicians.
There were many precursors to Vernon's handling of the concept. Karl Fulves, again in The Pallbearers Review - Close-up Folio #10, pp. 1025-6, presents a good history of the visual illusion on which the Depth Illusion depends. He cites a false insertion of a card into the deck by Cazeneuve (1839-1913), described by Camille Gaultier in La Prestidigitation sans appareils, 1914, published in English in 1945 as Magic without Apparatus, see p. 85. Cazeneuve held the deck upright, face outward, and pretended to insert a card into it while actually placing it behind the deck.
Instances can be found of inserting a card under the top card while suggesting the card is going deeper into the deck. Such a maneuver appears to be intended in the first method of Hofzinser's “Remember and Forget” as described by Ottokar Fischer in J. N. Hofzinser Kartenkünste, 1910, p. 91, or p. 90 of the Sharpe translation (J. N. Hofzinser's Card Conjuring, 1931). Another instance appears in Ralph W. Hull's Eye Openers, 1932, p. 5. In neither instance is a break used to create an illusion of the card going deeper into the deck. The deception is supported only by patter and previous honest insertions designed to condition the spectators' perceptions.
A refinement of this idea, in which a large break is secretly formed under the top card of the deck at the front end and a card is inserted into it, seems to have begun to circulate in the middle decades of the 1900s. This idea employed the illusion of depth, but used a frontal insertion. Howard Wurst and and Bill Pawson described this version in The Sphinx, Vol. 48 No. 11, Jan. 1950, p. 285. A distinctive variation of the idea — where the card was inserted from the side of the deck — was published by Edward Victor in Further Magic of the Hands, 1946, p. 24.
The feature that distinguishes Vernon's application of the Depth Illusion is the insertion of the card into a deep break at the rear of the deck, rather than at the more vulnerable front end.
Methods for forming a Tilt break using just one hand were devised, not surprisingly, by several magicians independently. In March 1974, Karl Fulves wrote in Epilogue, No. 20, p. 183, “Although a one-hand Tilt get-ready has not appeared in print, it seems to be widely used with many variations in circulation.” He published the first description of one of these in Methods with Cards (Part 1), 1975, p. 15. Bob White is also recognized for having come up with an early one-handed get-ready for Tilt, which circulated through the card underground for years before it was eventually published in Bob White's It's a Matter of Style, written by Jason Womack, 1997, p. 12.
The “Depth Illusion” moniker was originated by Conrad Bush.