“Ted’s Vermeer” is an irresistibly engaging documentary that might be described as a lab experiment in art history presented with Las Vegas-style showmanship. It focuses on two people: the seventeenth-century Dutch painter Johannes Vermeer, whose paintings possess such uncanny detail that they might be mistaken for perfectly-composed photographs, and Tim Jenison, a wealthy American who set himself the task of not only figuring out how the artist accomplished what he did but reproducing the technique himself.

Jenison’s Vermeer project derives from the idea espoused in two 2001 books: artist David Hockney’s “Secret Knowledge,” which argued that many past masters used devices like the camera obscura to achieve their effects, and Philip Steadman’s “Vermeer’s Camera,” which theorized that the artist used a complicated mirrored contraption to achieve such detailed, realistic precision on his canvases. Jenison’s dream was basically to replicate Vermeer’s methodology—a process that required him not only to build the mechanism (something that depended on his background in computer graphics and software construction, as well as his personal fortune) but to test it by reproducing one of Vermeer’s most famous works, “The Music Lesson” using it—though he had never put brush to canvas before.

That in turn necessitated building an exact replica of the artist’s studio, the painting’s setting, in a warehouse in San Antonio, filling it with exact copies of everything found in the painting, and then employing the painstakingly constructed device (as well as pigments made to the same specifications as those Vermeer would have had at his disposal) to paint “his” Vermeer. The entire project took well over a year, including more than two hundred days to build the tableau and more than a hundred in the actual painting. But the result, which the artist finally got to compare to the original (owned by English royal house), certainly impressed Hockney and Steadman (as well as Keeper of the artwork in Buckingham Palace) though others remain unconvinced.

Of course, the entire effort undertaken by Jenison—which might be considered just a quirky obsession by many—would have remained a largely unknown curiosity were it not for the decision of magician Penn Jillette and his partner Teller (the former acts as narrator, the latter as director) to document it. But there’s none of their sleight of hand here, except in the deftness with which they combine with Jenison to turn what might threaten to become a tedious slog into a surprisingly entertaining journey through a weird but fascinating experiment. Together with cameraman Shane F. Kelly, editor Patrick Sheffield and composer Conrad Pope, they’ve contrived to transform a potentially tiresome effort into something as witty and charming as one of Penn and Teller’s stage routines.

Of course “Tim’s Vermeer’s” doesn’t answer the essential question that it raises definitely. It proves that Johannes Vermeer could have used the sort of optical device that Jenison constructed. It doesn’t prove that he actually did. But it unquestionably makes the question all the more tantalizing by presenting it in concrete rather than merely theoretical terms.