Fine art and technology combine in this fascinating documentary about how an obsessive amateur was able to recreate an astonishingly precise replica of one of Johannes Vermeer's most famous paintings.

Magicians Penn and Teller introduce their self-made millionaire friend, NewTek computer graphics inventor Tim Jenison, who marvels at how the 17th-century Dutch master Vermeer (1632-1675) was able to paint with a luminous, photographic clarity that rivals photo-realism, long before the modern-day camera was invented. Then -- with no previous training in painting -- Jenison was able to reproduce "The Music Lesson" in 1,825 days. How did he do it?

After reading artist David Hockney's "Secret Knowledge: Rediscovering the Lost Techniques of the Old Masters" and studying the mathematical calculations in architect/professor Philip Steadman's "Vermeer's Camera: Uncovering the Truth Behind the Masterpieces," Jenison decided to explore American photographer Joseph Pennell's controversial 1891 assertion that Vermeer was able to achieve his exceptional effects through projected optical images, using primitive mirrors and lenses.

Directed by non-speaking Teller, Jenison chats amiably with Penn Jillette, while demonstrating how his relentless research unraveled the mystery that has stumped scholars for decades.

After learning to read Dutch, studying Vermeers in Amsterdam's Rijksmuseum and visiting the artist's hometown of Delft, Jenison recreates Vermeer's studio in a San Antonio, Texas, warehouse, complete with window decor, furniture, rugs and costumed models.

To ensure accuracy, Jenison inveigles his way into Buckingham Palace to view the "original" in the queen's private collection; grinds his own pigments, using only ingredients that were available to Vermeer; and spends months hunched over a 29-by-25-inch canvas, squinting through a variety of lenses in the kind of camera obscura that Vermeer must have used. And every detail is duplicated with painstaking precision.

While art history academics debate whether Vermeer "cheated," it becomes obvious that Vermeer was one of the first ingenious artists to combine painting with technology, inventing new techniques.

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On the Granger Movie Gauge of 1 to 10, "Tim's Vermeer" is an intriguing 8, delineating an experiment that should appeal to an art-house audience.