Heather Pringle at Archaeology has this bit on the Shroud of Turin:
Many believe the Shroud of Turin is the winding cloth that covered the body of Jesus of Nazareth after his crucifixion. It bears a faint and terribly sad image of a man. In 1988, the Catholic Church gave the University of Arizona and two other institutions the task of dating the Shroud of Turin, hoping to shed light on its mysterious origins. On the morning of April 21, 1988, a group of scientists and clerics convened in the sacristy of Turin Cathedral to trim tiny samples from the famous shroud. Each of the labs then received four identical stainless steel containers, one holding a shroud sample and three containing samples from other ancient textiles to allow blind studies.
The labs ran Accelerator Mass Spectrometry (AMS) tests on snippets from samples. These tests revealed that the shroud was much younger than previously believed. It dated to the medieval period, between A.D. 1250 and 1390. The faithful were much dismayed. So recently, explains Freer, the University of Arizona began running further tests on tiny swatches of the shroud sample. The researchers hope to determine whether contaminants on the cloth had skewed the accelerator dates, or whether the samples came from a medieval repair to the shroud.
In search of answers, Freer examined the fibers by polarized light microscopy. The resulting image, an almost psychedelic cascade of arching blue, orange and green lines, revealed fibers made from plant stems—most likely linen produced from flax. And Freer’s other studies showed that the sample’s overall weave structure was identical to that of the rest of the textile, likely ruling out the theory of a later repair. She is now working on an analysis of possible contaminants.