Here’s a lead i found in www.clairval.com:
"The most moving experience of my life
In 1936, an examination conducted on two fibers from the tilma, one red and the other yellow, led to an astounding finding—the fibers contained no known coloring agent. Ophthalmology and optics confirm the inexplicable nature of the Image—it seems to be a slide projected onto the fabric. Closer analysis shows that there is no trace of drawing or sketching under the color, even though perfectly recognizable retouches were done on the original, retouches which moreover have deteriorated with time. In addition, the background never received any primer, which seems inexplicable if it is truly a painting, for even on the finest fabric, a coat is always applied, if only to prevent the fabric from absorbing the painting and the threads from breaking the surface. No brush strokes can be detected. After an infrared analysis conducted on May 7, 1979, a professor from NASA wrote, «There is no way to explain the quality of the pigments used for the pink dress, the blue veil, the face and the hands, or the permanence of the colors, or the vividness of the colors after several centuries, during which they ordinarily should have deteriorated… Studying this Image has been the most moving experience of my life.»"
I’m now off to find something more specific to those findings!
A letter or email to the above website may be a good starting point.