I think the convergence of evidence - the cumulative evidence - is clear: the Shroud of Turin is authentic.
The Carbon 14 dating of the Shroud to the Middle Ages was demonstrated to be inaccurate due to a contaminated sample of the Shroud being tested. Raymond Rogers, who served as Director of Chemical Research for the Shroud of Turin Research Project (STURP) in 1978, debunked the myth that the Shroud of Turin was a Middle Ages forgery:
Rogers’ continual study of the Shroud resulted from a 2000 study by Joseph Marino and Sue Benford, based on x-ray analysis of the sample sites, shows a probable seam from a repair attempt running diagonally through the area from which the sample was taken. These researchers conclude that the samples tested by the three labs were more or less contaminated by this repair attempt. They further note that the results of the three labs show an angular skewing corresponding to the diagonal seam: the first sample in Arizona dated to 1238, the second to 1430, with the Oxford and Swiss results falling in between. They add that the variance of the C-14 results of the three labs falls outside the bounds of the Pearson’s chi-square test, so that some additional explanation should be sought for the discrepancy.[3] The claims by Marino and Benford on the lack of statistical consistency of the results of the 1988 radiocarbon test were in contrast with the conclusions of J.A. Christen, who, in 1994, claimed to have applied a “robust approach” (Bayesian) to the radiocarbon data and concluded that the given age for the Shroud was correct, from a statistical point of view.[4]
When Rogers saw the paper by Marino and Benford, his reaction was that they were not scientists,[5] their theory was ridiculous, and that he still had fiber samples he had taken from the Shroud that could disprove their theory. Upon examining the fibers under a microscope, however, he concluded that, as they had hypothesized, a cotton patch had been woven into the linen fibers and then dyed to match the color of the linen. This was possible because linen is strongly resistant to dyes but cotton is not. Rogers claimed that the repair had gone undetected because it was expertly done, there was no record of it, none of the STURP team were textile experts, and the area had not previously been a major focus of any major Shroud researchers’ attention because it was outside the image area.
Rogers claimed that under the microscope he could see the undyed linen fibers, the cotton fibers and the dye on the cotton fibers. Because he knew he had terminal cancer he contacted his friend and fellow STURP researcher Barrie Schwortz to record interviews, etc.[6] He also sent some of the fibers to a research lab for independent examination. When they were preparing samples, in one case they accidentally pulled apart the cotton and linen sections of one fiber. Schwortz reexamined false-color x-ray fluorescent photographs of the Shroud taken by STURP and pointed out that the sample for radiocarbon dating was taken from the only section that showed up green, indicating it had different chemical properties from the rest of the Shroud, but no one had previously paid attention to the color difference because the green portion is from a section that does not contain part of the image. In December 2008 the Discovery Channel in the United States presented a documentary titled Unwrapping the Shroud: New Evidence containing a detailed explanation of the repair and footage of Schwortz and of Rogers discussing their new findings.[7] Few month before his death Rogers submitted an article describing his findings to a peer-reviewed journal and it was published less than two months before Raymond Rogers died.[8] The essential conclusion of the article is that the radiocarbon datings were accurate, but because the samples were from cloth that was not part of the original Shroud, they are irrelevant regarding the age of the image area.
en.wikipedia.org/wiki/Raymond_Rogers