According to scripture: John 20:6-7, the shroud of turin could not possibly be authentic. It is clear from the record the real shroud was in two pieces. A smaller piece about the head and a larger piece about the body.
The shroud of turin is one complete piece approximately 14 feet in length not matching the discription in scripture.
The shroud only presents a controversy for those who don't pay attention to the scriptural record.
And those who cite the English translation of Scripture fail to understand the definitions and uages of the words in the original Greek. It is also helpful to understand the customs and practices of the time and place the Gospels are describing.
As a matter of fact, the Sudarion of Oviedo, a piece of blood stained, dirty linen about 30" on a side) has been kept in a Cathedral in Oviedo, Spain, since at least the ninth Century. It is believed to be the second cloth, the head cloth, of which you speak.
Forensic scientists have determined that the Sudarion and the Shroud have matching blood flows from identical wounds in identical locations, share the same blood type (if the blood typing is accurate), and that the head both cloths covered match in demension and form; their conclusion is that BOTH cloths covered the same dead body at different times within minutes or hours of each other.
Analysis indicates the Sudarion was placed over the dead man's head while his body was still suspended on the cross. It was removed and most likely used as a binding to keep the mouth closed by being wrapped under the jaw and over the top of the head under the hair just in front of the ears and then tied in a knot at the crown of the head. This comports with known Jewish burial practices of the 1st Century. Other twisted strip bindings would be used to tie the wrists and the ankles to keep them from flopping to the side when rigor mortis passed in a few hours or days.
With the understanding of HOW Jews prepared their dead for burial, the descriptions of the grave clothes in the Gospels and the evidence of the Shroud are not incompatible. In fact, this understanding explains a lot. For example, the first people into the tomb found the shroud lying in the niche where the body had been left... but the head cloth, the sudarion, lying "folded" (actually the original Greek is better translated as "rolled") by itself some distance away. One can picture the risen Christ, leaving his shroud, walking toward the opening and reaching up and pulling the jaw binding "head cloth" off as He walks and dropping it, casting off the garments of death.