I have heard about you and about your cures, which are done by you without drugs; for example you make the blind see again; you make the lame walk; you cleanse lepers; you drive out unclean spirits; you heal those who have been tormented by disease over long periods. Having heard all this of you I had one of two ideas: either that you are Son of God, who do these things, or that you are God. So then I write to you and ask you to and to come to me to cure the suffering I have, and then to be with me; for I have also heard that the Jews murmur against you and wish to do you ill. My city is very small but distinguished and adequate for both of us to live here in peace. (http://anastasis.org.uk/16august.htm)]
Ananias arrived in Jerusalem and saw the Lord surrounded by people. He was not able to get close to Him because of the large throng of people listening to the preaching of the Savior. Then he stood on a high rock and attempted to paint the portrait of the Lord Jesus Christ from afar, but this effort was not successful. The Savior saw him, called to him by name and gave him a short letter for Abgar in which He praised the faith of this ruler. He also promised to send His disciple to heal him of his leprosy and guide him to salvation.
[Blessed are you, Agbar, who have believed in me, though you have not seen me. For it is written of me that those who have seen me do not believe in me so that those who have not seen me may believe and live. As to what you wrote about my coming to you, it is necessary that I accomplish all that I was sent out to do and, after I have accomplished it, to be taken up to the Father who sent me. And when I have been taken up I will send you one of my Disciples, named Thaddaios, he will heal your disease and grant you and those with you eternal life and peace, and he will make your city such that no enemy can prevail against it.
[The Persians had built a huge fire outside the city wall; when the Bishop approached with the Holy Napkin, a violent wind fell upon the fire, turning it back upon the Persians, who fled in defeat. (http://goarch.org/chapel/saints_view?contentid=167)]
For the original Greek text by Emperor Constantinos Porphyrogenitos on the Holy Mandylion (Narratio de imagine Edessena), see here.
A full English translation of this account by Emperor Constantinos Porphyrogenitos (944AD) is available in the dissertation by Mark Guscin.
Of note, as alluded to, the Emperor discusses the commonly-held story about the origin of the Holy Mandylion, but also discusses an alternative having to do with the Passion of Christ:
And and additional translation of other original source documents.
Orthodox tradition has long seen the Mandylion (the cloth that Christ imprinted His image on in life) as distinct from the burial cloths of Christ. A few modern researchers (heterodox and some Orthodox) however have proposed that the Mandylion of Orthodox tradition is in fact the burial shroud of Christ (i.e. the Shroud of Turin) upon which His image was imprinted.
(Of course this isn't the juncture to fully discuss the authenticity of the Shroud of Turin from a scientific perspective. See the link below the quote for a full article about it, or pictures here from an Orthodox service before the Shroud this past year: http://www.mospat.ru/en/2010/05/18/news18357/)
The following is an excerpt from an article by an Orthodox source on the Shroud of Turin:
"A 6th century text refers to the Mandylion as a "tetradiplon'--"doubled in four." A most curious choice of word, according to Cambridge University's Professor Lampe, editor of the 'Lexicon of Patristic Greek'; in all literature it occurs only in association with the image of Edessa, being scarcely, therefore, an idle turn of phrase."  As Wilson convincingly suggests, if the Shroud of Turin were folded in this manner, i.e., doubled four times, the viewer would see nothing but the head. And if this folded cloth were attached to a board (as the Mandylion is said to have been), those who venerated the holy image could well have been ignorant of the fact that they were looking at but a portion of what was actually a full-length image, particularly if this image had been sealed up for so many years.
But none of this, as fascinating as it is, has been conclusively proven. We can only say that the historical evidence thus far uncovered, and the scientific evidence of the Shroud of Turin itself, does indeed suggest this explanation, But the point is that if the Shroud is also the Mandylion, not only does it have an Orthodox history, but it also explains why it seems to have no separate feast or service."
Another excerpt to summarize some of the historical documents from Constantinople:
"To sum up the points made in this paper: a linen cloth or cloths described as the burial wrappings of Jesus are attested in many Constantinople documents from 944 to 1203, twice with his image if one counts Mesarites (Doc. XI), and several times described as bloodied. No record exists of the arrival of Jesus’ burial cloth in the capital, and no celebration such as accompanied the Edessa cloth in 944. [Note: This is a very important point from the Byzantine perspective, as the Church of Constantinople preserves feasts for the finding and translation of almost all the Holy Relics treasured in the City, such as the Finding of the Precious Cross and Holy Nails on March 6th, the Exaltation of the Cross on September 14th, the translation of the Robes of the Theotokos on July 2nd and August 31st, etc. It seems unlikely that the Burial Shroud of Christ (arguably one of the most precious spiritual treasures, similar to the Holy Cross) could have made it to Constantinople without having been noticed, and without a feast or record. However, the Holy Mandylion is widely documented to have come to the City in 944 to great fanfare, and continues to be festally celebrated on August 16th annually.] Yet it was there. Judging from copious documents and artistic representations made in Constantinople and elsewhere from 944 to 1150, the Edessa towel always with the image of Jesus’ face may be identical with Jesus’ Shroud in folded form, enclosed in a case with face exposed. Before that, from at latest 544 to 944, this cloth was certainly in Edessa. If the Edessa cloth and Jesus’ purported shroud are indeed one and the same object, that assumed burial cloth may have a pedigree back at least to 544, and if the Abgar legend has any historical worth, to the 4th c. and even, accepting the descriptive evidence, to the very time of Christ. If the pieces of this elaborate puzzle truly fit as they seem to, the blood-stained burial cloth with faint unpainted image would have a documented history back to palaeochristianity and may in fact be the actual tomb wrapping of Jesus."(source)
For more information, here is another presentation by an Orthodox physician on the subject.
And another article from Orthodox sources, that reviews many of the scientific analyses and also the historical record from an Orthodox perspective.
I honour the imprint of your face, O Saviour.
Alive you wiped your face upon a cloth,
A final burial cloth you wore when dead.
Maker of all, my Christ, a tile once made
By hand now bears your form not made by hand.