do we have information on the image of the snake on the pole? And how would that relate to the medical insignia for a physician?
From the article (with some amplifications and abridgments)
When the people of Israel in the wilderness sinned and were bitten by snakes, God provided a way of escape that prefigured His Sons death on a cross. All the Israelites had to do to be saved was look at the snake mounted on a pole (Numbers. 21:4-9). In Cranachs painting, this is shown in the background on the paintings right...
Directly in front, Martin Luther is standing with open Bible in hand.... Of three passages written in German on the open Bible, the third one reads, Just as Moses lifted up the serpent in the desert, so also must the Son of man be lifted up, so that all [who believe] in [him may have eternal life] (John 3:14)
The connection between serpents and physicians extends to Greek mythology; the constellation Aesculapius ("the serpent-holder") is to represent a physician who is depicted among the stars as holding a fractured snake, the head part in one hand, the tail part in another. But the bronze serpent of the book of Numbers in the Pentatuch predates the Greek legend by many centuries.