Objection 1. It would seem that the name of Image is not proper to the Son; because, as Damascene says (De Fide Orth. i, 18), "The Holy Ghost is the Image of the Son." Therefore Image does not belong to the Son alone.
Objection 2. Further, similitude in expression belongs to the nature of an image, as Augustine says (QQ. lxxxiii, qu. 74). But this belongs to the Holy Ghost, Who proceeds from another by way of similitude. Therefore the Holy Ghost is an Image; and so to be Image does not belong to the Son alone.
Objection 3. Further, man is also called the image of God, according to 1 Corinthians 11:7, "The man ought not to cover his head, for he is the image and the glory of God." Therefore Image is not proper to the Son.
On the contrary, Augustine says (De Trin. vi, 2): "The Son alone is the Image of the Father."
I answer that, The Greek Doctors commonly say that the Holy Ghost is the Image of both the Father and of the Son; but the Latin Doctors attribute the name Image to the Son alone. For it is not found in the canonical Scripture except as applied to the Son; as in the words, "Who is the Image of the invisible God, the firstborn of creatures" (Colossians 1:15) and again: "Who being the brightness of His glory, and the figure of His substance." (Hebrews 1:3).
Some explain this by the fact that the Son agrees with the Father, not in nature only, but also in the notion of principle: whereas the Holy Ghost agrees neither with the Son, nor with the Father in any notion. This, however, does not seem to suffice. Because as it is not by reason of the relations that we consider either equality or inequality in God, as Augustine says (De Trin. v, 6), so neither (by reason thereof do we consider) that similitude which is essential to image. Hence others say that the Holy Ghost cannot be called the Image of the Son, because there cannot be an image of an image; nor of the Father, because again the image must be immediately related to that which it is the image; and the Holy Ghost is related to the Father through the Son; nor again is He the Image of the Father and the Son, because then there would be one image of two; which is impossible. Hence it follows that the Holy Ghost is in no way an Image. But this is no proof: for the Father and the Son are one principle of the Holy Ghost, as we shall explain further on (36, 4). Hence there is nothing to prevent there being one Image of the Father and of the Son, inasmuch as they are one; since even man is one image of the whole Trinity.
Therefore we must explain the matter otherwise by saying that, as the Holy Ghost, although by His procession He receives the nature of the Father, as the Son also receives it, nevertheless is not said to be "born"; so, although He receives the likeness of the Father, He is not called the Image; because the Son proceeds as word, and it is essential to word to be like species with that whence it proceeds; whereas this does not essentially belong to love, although it may belong to that love which is the Holy Ghost, inasmuch as He is the divine love.
Reply to Objection 1. Damascene and the other Greek Doctors commonly employ the term image as meaning a perfect similitude.
Reply to Objection 2. Although the Holy Ghost is like to the Father and the Son, still it does not follow that He is the Image, as above explained.
Reply to Objection 3. The image of a thing may be found in something in two ways. In one way it is found in something of the same specific nature; as the image of the king is found in his son. In another way it is found in something of a different nature, as the king's image on the coin. In the first sense the Son is the Image of the Father; in the second sense man is called the image of God; and therefore in order to express the imperfect character of the divine image in man, man is not simply called the image, but "to the image," whereby is expressed a certain movement of tendency to perfection. But it cannot be said that the Son of God is "to the image," because He is the perfect Image of the Father.
Source: Summa Theologica (New Advent)