Images involving the Trinity were in particular rather problematic.
A major problem arose as a result of the devotions surrounding Maria Crescentia Höss (1682–1744) of Kaufbeuren. Kaufbeuren is north of Lake Constance in the Diocese of Augsburg.
Laudatory reports about her had reached the Pope (Pope Benedict XIV) even during her lifetime.
She had a vision of the Holy Spirit under the appearance of a beautiful young man .
There were distributed small pictures representing him (see above). Further, a new technique had come into being: flat, angular woodcuts were replaced by realistic copper engravings. These cheap reproductions gave the image a new kind of presence in every household and prayer book.
Apparently at the time it was not unknown for the Holy Spirit to be represented in this way
Benedict XIV disapproved of this practice. On October 1st, 1745, he issued a Bull, Sollicitudini Nostrae. (Bull. Lux., XVI., 318-323). He set out in some detail what depictions were permitted of the Holy Trinity and the persons who composed it.
Extracts from the Bull are set out in pages 139 et seq in The Image of God the Father in Orthodox Iconography and Other Studies By Steven Bigham Published by St Vladimir's Seminary Press, 1995 ISBN 1879038153, 9781879038158 (can be accessed through Google Books)
For Benedict XIV, the key test for depicting the Trinity was Scripture.
Therefore, in depicting the Holy Spirit, a dove (the baptism of Jesus) or tongues of fire (Pentecost) were the only applicable images. However he did go on to say that the image of the Trinity as three identical men (based on the three visitors appearing to Abraham) would be tolerated.
What would not be allowed would be: the Holy Spirit as a human being; the Trinity as a man with three faces or double-headed with a dove in the middle.
It should be pointed out for the sake of completeness that despite what Pope Benedict XIV wrote, the vision of St Crescentia does not appear to have barred her cause for canonisation.