The purgation/illumination/contemplation model is ancient and present in the Church Fathers. St. Dionysius the Areopagite ("Pseudo-D") based all of his works on it. He also sees the sacramental framework mirroring this process. It only makes sense. You suffer, you learn, you draw near to God.
Also, the Old Testament temple complex foreshadowed it:
Purgation: The altar outside the temple was a place where the priests burned victims through fire. It was the place of holocaust (Greek for burnt offering).
Illumination: The holy place was the place of illumination - where the golden lampstand stood.
Contemplation: The holy of holies was the place of union with God - the dark inner sanctum of God's presence.
The spiritual life moves along this "temple pathway". And to "contemplate" is etymologically related to "temple" and "template". It's all connected.