As has been discussed before on this blog, incense, among its many qualities, is known to be repulsive to demons. It is also a part of the ceremonies of the Mass in every rite I have ever experienced. Why then, is there so much opposition among the faithful to its use?
When we get to the offertory of the Mass, why would anyone not want to see incense rising from around the altar? Americans have a tendency to claim allergies to incense. Often the same people have allergies to the confessional, but that is another story. However, one has to wonder, when the coughing starts before the incense is even imposed, just how much is related to allergies, and how much is their imagination.
As the incense is imposed, it is blessed by the Priest. Traditionally, the prayer Ab illo benedicaris, in cuius honore cremaberis. is said as the incense is being imposed. It is blessed silently. Then the thurible is handed by the deacon to the Priest. First the Oblation itself is incensed. As a rupture from the past, the rubrics of the Ordinary Form call for there to be three swings (double) or a cross. This sad clarification in the General Instructions of the Roman Missal's most recent edition means that the Priest is no longer free to incense the Oblation with three crosses and three circles. After the Oblation is incensed, the Altar Cross and Altar are incensed as well. This is done with single swings of the thurible over or toward the altar.
A hermeneutic of continuity would lead one to incense the mensa (top) of the altar, then the sides, then continue around the back side (or as is the case in disoriented worship, around the front side) of the mensa, stopping, if necessary in the middle to incense the Cross. The other side of the Altar, and the Gospel Side of the mensa are incensed, followed by the front of the Altar. After this, the Priest hands the thurible to the Deacon, who incenses him and then the congregation. In the midst of this can be added any concelebrants, Deacons, Acolytes, or clerics in choir. The Priest and people are incensed as a sign of their being offered as part of the oblation to God the Father.