Multimeridional apparent frontoparallel plane: relation between stimulus orientation angle and compensating tilt angle.

The classical apparent frontoparallel plane (AFPP) setting is typically obtained by having the subject move a series of parallel rods farther or closer until they line up in a plane perceived to be parallel to the face plane. If there is a size difference between the two ocular images, the AFPP setting defined by the rods will exhibit a tilt from the objective frontoparallel plane, about an axis parallel to the rods. The multimeridional apparent frontoparallel plane (MAFPP) is an extension of this procedure to rod orientations other than the vertical meridian. In previous studies, it was found that oblique tilt angle settings corresponding to rod orientations of 45 degrees and 135 degrees are equal to square root 2 times the tilt angle for the vertical rod orientation for the same interocular magnification difference along the meridian perpendicular to the rods. In this study, we measured the tilt angles produced by a series of oblique rod orientations between 15 degrees and 165 degrees, inclusive. Throughout the 150 degrees range tested, the tilt angles were found to be consistently proportional to the cosecant of the rod orientation angle, the factor square root 2 previously used being a specific example of this relation. Within this range, neither empirical cues nor the induced effect cause the cosecant relation to break down. It is suggested that the MAFPP procedure can be applied more extensively than previously anticipated.