topography topics

Learning the Intricacies of Axial and Tangential Maps

BY KENNETH A. LEBOW, OD, FAAO
September 1999

Mapping strategies are one of the most important, yet most often misunderstood concepts in corneal topography. Simply put, they represent the mathematical analysis (i.e., algorithm) that the corneal topographer uses to present the raw data into various topography maps.

Axial and tangential maps are the two most important and frequently used mapping strategies.

Axial Maps

Axial maps, also referred to as power or sagittal maps, report reference distances across the corneal surface. They do not represent values of dioptric power and they incur more smoothing of data by representing a running average of scaled curvatures. Extreme values are averaged out of the calculation. Axial maps are spherically biased and are calculated on the assumption that all rays of light striking the corneal surface are refracted, forcing a focal point through the optical axis as a reference axis (Fig. 1).

Axial maps produce patterns that appear larger and have a more diffuse color range, where specific corneal details are generally represented in a more peripheral location. Subsequently, this global representation of corneal shape generally provides more accurate central detail, which is helpful in base curve selection and lens fitting.

Tangential Maps

Tangential maps, also referred to as instantaneous, local or "true" maps, are based on the fact that all refracted light does not fall nicely on a central reference axis.

Unlike axial maps, the scaled curvatures used in tangential maps are not forced to stop along the reference axis (Fig. 1). This occurs because extreme peripheral curvatures are included in the calculation. Hence, tangential maps are much more sensitive to local changes in the corneal surface and are able to show transitions in curvature with much greater sensitivity and less smoothing of data than axial maps.

Compared with axial maps, tangential maps show smaller patterns with details that are more centrally located and they also provide a better visualization of the exact location of a corneal defect.

Remember that each map presents a different picture of the same corneal shape. The differences in readings become clinically significant at the extreme ranges of corneal curvature. Axial maps offer larger-sized images with flatter steep curvatures and steeper flat curvatures than tangential maps. They are helpful in viewing central curvature detail, but not in viewing peripheral details. Tangential maps are visually smaller and offer a truer picture of the corneal shape. They locate specific details more centrally and are excellent for locating the apex of the cone in keratoconus. 

FIG. 1: Line drawings of axial and tangential assumptions showing how the axial assumption forces the focus along the optical axis while the tangential assumption allows for off-axis focal lengths.

Dr. Lebow is a member of the AOA and a Fellow of the AAO. He is in private practice in Virginia Beach, Virg.