Arc Step Reconstruction....


.........the science behind the Keratron family of Topographers.


Introduced in 1994, the Keratron was the first hardware platform designed to utilize the full potential of ARC STEP surface reconstruction. Accuracy and sensitivity, without smoothing of data or extrapolating to fill in shadows, is unmatched. The unique method produces five richly detailed maps of the cornea: Arc Step-IROC/True Curvature (shape), Axial (spherical bias), Refractive (Snell’s Law/Ray Tracing), True Height (topographical height data in microns), and Contact Lens.


Arc Step Corneal Reconstruction


Our unique ARC STEP method begins with it’s patented infra-red vertex detector. This sensor determines the exact location of the corneal vertex and begins outwardly constructing a web of "Arcs" between the intersections of 26 rings and 256 meridians. Defining and starting from corneal vertex is the foundation of the our extreme accuracy. Curvature and height are simultaneously derived from the length and shape of each arc. Since mapping begins at vertex, the our topographers easily pick up central islands. Error is minimal since each data point of the "web" is related to one another. (Other topographers "concentric rings method" of  measures each point independently, resulting in much greater error.)


The Keratron ARC STEP method directly derives an axial curvature map, instantaneous curvature map, and corneal height map (in microns). All of the maps are derived separately without resorting to converting data from one type of data to another. Some systems first create an axial map and then convert the axial data into other maps. Other systems create a height map and then convert the data to curvature maps. Anytime data is converted from one format to another, map error increases. Since the Keratron does not convert data, map error is minimal in all maps.



Each point on the ARC STEP web is related to one another, resulting in better maps (above). The ARC STEP method reconstructs the entire corneal profile (heights, tangents and curvatures) starting from the vertex through all points at reflections and reaches point B with a unique possible sequence of joined arcs.




None of the points on spherically biased topography systems are related to one another, resulting in less detailed, increasingly inaccurate maps. Limits of the spherically biased method. The analysis of individual reflections does not allow us to identify if a ray was coming from point B instead of point A. Paraxial radius of A and B is approximately the same, but the resulting error in curvature and height is large.


Arc Step versus Tangential IROC


Local (IROC) curvature maps, extremely useful in refractive surgery and contact lens fitting, better describe the shape of the cornea. The Keratron IROC maps are directly derived from the "web". Topographers using the "concentric rings method" indirectly derive IROC, typically through "conversion from axial to tangential radius based on an algorithm that assumes a basic elliptical shape."1 The conversion retains the spherical bias from the original axial measurement while assuming the corneal profile is elliptical. The resulting Tangential IROC maps have reduced accuracy and sensitivity. The Keratron, Scout and Piccolo, not required to convert data, has extremely small IROC error. Less error means better post op management and contact lens fits.


Arc Step Height Maps


The Keratron's "web" also directly maps corneal height (elevations). Height maps are rapidly becoming recognized for their added value. Since height data are not converted, the Keratron’s maps are "within 0.25 microns at less that 3mm from the keratoscope axis and were generally within 1 micron".2 Again, "concentric rings" topographers, when they do provide height data, must indirectly derive data through conversion with the resultant error.


1 Accuracy of Videokeratograph Tangential Radius in Keratoconus (J.S. Chan, R.B. Mandell, et al) School of Optometry, UC, Berkeley, ARVO, 1995


2 "Assessment of Radial Aspheres by the Arc-Step Algorithm as implemented by the Keratron Keratoscope", AJO, Nov. 1995

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