# Zernike representation of corneal topography height data after nonmechanical penetrating keratoplasty.

PURPOSE: To demonstrate a mathematical method for decomposition of discrete corneal topography height data into a set of Zernike polynomials and to demonstrate the clinical applicability of these computations in the postkeratoplasty cornea. METHODS: Fifty consecutive patients with either Fuchs' dystrophy (n = 20) or keratoconus (n = 30) were seen at 3 months, 6 months, and 1 year (before suture removal) and again after suture removal following nonmechanical trephination with the excimer laser. Patients were assessed using regular keratometry, corneal topography ( TMS-1, simulated keratometry [SimK]), subjective refraction, and best-corrected visual acuity (VA) at each interval. A set of Zernike coefficients with radial degree 8 was calculated to fit two model surfaces: a complete representation (TOTAL) and a representation with parabolic terms only to define an approximate spherocylindrical surface (PARABOLIC). The root mean square error (RMS) was calculated comparing the corneal raw height data with TOTAL (TOTALRMS) and PARABOLIC (PARABOLICRMS). The cylinder of subjective refraction was correlated with the keratometric readings, the SimK, and the respective Zernike parameter. Visual acuity was correlated with the tilt components of the Zernike expansion. RESULTS: The measured corneal surface could be approximated by the composed surface 1 with TOTALRMS < or = 1.93 microm and by surface 2 with PARABOLICRMS < or = 3.66 microm. Mean keratometric reading after suture removal was 2.8+/-0.6 D. At all follow-up examinations, the SimK yielded higher values, whereas the keratometric reading and the refractive cylinder yielded lower values than the respective Zernike parameter. The correlation of the Zernike representation and the refractive cylinder (P = 0.02 at 3 months, P = 0.05 at 6 months and at 1 year, and P = 0.01 after suture removal) was much better than the correlation of the SimK and refractive cylinder (P = 0.3 at 3 months, P = 0.4 at 6 months, P = 0.2 at 1 year, and P = 0.1 after suture removal). Visual acuity increased from 0.23+/-0.10 at the 3-month evaluation to 0.54+/-0.19 after suture removal. After suture removal, there was a statistically significant inverse correlation between VA and tilt (P = 0.02 in patients with keratoconus and P = 0.05 in those with Fuchs' dystrophy). CONCLUSIONS: Zernike representation of corneal topography height data renders a reconstruction of clinically relevant corneal topography parameters with a marked reduction of redundance and a small error. Correlation of amount/axis of refractive cylinder with respective Zernike parameters is more accurate than with keratometry or respective SimK values of corneal topography analysis.[1]## References

**Zernike representation of corneal topography height data after nonmechanical penetrating keratoplasty.**Langenbucher, A., Seitz, B., Kus, M.M., Naumann, G.O.*Invest. Ophthalmol. Vis. Sci.*(1999) [Pubmed]

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