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Performance of Zernike polynomials in reconstructing raw-elevation data captured by Pentacam HR, Medmont E300 and Eye
Yueying Wei1,2, Bernardo T Lopes3,4, Ashkan Eliasy3
1Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Ontario, Canada.
Purpose:
To investigate the capability of Zernike polynomials fitting to reconstruct corneal surfaces as measured by Pentacam HR tomographer, Medmont E300 Placido-disc and Eye Surface Profiler (ESP).
Methods:
The study utilised a collection of clinical data of 527 participants. Pentacam HR raw elevation data of 660 eyes (430 healthy and 230 keratoconic) were fitted to Zernike polynomials of order 2 to 20. Same analyses were carried out on 158 eyes scanned by Medmont E300 Placido-disc and 236 eyes were scanned by ESP for comparison purposes. The Zernike polynomial fitting was carried out using a random 80% of each individual eye surface's data up to a corneal radius of 5 mm and the root means squared fitting error (RMS) was calculated for the unused 20% portion of the surface data. The process was carried out for the anterior and posterior surfaces of the corneal measurements of the Pentacam HR and the anterior surfaces only with the ESP and the Medmont E300 measurements.
Results:
Statistical significances in reduction of RMS were noticed up to order 14 among healthy participants (p < 0.0001 for right eyes, p = 0.0051 for left eyes) and up to order 12 (p < 0.0001 for right eyes, p = 0.0002 for left eyes) in anterior surfaces measured by the Pentacam. Among keratoconic eyes, statical significance was noticed up to order 12 in both eyes (p < 0.0001 for right eyes, p = 0.0003 for left eyes). The Pentacam posterior corneal data, both right and left, healthy and keratotic eyes recorded significance (p < 0.0001) in reduction of RMS up to order 10 with same RMS values of 0.0003 mm with zero standard deviation. RMS of fitting Zernike polynomials to Medmont data up to order 20 showed a consistent reduction in RMS with the increase of the fitting order with no rise at high fitting orders. Minimum RMS = 0.0047 ± 0.0021 mm, 0.0046 ± 0.0019 mm for right and left eyes respectively were recorded at order 20 and were more than 15 times the minimum RMS of the Pentacam. RMS of fitting Zernike polynomials to ESP data also showed a consistent reduction in RMS with the increase of the fitting order with no sign of any rise at high fitting orders. Similar to the Medmont, minimum RMS of 0.0005 ± 0.0003 mm, 0.0006 ± 0.0003 mm was recorded at order 20 for right and left eyes respectively and was 2 times the minimum RMS of the Pentacam for right eyes and 1.7 times the minimum RMS of the Pentacam for left eyes.
Conclusions:
Orders 12 and 10 Zernike polynomials almost perfectly matched the raw-elevation data collected from Pentacam for anterior and posterior surfaces, respectively for either healthy or keratoconic corneas. The Zernike fitting could not perfectly match the data collected from Medmont E300 and ESP.
