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S. Somani, C. Campbell, L. Chen; Determination of Sphero-Cylindrical Correction Through Direct Fourier Transform of Shack-Hartmann Spot Images. Invest. Ophthalmol. Vis. Sci. 2007;48(13):994.
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© ARVO (1962-2015); The Authors (2016-present)
Shack-Hartmann sensors (SHS) are widely used for measuring the ocular wavefront. In this measurement process the low orders of aberration –sphere and cylinder –are usually estimated by fitting the measured wavefront slope to a set of Zernike polynomials. Wavefront measurement as well as auto-refraction by SHS would be improved by more efficient sphere and cylinder estimates and the ability to cover a longer dynamic range. This study presents an alternative method of taking wavefront measurements based on direct Fourier Transform of SHS spot images.
A new algorithm was developed that consisted of Fourier Transform applied to the discrete SHS spot image. Using this method there is no need to find the centroid of each valid spot in the SHS image. The sphere and cylinder in the sampled wavefront distort the SHS grid of spots. A relationship between the distorted grid and its Fourier Transform was analytically derived. The locations of the first order spectra were determined from the Fourier Transform. Sphere, cylinder, and axis were then calculated from the coordinates of these spectral peaks. The algorithm was implemented in MATLAB and was tested using data collected on an SHS device. The data were from a test setup on which a flat wavefront was propagated through 8 sample glass lenses one by one. The resulting defocus was in the range of -4 D to +4 D including both sphere and cylinder.
The power calculated by the new method was within 0.15 D, and the calculated axis was within 1 degree in all of the test lenses. The computation was faster than the current Zernike-fit method. The secular reflections and background illumination did not affect the accuracy of the results. With higher amounts of defocus the spots grew large and blurry, however this method worked accurately over a wide range of defocus in the SHS data.
The direct Fourier Transform method is fast, efficient, and accurate over a large range of defocus. This method also performs well in the presence of data artifacts such as stray reflections, background scatter, missing spots, and partially formed spots at the edges. The proposed method appears to be a better choice for measuring defocus in wavefront data or for SHS-based auto-refractors.
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