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Alexander Leube, David Kern, Arne Ohlendorf, Siegfried Wahl; Radial averaging of the optical modulation transfer function and its impact on image quality. Invest. Ophthalmol. Vis. Sci. 2017;58(8):1123. doi: https://doi.org/.
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© ARVO (1962-2015); The Authors (2016-present)
The currently used method for radial averaging of the modulation transfer function (MTF) (Thibos, 2004) results in tight fluctuations regarding the outcomes. The purpose of the study was to develop a novel method to average the MTF radially and to evaluate the impact on image quality.
The MTF was calculated from wavefront aberrations up to the 7th radial order (i.Profiler plus, Carl Zeiss Vision) using a Fourier based approach. Applying a 2-D bi-cubic interpolation algorithm (Matlab 2015b, MathWorks), the MTF was resampled for each radial orientations in 1.0° steps for a step size of spatial frequencies (SF) of 1.0 cpd from 1 cpd up to 60 cpd. Each SF was averaged from 0° to 359° separately, using the same number of given values. To evaluate the impact on image quality of the proposed averaging method, six image quality metrics (IQM) (visible area under the MTF and OTF (AUC), cut-off frequencies for MTF and OTF (SFcutoffMTF, SFcutoffOTF), Square root integral (SQRI) and integrated contrast sensitivity (ICS)) were calculated for natural wavefront errors and artificial combinations of primary coma C(3,-1) and trefoil C(3,-3) from -0.8 µm to +0.8µm.
Bi-cubic pre-sampling of the MTF resulted in a radial averaged MTF (rMTF), representing the mathematically correct mean and results in a smooth outcome without random fluctuations even for asymmetric MTF curves (see Fig. 1). IQMs showed no significant difference for natural wavefront errors (pAll>0.05, t-test) and high correlations (r>0.92, p<0.001, Pearson) between the two rMTF methods. For combinations of C(3,-1) and C(3,-3) that differed in the sign, AUC-based metrics result in significantly lower values, when the proposed rMTF method was used (ΔAUCMTF=-0.04, p=0.04; ΔAUCOTF=-0.05, p=0.002; ΔICS=-95.33, p=0.02; t-test). SFcutoffMTF and SQRI metric performed equally well in both methods (r>0.90, p<0.05, Pearson; p>0.05, t-test) while artificial wavefront errors were used.
The proposed method of pre-sampling the MTF using bi-cubic interpolation, provides a mathematically correct mean rMTF and offers a better estimation of image quality, using area under the curve based metrics, especially in highly asymmetric wavefronts.
This is an abstract that was submitted for the 2017 ARVO Annual Meeting, held in Baltimore, MD, May 7-11, 2017.
Fig. 1: Example for radial average of modulation transfer function (rMTF) calculated from original data (grey) with the proposed method (red) and the conventional method (black).
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