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Boris I. Gramatikov; A Method of Detecting and Monitoring Central Fixation Using the Continuous Wavelet Transform. Invest. Ophthalmol. Vis. Sci. 2011;52(14):6340.
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Techniques for amblyopia screening using the form birefringence properties of the Henle fibers surrounding the fovea have been reported earlier. A periodic signal s(t) is produced by circular scanning around the center of the fovea, generating a frequency of central fixation f2 =k2* fs, where fs is the scanning frequency. With no central fixation, f1=k1*fs is generated. The constants k1 and k2 depend on the optical design. All existing instruments analyze consecutive sub-epochs of s(t), with gaps in-between, during which the Fast Fourier Transform (FFT) is performed and signal analysis takes place. FFT power spectrum tells to what extent f1 and f2 are represented in the epoch analyzed, but it does not tell exactly where these frequencies appear. With pediatric patients, where subject cooperation is a problem, short lasting moments of central fixation (f2) may easily be lost. Moreover, in the gaps between the sub-epochs, valuable instants of central fixation may be missed.
To solve this problem, time-frequency distributions obtained by means of the Continuous Wavelet Transform (CWT) are proposed. CWT allows excellent localization in both time- and frequency domains and permits analysis of continuous signal epochs of any duration without any gaps.
Panel A of the figure shows the time domain scan signal s(t) (RE, 7 year old boy) of duration 400 ms (fs=96Hz; k1=1, k2=2). Panel C shows the FFT power of the same signal. One can see the two frequencies, but cannot tell where in time they appear. Panel B shows the CWT of the same signal. Here f1 and f2 episodes can easily be localized in time.
The Continuous Wavelet Transform is superior to the FFT in localizing fixation frequencies in both the time- and frequency domains. It is an excellent tool for precisely identifying central fixation in an uninterrupted manner, thus improving device reliability and shortening test time. Using modern digital signal processing hardware, the CWT can be performed in real time, and is expected to improve significantly detection sensitivity when testing uncooperative subjects.
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