February Fourier Talks 2016

In recent years, the birefringent (polarization-changing) properties of the Henle fibers surrounding the fovea of a person's eye have been used to identify the position of the fovea and the direction of gaze. This allows for one to check for eye alignment and strabismus, a risk factor for amblyopia ("lazy eye"). The author's lab has developed screening techniques that are based on the birefringence signal derived from foveal circular scanning. In this approach, a signal s(t) consisting of several frequency components (f1=k1*fs, f2=k2*fs, f3=k3*fs, etc.) is produced, where each frequency is a multiple of the scanning frequency fs. Some frequencies prevail during central fixation, while others appear at para-central fixation. In the simplest case, f2=2fs is produced during central fixation, while f1=fs prevails during off-central fixation. Existing instruments acquire consecutive epochs of s(t),with gaps between them, during which an FFT is performed. A problem with this approach is that the FFT power spectrum is a global measure, i.e., it provides information on how much of f1 and f2 are represented in the whole epoch analyzed, but it does not provide information on exactly where these frequencies appear and for how long. With less-cooperative patients, important short lasting moments of central fixation (f2) may easily be hidden behind large low-frequency (f1) components, and thus remain undetected. Analyzing short time intervals is desirable, but this is where the FFT becomes prone to noise and loses spectral resolution. As shown in this presentation, the problem can be solved by using Time-Frequency Distributions (TFD) obtained by means of the Continuous Wavelet Transform (CWT), or other time-frequency methods. The CWT allows sufficient localization in both time- and frequency domains, is computationally efficient, and allows the analysis of continuous signal epochs without gaps, i.e. without loss of data. Another approach to analyze short-lasting non-stationary segments of the scanning signal is the autoregressive (AR) spectral estimation. AR has an advantage over FFT that, it can be designed to employ shorter records while preserving good spectral resolution. Results obtained from human subjects with both the CWT and the AR estimation of the power spectrum density are presented.