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Boris I. Gramatikov; Detecting Central Fixation with Autoregressive Modeling during Retinal Birefringence Scanning. Invest. Ophthalmol. Vis. Sci. 2012;53(14):3883.
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© ARVO (1962-2015); The Authors (2016-present)
The birefringent properties of the Henle fibers surrounding the fovea have been used to to identify the position of the fovea and the direction of gaze. This allows checking for eye alignment and strabismus - a risk factor for amblyopia. Screening techniques have been reported, based on the birefringence signal derived from foveal circular scanning. 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 cental fixation, while others appear at paracentral fixation. The existence and the mixture of frequencies depends on the opto-mechanical design. In the simplest case, discussed here, 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 FFT is performed. The problem is that the FFT power spectrum tells how much of f1 and f2 are represented in the whole epoch analyzed, but it does not tell exactly where these frequencies appear and for how long. With less-cooperative patients, important short lasting moments of central fixation (f2) may be hidden behind large low-frequency (f1) components. Analyzing short time intervals is advantageous, but this is where FFT becomes prone to noise and loses spectral resolution.
Autoregressive (AR) spectral estimation is proposed to analyze short-lasting non-stationary segments of the scanning signal. AR has an advantage over FFT that, it uses shorter records and has better spectral resolution at that scale.
Figure 1 illustrates the AR-based analysis during central fixation (left column), and lack thereof (right column). The upper row shows the time domain scan signal (5 ms, scanning frequency fs=96 Hz, sampling rate SR=10 kHz). The middle row is the FFT power of the same signal, having a spectral resolution of 200 Hz. The lower row shows continuous AR power spectral densities, capable of detecting intermediate frequencies.
AR spectral estimation is superior to FFT in analyzing short segments. With modern DSP technology, it can be performed fast, thus reducing signal gaps while increasing temporal resolution.
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