We introduce a simple and cheap method for phase-shifting Fourier domain optical coherence tomography (FDOCT) that does not need additional devices and can easily be implemented. A small beam offset at the fast beam-scanning mirror introduces a causal phase shift, which can be used for B-scan-based complex image reconstruction. We derive the conditions for optimal conjugate suppression and demonstrate the method on human skin in vivo for spectrometer-based FDOCT operating at 1300 nm employing a handheld scanner. Employing phase-shifting techniques in Fourier domain optical coherence tomography (FDOCT) is a common method to suppress complex ambiguity terms due to the signal reconstruction. The terms are a direct result of taking the Fourier transform of the recorded spectral interference pattern, which is a real-valued function. The first attempts to produce the complex FDOCT signal were phase stepping techniques known from white-light interferometry [1,2]. However, keeping a clear phase relation over several frames becomes difficult in the case of in vivo measurements. The reduction to two frames allowed motion artifacts to be kept small [3]. Still, the phaseshifting process is highly chromatic, leading to phase errors and failure of mirror term suppression. The use of frequency shifters allows a complete achromatic heterodyne signal reconstruction [4]. The advantages of complex reconstruction techniques in FDOCT are doubling of the achievable depth range, the suppression of mirror terms that might obscure the sample structure, and the possibility of exploiting the high sensitivity across the zero delay. For clinical systems the suppression of mirror terms-avoiding folding of structure terms at the zero delayincreases instrument quality and facilitates the system operation. The drawback of employing phaseshifting devices such as electro-optic modulators, acousto-optic frequency shifters, or piezo transducers is the increased complexity of the system concerning synchronization electronics as well as the price of the elements themselves. In particular for common-path configurations [5], where the reference arm is included in a fiber-coupled hand-held applicator, it is difficult to include such phase-shifting devices. In the present Letter we will show how to realize a simple FDOCT system that allows complex signal reconstruction without additional phase-shifting devices. It is already known from en face time domain OCT that a heterodyne frequency can be obtained by simply offsetting the probing beam from the pivot point of the scanning mirror [6]. Consider the schematics in Fig. 1(a): the offset ⌬x from the center of rotation (CR) of the scanner mirror causes a change in optical path length ␦z during scanning. For small angles of rotation ␦␣ the path length change reads as ␦z =2␦␣⌬x / ͑1−␦␣͒. Of particular interest is the differential path length change between successive depth scans, i.e., during the detection line period T. With the relation between the angular scanner frequency and the differential angular chan...

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Abstract-We address the problem of estimating the instantaneous frequency (IF) of a phase signal using its level-crossing (LC) information based on front-end auditory processing motivation. We show that the problem of IF estimation using LC information can be cast in the framework of estimation from irregularly sampled data. The formulation has the generality of estimating different types of IF without the need for a quasistationary assumption. We consider two types of IF-polynomial and bandlimited; we use polynomial interpolating functions for the former, and for the latter, we propose a novel "line plus sum of sines" model.

We address the problem of estimating instantaneous frequency (IF) of a real-valued constant amplitude time-varying sinusoid. Estimation of polynomial IF is formulated using the zero-crossings of the signal. We propose an algorithm to estimate nonpolynomial IF by local approximation using a low-order polynomial, over a short segment of the signal. This involves the choice of window length to minimize the mean square error (MSE). The optimal window length found by directly minimizing the MSE is a function of the higher-order derivatives of the IF which are not available a priori. However, an optimum solution is formulated using an adaptive window technique based on the concept of intersection of confidence intervals. The adaptive algorithm enables minimum MSE-IF (MMSE-IF) estimation without requiring a priori information about the IF. Simulation results show that the adaptive window zero-crossing-based IF estimation method is superior to fixed window methods and is also better than adaptive spectrogram and adaptive Wigner-Ville distribution (WVD)-based IF estimators for different signal-to-noise ratio (SNR).

We address the problem of exact signal recovery in frequency domain optical coherence tomography (FDOCT) systems. Our technique relies on the fact that, in a spectral interferometry setup, the intensity of the total signal reflected from the object is smaller than that of the reference arm. We develop a novel algorithm to compute the reflected signal amplitude from the interferometric measurements. Our technique is non-iterative, non-linear and it leads to an exact solution in the absence of noise. The reconstructed signal is free from artifacts such as the autocorrelation noise that is normally encountered in the conventional inverse Fourier transform techniques. We present results on synthesized data where we have a benchmark for comparing the performance of the technique. We also report results on experimental FDOCT measurements of the retina of the human eye.