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...

We present a lamellar grating interferometer realized with microelectromechanical system technology. It is used as a time-scanning Fourier-transform spectrometer. The motion is carried out by an electrostatic comb drive actuator fabricated by silicon micromachining, particularly by silicon-on-insulator technology. For the first time to our knowledge, we measure the spectrum of an extended white-light source with a resolution of 1.6 nm at a wavelength of 400 nm and of 5.5 nm at 800 nm. The wavelength accuracy is better than 0.5 nm, and the inspected wavelength range extends from 380 to 1100 nm. The optical path difference maximum is 145 mm. The dimensions of the device are 5 mm 3 5 mm.Spectrometry is widely used in industry and research laboratories. There are many different methods that are used in a variety of fields. In particular, Fourier-transform spectroscopy is a powerful technique for investigating weak sources with high resolution. At present, an extended range of Fourier spectrometers is commercially available. However, high resolution involves an elevated degree of mechanism precision and therefore large size and high cost. Recently, lower-resolution miniature spectrometers have become attractive because of new applications, expanding opportunities in a remarkable variety of disciplines and industries.

Resonant Doppler Fourier domain optical coherence tomography (FDOCT) is a functional imaging tool for extracting tissue flow. The method is based on the effect of interference fringe blurring in spectrometer-based FDOCT, where the path difference between structure and reference changes during camera integration. If the reference path length is changed in resonance with the Doppler frequency of the sample flow, the signals of resting structures will be suppressed, whereas the signals of blood flow are enhanced. This allows for an easy extraction of vascularization structure. Conventional flow velocity analysis extracts only the axial flow component, which strongly depends on the orientation of the vessel with respect to the incident light. We introduce an algorithm to extract the vessel geometry within the 3-D data volume. The algorithm calculates the angular correction according to the local gradients of the vessel orientations. We apply the algorithm on a measured 3-D resonant Doppler dataset. For validation of the reproducibility, we compare two independently obtained 3-D flow maps of the same volunteer and region.

We report on a novel method combining achromatic complex FDOCT signal reconstruction with a common path and dual beam configuration. The complex signal reconstruction allows resolving the complex ambiguity of the Fourier transform and to enhance the achievable depth range by a factor of two. The dual beam configuration shares the property of high phase stability with common path FDOCT. This is of importance for a proper complex signal reconstruction and is in particular useful in combination with handheld probes such as in endoscopy and catheter applications. The advantage of the presented approach is the flexibility to choose arbitrarily positioned interfaces in the sample arm as reference together with the possibility to compensate for dispersion. The method and first experimental results are presented and its properties concerning SNR and dynamic range are discussed.

We present a lamellar grating interferometer (LGI) realized by silicon micro-machining. The LGI is a binary grating with a variable depth. The motion is carried out by an electrostatic comb drive actuator fabricated by silicon-oninsulator (SOI) technology. It is used as Fourier transform spectrometer (FTS). We have measured an optical path difference maximum of 82 µm. The measured resolution of the spectrometer after the phase correction is 6 nm at a wavelength of 633 nm. A preliminary measurement with a xenon arc lamp is shown.A lamellar grating interferometer (LGI) is a grating that operates in the zeroth order. This particular type of apparatus was invented by Strong [1]. A scheme of the principle is illustrated in Fig. 1a. The LGI is used as FTS, but contrary to the Michelson interferometer that splits wave amplitudes at the beamsplitter, the LGI divides the wavefront. At the grating, the wavefront is divided such that one half of the beam is reflected from the front facets (fixed mirrors in Fig. 1b) and one half from the back facets (mobile mirrors in Fig 1b). The distance d between the two series of mirrors determines the optical path difference (OPD = 2d) between the two parts of the wave. The enormous advantage of this configuration, compared with a Michelson interferometer, is the absence of a beamsplitter. Indeed, any additional micro-optical component is a limitation in the particular case of micro-sized spectrometers. In general, this type of spectrometer is used for wavelengths larger than 100 µm; below, the tolerances are too tight for most machine shops. Silicon micromachining is the ideal technology to overcome these limitations for shorter wavelengths. where a is the grating period, α is the diffraction angle, λ is the wavelength, andis the phase delay introduced by the displacement d. At the zeroth order of the grating (α = 0), Eq. (1) To characterize the performance of our device, we have recorded the zeroth order I 0 (d) of the diffraction pattern produced by a collimated HeNe laser on the grating. To get rid of the non-linearity of the driving system, a phase correction is effectuated. The phase correction is described in reference [3]. We have measured an OPD nonlinearity ∆ OPD of ±0.6 µm for a displacement of 82 µm. Figure 2 shows the spectrum of a He-Ne laser before and after the phase correction. The measured resolution of the spectrometer after the phase correction is 6 nm at a wavelength of 633 nm. To achieve the maximum displacement, we have applied a variable voltage V 0 of ±8.5 V and the constant tensions V A and V B were 85 V, respectively -91 V. In addition, measurements with an extended white light source have been carried out. Figure 3 shows the interferogram and the spectrum of a xenon low-pressure arc lamp. In this experiment, the light coming from a multimode fiber is collimated and then focused with a cylindrical