Measurement of angular distributions by use of low-coherence interferometry for light-scattering spectroscopy

We present a novel interferometer for measuring angular distributions of backscattered light. The new system exploits a low-coherence source in a modified Michelson interferometer to provide depth resolution, as in optical coherence tomography, but includes an imaging system that permits the angle of the reference field to be varied in the detector plane by simple translation of an optical element. We employ this system to examine the angular distribution of light scattered by polystyrene microspheres. The measured data indicate that size information can be recovered from angular-scattering distributions and that the coherence length of the source influences the applicability of Mie theory.     

Fourier-domain angle-resolved low coherence interferometry through an endoscopic fiber bundle for light-scattering spectroscopy

We present a novel endoscopic fiber bundle probe incorporated in a Fourier-domain angle-resolved low coherence interferometry system for the measurement of depth-resolved angular scattering distributions to permit the determination of scatterer size via elastic scattering properties. Depth resolution is achieved with a superluminescent diode via a Mach-Zehnder interferometer. The sample is illuminated with a collimated beam, and a Fourier plane image of the backscattered light is collected by a coherent fiber bundle. The angular scattering distribution relayed by the fiber bundle is mixed with the reference field and made to coincide with the input slit of an imaging spectrograph. The data collected are processed in real time, producing a depth-resolved angular scattering distribution in 0.37 s. The data are used to determine the sizes of polystyrene microspheres with subwavelength precision and accuracy.     

Fourier-domain low-coherence interferometry for differential mode delay analysis of an optical fiber

We propose a novel mode analysis and differential mode delay measurement method for an optical fiber using Fourier-domain low-coherence interferometry. A spectral interferometer based on a Mach-Zehnder interferometer setup was used with a broadband source and an optical spectrum analyzer to detect relative temporal delays between the guided modes of a few-mode optical fiber by analyzing spectral interference signals. We have shown that experimental results of the proposed method agree well with those results obtained by using a conventional time-domain measurement method. We have demonstrated that this new mode analysis technique has high sensitivity (<60 dB) and very good resolution (<1 ps/m).     

Fiber-optic temperature sensor using low-coherence interferometry

Low-coherence interferometric sensors are an important group of optical fibre sensors. Combining high measurement resolution with broad measurement range, these sensors can measure accurately several physical quantities e.g. temperature. In this article we present the fiber-optic temperature sensor using low-coherent interferometry, which has been designed and elaborated.     

Needle-based refractive index measurement using low-coherence interferometry

We present a novel needle-based device for the measurement of refractive index and scattering using low-coherence interferometry. Coupled to the sample arm of an optical coherence tomography system, the device detects the scattering response of, and optical path length through, a sample residing in a fixed-width channel. We report use of the device to make near-infrared measurements of tissues and materials with known optical properties. The device could be used to exploit the refractive index variations of tissue for medical and biological diagnostics accessible by needle insertion.     

Profilometry with compact single-shot low-coherence time-domain interferometry

We describe the performance of a compact single-shot low-coherence interferometric scheme that can be capable of measuring three-dimensional surface profiles and shape. This technique utilizes a polarizing Michelson interferometer and a four-channel polarization phase-stepper optics, which is based on a paired wedge prism, a combined wave plate and a Wollaston prism. The coherence gated surface image can be calculated by the simultaneous acquisition of two interferograms and a DC image on a single CCD camera. The image calculation is based on a novel algorithm to calibrate the imbalanced intensity as well as the deviated arbitrary relative phase of each of the imaging channels. The system can display the transverse cross-sectional images in real-time. To demonstrate the feasibility of this system, a Japanese coin is presented as a 3-D shape measurement example with an image size of 4 mm (horizontal) × 4 mm (vertical) × 160 μm (depth).     

Fiber-modes and fiber-anisotropy characterization using low-coherence interferometry

An optical low-coherence interferometry technique has been used to simultaneously resolve the mode profile and to measure the intermodal dispersion of guided modes of a few-mode fiber. Measurements are performed using short samples of fiber (about 50 cm). There is no need for a complex mode-conversion technique to reach a high interference visibility. Four LP mode groups of the few-mode fiber are resolved. Experimental results and numerical simulations show that the ellipticity of the fiber core leads to a distinct splitting of the degenerate high-order modes in group index. For the first time, to the best of our knowledge, it has been demonstrated that degenerate LP11 modes are much more sensitive to core shape variations than the fundamental modes and that intermodal dispersion of high-order degenerate modes can be used for characterizing the anisotropy of an optical waveguide.     

High-performance fiber-optic temperature sensor using low-coherence interferometry

A temperature-sensor system based on low-coherence interferometry with a fiber Mach-Zehnder interferometer as a phase modulator was implemented. A measurement range of 20 to 800 degrees C with a resolution of 0.025 degrees C (corresponding to 0.0004 fringe) was achieved with a 1-mm-long fiber Fabry-Perot interferometer as the sensing element.     

Self-referenced method for optical path difference calibration in low-coherence interferometry

A simple method for the calibration of optical path difference modulation in low-coherence interferometry is presented. Spectrally filtering a part of the detected interference signal results in a high-coherence signal that encodes the scan imperfections and permits their correction. The method is self-referenced in the sense that no secondary high-coherence light source is necessary. Using a spectrometer setup for spectral filtering allows for flexibility in both the choice of calibration wavelength and the maximum scan range. To demonstrate the method's usefulness, it is combined with a recently published digital spectral shaping technique to measure the thickness of a pellicle beam splitter with a white-light source.     

Gradient-index fiber-optic microprobes for minimally invasive in vivo low-coherence interferometry

We describe the design, construction, and application of what are believed to be the smallest fiber-optic probes used to date during imaging or diagnosis involving low-coherence interferometry (LCI). The probes use novel fiber-optic gradient-index (GRIN) lenses fabricated by a recently developed modified chemical-vapor-deposition (MCVD) process that avoids on-axis aberrations commonly marring MCVD-fabricated GRIN substrate. Fusing GRIN fiber lenses onto single-mode fiber yields automatically aligned all-fiber probes that insert into tissue through hypodermic needles as small as 31-gauge (inner diameter, 127 mum). We demonstrate the use of such probes with LCI by measuring microscopic brain motions in vivo.     

An effective optical evaluation technique using visible low-coherence interferometry

An easy and effective path length deviation detection technique is described which uses low-coherent visible light source and Michelson interferometer configuration. This technique uses large-amplitude piezoelectric modulation of a mirror, which probes portions of a complete interferogram. The maximum ambiguity in determining the center position of white light fringes is confined to half the source wavelength. Using this technique, the physical thickness and group index of an optical material are measured with an error around 0.1%. The method of improving the accuracy is also discussed.     

Quantitative phase imaging using actively stabilized phase-shifting low-coherence interferometry

We describe a quantitative phase-imaging interferometer in which phase shifting and noise cancellation are performed by an active feedback loop using a reference laser. Depth gating via low-coherence light allows phase measurement from weakly reflecting biological samples. We demonstrate phase images from a test structure and living cells.     

Measurement of ocular axial length using full-range spectral-domain low-coherence interferometry

We demonstrate a system for measuring the ocular axial length(AL) with high sensitivity and high speed using spectral-domain low-coherence interferometry(SD-LCI). To address the limit in measuring such a large range by using SD-LCI, we propose a full-range method to recognize the positive and negative depths. The reference arm length is changed synchronously with the shift of the focal point of the probing beam. The system provides a composite depth range that is sufficient to cover the whole eye. We demonstrate the performance of the presented system by measuring the ALs of five volunteers. This system can provide the A-scan ocular biometric assessment of the corneal thickness and AL in 0.1 s.     

Differential phase measurements in low-coherence interferometry without 2pi ambiguity

Quantitative phase measurements by low-coherence interferometry and optical coherence tomography are restricted by the well-known 2pi ambiguity to path-length differences smaller than lambda/2 . We present a method that overcomes this ambiguity. Introducing a slight dispersion imbalance between reference and sample arms of the interferometer causes the short and long wavelengths of the source spectrum to separate within the interferometric signal. This causes the phase slope to vary within the signal. The phase-difference function between two adjacent sample beam components is calculated by subtraction of their phase functions obtained from phase-sensitive interferometric signal recording. Because of the dispersive effect, the phase difference varies across the interferometric signal. The slope of that phase difference is proportional to the optical path difference, without 2pi ambiguity.     

Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers

We describe fiber-based quadrature low-coherence interferometers that exploit the inherent phase shifts of 3 x 3 and higher-order fiber-optic couplers. We present a framework based on conservation of energy to account for the interferometric shifts in 3 x 3 interferometers, and we demonstrate that the resulting interferometers provide the entire complex interferometric signal instantaneously in homodyne and heterodyne systems. In heterodyne detection we demonstrate the capability for extraction of the magnitude and sign of Doppler shifts from the complex data. In homodyne detection we show the detection of subwavelength sample motion. N x N (N > 2) low-coherence interferometer topologies will be useful in Doppler optical coherence tomography (OCT), optical coherence microscopy, Fourier-domain OCT, optical frequency domain reflectometry, and phase-referenced interferometry.     

Measurement of complex refractive index of human blood by low-coherence interferometry

In this article, the usefulness of the optical technique for measurements of blood complex refractive index has been examined. Measurement of optical properties of human blood is difficult to perform because of its nonuniform nature. However, results of my investigation have shown the usefulness of low-coherence interferometry for measurement complex refractive index of human blood. Furthermore, mathematical analysis of spectrum of measured signal have made possible to determined relationship between complex refractive index and hematocrit level in human blood.     

Using dynamic low-coherence interferometry to image Brownian motion within highly scattering media

Dynamic low-coherence interferometry was used to measure Brownian motion of submicrometer particles within highly scattering media. Strong rejection of multiply scattered light was obtained by combination of a coherence gate with a confocal microscope, thus allowing particle characterization methods generally reserved for optically dilute materials to be applied to optically concentrated suspensions. The Brownian diffusion coefficient of highly scattering media was determined with an accuracy better than 5%. Furthermore, we show that spatial variations in the Brownian diffusion coefficient can be imaged with an axial resolution determined by the coherence length of the light source (~30 mum) . The experiments also show broadening of the power spectrum as a function of depth into the sample, most likely as a result of detecting multiply scattered light.     

Random depth access full-field low-coherence interferometry applied to a small punch test

In small punch testing, with approximate preknowledge of the sample deformation, profile measurement need only be made at selected locations in depth. To date, profilometry through full-field low-coherence interferometry has not been applied to small punch testing—conventional methods typically measure the maximum displacement as the sample is deformed, ignoring useful shape and profile information. A modification of full-field low-coherence interferometry is presented, where a digital stepper motor is combined with piezoelectric transducer scanning to achieve random depth access three-dimensional micrometer profile measurement. Offering a rapid, inexpensive, and functional machine vision system, the measurement technique is applied to a small punch test.     

Measurement of dye diffusion in agar gel by use of low-coherence interferometry

We demonstrate low-coherence interferometry for diffusion measurements. We have measured the diffusion coefficient of a phthalocyanine dye in 1.5% agar gel with a two-wavelength interferometer; one wavelength was matched to the absorption peak of the dye at 675 nm, while the other, 805 nm, was not affected by the dye. The diffusion coefficient of the dye was found by fitting a mathematical model for the interferometer signal to the measured low-coherence interferometry amplitude. A 95% confidence interval for the diffusion coefficient was found to be D = (2.5 +/- 0.2) x 10(-10) m2/s. The influence of speckle averaging and experiment time on the determination of the diffusion coefficient has been studied. The presented technique allows in situ characterization of diffusion in semitransparent media.     

Non-linear Sagnac interferometry for pump-probe dispersion spectroscopy

We explore pump-probe non-linear Sagnac interferometry as a tool to measure the dispersive properties of a medium. We introduce the background theory, and show experimental spectra obtained on the D₂ transition with ⁸⁵Rb and ⁸⁷Rb. The measured dispersion spectra are in excellent agreement with the Kramers-Kronig relations. In addition, as both beams traverse identical optical paths, Sagnac interferometry is very robust against mechanical vibrationReceived: 5 June 2003, Published online: 16 September 2003PACS: 39.30. + w Spectroscopic techniques - 33.55.Ad Optical activity, optical rotation; circular dichroismG. Jundt: Present address: Institute of Quantum Electronics, Department of Physics, ETH Zürich, Hönggerberg 8093, Switzerland.