Optical Phase Measurement Research Articles

Optical pulse intensity and phase measurement bytime-to-space conversion based on time-lens operation

A method for measuring the phase profile of optical pulses, based on time-to-space conversion by a time lens, is presented. Experimental results are shown for semiconductor laser pulses.

Frequency–Time Method of Processing Phase Measurements in Geophysics

A frequency–time method is proposed for analyzing geophysical phase information whose implementation approaches the results of the operation of an ideal filter. The method is based on the principle of expanding an observed signal over a system of basis functions. The procedure developed makes it possible to determine the phase of the signal and to estimate the operational stability of the phase measuring system. The procedure can be used when designing geophysical measuring devices utilizing optical phase measurements.

Multichannel fiber-optic interferometric sensor for measurements of temperature and vibrations in composite materials

A multichannel fiber-optic interferometric sensor for measuring temperature and vibrations in composite materials is presented. The fiber-optic sensor is designed for simultaneous monitoring of all channels with optical fibers embedded in the structure. The multichannel arrangement with a common reference path and the transducer principle, based in optical phase measurements, provide a high sensitivity sensing of two parameters, their spatial distributions, and the rules of calibration. Our results show that the temperature gradient and the propagation of vibrations along a carbon fiber board are obtained at the same time using the proposed technique as well as their dynamic behavior.

Measurement of the relative optical phase between amorphous and crystalline regions of the phase-change media of optical recording

We describe a method of measuring the relative optical phase on reflection between amorphous and crystalline regions of the phase-change media of optical data storage. With a red He-Ne laser (wavelength, 632.8 nm) the relative phases on two quadrilayer optical disk stacks were measured and found to be ~40 degrees . The results are in good agreement with the calculated values based on the known layer thicknesses and refractive indices of the stacks. For calibration purposes the height of a known step on an otherwise flat silicon substrate was measured with the same apparatus. The proposed method is fairly simple to set up, can measure both front-surface and through-substrate types of optical disk, and can be used with any laser that has long coherence length.

Direct measurement of optical phase in the near field

To fully characterize photonic crystal guided wave optical devices, one needs to measure the spatial variation of both the phase and amplitude of the electromagnetic field. In this work, we simultaneously measure the intensity and phase in the near field of both propagating and evanescent fields by incorporating a scanning near-field optical microscope into one arm of a Mach–Zehnder interferometer. We demonstrate the technique by imaging the phase fronts of an evanescent wave formed by total internal reflection and by measuring the phase variation in the LP11 mode in an overmoded optical fiber.

Phase properties of the optical near field

This paper presents a theoretical and numerical study of the phase properties of the optical near field. A model based on the first Rytov approximation for three-dimensional electromagnetic vector fields describes the relationship between the phase variations and both the topographic and optical properties of the scatterer. It is shown that strong polarization effects can lead to subwavelength phase variations around nanometric structures. The conclusions of the model are illustrated by exact numerical calculations. This study should find broad experimental applications in near-field optical interferometric phase measurements.

Quantitative investigation of optical phase-measuring techniques for ultrashort pulse lasers

We have performed a quantitative investigation into the capabilities and the limitations of two phase-measuring techniques: second-harmonic-generation frequency-resolved optical gating and direct optical spectral phase measurement. In particular, we have studied the reproducibility and the accuracy of these techniques in measuring the frequency-dependent phase of ultrashort pulses with varying amounts of cubic and quadratic phase. We find that both of these techniques are accurate to within 5% in measuring phase distortions in optical pulses.

Programmable liquid crystal waveplates in ellipsometric measurements

High-birefringent, nematic liquid crystal waveplates, using low-voltage electrical drive signals to provide programmable retardances over several hundred nanometres, have recently become commercially available. Using one of these electro-optic devices for both phase and polarization modulation, we have developed a simple, semi-automatic, null, broadband ellipsometer. This instrument measures the ellipsometric parameters and by a technique that does not require measurement of either optical phase or intensity. The operating principle of the ellipsometer is described in detail together with brief details of its construction. Its performance is illustrated by reference to specific optical constant measurements made on a variety of materials including thin films and overcoated magneto-optic recording media.

Surface Topography Measurement Using Digital Moirè Contouring—Errors and Limitations

Moiré contouring is a technique that enables the surface topography of an object to be measured in a single view and has a wide range of potential applications in manufacturing. However, to be useful, it is necessary to be able to calibrate the system and establish the traceability of the calibration. In this paper, the factors that determine the accuracy of the technique are identified, methods of calibration proposed and attainable accuracies estimated. These include the optical magnification, phase measurement and sensitivity, all of which contribute to measurement errors in the technique. The methods are illustrated with results from a digital moiré system, and the improvements required to obtain maximum accuracy are outlined.

Characterization of laboratory-generated turbulence by optical phase measurements

The resolution achieved by an optical imaging system in the presence of the random effects of the atmosphere is severely degraded from the theoretical diffraction limit. Techniques exist for recovering near diffraction-limited performance of an imaging system in the presence of atmospheric turbulence. These image enhancement techniques include speckle imaging, deconvolution, and adaptive optics. A turbulence chamber has been designed and built for laboratory testing of current and future adaptive optics and image enhancement techniques. The turbulence is produced within a chamber consisting of two small fans and a heating element. The effects of the generated turbulence on optical propagation are directly measured by sensing the perturbed wavefront phase. The wavefront phases are measured using a shearing interferometer. The statistical properties of the turbulence are then characterized by means of estimating the phase structure function from the wavefront phase measurements. We found that the estimate of the phase structure function depends only on the magnitude of the separation between two points on the optical wavefront and follows the Kolmogorov 5/3 power law.

Interferogram Analysis: Digital Fringe Pattern Measurement Techniques

Introductory digital image processing optical techniques intensity based analysis methods temporal phase measurement methods spatial phase measurement methods phase unwrapping methods analysis methods in speckle photography and PIV applications.

Quantum sensitivity limits of an optical magnetometer based on atomic phase coherence.

An optical magnetometer based on atomic coherence effects is analyzed using a quantum Langevin approach. The large dispersion of a phase-coherent atomic medium (``phaseonium'') at a point of vanishing absorption is used to detect magnetic level shifts via optical phase measurements in a Mach-Zehnder interferometer with sensitivities potentially superior to state-of-the-art devices. Effects of Doppler broadening and fluctuations of the driving field are discussed and a comparison to standard optical-pumping magnetometers is made.

Many-port homodyne detection of an optical phase.

We present a quantum analysis of the measurement of a relative optical phase using a many-port method that can be implemented using arrays of photodetectors in the limit of a large number of detector elements. Its application to coherent states and states not describable by the semiclassical theory shows that the many-port method has in principle several advantages compared to an eight-port method previously studied. In some cases, especially for very weak fields, the many-port method provides a more faithful characterization (i.e., a smoother distribution) of the distribution of the relative phase than does the eight-port method. The definition used here for the relative phase between two fields is an operational one, not corresponding to any presently known Hermitian phase operator. We discuss the conditions under which our phase definition corresponds to the best estimate in the maximum-likelihood sense. We find that if the many-port data set is analyzed in a way that retains the contributions from zero photon counts, the many-port phase distribution takes on a character that resembles other phase distributions, such as the Pegg-Barnett or Wigner phase distributions, that show very small modulation depth in the case of weak fields.

Quantum-noise-limited interferometric phase measurements

Two schemes for interferometric optical phase measurement, with sensitivity limited only by quantum noise in the light, are analyzed. Direct detection is applicable to signals at modulation frequencies away from the technical noise of the light, so that quantum noise dominates the measurement. Alternatively signals otherwise obscured by classical optical noise may be recovered with a phase-modulation technique that shifts the signals to a quantum-noise-limited region of the photocurrent spectrum. The analysis is tested experimentally by using a polarimetric electric-field sensor. In the direct-detection scheme quantum-noise-limited performance produced a phase sensitivity of 0.25 µrad. The indirect scheme allowed subkilohertz signals to be extracted from classical noise 67 dB greater with sensitivity approaching the quantum noise limit.

Frequency domain analysis of an optical FM discriminator

Measurement of optical phase and frequency deviations using a frequency-domain network analysis approach is described. The frequency domain transfer functions are given which relate the conversion of optical phase, frequency, and intensity modulation into photodetector current after passing through a quadrature biased Mach-Zehnder interferometer. It is shown that the error term in the phase and frequency transfer functions depends only to second order on any accompanying intensity modulation. Experimental data are given illustrating the analytical results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Noise in interferometric optical systems: an optical Nyquist theorem

The index of refraction of an optical medium at a temperature above absolute zero undergoes statistical fluctuations, which in turn introduce fluctuations in the phase of an optical signal propagating in the medium. The magnitude and spectral density of these phase fluctuations are calculated, and it is shown that they can be larger than the phase uncertainty due to quantum noise. Barring the onset of nonlinearities, these fluctuations and not quantum noise set the limit to the measurement of optical phase.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Ultimate quantum limits on phase measurement.

The Susskind-Glogower (SG) phase operator is shown to be the maximum-likelihood (ML) quantum measurement of optical phase for all input states. The ML performance of the SG measurement is optimized, at average photon number N, by an input state with number-ket representation of the form ${\mathrm{\ensuremath{\psi}}}_{\mathrm{n}}$=A/(1+n), for 0\ensuremath{\le}n\ensuremath{\le}M&lt;\ensuremath{\infty}. The optimum phase-error behavior, measured by the reciprocal peak-likelihood, is proportional to 1/${\mathrm{N}}^{2}$, as opposed to the 1/ \ensuremath{\surd}N and 1/N dependences of coherent-state and optimum squeezed-state interferometers.

Measurement of optical phase with subpicosecond resolution by time-domain interferometry

A new and extremely general interferometric technique has been experimentally demonstrated that permits the direct measurement of optical phase on a subpicosecond time scale. The intensity is characterized by cross correlation, and thus the optical field is completely determined.

Subpicosecond transient excitation of atomic vapor and the measurement of optical phase

The transient behavior of a frequency-swept optical pulse transmitted through a resonant vapor cell is observed by an optical sampling technique with ~20-fsec time resolution. The observed 200-fsec transients are the fastest intensity sampling measurement ever made on an atomic vapor and provide a precise determination of the time-varying phase of the pulse. The observed phase shows deviations from a linear frequency sweep, which may account for previous limits on pulse compression.

Three-beam heterodyne interferometer

The heterodyne technique has been applied to three-beam interference, and three interferometer arrangements are discussed. These arrangements are suitable for electronic measurement of optical phase. A three-beam heterodyne interferometer is demonstrated.