Showing papers on "Phase (waves) published in 1985"

Phase-shifting speckle interferometry

Abstract: Speckle patterns have high frequency phase data, which make it difficult to find the absolute phase of a single speckle pattern; however, the phase of the difference between two correlated speckle patterns can be determined. This is done by applying phase-shifting techniques to speckle interferometry, which will quantitatively determine the phase of double-exposure speckle measurements. The technique uses computer control to take data and calculate phase without an intermediate recording step. The randomness of the speckle causes noisy data points which are removed by data processing routines. One application of this technique is finding the phase of deformations, where up to ten waves of wavefront deformation can easily be measured. Results of deformations caused by tilt of a metal plate and a disbond in a honeycomb structure brazed to an aluminum plate are shown.

Multiple-wavelength phase-shifting interferometry

Abstract: This paper describes a method to enhance the capability of two-wavelength phase-shifting interferometry. By introducing the phase data of a third wavelength, one can measure the phase of a very steep wave front. Experiments have been performed using a linear detector array to measure surface height of an off-axis parabola. For the wave front being measured the optical path difference between adjacent detector pixels was as large as 3.3 waves. After temporal averaging of five sets of data, the repeatability of the measurement is better than 25-A rms (λ = 6328 A).

Phase shifter calibration in phase-shifting interferometry.

Abstract: This paper describes some practical methods to calibrate the phase shifter in phase-shifting interferometry (PSI). The phase shifter used in the experiment is a piezoelectric transducer (PZT) that has a nonlinearity of <1%. Using the quantitative method described in this paper, the repeatability in the measurement of the phase-shifting angle is ~0.046° rms, and the 3σ value is 0.139°. A calibration-insensitive phase calculation algorithm is discussed and compared with other synchronous detection equations (e.g., the three-bucket or the four-bucket method). Experimental results verify the calibration-insensitive mechanism of the self-calibrating algorithm.

Automated phase-measuring profilometry: a phase mapping approach.

Abstract: When a sinusoidal grating is projected on either a reference plane or a diffuse object to be measured, every point along a line normal to the grating lines, on the reference plane as well as the object, can be characterized by a unique phase value. By measuring this phase accurately using phase modulation methods and by determining points on the reference plane and the object having identical phases, it is shown that the object height can be computed. A working system requires a projector, a translatable sinusoidal grating, and a detector array interfaced to a microcomputer. Results of measurements on diffuse test objects are described and errors are analyzed.

It's Just a Phase We're Going Through: A Review and Synthesis of OD Phase Analysis

Abstract: This article identifies the description of OD phases as one of the fundamental theoretical problems in the field of organization de velopment. Although phase models have been proposed for over 30 y...

Residual amplitude modulation in laser electro-optic phase modulation

Abstract: An important practical limitation to the sensitivity of frequency-modulation spectroscopy arises because of imperfect phase modulation of the laser beam. This imperfection manifests itself as residual amplitude modulation (RAM), and we present data from a careful series of experiments designed to elucidate its origin. Experimentally, we find two components to the RAM, one that depends for its intensity on the laser frequency and one that does not. We present a model that correctly accounts for the intensity and rf phase and frequency behavior of the laser-frequency-dependent component. We are unable to offer a plausible explanation for the laser-frequency-independent component.

Synchronous cavity mode and feedback wavelength scanning in dye laser oscillators with gratings

Abstract: A simple result of scalar diffraction theory is used to derive the round trip phase accrual of a plane wave in dye laser oscillators containing gratings. This is used to determine configurations where the standing wave condition is satisfied at the feedback wavelength throughout an angle scan. We find that at least one such exactly synchronous configuration always exists regardless of oscillator type.

Optical phase conjugation by backscattering in barium titanate

Abstract: We demonstrate optical-beam phase conjugation by the process of two-beam coupling in photorefractive barium titanate The incident, image-bearing beam causes exponential gain for counterpropagating waves, which are fed by noise and emerge with a power of the order of 10% of the incident beam and phase conjugate to it This is expected from the calculated plane-wave gain plus the analogy to the theory of phase conjugation of complex wave fronts by stimulated Brillouin backscattering We conjugate beams at either 515 or 488 nm at between 10- and 50-mW power, and find, as expected, no frequency shift (<1 Hz) in the process

Shearing interferometer for phase shifting interferometry with polarization phase shifter.

Abstract: A cyclic interferometer can be used for both lateral and radial shearing. Being common-path this interferometer is quite stable. The use of a cyclic shear interferometer for phase shifting interferometry is discussed. The phase shifting is provided here by polarization techniques. Some useful cyclic phase shifting interferometer arrangements are discussed, and the working of a polarization phase shifting cyclic shear interferometer is demonstrated.

Magnetic resonance imaging the velocity vector components of fluid flow.

Abstract: Encoding the Precession phase angle of proton nuclei for Fourier analysis has produced accurate measurement of fluid velocity vector components by MRI. A Pair of identical gradient pulses separated in time by exactly ½ TE, are used to linearly encode the phase of flow velocity vector components without changing the phase of stationary nuclei, Two-dimensional Fourier transformation of signals gave velocity density images of laminar flow in angled tubes which were in agreement with the laws of vector addition. These Velocity profile images provide a quantitative method for the investigation of fluid dynamics and hemodynamics.© 1985 Academic Press,Inc.

Contouring Aspheric Surfaces Using Two-wavelength Phase-shifting Interferometry

Abstract: Two-wavelength holography and phase-shifting interferometry are combined to measure the phase contours of deep wavefronts and surfaces, such as those produced by aspherics, with a variable sensitivity. When interference fringes are very closely spaced, the phase data contain high frequencies where 2 ~ ambiguities cannot be resolved. In this technique, the surface is tested at a synthesized longer equivalent wavelength. The phase of the wavefront is calculated modulo 2φ using phase-shifting techniques at each of two visible wavelengths. The difference between these two phase sets is the phase of the wavefront as it would be measured at λeq=λ1λ2/|λ1 − λ2 |, assuming that 2π ambiguities can be removed at λeq. This technique enables surfaces to be contoured to an accuracy of λeq/100.

Optical profiler using improved phase shifting interferometry

Abstract: An optical profiler includes a two-beam interferometer. An interference pattern produced thereby is focused onto an array of photocells. Phase shift in a reference beam of the interferometer is produced by accelerating a piezoelectric transducer supporting the interferometer mirror to a constant velocity. The velocity is maintained constant for at least 360° of phase shift, during which four integrated buckets are obtained from each photocell. The outputs of the photodetector array are continuously integrated and effectively read out every 90° of phase shift of the reference beam by a computer that computes a first value of phase corresponding to each photocell output from the first, second, and third integrated buckets produced by that photocell and a second phase value from the second, third, and fourth integrated bucket values obtained from that photocell. The two phase values are averaged, eliminating the effects of sinusoidal noise produced by inaccuracies in the reference beam phase at which integrated buckets are initiated and terminated. Data points at which intensity modulation produced by the reference beam phase variation is less than a noise threshold are masked from phase calculations. The intensity of the interferometer light source is automatically controlled by averaging intensity of the intereference pattern at angles that differ by 180° to cancel out the effects of the interference and obtain an average intensity. The lamp voltage is automatically adjusted to maintain the average intensity.

Coherent interactions in pump-probe absorption measurements: the effect of phase gratings

Abstract: We show that in order to describe completely the coherent coupling between the pump and probe pulses in a pump– probe measurement of transient absorption, the influence of induced phase gratings must be included. The importance of phase gratings is demonstrated experimentally for the case of a bleachable dye and analyzed in terms of transient four-wave mixing. These results are relevant to the interpretation of pump–probe measurements on all time scales performed with pulses from a single laser, particularly when the pulse duration is comparable with the material response time.

Quasi- heterodyne hologram interferometry

Abstract: Wider use of hologram interferometry for quantitative measure-ments has been delayed by the fact that interpolation between the fringe maxima and minima to obtain the optical path difference at a particular point in the field is laborious and inaccurate. A solution to this problem is quasi-hetero-dyne interferometry, which permits rapid and accurate measurements simultaneously at a number of points distributed over the interference pattern. In this technique a television camera is used in conjunction with digital electronics to measure and store the irradiance values at points on a rectangular sampling grid covering the real-time interference fringes. The phase difference between the interfering wavefronts at each point is then calculated from the irradiance values obtained from successive scans of the camera made while the phase of one of the wavefronts is shifted either continuously or in steps. A practical system is described with which values of the optical path difference for 10,000 data points can be obtained with an accuracy of ± A/200 in less than 10 s. The application of quasi-heterodyne hologram interferometry to the measurement of vector displacements and to holographic contouring is discussed.

Investigation of a surface field phase perturbation technique for scattering from rough surfaces

Abstract: We present initial results from the investigation of a surface field phase perturbation method for the calculation of the wave field scattered by a rough surface. This technique is based on the extinction theorem and uses a perturbation expansion of a function closely related to the complex phase of the surface field. This approach was suggested earlier, but we use the expansion in a different way. In the present work we consider only deterministic periodic surfaces, rough in one dimension, on which the total field is zero. We find that, for surfaces with modest slope and curvature, this technique can be used to calculate scattered fields even when surface relief is significant compared to the wavelength of the incident radiation.

The effect of phase-shifter errors on the performance of an antenna-array beamformer

Abstract: The paper considers the random phase errors in the phase shifters which are used in an antenna array to steer the beam in the look direction, and analyzes the effect of these errors on the performance of the optimal processor which maximizes the output SNR by deriving the expressions for the output signal power, residual interference power, output SNR, and the array gain as a function of the variance of these errors. The paper also considers the phase quantization error which arises in the digital phase shifters and shows how the performance of the optimal processor depends on the number of bits of the digital phase shifters.

Light demodulator and method of communication employing the same

Abstract: A light modulator for generating a beam of phase modulated light including a source of polarized light, at least one and preferably two liquid crystal cells having a thin layer of nematic liquid crystals of positive dielectric anistropy through which the polarized light is directed to produce a beam of light having a phase shift corresponding to a modulating electrical signal which is applied to each of the liquid crystal cells. The liquid crystal cells in addition have a continuing electrical bias applied across the layers in order to achieve the rapid response times necessary to achieve modulation of the polarized light. Demodulation of the polarized light occurs by splitting the modulated light beam into its quadrature components and developing an electrical signal corresponding to the phase difference between the two quadrature components. A communication system involving its modulators and demodulators delivers communication through light as a transmission medium.

Representation of Gaussian beams by complex rays.

Abstract: This paper shows that a fundamental Gaussian beam propagating in a lenslike medium with cylindrical symmetry can be generated by the rotation about its axis of a skew ray which obeys the laws of geometrical optics. A complex representation: X(z) = ξ(z) + jη(z), where ξ(z) and η(z) are the projections of the skew ray on two perpendicular meridional planes, is discussed. It is found that the beam radius is equal to the modulus of X(z) and the on-axis phase to the phase of X(z). Using this representation, we derive a general expression for the on-axis phase shift ΔΦ experienced by a beam with an input complex beam parameter q through an optical system whose ray matrix is [ABCD]:ΔΦ=phase of(A+B/q). When the beam is matched to the optical system (output q = q), ΔΦ can be written cos–1(A + D)/2. This representation also provides a useful beam tracing method which is demonstrated and a simple interpretation for the known representation of Gaussian modes by ray packets.

Enhanced four-wave mixing by use of frequency-shifted optical waves in photorefractive BaTiO3.

Abstract: We present theory and experiments to show that the efficiency of four-wave mixing in photorefractive materials can be enhanced by use of optical waves of slightly different frequencies The optimum frequency shift scales inversely with the response time of the material We show that the \ensuremath{\sim}1-Hz frequency shift previously observed in the output of a self-pumped phase conjugator that used photorefractive BaTi${\mathrm{O}}_{3}$ is the result of this inherent property of four-wave mixing

Passive harmonic source ranging in waveguides by using mode filter

Abstract: The conventional beam‐forming technique cannot be used for source location in a waveguide because of the modal interference structure of the field. In this paper a new method of passive source ranging in a layered waveguide is proposed. The mode filtering processor was used to process the field data of a vertical array to obtain individual modes. The source range information can be extracted by measurement of three individual mode phases. The source range was expressed in terms of the ‘‘mode interference distance’’ as follows: r=Li j*Di j+Δri j; Δri j=Di j ×(δφi j/2π), where Li j is a certain integer, δφi j is the phase difference of the ith and jth modes, Di j is the ‘‘mode interference distance’’ defined by Di j=2π/(ki−k j), and ki is the wavenumber of the ith mode given by a numerical mode code. The information of Li j can be estimated by means of comparison with the phase of the jth mode with another mode, say the mth mode, and then Li j would be estimated by solving the following equation: (δφ jm/2π)...

Voltage-controlled optical/RF phase shifter

Abstract: A new fiber-optic device designed to steer the radiation beam of a phased-array antenna has been demonstrated. A radiofrequency (RF) signal at 125 MHz is generated via photomixing at the output of a single-mode fiber-optic interferometer. The phase of the electrical signal is shifted over several cycles in direct proportion to a voltage applied to an optical controller. The controller consists of a Pockels-type optical phase modulator located in one arm of the heterodyne interferometer. Rapid changes in RF phase are feasible. A miniature low-voltage version of the device, based upon integrated optics, is proposed.

Image formation in terms of the transport equation

Abstract: A scheme for recovering phase using irradiance data alone, without interferometric techniques, is developed using the transport equations for phase and irradiance. For the case of one transverse dimension a general solution, for an arbitrary irradiance distribution, of the transport equation for the optical phase is already given by an application of the divergence theorem. Numerical simulation results are given that indicate that the phase-recovery scheme works well even in the presence of large pupil-plane aberrations if the signal-to-noise ratio is sufficiently high. In particular, pupil-plane phase aberrations may be determined from irradiance measurements in two planes that are near the image plane.

Image transmission and interferometry with multimode fibers using self-pumped phase conjugation

Abstract: A double‐pass image transmission through a single multimode fiber is demonstrated, using a passive phase conjugate mirror. An application to interferometry based on phase sensing is demonstrated, by implementing the multimode fiber and the passive phase conjugate mirror as one arm of a Michelson interferometer. Due to the unique properties of the self‐pumped conjugator, nonuniform distortions caused by modal dispersion in the fiber and other aberrations are cancelled out, while uniform phase changes are detected.

Frequency shift and cavity length in photorefractive resonators.

Abstract: Photorefractive resonators exhibit an extremely small frequency difference (Deltaomega/omega~10(-15)) between the oscillating and pumping beams. The observed frequency difference is proportional to cavity-length detuning. This dependence is explained by a photorefractive phase shift that is due to slightly nondegenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for steady-state oscillation. The measured onset or threshold of oscillation as a function of photorefractive gain and intensity agrees with theory.