Phase-shifted Interferograms Research Articles

Tilt-compensating algorithm for phase-shift interferometry

A self-calibrating algorithm for phase-shift interferometry is described that is able to cancel the effect of accidental relative tilts that may occur during phase stepping. The algorithm is able to retrieve both the phase steps and the tilts that accompany them. Only three phase-shifted interferograms are needed, and no other information about the intentional phase shifts or possible tilts has to be supplied. This purpose is achieved by division of the interferogram space into blocks on which a previously reported self-calibrating algorithm is applied and the actual values of the local phase shifts are calculated. The information thus obtained is used for extracting the global shift and tilt values. Further improvement in the results is achieved by means of a fitting routine.

Fringe compensation measurement in holographic interferometry using phase-shifted interferograms

A new fringe compensation method for holographic interferometry is presented. Virtual displacement fields are used to compensate the displacement of the investigated object. The virtual displacement fields are built from phase-shifted reconstructions of the recorded interferogram. The sensitivity of the measurement can be changed after the recording of the interferogram. The fringe density at highly deformed points of the object can be decreased; the defect detection can be simplified.

Frame rate phase-shifting interferometer with a frequency-modulated laser diode

We develop a laser-diode phase-shifting interferometer that can capture frame-rate phase-shifted interferograms on a video tape with a high capacity for their storage. The number of the video frame is simultaneously recorded on an audio track of the video tape. In a four- step manner, the injection-current variation of the laser diode is synchro- nized with the field pulse of a CCD camera to producep/2-step phase shifts at a frame rate of 1/30 s. An intensity distribution of the interfero- gram on any frame can be determined through a video tape with a frame memory using the recorded frame number. The four successive phase- shifted interferograms are used to calculate a distribution of frozen phase by a phase-extraction algorithm. The phase error due to the frame-by- frame intensity repeatability is theoretically analyzed. © 1999 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(99)01812-7)

Phase Retrieval of Phase-Shifting Interferometry with Iterative Least-Squares Fitting Algorithm: Experiments

We report our experimental results of phase-shifting interferometry with an iterative least-squares fitting technique to estimate both the wave front phases and the phase shifts. The method allows phase retrieval from phase-shifting interferograms even though the calibration data of the phase shifter is unknown. The algorithm is used to analyze two sets of experimental interferograms. One records by moving a piezoelectric transducer shifter randomly and therefore has embedded random phase shifter errors, and the other samples the interference movie recorded by a video recorder while driving a stepping motor and therefore has embedded random intensity noises. The results are comparable with that of the conventional M-frame algorithm. Investigation of the effects of the intensity noises and phase shift errors shows the algorithm to perform well in both. Problems such as convergence, unique solution and reliability are also discussed.

Phase-shifted interferometry without phase unwrapping: reconstruction of a decentered wave front

We apply the method of the line integration of the phase gradient to determine unambiguously the phase from several phase-shifted interferograms (intensity fringe patterns) without phase unwrapping. The ambiguities introduced owing to the multiple values of the arctangent function and to the necessity to invoke a priori knowledge in the regions of high-intensity gradients are avoided. A decentered wave front with circular boundaries is reconstructed from high-fringe-density interferograms with an error of less than 0.1 percent, thus demonstrating the feasibility of testing the off-axis optical elements with approximate reference components.

Phase-shifting interferometry using a two-dimensional regularized phase-tracking technique

Phase-shifting interferometry is the most used method whenever the optical stability of the interferometer remain high when several phase-shifted interferograms are taken. In this work we present a two-dimensional regularized phase-tracking (RPT) technique applied to demodulate multiple phase-shifted interferograms. The main advantage of this technique with reference to classical phase-shifting interferometry is its higher signal-to-noise rejection as well as a higher signal′s harmonics rejection. In the RPT technique the unwrapping process is implicit; so it is achieved simultaneously with the phase estimation process; then, no additional unwrapping process is required.

Statistical self-calibrating algorithm for phase-shift interferometry based on a smoothness assessment of the intensity offset map

By processing a set of three phase-shifted interferograms one can determine the actual phase steps between recordings by assuming that the calculated map of the intensity offset has the smallest pixel to pixel variations when the supposed values of the phase steps match the actual ones. Based on this principle a new statistical self-calibrating algorithm for phase-shift interferometry is presented. Numerous tests were carried out to check the ability of the new algorithm to find the correct values of the actual phase steps. Algorithm limitations are discussed.

Quantitative vibration amplitude measurement with time-averaged digital speckle pattern interferometry

A new method of using time-averaged digital speckle pattern interferometry for the quantitative measurement of vibration amplitude was developed. Signal processing techniques especially the Hilbert transformation for quantitative evaluation of the Bessel fringes obtained in time-averaged digital speckle pattern interferometry were explored. The quadrature signal after Hilbert transformation is equivalent to a 90° phase-shifted interferogram for a monotonically increasing or decreasing phase function. An algorithm was developed for Bessel fringe contrast enhancement and phase extraction. The techniques were tested numerically and experimentally. Sub-fringe quantification of the time-averaged vibration fringes is realised with the proposed method. Compared with the commonly used phase shift method which requires a minimum of two images for image processing, this method requires only one fringe pattern for data extraction.

Self-calibrating algorithm for three-sample phase-shift interferometry by contrast levelling

A new statistical self-calibrating algorithm for phase-shift interferometry is presented. The algorithm can be applied to the case of three phase-shifted interferograms for which the assumption of a constant fringe contrast over the viewing field can be made. Self-calibration is achieved by minimizing the non-uniformity that appears in the map of the calculated contrast when incorrect phase shifts are supposed. No information on the actual phase shifts has to be supplied, the only input needed is the set of three interferograms. The residual errors of the algorithm are as low as in usual conditions.

Direct deduction of the Sellmeier dispersion function from the hook and phase-shift spectrograms

A double-layer interferometer is used to produce the hook and the phase-shift interferograms with a tube- and flame-excited D-line of Na atoms. New equations are derived to express the order shift of the perturbed fringes in terms of the coefficients of the Sellmeier dispersion function. A least-squares fit of this function to the experimental data enables its coefficients to be found so that the level population can be more precisely determined than hitherto given. The precision is enhanced at the expense of using a multiray interferometer and a data collection over a relatively wide spectral interval extending from the line core to its far wings.

Evaluation of a method to determine interferometric phase derivatives

A recently published method for the determination of phase derivatives maps by direct manipulation of three or more phase-shifted interferograms is tested for accuracy. The method is evaluated on computer-simulated holographic and electronic speckle pattern interferometry fringes and the results are assesed through the calculation of two comparative parameters: the relative image difference and the linear correlation coefficient. It is shown that errors in the phase derivative strongly depend on the filtering method used for smoothing the fringe patterns. An experimentally recorded ESPI fringe pattern is used to confirm the predictions of the numerical simulations.

Derivatives of displacement obtained by direct manipulation of phase-shifted interferograms

The maps of phase derivatives are extracted here by direct manipulation of phase-shifted interferograms. There are three main advantages: There is no need for prior phase evaluation or unwrapping procedures, and only a short processing time is needed. By digital integration of the derivatives the absolute phase map can also be retrieved without unwrapping procedures. A general description of the method is presented and discussed. For example, the proposed technique has been applied to the study of the deformation of a test object by the manipulation of four phase-shifted interferograms.

Optical and electronic design of a calibrated multichannel electronic interferometer for quantitative flow visualization

Calibrated multichannel electronic interferometry is an electro-optic technique for performing phase shifting of transient phenomena. The design of an improved system for calibrated multichannel electronic interferometry is discussed. This includes a computational method for alignment of three phase-shifted interferograms and determination of the pixel correspondence. During calibration the phase, modulation, and bias of the optical system are determined. These data are stored electronically and used to compensate for errors associated with the path differences in the interferometer, the separation of the phase-shifted interferograms, and the measurement of the phase shift.

Modulation analysis of phase-shifted holographic interferograms

A new evaluation technique for phase-shifted holographic interferograms is developed and verified by experiments. In evaluating the interferograms, both the discrete phase distribution and the intensity modulation of interference fringes are calculated and a binary control mask is generated by analysing histograms and tracing local minima of the intensity modulation distribution. The control mask is used to identify valid and invalid areas of the discrete phase distribution in subsequent phase unwrapping and phase interpolation, and to control the path of phase unwrapping. The evaluation of experimentally obtained phase-shifted holographic interferograms shows that this method can be successfully applied for the processing of complex interference patterns, even if the interferograms have fringe discontinuities and shaded areas.

Calibrated multichannel electronic interferometry for quantitative flow visualization

Calibrated multichannel electronic interferometry, a new technique for quantitative flow visualization of transient phenomena, is discussed. This technique uses an interferometer combined with diffraction gratings to generate three phase shifted interferograms simultaneously which are used to perform multichannel phase shifting. The optical system is calibrated with no phase object present using standard piezoelectric phase shifting, and this calibration information is stored as an electro-optic hologram. The calibration information is used along with the three phase-shifted interferograms that exist with a phase object present to perform time-resolved phase shifting. Examples using natural convection and separated flows are presented.

Electronic speckle pattern interferometer with polarization phase-shift technique

An electronic speckle-pattern interferometer with a polarization phase-shift technique for the deformation measurement of a diffuse surface is proposed. A common-path optical phase-shift arrangement is adopted in the interlerometer to improve the stability of the optical system. A polarization phase-shift technique is used to obtain precisely phase-shifted interferograms. A phase map of a fringe pattern, which is capable of distinguishing surface depressions from elevations, can be automatically and accurately obtained from four interferograms by the computer data processing. The numerical data representing the deformation over the entire field can be easily extracted from the phase map. An example of deformation measurement using this interferometer is presented.

Linearization and flattening technique for fringe analysis and its application to holographic interferometry

A simple technique for correcting the nonlinearity of a camera-digitizer system is presented. With this technique cameras that are extremely nonlinear but which enhance fringe contrast can be used. The technique can also reduce the number of phase-shifted interferograms required for quantitative analysis from three to two or (with some restrictions) to one. The last option is important for the interpretation of transient phenomena. The technique is demonstrated for the strain analysis of a pressure vessel by holographic interferometry (HI). The contribution to suitable noise elimination is also described.

A Parallel Fringe-scanning Algorithm for Phase-shifting Interferometry

Abstract In connection with digital interferometry, the evaluation of phase-shifted interferograms can be speeded up by a digital image processor. A special parallel algorithm has been designed for scanning the saw-tooth shaped fringes. It is shown that the number of image passes (TC cycles) for a 2 j × 2 j pixel image is reduced to j instead of 2j. Fringe scanning of a saw-tooth phase image and a pseudocoloured display of the continuous phase is obtained after 1·4s for 512 × 512 points.

Vibration measurement using phase-shifting time-average holographic interferometry

Computer image processing techniques for the measurement of vibration amplitude are presented, which utilize phase-shifted time-average holographic interferograms. The calculation of the square root and division with phase-shifted interferograms gives a high contrast fringe pattern which contours the vibration amplitude. The arctangent calculation with phase-shifted fringe patterns also gives the phase distribution proportional to the optical path difference of the measured object before and after vibration. The detection of the phase discontinuity of ±π in the phase image gives exactly the center line of the dark fringe. The distribution of the vibration amplitude can be obtained by the fringe-order determination and its interpolation. The bias deformation of the vibration is obtained by the correction of phase discontinuities of ±2π and ±π in the phase images before and after vibration.

Vibration measurement using phase-shifting speckle-pattern interferometry

Digital speckle-pattern interferometries for the measurement of a vibration amplitude are presented, based on phase shifting of a speckle interferogram. The calculation of the square root and division with phase-shifted speckle interferograms give a high contrast fringe pattern, which contours a vibration amplitude regardless of a bias deformation of the vibration. The arctangent calculation with phase-shifted fringe patterns gives the phase distribution proportional to the bias deformation of the vibration, which is obtained by the correction of phase discontinuities of ±2π and ±π in the phase image. The detection of the phase discontinuity of ±π in the phase image gives the center line of a dark fringe in the calculated fringe pattern. The fringe-order numbers are determined by referring to the new calculated fringe pattern. The distribution of the vibration amplitude is obtained by the interpolation of the fringe-order numbers.