Vibration-resistant phase-shifting interferometry

Applied Optics, 2009

A new method for reducing the influence of vibrations in phase-shifting interferometry uses spatial information to achieve a 100X reduction in vibrationally induced surface distortion for small-amplitude vibrations. The technique does not require high density spatial carrier fringes and maintains full lateral sampling resolution. The principles of the technique are discussed and calculations highlight the capabilities, supported by real measurements under a variety of vibration conditions.

Optics Express, 2011

The presence of uncontrolled mechanical vibrations is typically the main precision-limiting factor of a phase-shifting interferometer. We present a method that instead of trying to insolate vibrations; it takes advantage of their presence to produce the different phase-steps. The method is based on spatial and time domain processing techniques to compute first the different unknown phase-steps and then reconstruct the phase from these tilt-shifted interferograms. In order to compensate the camera movement, it is needed to perform an affine registration process between the different interferograms. Simulated and experimental results demonstrate the effectiveness of the proposed technique without the use of any phase-shifter device.

The largest limitation of phase-shifting interferometry for optical testing is the sensitivity to the environment, both vibration and air turbulence. An interferometer using temporal phase-shifting is very sensitive to vibration because the various phase shifted frames of interferometric data are taken at different times and vibration causes the phase shifts between the data frames to be different from what is desired. Vibration effects can be reduced by taking all the phase shifted frames simultaneously and turbulence effects can be reduced by averaging many measurements. There are several techniques for simultaneously obtaining several phase-shifted interferograms and this paper will discuss two such techniques: 1) Simultaneous phase-shifting interferometry on a single detector array (PhaseCam) and 2) Micropolarizer phase-shifting array. The application of these techniques for the testing of large optical components, measurement of vibrational modes, the phasing of segmented optical components, and the measurement of deformations of large diffuse structures is described.

Optics Letters, 1998

We describe a method and algorithm for reducing the sensitivity of phase-shifting interferometry to external vibrations. Using an interline-transfer camera, a shutter, and a fast phase shifter, we acquire a series of paired interferograms in quadrature, with the pairs spaced to maximize residual phase-error cancellation. The rapid acquisition of quadrature pairs significantly improves resistance of interferometry to low-frequency vibrations.

Applied Optics, 1996

Computer simulations predict the expected rms measurement error in a phase-shifting interferometer in the presence of mechanical vibrations. The simulations involve a numerical resolution of a nonlinear mathematical model and are performed over a range of vibrational frequencies and amplitudes for three different phase-shift algorithms. Experimental research with an interference microscope and comparison with analytical solutions verify the numerical model. r 1996 Optical Society of America

Journal of the Optical Society of America A, 2007

The introduction of high-resolution phase-shifting interferometry methods such as annihilation filter, state space, multiple-signal classification, minimum norm, estimation of signal parameter via rotational invariance, and maximum-likelihood estimator have enabled the estimation of phase in an interferogram in the presence of harmonics and noise. These methods are also effective in holographic moiré where incorporating two piezoelectric transducers (PZTs) yields two orthogonal displacement components simultaneously. Typically, when these methods are used, the first step involves estimating the phase steps pixelwise; then the interference phase distribution is computed by designing a Vandermonde system of equations. In this context, we present a statistical study of these methods for the case of single and dual PZTs. The performance of these methods is also compared with other conventional benchmarking algorithms involving the single PZT. The paper also discusses the significant issue of an allowable pair of phase steps in the presence of noise using a robust statistical tool such as the Cramér-Rao bound. Furthermore, experimental validations of these high-resolution methods are presented for the estimation of single phase in holographic interferometry and for the estimation of multiple phases in holographic moiré.

Optics and Lasers in Engineering, 2005

A sample of phase-shifting algorithms suitable for accommodating arbitrary phase steps is passed in review. Although not exhaustive in nature, the paper describes a wide range of concepts which have been applied to generalized phase shifting interferometry. Linear phase shift miscalibrations and nonlinear sensitivity of the piezo electric device are known to introduce errors in phase measurement. The study reveals that of the various algorithms proposed most are suitable for compensating only one of these two error sources. Application of a direct search stochastic algorithm would appear to be a promising step towards characterizing the nonlinear response of the PZT. r

Optics letters, 2007

Phase-shifting interferometry [1] and holography [2] are powerful tools that have been in use for many years. In such systems, the phase of the reference arm of an interferometer is shifted by a mirror mounted on a piezoelectric transducer (PZT), and the interference pattern is ...

Optics Letters, 2008

To extract phase distributions, which evolve in time using phase-shifting interferometry, the simultaneous capture of several interferograms with a prescribed shift has to be done. Previous interferometric systems aimed to fulfill such a task were reported to get only four interferograms. It is pointed out that more than four suitable interferograms can be obtained with an interferometer that uses two windows in the object plane, a phase grid as a pupil, and modulation of polarization for each diffraction orders in the image plane. Experimental results for five, seven, and nine interferograms are given.

Interferometry XIV: Techniques and Analysis, 2008

An alternative to the conventional linear phase shift in optical testing interferometers is a sinusoidal phase shift, which has the benefit of relaxing requirements on the phase-shifting mechanism. We propose error-compensating phasedemodulation algorithms and provide a new, comprehensive sensitivity analyses to random noise, nonlinearity, vibrations and calibration error to demonstrate that sinusoidal phase shifting can be as robust and computationally efficient as the more established linear phase-shift techniques.