Phase-step calibration for phase-stepped interferometry

A high accuracy measurement method based on vortex polar axis rotation phase-shifting interferometry (VPAR-PSI)

For higher precision phase shift measurement, based on the characteristics of vortex beam, the manuscript introduces phase shift directly through the polar axis rotation of the vortex beam. Compared to traditional grey-scale modulation, the proposed VPAR-PSI method introduces a phase-shifting directly instead of changing the grey-scale, which not only can largely reduce the deviation caused by traditional PSI phase modulation via grey-scale change, but also can effectively avoid the non-linearity between grey-scale and phase of traditional PSI. For verifying the effectiveness of the method proposed in this manuscript, a simulation experiment, sample experiment, and VPAR-PSI and PSI comparison experiment were conducted. The results show that the proposed VPAR-PSI has a high phase-shifting and demodulation accuracy, and can be well implemented to measurement of optical components. The comparative experimental show that compared to conventional PSI, the measurement results of VPAR-PSI have smaller envelope values (mean envelope reduction of 1.4202λ), smaller RMS and standard deviation (the values decreased by 0.3515, 0.3067, and the percentage decreases were 59.69%, 59.71% respectively), proving that the VPAR-PSI technique are more accurate and stable. © 2020 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Global Science and Technology Forum Pte Ltd.

Characterization of the phase modulation property of a free-space electro-optic modulator by interframe intensity correlation matrix

Characterization of a phase modulator or phase shifter has always been an integral part of phase-modulating or phase-adjusting applications. We propose a simplified approach to characterize a phase modulator by investigating the performance of phase shifts from grabbed interferograms using the phase extraction method. After reviewing some phase analysis techniques, the interframe intensity correlation (IIC) matrix method is introduced to the investigation. The proposed strategy is illustrated by the measurement of a free-space electro-optic modulator (EOM). Placing the modulator in one arm of a Michelson interferometer, the global phase shifts are estimated by the IIC method from the phase-stepped interferograms. Experimental results demonstrate the tested EOM has a phase modulation response of at least 2π  rad with a π/20  rad modulation precision for λ=1064  nm. In addition, our method is applicable to various types of phase modulator or phase shifter calibration, e.g., electro-optic phase modulator, spatial light modulator, or piezoelectric transducer (PZT).

Phase-shifts n pi/2 calibration method for phase-stepping interferometry

A novel phase-shifts n pi/2 calibration method for phase-stepping interferometry, in which the sum intensities and the squared sum of a series of phase-shifted interferograms are firstly calculated, and then by the minimization of the variances of these sums perform the n pi/2 phase-shifts calibration, is proposed in this paper. The proposed method can overcome effectively the effect of the variations of background and modulation intensities in interferograms with any phase structure, and it is also insensitive to the nonlinearity of phase shifter. Numerical simulation and experiments are implemented to verify the effectiveness of this method.

Iterative least square phase-measuring method that tolerates extended finite bandwidth illumination

Iterative least square phase-measuring techniques address the phase-shifting interferometry issue of sensitivity to vibrations and scanner nonlinearity. In these techniques the wavefront phase and phase steps are determined simultaneously from a single set of phase-shifted fringe frames where the phase shift does not need to have a nominal value or be a priori precisely known. This method is commonly used in laser interferometers in which the contrast of fringes is constant between frames and across the field. We present step-by-step modifications to the basic iterative least square method. These modifications allow for vibration insensitive measurements in an interferometric system in which fringe contrast varies across a single frame, as well as from frame to frame, due to the limited bandwidth light source and the nonzero numerical aperture of the objective. We demonstrate the efficiency of the new algorithm with experimental data, and we analyze theoretically the degree of contrast variation that this new algorithm can tolerate.

Interference fringe analysis based on centroid detection

Phase measurement of interference fringes is an integral part of several fields in optics. Using simple straight sinusoidal fringe patterns, we describe the relationship between fringe position or phase to the centroid position when these fringes are incident on a position sensitive detector. With detailed descriptions and some experimental results, we show that a phenomenal sensitivity is possible in principle with what we believe is a new approach of phase measurement, and excellent sensitivity is readily achieved.

Phase-step calibration technique based on a two-run-times-two-frame phase-shift method

A novel phase-step calibration technique is presented on the basis of a two-run-times-two-frame phase-shift method. First the symmetry factor M is defined to describe the distribution property of the distorted phase due to phase-shifter miscalibration; then the phase-step calibration technique, in which two sets of two interferograms with a straight fringe pattern are recorded and the phase step is obtained by calculating M of the wrapped phase map, is developed. With this technique, a good mirror is required, but no uniform illumination is needed and no complex mathematical operation is involved. This technique can be carried out in situ and is applicable to any phase shifter, whether linear or nonlinear.

Interframe intensity correlation matrix for self-calibration in phase-shifting interferometry

A new method of estimating reference phase shifts in phase-shifting interferometry is proposed. The reference phase shifts are determined from a matrix that represents the interframe intensity correlation (IIC) of phase-shifted interferograms. The root-mean-square error of intensity measurement is automatically obtained from the smallest eigenvalue of the IIC matrix. The proposed method requires only four interferograms, unlike others, and can extract phase shifts reliably even from interferograms without well-defined fringes, such as speckle patterns. In typical conditions, reference phase shifts and wave-front phases can be determined with an accuracy of lambda/6310 and lambda/150, respectively. The validity of the method is tested by comparing it with other methods in experiments and simulations.

Phase-shift calibration algorithm for phase-shifting interferometry

We propose a novel phase-shift calibration algorithm. With this technique we determine the unknown phase shift between two interferograms by examining the sums and differences of the intensities on each interferogram at the same spatial location, i.e., I1(x, y) +/- I2(x, y). These intensities are normalized so that they become sinusoidal in form. A uniformly illuminated region of the interferograms that contains at least a 2pi variation in phase is examined. The extrema of these sums and differences are found in this region and are used to find the unknown phase shift. An error analysis of the algorithm is provided. In addition, an error-correction algorithm is implemented. The method is tested by numerical simulation and implemented experimentally. The numerical tests, including digitization error, indicate that the phase step has a root-mean-square (RMS) phase error of less than 10(-6) deg. Even in the presence of added intensity noise (5% amplitude) the RMS error does not exceed 1 deg. The accuracy of the technique is not sensitive to nonlinearity in the interferogram.