Design of new window function of phase extraction algorithm in wavelength tuning Fizeau interferometer

Optical absorption in asymmetric triple quantum well structures

Laser-diode interferometry

In this day of digitalization, you can work within the technology of optics without having to fully understand the science behind it. However, for those who wish to master the science, rather than merely be its servant, it's essential to learn the nuances, such as those involved with studying fringe patterns produced by optical testing interferometers.When Interferogram Analysis for Optical Testing originally came to print, it filled the need for an authoritative reference on this aspect of fringe analysis. That it was also exceptionally current and highly accessible made its arrival even more relevant. Of course, any book on something as cutting edge as interferogram analysis, no matter how insightful, isn't going to stay relevant forever. The second edition of Interferogram Analysis for Optical Testing is designed to meet the needs of all those involved or wanting to become involved in this area of advanced optical engineering. For those new to the science, it provides the necessary fundamentals, including basic computational methods for studying fringe patterns. For those with deeper experience, it fills in the gaps and adds the information necessary to complete and update one's education. Written by the most experienced researchers in optical testing, this text discusses classical and innovative fringe analysis, principles of Fourier theory, digital image filtering, phase detection algorithms, and aspheric wavelength testing. It also explains how to assess wavefront deformation by calculating slope and local average curvature.

Phase extraction based on iterative algorithm using five-frame crossed fringes in phase measuring deflectometry

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)

The surface flatness and the uniformity in thickness and refractive index of a mask-blank glass have been requested in semiconductor industry. The absolute optical thickness of a mask-blank glass of seven-inch square and 3mm thickness was measured by three-surface interferom etry in a wavelength tuning Fizeau interferometer. Wavelength-tuning interferometry can separate in freq uency space the three interference signals of the surface shape and the optical thickness. The wavelength of a tunable laser diode source was scanned linearly from 632 nm to 642 nm and a CCD detector recorded two thousand interference images. The number of phase variation of the interference fringes during the wavelength scanning was counted by a temporal discrete Fourier transform. The initial and final phases of the interferograms before and after the scanning were measured by a phase shifting technique with fine tunings of the wavelengths at 632 nm and 642 nm. The optical thickness defined by the group refractive index at the central wavelength of 337 nm can be measured by this technique. Experimental results show that the cross talk in multiple-surface interferometry caused a systematic error of 2.0 microns in the measured optical thickness. Keywords: Phase measurement, absolute optical path difference, wavelength scanning, optical thickness distribution measurement, phase shift, Fizeau interferometer

A new window function for the spectral analysis of effect of celestial body on Taiji mission below 0.1 mHz

To accurately obtain the phase distribution of an optical surface under test, the accurate phase extraction algorithm is essential. To overcome the phase shift error, a random two-step phase shifting algorithm, which can be used in the fluctuating and non-uniform background intensity and modulation amplitude, Lissajous ellipse fitting, and least squares iterative phase shifting algorithm (LEF&LSI PSA), is proposed; pre-filtering interferograms are not necessary, but they can get relatively accurate phase distribution and unknown phase shift value. The simulation and experiment verify the correctness and feasibility of the LEF & LSI PSA.

In this paper the mechanisms causing phase drift in the dual active bridge topology are presented and two compensation methods are proposed to overcome their effects. The phase drift causes discrepancy between the predicted phase shift and the actual phase shift measured from the transformer primary and secondary voltages. The error in the phase shift causes the input power to be larger or smaller than predicted and it can also interfere with the operation of several modulation methods. By using the phase drift compensation methods presented in this paper the converter input power can be predicted accurately by using the classical power equation. The effects of dead-time on the phase drift are also discussed and a method to calculate a suitable dead-time with respect to the converter operating point is proposed. The value of the phase drift compensation is presented along with a variable frequency modulation method, which enables zero voltage switching at a wide load range with a minimal circulating current.

An algorithm is proposed for extraction of the unknown phase shift steps and correction of the phase shift error in partially coherent illuminated phase-shifting digital holography. The mean contrast of noise (MCN) of the reconstructed amplitude image is developed to evaluate the noise level resulting from phase shift error. Actual phase shift steps are first extracted by minimizing the MCN. Then the extracted actual phase shift steps are used to retrieve the original object wave without phase shift error. The validity of the proposed method is verified by simulations, and then implemented in partially coherent illuminated phase-shifting digital holography where a spatial light modulator with unknown phase modulation characteristic is used as the phase shifter. The results demonstrated that the actual phase shift steps can be extracted and the phase shift error is corrected effectively.

A common material for read-write sliders is a composite of alumina (Al(2)O(3)) and titanium carbide (TiC), with a grain size of the order of 1 mum. I derive the effective complex reflectivity of this material, using scalar diffraction theory and the known indices of refraction of Al(2)O(3) and TiC. The effective reflectivity is a function of the relative surface area of the exposed TiC grains as well as of the numerical aperture of the collection optics. The theory resolves several known discrepancies between ellipsometry and reflectometry of Al(2)O(3)-TiC. The theory also predicts a systematic error in the phase shift on reflection calculation. These results are of considerable interest for surface shape metrology of the slider as well as for optical flying-height testing and control of pole-tip recession.

Spline algorithms are described for solving the radial equation for continuum states. The Galerkin method leads to a generalized eigenvalue problem for which the eigenvalue is known so that inverse iteration can be used to determine the eigenvector. Three cases are considered: the equation whose solution is sin κr, the Coulomb problem, and the hydrogen scattering problem. Plots are presented for the first two cases that show the dependence of the error in the phase shift on spline parameters and execution time. The results for the scattering problem are compared with earlier values.

Two dominant systematic errors in the absolute interferometric test of high numerical-aperture sphericals are discussed and measured experimentally in pursuit of an accuracy of λ=100. Gravitational sag deformation of a 4-inch spherical concave surface was measured in a vertical phase-shifting Fizeau interferometer. The surface shapes of two identical transmission spherical concaves were measured via the two-surface comparison method using three positional measurements. One of the surfaces was then rotated around the optical axis and the interference phases were averaged to extract a rotationally symmetric component of the aberration. The gravitational sag was then determined by the aberration component independent of the rotation. The geometrical error in the phase shift is also estimated theoretically and corrected in the experiment. Experimental results show that the both errors amount to 6 to 7 nm peak-to-valley lengths, the magnitudes of which are comparable to that of the total aberration of the spherical surface.

The phase shift interferometer can be used to detect the wavefront phase of optical system and the piezoelectric transducer is widely used as a phase shifter in phase shift interferometer. However, the displacement of piezoelectric transducer presents hysteresis nonlinearity. Hence, when the equal-step phase shift algorithm (e.g. the Schwider-Hariharan phase-shifting algorithm which obtains five images and sets the phase-shifting between images to 90 degrees) is used in the phase shift interferometer to calculate the wavefront phase, the nonlinearity of piezoelectric transducer will introduce error to the 90 degrees phase-shifting between images. Then the calculated wavefront phase will contain the error. Hence, it is necessary to propose a method to diminish the phase error. The method by choosing an optimized phase-shifting algorithm has been used to mitigate the phase error. However, the method does not directly focus on piezoelectric transducer itself. In the paper, we propose a method by compensating for the hysteresis nonlinearity displacement of piezoelectric transducer to mitigate the phase error. We analyze the relationship between the nonlinearity displacement of piezoelectric transducer and phase shift error and establish the error models to analyze the relationship between the phase shift error and phase error. Furtherly, we propose the Proportion Integration Differentiation (PID) closed-loop feedback control method to compensate for the hysteresis nonlinearity displacement of piezoelectric transducer. The results indicate that, with compensated, the maximum tracking error is reduced from 18.89 % to 5.5 %. And in the ascending stage, the PV error and RMS error with compensated are less 12.35nm and 4.34nm than the PV error and RMS error without compensated. In the descending stage, the PV error and RMS error with compensated are less 19.15nm and 6.76nm than the PV error and RMS error without compensated. Hence, the proposed compensation method can improve the detection accuracy of the phase shift interferometer.

A phase shift selection method is proposed to design algorithms immune against phase shift errors in two-step generalized phase-shifting interferometry. A general formula for wavefront reconstruction error is derived, and its specific expressions for two common errors are also given. Calculation results suggest that the proper range of phase shift for general application is about from 0.5 to 2.0 rad for both the fixed and linear phase shift errors. Computer simulations have demonstrated the effectiveness of this phase shift selection method by decreasing the wave reconstruction errors to one-fifth.