Zongtao Ge

Coordinate-transform technique for closed-fringe analysis by the Fourier-transform method

A coordinate-transform technique is proposed that enables the Fourier-transform method to analyze an interferogram that includes a closed-fringe pattern. First, the closed-fringe pattern is converted to an open-fringe pattern by transformation of the Cartesian coordinate system to a polar coordinate system. Then the phase distribution for the open-fringe interferogram is determined by the conventional Fourier-transform method. The phase distribution for the original closed-fringe pattern is obtained by inverse coordinate transformation from the polar coordinate system back to the Cartesian coordinate system. Computer simulation and experiments were performed for a closed-fringe pattern generated by interference of a spherical wave with a reference plane wave, and results are presented that demonstrate the validity of the proposed technique.

High-resolution two-dimensional angle measurement technique based on fringe analysis

A novel angle-measurement technique based on fringe analysis for phase-measuring profilometry is proposed. A two-dimensional (2-D) angle between two mirror surfaces is determined by least-squares fitting of a plane to the 2-D distribution of the phase difference introduced by the 2-D tilt angle. To evaluate the performance of the proposed technique, numerical simulations that use the Fourier-transform technique and the phase-shift technique for fringe analysis were performed, and the results are compared. A 2-D angle-measurement interferometer based on a Mirau interference microscope was developed that demonstrated the validity of the proposed principle. It is shown by simulation and experiment that the proposed 2-D angle-measurement technique can achieve both a wide measurement range and a high angular resolution simultaneously.

High-precision measurement of a fiber connector end face by use of a Mirau interferometer

What we believe to be a new instrument for measuring the end-face geometrical parameters of fiber connectors is described. In this apparatus, a Mirau-type interferometric objective is employed to measure a small area of the connector end face and generate an interferogram corresponding to the surface profile. Various new technologies are used to ensure excellent performance and high measurement repeatability. A multipoint method is proposed to adjust the inclination of the physical contact sample stage. The physical contact angle of the sample stage is adjusted directly on the instrument by use of a special tool whose angle is calibrated with the reversal method. Measurement results of important parameters of the fiber connector end face are compared with those inspected by a commercial profiler or with a standard sample. Optical insertion losses of connectors inspected by the developed system are also evaluated.

Precision interferometry for measuring wavefronts of multi-wavelength optical pickups

A novel wavefront measurement interferometer is developed that enables the user to evaluate the wavefronts of multi-wavelength optical pickups. In this interferometer, instead of transparent pinholes used in Mach-Zehnder interferometers, reflection dot pinhole mirrors are used to generate reference wavefronts for different wavelengths which make the optical system very flexible and simple compared with those using transparent pinholes. The interferometer is designed to operate at wavelengths of 405 nm, 650 nm and 780 nm over an NA range of up to 0.95, which is very difficult to realize when transparent pinholes are used for generating reference wavefronts. The three-beam problem is solved and the optics of the interferometer is simplified by employing a software filter instead of using spatial filters in the optics of the interferometer. The instrument has an equal optical path length that enables the user to measure pickups with a very short coherence length. A new method by which asymmetric aberration components, such as astigmatic and coma aberrations, can be calibrated by rotating the measured lens with 90 and 180 degrees is proposed and the calibration results are verified by using a high precision reference point source. System accuracy is also evaluated by comparing with the measurement results obtained by commercial Fizeau type interferometer and a good agreement is achieved.

High-precision 2D-angle measurement interferometer

Fourier transform method and phase shift method are widely used to analyze fringe patterns to obtain surface profiles. In these ordinary fringe analysis methods, tilt or angle in the measured surface is often cancelled by certain operations. On the other hand, tilt can be considered as part of the measured surface, and obtained by fitting the measured surface profile with a line or plane. Therefore, we proposed a high-precision angle measurement method using fringe analysis techniques. In this paper, a 2-dimensional angular measurement interferometer is constructed to realize the proposed method, and the output curve of the measurement system is calibrated using a high-resolution autocollimator and a PZT driven lever system as the references. Fringe patterns obtained by the experiments are analyzed by both of the Fourier transform method and phase shift method, and the experimental results are compared with each other. Furthermore, the characteristics of the measurement system, including stability, resolution, and accuracy are evaluated and analyzed. Experiments verified that it could achieve both a wide measurement range of over +/- 2160 arcsec (+/- 0.6Degree) and a high angular resolution of 0.01 arcsec, simultaneously.

Self-reference method for phase-shift interferometry

A self-reference method (SRM) is proposed to realize high precision fringe analysis for phase-shifting interferometry when translation and tilt errors exist in phase shifters. In this method, arbitrary pixel-dependent phase shifts including those caused by tilt are directly estimated from a single interferogram by the Fourier transform method without using any extra reference mirror. The obtained phase shifts are then used to reconstruct the original wave front according to the algorithm of the proposed self-reference method. Computer simulations demonstrate the feasibility of the proposed method. Precision of shifted phases and tilts estimation is also evaluated, and some error sources are analyzed. It is shown that the self-reference 3-step method can give better accuracy than that of the popular 5-step method even when the tilt error exists in the reference surface.

A new instrument for fiber connector endface measurement

A new instrument for measuring end surface geometrical parameters of APC connectors is described. In this apparatus, a Mirau type interferometric objective is employed to measure a small area of the connector end surface and generate interferogram corresponding to the surface profile. Various new technologies are used to ensure high performance and high measurement repeatability. A multi-point method is proposed to adjust the inclination of the PC sample stage. APC angle of the sample stage is adjusted directly on the instrument using a special tool whose angle is calibrated by using the reversal method. Measurement results of important parameters of fiber connector end faces are compared with those inspected by commercial profiler or a standard sample. Optical insertion losses of connectors inspected by the developed system are also evaluated.

High-precision 2D angle measurement using fringe analysis techniques

In this paper, a novel angle measurement method using the fringe analysis techniques is proposed. In this method, a 2D surface profile including a tilt is obtained by fringe analysis, and the tilt in the 2D surface profile is determined by fitting the obtained surface profile with a plane. From the fitted plane, 2D angles can be easily obtained. Simulations using the Fourier transform and phase- shift methods are performed, and the results are compared with each other. Simulations show that 2D angle measurement using the fringe analysis techniques can achieve simultaneously a wide measurement range and high precision.

Coordinate transform method for closed fringe analysis

A coordinate transform method is proposed which enables the Fourier transform method to analyze interferograms including closed fringe patterns. According to the principle of the proposed method, closed fringe patterns in an interferogram can be converted to open fringe patterns by transforming the Cartesian coordinate system to a polar coordinate system. Phases corresponding to the open fringe interferograms can be obtained by analyzing the open fringe interferograms using the conventional Fourier transform method. Subsequently, the original phases corresponding to the closed fringe interferograms can be acquired by inverse coordinate transform. Computer simulation and experiments show that spherical wave fronts are accurately recovered by using the proposed method.