Yongmo Zhuo

Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces

A point diffraction interferometer (PDI) with adjustable fringe contrast is presented for the high-precision testing of spherical surfaces. The polarizing components are employed in the PDI to transform the polarization states of the test and reference beams, and a good fringe contrast can be realized by adjusting the relative intensities of interfering waves. The proposed system is compact and simple in structure, and it provides a feasible way for high-precision testing of spherical surfaces with low reflectivity. The theory of the interferometer is introduced in detail, along with the properties of optical components employed in the system, numerical analysis of systematic error, and the corresponding calibration procedure. Compared with the testing results of the ZYGO interferometer, a high accuracy with RMS value about 0.0025λ is achieved with the proposed interferometer. Finally, the error consideration in the experiment is discussed.

Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer

Transient, high repetition pulse laser can be applied to test numerous physical parameters, where in situ, real time measurement and isolation of vibration is highly demanded. Because of its short half-width, high power, high repetition, and even large distortion, the laser presents unique challenges to conventional diagnosing methods. A system based on a novel cyclic radial shearing interferometer is proposed to diagnose the transient, high repetition pulse laser with common path, no reference plane, and high precision. With the spatial-carrier methods, the system needs only one interferogram to reconstruct amplitude and wavefront of the laser. The theories of amplitude and wavefront reconstruction have been validated by computer simulation, and errors less than 1/1000lambda are obtained for both. Comparing with the results of the ZYGO interferometer, an error less than 1/20lambda for both peak-valley and root-mean-square values is gained with good repeatability for the wavefront. The calibration process and real time diagnosis of a high repetition pulse laser are presented then. Finally, the error consideration and system optimization are discussed in detail.

Misalignment aberrations calibration in testing of high-numerical-aperture spherical surfaces

The calibration of misalignment aberrations is a key issue in the testing of high-numerical-aperture spherical surfaces, and it is hard to separate the high-order aberrations introduced by misalignment from the measured data. The traditional calibration method is still applicable in the case of only wavefront tilt, but no longer effective in the existence of defocus. A calibration technique based on the wavefront difference is proposed to calibrate the misalignment aberrations in the presence of wavefront defocus, and it can be carried out without foreknowledge of the spherical surface under test. With the wavefront difference method, the calibration needs two separate measurements to separate the high-order aberrations. Both the computer simulation and experiments with the ZYGO interferometer have been carried out to validate the proposed calibration technique, with the accuracies better than 0.0005λ RMS and 0.0010λ RMS achieved, respectively. The proposed calibration method provides a feasible way to lower the requirement on the adjustment in the measurement, while retaining good accuracy.

Demodulation of a single complex fringe interferogram with a path-independent regularized phase-tracking technique.

The two-dimensional regularized phase-tracking (RPT) technique is one of the most powerful approaches to demodulate a single interferogram with either open or closed fringes. However, it often fails in the cases of complex interferograms and needs well-defined scanning strategies. An improved algorithm based on the RPT is presented in this paper. We use a paraboloid phase model to approximate the phase function and modify the cost functional to search the smoothest phase solutions in the function space C(2). With these modifications, the phase tracker preserves the robustness of the RPT while at the same time it is no more sensitive to stationary points and is capable of demodulating complex interferograms with arbitrary scanning schemes. Moreover, the phase reconstructed by the proposed algorithm is normally more accurate than that of the RPT both for noiseless and noisy interferograms under the same conditions. Computer simulations and experimental results are both presented.

Nonnull interferometer simulation for aspheric testing based on ray tracing.

The nonnull interferometric method that employs a partial compensation system to compensate for the longitude aberration of the aspheric under test and a reverse optimization procedure to correct retrace errors is a useful technique for general aspheric testing. However, accurate system modeling and simulation are required to correct retrace errors and reconstruct fabrication error of the aspheric. Here, we propose a ray-tracing-based method to simulate the nonnull interferometer, which calculates the optical path difference by tracing rays through the reference path and the test path. To model a nonrotationally symmetric fabrication error, we mathematically represent it with a set of Zernike polynomials (i.e., Zernike deformation) and derive ray-tracing formulas for the deformed surface, which can also deal with misalignment situations (i.e., a surface with tilts and/or decenters) and thus facilitates system modeling extremely. Simulation results of systems with (relatively) large and small Zernike deformations and their comparisons with the lens design program Zemax have demonstrated the correctness and effectiveness of the method.

Generalized data reduction approach for aspheric testing in a non-null interferometer

Data reduction in non-null tests is difficult due to the presence of retrace error. We propose a simple yet effective data reduction approach for aspheric testing in a non-null interferometer. The new approach gives figure error of the aspheric by just subtracting the theoretical wavefront and first-order errors from the real wavefront obtained in the non-null interferometer. Precise prediction of the theoretical wavefront can be achieved by accurate calibration of the partial compensation system. The approach can be considered a generalization of the traditional data processing method in null tests, and errors that may affect its accuracy are discussed. A set of experiments have been carried out to demonstrate its validity and feasibility.

Demodulation of a single-image interferogram using a Zernike-polynomial-based phase-fitting technique with a differential evolution algorithm

We propose a simple and robust polynomial-based phase-fitting (PPF) technique for single interferogram demodulation. Based on the smoothness assumption, the method employs a set of Zernike polynomials (ZPs) to fit the phase and estimates the expansion coefficients using a global optimization algorithm, i.e., differential evolution. The fitting order of the ZPs and the bounds of the coefficients can be intuitively determined according to the shape and number of fringes of the interferogram. Different from classical methods that need predefined scanning paths to guide the phase estimator, the PPF demodulates an interferogram globally and is insensitive to local defects, which allows it to deal with very noisy interferograms. Moreover, as the PPF gives the reconstructed phase by use of the ZPs, no further phase-unwrapping or wavefront-fitting procedures are needed. Experimental results have demonstrated the robustness and effectiveness of the method.

Regularized frequency-stabilizing method for single closed-fringe interferogram demodulation

We present a simple and fast regularized frequency-stabilizing method for single open- or closed-fringe interferogram demodulation. The proposed method recovers the phase maps of interferograms by establishing a cost function, according to prior knowledge. Because only the phase field to be estimated is employed in the cost function, the optimization process is fast. Moreover, the recovered phase is continuous, and no further phase unwrapping is necessary. Computer simulation and experimental results have demonstrated both the rapidity and the efficiency of the method.

Non-null interferometric aspheric testing with partial null lens and reverse optimization

With respect to null test, non-null test is more flexible and can provide fast, general test with acceptable accuracy. A non-null interferometric aspheric testing system, which employs partial null lens and reverse optimization reconstruction, is proposed. The partial null lens compensates most of the longitude aberration of the aspheric under test and keeps the slope of the non-null wavefront within the resolution of the detector. The reverse optimization reconstruction procedure reduces the retrace error of the non-null test and reconstructs the figure of the test aspheric. The characteristic, design process of the partial null lens and especially the implement of the reverse optimization reconstruction are discussed in detail. Computer simulation shows the reverse optimization reconstruction procedure can reconstruct the aspheric figure error with an accuracy better than 1/200wave within 5 mins. The error analysis is also considered and some conclusions are given. This research is of great importance for general aspheric surfacing and testing.

System optimization of radial shearing interferometer for aspheric testing

The large slope of the aspheric departure presents great difficulty for optical testing researchers to test aspheric surfaces and wavefronts. The instrument dynamic range of traditional interferometers does not support the high number of fringes due to the steep slopes commonly found in aspherics. The radial shearing interferometer, which can greatly reduce the slope of the aspheric wavefront under test, is always adopted to test aspherics. In this paper, the two evaluating parameters of a radial shearing interferometer, the wavefront slope tolerance and the wave phase sensitivity, are proposed. The effective radial shear plays important role in reduction of the wavefront slope and that of the wave phase sensitivity. How the two parameters effect the radial shearing interferometer is discussed in detail. Computer simulation shows that by properly choosing the effective radial shear, the radial shearing interferometer can obtain the best performance when testing an arbitrary aspheric wavefront. This research is of greatly importance to the design of the radial shearing interferometer for aspheric testing.