In the development of a high-precision vertical Fizeau interferometer with 300-mm aperture, uncertainty evaluation is a significant method to assess the accuracy of interferometer. In this paper, we reported an uncertainty evaluation method. Then, the uncertainty evaluation of a 300-mm-aperture vertical Fizeau interferometer was carried out based on the method. The uncertainties of interference cavity measurement and absolute testing (e.g., three-flat method) were used as indicators of uncertainty evaluation. In addition, the gravity-induced deformation of three-flat method can be compensated accurately by finite element method modeling. Finally, we obtained the uncertainties of interference cavity measurement and three-flat method. With 300-mm aperture, the expanded uncertainty of interference cavity measurement is 3.7×10-3 λ, and the expanded uncertainty of three-flat method is 1.47×10-2 λ.
When the optical homogeneity of parallel plates is measured using wavelength phase shifting interferometers, the nonlinearity of phase shifts caused by nonlinear wavelength tuning results in spectrum aliasing, and thus the optical homogeneity cannot be obtained accurately. We propose a nonuniform fast Fourier transform algorithm based on low-rank approximation and Taylor expansion (LRTE-NUFFT) to solve the problem. The principle of the LRTE-NUFFT method is introduced and compared with the FFT method and the nonuniform fast Fourier transform algorithm based on fast Gauss gridding (FGG-NUFFT) method proposed earlier through simulations and experiments. The results show that LRTE-NUFFT can improve the accuracy of the optical homogeneity measurement of parallel plates compared with the FFT method, and it can also improve the computational efficiency compared with the FGG-NUFFT method.
For a simultaneous phase-shifting interferometer (SPSI), typically four interferograms with different phase shifts are captured at different areas on the detector target by a single-shot capture method. Prior to calculating phase distribution, the region segmentation should be conducted to obtain four separated interferograms. A registration method is also necessary to eliminate the mismatch errors between the interferograms. A spatial mismatch calibration method based on fast partial phase correlation is proposed to register the spatial positions between the phase-shifting interferograms. By tilting the reflective flat, four carrier interferograms are captured to extract four phase distributions using the Fourier transform technique. Partial phase distribution is used as match characteristics to register the interferograms rapidly by employing the correlation operation. The simulation and experimental results show that the ripple error generated by spatial mismatch is suppressed well by the proposed method.
A simultaneous phase-shifting Twyman interferometer with a point source array is proposed. We use a point source in combination with a grating and select the four (±1,±1) diffraction orders to generate a point source array. With this configuration, we can acquire four independent Twyman interferometers. Adjust the offset amounts of each point source to introduce different phase shifts in the interferograms, and realize dynamic measurement. We introduce 0, π/2, π, and 3π/2 in the interferograms. The initial phase will be exactly retrieved by employing the four-bucket algorithm. The experimental results show the feasibility and precision of the interferometer.
A spatial-temporal phase shifting interferometry is proposed to suppress the phase errors in dynamic Fizeau
interferometer. The process of phase errors suppression in this interferometry includes three steps: (1) utilizing the
spatial phase shifting interferometry to calculate the initial phase; (2) viewing all the effects of the error sources as a
complex; (3) utilizing the temporal phase shifting interferometry to obtain multiple different initial phases and calculate
the average phase. Experimentally, the phase errors are suppressed effectively and the measurement results are in good
agreement with those obtained by Zygo GPI interferometer, which verifies that the proposed interferometry is a powerful
tool for phase errors suppression in dynamic interferometer.
Optical inhomogeneity is an important index to evaluate optical transmission material. We propose an absolute measurement method for optical inhomogeneity of the parallel plate with phase-shifting interferometry (PSI). Compared with the window-flipping method, we introduce another transmission flat and add two cavity measurements between the two transmission flats and the reflective flat with the assistance of a Fizeau interferometer. Simulation and experiment results show that the method can effectively eliminate the disturbances of both surfaces of the parallel plate, the reflective flat, and the system error of the interferometer. It reduces the requirement for surface accuracy of the transmission and reflective flats. It is an absolute measurement method for the optical inhomogeneity of the parallel plate, which can be realized with traditional phase-shifting interferometry.
Off-axis paraboloid (OAP) is widely used in optical system of large diameter, such as astronomical instruments, space optics and so on, for it produce no aberration at geometric focus. It simplifies the structure of optical system, improves imaging quality, reduces the size and weight, also cost of the system. The software Zemax was used to simulate the adjustment errors including high-low and pitch, tilt and off-axis distance, and the rotation around the secondary optical axis, by taking an off-axis paraboloid mirror with the diameter of 400mm, focal length of 4000mm, and the off-axis distance of 350mm for an example. Then the corresponding experiments were performed to verify the simulation results using PhaseCam6000 interferometer of 4D technology. It proves the simulation model in correct, will play an important role in adjusting an off-axis paraboloid mirror.
A near infrared reflective shearing point diffraction interferometer (NIRSPDI) is designed for large-aperture dynamic wave-front measurement. The PDI is integrated on the small substrate with properly designed thin film. The wave-front under test is reflected by the front and rear surfaces of the substrate respectively to generate an interferogram with high linear-carrier frequency, which is used to reconstruct the wave-front by means of the Fourier transform algorithm. In this article, the system error and the major parameters of NIRSPDI are discussed. In addition, we give an effective method to adjust NIRSPDI for fast measurement. Experimentally NIRSPDI was calibrated by a standard spherical surface and then it was applied to the dynamic wave-front with a diameter of 400mm. The measured results show the error of whole system which verifies that the proposed NIRSPDI is a powerful tool for large-aperture dynamic wave-front measurement.
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