Donghui Zheng

Lensless reflective point diffraction interferometer.

A lensless reflective point diffraction interferometer (LRPDI) is proposed for dynamic wavefront measurement. The point diffraction interferometer is integrated on a small substrate with properly designed thin film, which is used for generating the interferogram with high carrier frequency at a CCD target. By lensless imaging, the complex amplitude at the CCD target can be propagated to the conjugated plane of the exit pupil of an incident wavefront, which not only avoids the edge diffraction in the interferogram, but also eliminates systematic error. The accuracy of LRPDI is demonstrated by simulation and experiment, and a precision better than 1/150 wavelength is achieved. The new design with lensless imaging processing is suitable for dynamic wavefront measurement.

Dynamic wavefront measurement with a pinhole linear polarizer point-diffraction interferometer

We propose a pinhole linear polarizer point-diffraction interferometer (PLP-PDI) for dynamic wavefront measurements. The proposed interferometer uses a metallic wire grid linear polarizer that acts as a point-diffraction plate to generate an ideal spherical wave, from which we can obtain orthogonally polarized reference and test beams. The special polarization phase-shifting configuration allows four phase-shifted interferograms to be captured in a single shot with high precision and stability. The wavefront can then be reconstructed using a phase-unwrapping algorithm. In this paper, we describe the theory of the PLP-PDI and analyze the possible errors introduced by the device. The feasibility of the proposed PLP-PDI was verified by direct measurements of a wavefront. The experimental results show that the proposed PLP-PDI is an effective and efficient tool for the dynamic measurement of wavefronts.

Simultaneous phase-shifting interferometry: immune to azimuth error of fast-axes in retarder array

Simultaneous phase-shifting interferometry based on a 2×2 retarder array with random fast-axes (RARF-SPSI) is proposed for real-time wavefront measurements. The retarder array is used as the phase-shift component, where the phase retardances are π/2, π, 3π/2, and 2π and the four fast-axes of the four retarders can be somewhat random. In this paper, the mathematical model of RARF-SPSI is built by using a Stokes vector and a Mueller matrix, the phase demodulation method through solving equations is derived, and the coefficient matrix of the equations that is associated with the azimuth of the fast-axes is calculated by Fourier analysis. Then the corresponding simulation analysis is executed. In the experiment, four simultaneous phase-shifting interferograms are captured and the phase distribution under test is demodulated through the proposed method. Compared with the four-bucket phase-shifting algorithm adopted in traditional simultaneous phase-shifting interferometry, the ripple error is suppressed well. The advantage of the proposed RARF-SPSI is that there is no need to calibrate the fast-axes of the phase-shift component before measuring; in other words, the phase demodulation error caused by the azimuth error of fast-axes is eliminated.

Spatial-temporal phase shifting interferometry: suppressing phase errors in dynamic Fizeau 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.

Simultaneous phase-shifting Twyman interferometer with a point source array

Abstract. 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.

Defect detection based on a lensless reflective point diffraction interferometer

We propose a defect detection system to identify phase defects on optics based on a lensless reflective point diffraction interferometer (LRPDI). The optics under test are illuminated by a collimated beam to produce a signal wavefront carrying the defect information, and then the signal wavefront is recorded in a high carrier interferogram using the LRPDI. By lensless imaging, amplitude and phase defects, as well as the accurate phase of a phase defect, can be identified. The simulation and experiment demonstrate the success of the proposed system in detecting phase defects, and its high-accuracy and high-resolution dynamic detection abilities are verified.

Phase extraction from fringe pattern via light propagation

A phase demodulation method via light propagation is proposed, where one or two fringe patterns are viewed as the superposition of complex amplitudes, and then the phase is reconstructed by separating the light field via light propagation. Simulation and experimental results indicated that the proposed method can extract the phase from a single shot effectively, thereby realizing dynamic phase retrieval. In addition, the accuracy of phase reconstruction can be improved by adding another fringe pattern with an unknown phase shift. The carrier requirement is relatively low, and, thus, the proposed method can be applied to the measurements with an environment disturbance, an inaccurate phase shift, and the requirement of a high speed capture.

Absolute measurement for optical inhomogeneity of parallel plate using phase-shifting interferometry

Abstract. 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.

Research on adjusting and testing of off-axis paraboloid mirror with large aperture

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.

Near infrared reflective shearing point diffraction interferometer for dynamic wavefront measurement

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.