A novel aspherical surface measurement system based on randomly encoded hybrid grating (REHG) wavefront sensor is proposed. The system utilizes a non-null testing compensation lens to partially compensate the normal aberration of aspheric surface under test, which is more general than the null testing system. Different from the conventional interferometers, the REHG wavefront sensor exhibits strong anti-vibration ability and larger dynamic range due to its common path and self-reference characteristics, and is especially suitable for the measurement of aspherical surface. In this paper, a simulation model combing quadriwave lateral shearing interferometry based on the REHG and non-null aspheric testing technology is established. The generation mechanism of retrace error is analyzed. The iterative reverse optimization (IRO) retrace error correction method based on system modeling is discussed. Computer modeling is performed based on the actual experiment configuration, and an optimization function is set with polynomial coefficients of aspherics under test as variables. Through the reverse optimization with iterative ray tracing, the retrieved wavefront of the REHG sensor in the actual experiment system and the simulated wavefront in the system model will meet the constraint condition, and the figure error of aspheric surface can be then reconstructed by the optimal solution of polynomial coefficients in the model. The feasibility and accuracy of the aspherical surface non-null measurement system based on the REHG wavefront sensor are demonstrated by the simulation experiment result with different asphericities.
In this paper, a novel randomly encoded hybrid grating (REHG) interferometric wavefront sensor with the features of high-precision, high-resolution, high-dynamic-range and anti-vibration is proposed. The REHG consists of a randomly encoded binary amplitude grating and a phase chessboard. The far filed Fraunhofer diffractions only contain ±1 orders in two orthogonal directions. Different from the cross grating lateral shearing interferometer (CGLSI), there is no need of order selection mask for quadriwave lateral shearing interference. Without the influence of periodical Talbot effect, a continuously variable shear ratio can be obtained with the REHG, which makes it possible to control the dynamic range and measurement sensitivity of the wavefront sensor. A high-precision calibration method for shear ratio based on the shearing wavefront feature extraction and the generalized wavefront retrieval algorithm are employed to ensure the accuracy of the wavefront measurement results. The REHG wavefront sensor can work in collimated beam and convergent beam modes. Due to self-referenced and common-path characteristics, the REHG wavefront sensor can applied to different application fields in situ. Compared to the ZYGO interferometer, the results of the optical aberration and spherical surface measured by the REHG are highly precise and also show good repeatability. By applying two REHG wavefront sensors with different shear ratio, a wideband sensitivity-enhanced interferometric microscopy with real-time visualization can retrofit existing bright-field microscopes into quantitative phase microscopes.
A lateral shearing interferometer based on randomly encoded hybrid grating (REHG) is proposed to measure the optical system aberrations. According to the theory of Fraunhofer diffraction, the REHG is designed to be a combination of a randomly encoded binary amplitude grating and a phase chessboard. Compared with the conventional cross-grating lateral shearing interferometer, the REHG is more suitable for the general aberration testing since no order selection mask is needed. Collimated beam for aberration measurement will converge after passing through the optics system under test. Then the quadriwave lateral shearing interferogram containing the wave-front aberration information is then recorded by the CCD. By selecting its +1 order of the Fourier spectrum in both X and Y directions, the shearing wavefronts in both two orthogonal directions can be obtained employing phase unwarping algorithm. Zernike polynomials are used as basic functions for the original wave-front, and the coefficients of Zernike polynomials can be obtained with shearing wave-fronts. In the experiment, we employed a REHG with a grating pitch of 240μm to test a cemented doublet optics with an aperture of 50mm and a focal lengths of 90mm. The test results showed the peak-to-valley (PTV) aberration is 0.242λ while the root-mean-square (RMS) is 0.064λ. The test results by the REHG are very close to the results by the ZYGO GPI interferometer while the error of PTV is 0.003λ and the error of RMS is 0.007λ. The measurement of optical system aberrations by REHG can reach high precision and exhibit good immunity to environmental disturbance. The REHG can be applied to the optical testing of beam quality, optical system aberration and biomedical research.
The high precision ray tracing inside inertial confinement fusion (ICF) cryogenic targets plays an important role in the reconstruction of the three-dimensional density distribution by algebraic reconstruction technique (ART) algorithm. The traditional Runge-Kutta methods, which is restricted by the precision of the grid division and the step size of ray tracing, cannot make an accurate calculation in the case of refractive index saltation. In this paper, we propose an improved algorithm of ray tracing based on the Runge-Kutta methods and Snell's law of refraction to achieve high tracing precision. On the boundary of refractive index, we apply Snell's law of refraction and contact point search algorithm to ensure accuracy of the simulation. Inside the cryogenic target, the combination of the Runge-Kutta methods and self-adaptive step algorithm are employed for computation. The original refractive index data, which is used to mesh the target, can be obtained by experimental measurement or priori refractive index distribution function. A finite differential method is performed to calculate the refractive index gradient of mesh nodes, and the distance weighted average interpolation methods is utilized to obtain refractive index and gradient of each point in space. In the simulation, we take ideal ICF target, Luneberg lens and Graded index rod as simulation model to calculate the spot diagram and wavefront map. Compared the simulation results to Zemax, it manifests that the improved algorithm of ray tracing based on the fourth-order Runge-Kutta methods and Snell's law of refraction exhibits high accuracy. The relative error of the spot diagram is 0.2%, and the peak-to-valley (PV) error and the root-mean-square (RMS) error of the wavefront map is less than λ/35 and λ/100, correspondingly.
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