Fast method to detect and calculate displacement errors in a Littrow grating-based interferometer

Lu, Qiang; Liu, Zhaowu; Wang, Wei; Jiang, Shan; Bayanheshig,; Li, Wenhao

doi:10.1364/ao.58.003193

Cited by 12 publications

(4 citation statements)

References 24 publications

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“…The beam enters the symmetrically structured dual-grating interference region, where they are then directed into four beams through PBS2 and PBS3. Each beam is incident onto the dual-grating from four non-overlapping, symmetric, parallel optical paths at the Littrow angle [26,27]. The heights of the left and right incident spots are consistent, and their positions along the centerline of the grating are relatively consistent.…”

Section: Principle Of Dual-grating Homodyne Interferometer Calibrationmentioning

confidence: 98%

Research on Dual-Grating Spacing Calibration Method Based on Multiple Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise Combined with Hilbert Transform

Zhu,

Sun,

Guan

et al. 2024

Photonics

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The paper proposes a method for the calibration of spacing in dual-grating based on Multiple Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) combined with Hilbert Transform (HT), referred to as Multiple ICEEMDAN-HT. This method addresses the potential impact of nonlinear factors on phase extraction accuracy, consequently on ranging precision in the homodyne interference of the dual-grating. Building upon the ICEEMDAN algorithm, the signal undergoes iterative decomposition and reconstruction using the sample entropy criterion. The intrinsic mode functions (IMFs) obtained from multiple iterations are then reconstructed to obtain the complete signal. Through a simulation and comparison with other signal decomposition methods, the repeatability and completeness of signal reconstruction by Multiple ICEEMDAN are verified. Finally, an actual dual-grating ranging system is utilized to calibrate the spacing of the planar grating. Experimental results demonstrate that the calibration relative error of the Multiple ICEEMDAN-HT phase unwrapping method can be reduced to as low as 0.07%, effectively enhancing the signal robustness and spacing calibration precision.

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Section: Principle Of Dual-grating Homodyne Interferometer Calibrationmentioning

confidence: 98%

Research on Dual-Grating Spacing Calibration Method Based on Multiple Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise Combined with Hilbert Transform

Zhu,

Sun,

Guan

et al. 2024

Photonics

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“…When the grating pitch is in the range from 10 to 200 µm, the grating line distance is much larger than the source wavelength and the diffraction phenomenon can be neglected. Thus, the grating measurement can be analyzed by the occlusion effect of geometric optics [1]. At present, grating measurement technologies based on the principles of geometric optics, such as grating rulers, encoders, and roll angle measurement, have been widely used [2,3].…”

Section: Introductionmentioning

confidence: 99%

“…With regard to self-collimating optical instruments designed for various specialized fields, the focal length is one of the most important parameters of the collimator, and its accuracy plays a significant role in the use of precise optical systems [7,8]. However, the measurement accuracy of long focal length optical systems is easily affected by external factors, and the processing error of the lens in the manufacturing process also has significant influences on the measurement accuracy [1,9,10].…”

Section: Introductionmentioning

confidence: 99%

Research on Focal Length Measurement Scheme of Self-Collimating Optical Instrument Based on Double Grating

Yang

Wang

Shen

et al. 2020

Sensors

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In this paper, we propose a scheme for measuring the focal length of a collimating optical instrument. First, a mathematical model for measuring the focal length of a collimator with double gratings is derived based on the moiré fringe formula and the principles of geometric optics. Mathematical simulation shows that a slight difference in the focal length of two collimators has an important influence on the imaging law of moiré fringes. Our solution has a good resolution ability for focal length differences within 5‰, especially in the small angle range below 4°. Thus, the focal length of collimators can be measured by the amplification of the slight difference. Further, owing to the relative reference measurement, the measurement resolution at the symmetrical position of focal length is poor. Then, in the designed experiment, a corresponding moiré image at different angles is acquired using collimators with known focal length. The experimental results indicate that the root mean square error (RMSE) of the collimator corresponding to grating angles of 2°–4° is better than 4.7‰, indicating an ideal measurement accuracy of the proposed scheme. This work demonstrates that our proposed scheme can achieve an ideal accuracy in the measurement of a symmetrical optical path.

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“…Lv et al presented a fast and accurate method to calculate the displacement errors caused by grating surface errors and line errors in a grating-based interferometer with a Littrow configuration. The diffracted wavefronts were used to calculate the displacement errors at the 1st orders of the grating [12].…”

Section: Introductionmentioning

confidence: 99%

Large-Aperture Real-Time Compensated Collimating Wavefront Error Detection Method

et al. 2019

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This paper proposes a real-time compensated pentaprism scanning wavefront detection method to achieve real-time compensation for scanning errors occurring during prism movement along a guide rail. The method is based on existing pentaprism scanning wavefront detection technology and it is realized by applying self-collimation-based three-dimensional error compensation. Using theoretical and data analyses of a detection experiment, the reliability of the optimized pentaprism scanning detection method is verified, thus effectively ensuring the reasonable estimation of the interferometry surface measurement uncertainty.

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Fast method to detect and calculate displacement errors in a Littrow grating-based interferometer

Cited by 12 publications

References 24 publications

Research on Dual-Grating Spacing Calibration Method Based on Multiple Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise Combined with Hilbert Transform

Research on Dual-Grating Spacing Calibration Method Based on Multiple Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise Combined with Hilbert Transform

Research on Focal Length Measurement Scheme of Self-Collimating Optical Instrument Based on Double Grating

Large-Aperture Real-Time Compensated Collimating Wavefront Error Detection Method

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