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基于正交全息的台阶相位原位重建

郝爱花 黄静燕 张世纪 王志俊 王笑龙

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基于正交全息的台阶相位原位重建

郝爱花, 黄静燕, 张世纪, 王志俊, 王笑龙

In-situ reconstruction of step phase based on orthogonal holograms

HAO Aihua, Huang Jingyan, Zhang Shiji, Wang Zhijun, Wang Xiaolong
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  • 滤波技术是数字离轴全息精确相位重建的关键。由于CCD分辨本领和离轴全息技术本身的限制,台阶型相位物体在全息滤波过程常常伴随频谱损失、频谱混叠,以及全息图被截取非整数周期时的频谱泄露问题。目前频域滤波在针对单幅全息图的自适应滤波方面已有很多研究,但上述问题都无法得到根本解决。本文在分析一维空间滤波成像特性的基础上,提出了一种在对两个正交全息图分别进行一维傅里叶变换和一维全谱滤波的基础上,对重构的物光波利用泊松方程进行精确相位解缠绕的相位原位重建技术。该方法从根本上避免了滤波引起的频谱损失、频谱混叠和频谱泄露问题,且运算过程简单、重建精度高、适合于任何形状台阶物体的三维轮廓重建,为离轴全息的高精度相位重建提供了切实可行的途径。
    Filtering technology is the key to accurate phase reconstruction in off-axis digital holography. Due to the limitations of CCD resolution and off-axis digital holography itself, the filtering process of the step-phase objects is often accompanied by spectral loss, spectral aliasing and spectral leakage when non-integer periods are intercepted. At present, much research has been done on adaptive filtering in the frequency domain, but the above problems cannot be fundamentally solved. In this paper, the influence of spatial filtering on the accuracy of step-phase reconstruction is first analyzed theoretically. The analysis shows that even if the size of the filter window is equal to the sampling frequency of the CCD, the reconstructed object cannot retain all the spectral information of the object due to the limitation of the resolution power of the CCD itself. In addition, in the off-axis holographic recording process, considering the interference of zero-order terms and conjugate terms, the actual filter width is usually only 1/24 of the sampling frequency of the CCD, at which the average absolute error of the step is about 10% of the height of the step, the oscillation is relatively severe, and the details of the object are lost after further smoothing filtering, the edge is blurred and the tiny structure cannot be resolved. Second, according to the definition of discrete Fourier transform, the one-dimensional Fourier transform of a two-dimensional function is only integrated in one direction, leaving the other dimension unchanged. When the one-dimensional Fourier transform is performed along the direction perpendicular to the hologram interference stripe, and the one-dimensional full-spectrum filtering is performed, the distribution of the reconstructed object light wave in the direction parallel to the stripe follows the original distribution, which is not affected by the filtering, and is highly accurate. Therefore, an accurate two-dimensional differential phase can be obtained by combining the reconstructed light waves after one-dimensional full-spectrum filtering of two orthogonal off-axis holograms, which provides a fundamental guarantee for the accurate phase unwinding of the Poisson equation. Based on this, the spectral lossless phase reconstruction algorithm based on orthogonal holography and optical experiment method are proposed. In this paper, the ideal sample simulation, including irregular shapes such as gear, circle, V, diamond, drop, hexagon and pentagram, and the corresponding experiment based on USFA1951 standard plate and silicon wafer are carried out. The AFM-calibrated average step height of the standard plate is 100 nm, and that of the silicon wafer is 240 nm. The experimental results show that compared with the currently widely used adaptive filter phase reconstruction, the proposed method naturally avoids spectrum loss, spectrum aliasing and spectrum leakage caused by filtering, the reconstruction accuracy is high, and it is suitable for 3D contour reconstruction of any shape step object, which provides a practical way for high-precision phase reconstruction of off-axis holography.
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