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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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Keywords:
- digital holography /
- step phase /
- in-situ reconstruction
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