• Chinese Optics Letters
  • Vol. 13, Issue Suppl., S21001 (2015)
Yuanyuan Xu1, Yawei Wang1、2、*, Ying Ji2, Minjie Liang2, Weifeng Jin1, Min Bu2, Xuefu Shang2, and Hao Han2
Author Affiliations
  • 1School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China
  • 2Faculty of Science, Jiangsu University, Zhenjiang 212013, China
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    DOI: 10.3788/COL201513.S21001 Cite this Article Set citation alerts
    Yuanyuan Xu, Yawei Wang, Ying Ji, Minjie Liang, Weifeng Jin, Min Bu, Xuefu Shang, Hao Han. Fast phase retrieval method based on twice derivatives in phase-shifting interferometry with a blind phase shift[J]. Chinese Optics Letters, 2015, 13(Suppl.): S21001 Copy Citation Text show less
    Average-sized RBC: (a) 3D model; (b) cross section.
    Fig. 1. Average-sized RBC: (a) 3D model; (b) cross section.
    Phase reconstruction of a RBC using derivative method in off-axis interferometry: (a) and (b) two phase-shifted interferograms; (c) and (d) first-order derivatives of (a) and (b), respectively; (e) and (f) second-order derivatives of (a) and (b), respectively; (g) and (h) 2D display and 3D display, respectively, of the reconstructed phase; (i) thickness distribution.
    Fig. 2. Phase reconstruction of a RBC using derivative method in off-axis interferometry: (a) and (b) two phase-shifted interferograms; (c) and (d) first-order derivatives of (a) and (b), respectively; (e) and (f) second-order derivatives of (a) and (b), respectively; (g) and (h) 2D display and 3D display, respectively, of the reconstructed phase; (i) thickness distribution.
    Reconstructed phase of a RBC obtained by the following: (a) Hilbert transform, 2D display map; (b) twice filters algorithm, 2D display map; (c) Hilbert transform, 3D display map; (d) twice filters algorithm, 3D display map.
    Fig. 3. Reconstructed phase of a RBC obtained by the following: (a) Hilbert transform, 2D display map; (b) twice filters algorithm, 2D display map; (c) Hilbert transform, 3D display map; (d) twice filters algorithm, 3D display map.
    Reconstructed phase maps with different algorithms in slight off-axis interferometry: (a) Hilbert transform; (b) twice filters algorithm; (c) our method.
    Fig. 4. Reconstructed phase maps with different algorithms in slight off-axis interferometry: (a) Hilbert transform; (b) twice filters algorithm; (c) our method.
    Phase reconstruction of a RBC using derivative method in on-axis interferometry: (a) interferogram; (b) first-order derivative; (c) second-order derivative; (d) 2D display of the reconstructed phase; (e) 3D display of the reconstructed phase.
    Fig. 5. Phase reconstruction of a RBC using derivative method in on-axis interferometry: (a) interferogram; (b) first-order derivative; (c) second-order derivative; (d) 2D display of the reconstructed phase; (e) 3D display of the reconstructed phase.
    Preset α (rad)Calculated α (rad)Error α (rad)Max Thickness (μm)Mean Deviation (μm)
    π/80.393−0.00032.8440.0015
    2π/80.786−0.00062.8430.0014
    3π/81.179−0.00092.8430.0014
    4π/81.573−0.00222.8460.0026
    5π/81.965−0.00152.8450.0020
    6π/82.3520.00422.8510.0047
    7π/82.7470.00182.8470.0031
    Table 1. Phase Shift Extraction and the Calculated Thickness
    ApproachesStandard Deviation (rad)MSE (rad)Processing Time (s)
    Hilbert transform0.68500.0242.0625
    Twice filters0.68480.0172.512
    Our method0.68470.0171.8526
    Table 2. Standard Deviation, MSE, and Processing Time with Different Approaches
    Yuanyuan Xu, Yawei Wang, Ying Ji, Minjie Liang, Weifeng Jin, Min Bu, Xuefu Shang, Hao Han. Fast phase retrieval method based on twice derivatives in phase-shifting interferometry with a blind phase shift[J]. Chinese Optics Letters, 2015, 13(Suppl.): S21001
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