• 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

    Abstract

    A derivative method for phase retrieval in two-step phase-shifting interferometry (PSI) with a blind phase shift is proposed in this Letter. By numerically calculating the first-order and second-order derivatives of two PSI images, one can directly determine the phase shift and then obtain the quantitative phase image. We illustrate the method with both a theoretical analysis and some simulations of an average-sized red blood cell in different interferometry recording modes. From the results, the validity, accuracy, as well as efficiency of this method are verified. Moreover, this method can be applied to any quantitative phase imaging, including on-axis, off-axis, and slight off-axis interferometry.
    I1(x,y)=I0(x,y)+γ(x,y)cos[φ(x,y)+kx],(1)

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    I2(x,y)=I0(x,y)+γ(x,y)cos[φ(x,y)+kx+α],(2)

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    I1(1)=I1x=I0x+γxcos[φ+kx]+γ{sin[φ+kx]}[φx+k],(3)

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    I2(1)=I2x=I0x+γxcos[φ+kx+α]+γ{sin[φ+kx+α]}[φx+k].(4)

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    I1(1)=γ{sin[φ+kx]}[φx+k],(5)

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    I2(1)=γ{sin[φ+kx+α]}[φx+k].(6)

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    φ(x,y)=arctan[I1(1)sinαI2(1)I1(1)cosα]kx.(7)

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    I1(2)=2I1x2=γcos[φ+kx][φx+k]2γsin[φ+kx]2φx2,(8)

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    I2(2)=2I2x2=γcos[φ+kx+α][φx+k]2γsin[φ+kx+α]2φx2.(9)

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    2φ(x,y)x20.(10)

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    I1(2)=γcos[φ+kx][φx+k]2,(11)

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    I2(2)=γcos[φ+kx+α][φx+k]2.(12)

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    α=arccos[I2(2)I2(1)+I1(2)I1(1)I1(2)I2(1)+I2(2)I1(1)].(13)

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    φ(x,y)=arctan[I1(1)sinαI2(1)I1(1)cosα].(14)

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    z(ρ)=[1(ρa)2]1/2[0.72+4.125(ρa)23.426(ρa)4].(15)

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    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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