DigitalHolography

Documentation for DigitalHolography.

Note

When the object wave is denoted as $u_{o} = ae^{i\phi}$ and the reference wave as $u_{r} = be^{i\delta}$, the interference fringe $I$ can be represented as $I = |u_{o} + u_{r}|^{2} = a^{2} + b^{2} + 2ab\cos(\phi - \delta)$.

DigitalHolography.GeneralizedPSDH — Method
GeneralizedPSDH(I)

return object wave extracted by the generalized phase-shifting method. See (Creath, 1988), (Schreiber and Bruning, 2006). Store N interferograms in a three-dimensional array as I[:,:,1], I[:,:,2], ..., I[:,:,N]. Phase difference $\delta_{n}$ corresponding to the n-th interferogram is assumed to be $\delta_{n} = \dfrac{2\pi}{N}n$.

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DigitalHolography.PSDH2 — Method
PSDH2(I₁, I₂, Iᵣ, δ)

return object wave extracted by the two-step phase-shifting method (see Ref. 1).

Arguments

  • I₁, I₂: Interferograms corresponding to phases $\phi$ and $\phi - \delta$, respectively.
  • Iᵣ: intensity of reference wave.
  • δ: phase difference $\delta$.
  1. X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, "Two-step phase-shifting interferometry and its application in image encryption," Opt. Lett. 31, 1414-1416 (2006)
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DigitalHolography.PSDH3 — Method
PSDH3(I₁, I₂, I₃, δ)

return object wave extracted by the three-step phase-shifting method (see Ref. 1, 2). Phases of I₁, I₂, and I₃ correspond to $\phi - \delta$, $\phi$, and $\phi + \delta$, respectively.

  1. Katherine Creath, "V Phase-Measurement Interferometry Techniques," Progress in Optics 26, 349-393 (1988)
  2. Horst Schreiber, and John H. Bruning, "Phase Shifting Interferometry," in Daniel Malacara (ed.), Optical Shop Testing, John Wiley & Sons, Ltd, pp. 547-666 (2006)
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DigitalHolography.PSDH4 — Method
PSDH4(I₁, I₂, I₃, I₄)

return object wave extracted by the four-step phase-shifting method. See (Creath, 1988), (Schreiber and Bruning, 2006). Phase difference δ corresponding to I₁, I₂, I₃, and I₄ are assumed to be $\delta = 0, \dfrac{\pi}{2}, \pi$, and $\dfrac{3\pi}{2}$, respectively.

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DigitalHolography.ParallelPSDH — Method
ParallelPSDH(I)

return object wave extracted by the parallel four-step phase-shifting method (see Ref. 1, 2). Using 2x2 pixels with phase differences of $\dfrac{\pi}{2}$ each as units, the object wave is extracted through the four-step phase-shifting method.

  1. Y. Awatsuji, M. Sasada, and T. Kubota, "Parallel quasi-phase-shifting digital holography," Appl. Phys. Lett., 85, 1069-1071 (2004).
  2. Yasuhiro Awatsuji, "Parallel Phase-Shifting Digital Holography," in Bahram Javidi, Enrique Tajahuerce, Pedro Andrés (eds.), Multi-Dimensional Imaging, John Wiley & Sons, Ltd, pp. 1-23
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