## Abstract

A parallel two-step spatial carrier phase-shifting common-path interferometer with a Ronchi grating placed outside the Fourier plane is proposed in this paper for quantitative phase imaging. Two phase-shifted interferograms with spatial carrier can be captured simultaneously using the proposed interferometer. The dc term can be eliminated by subtracting the two phase-shifted interferograms, and the phase of a specimen can be reconstructed through Fourier transform. The validity and stability of the interferometer proposed are experimentally demonstrated via the measurement of a phase plate.

© 2013 OSA

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### Equations (9)

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(1)
$${f}_{0}=\Delta x/\lambda f.$$
(2)
$$\mathrm{sin}\theta =\frac{\lambda}{d}=\mathrm{tan}\theta =\frac{\Delta x}{\Delta f}.$$
(3)
$${f}_{0}=\frac{\Delta f}{f\cdot d}.$$
(4)
$${I}_{1}\left(x,y\right)=a\left(x,y\right)+c\left(x,y\right)\mathrm{exp}\left(i2\pi {f}_{0}x\right)+c*\left(x,y\right)\mathrm{exp}\left(-i2\pi {f}_{0}x\right),$$
(5)
$${I}_{2}\left(x,y\right)=a\left(x,y\right)+c\left(x,y\right)\mathrm{exp}\left(i\alpha \right)\mathrm{exp}\left(i2\pi {f}_{0}x\right)+c*\left(x,y\right)\mathrm{exp}\left(-i\alpha \right)\mathrm{exp}\left(-i2\pi {f}_{0}x\right)$$
(6)
$$c\left(x,y\right)=A\mathrm{exp}\left[i\phi \left(x,y\right)\right],$$
(7)
$$Rr=\mathrm{exp}\left(-i2\pi {f}_{0}x\right)=\mathrm{exp}\left(-i2\pi \frac{\Delta f}{f\cdot d}x\right).$$
(8)
$${c}^{\prime}\left(x,y\right)=c\left(x,y\right)\left[1-\mathrm{exp}\left(i\alpha \right)\right]=IFT\left\{FT\left\{Rr\left({I}_{1}-{I}_{2}\right)\right\}\cdot LF\right\},$$
(9)
$$\phi \left(x,y\right)=\frac{\mathrm{Im}\left[{c}^{\prime}\left(x,y\right)\right]}{\mathrm{Re}\left[{c}^{\prime}\left(x,y\right)\right]}-{\phi}_{C},$$