Abstract

We present a method for phase retrieval in off-axis interferometric systems. By numerically calculating the transverse 1st and 2nd order derivatives of the interferogram, we show that one can directly retrieve the quantitative phase image, without the need for Fourier or Hilbert transformations. Because of this, the method is significantly faster than the current approaches. We illustrate our method using biological specimen data from three different off-axis quantitative phase imaging techniques.

© 2012 Optical Society of America

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References

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2012

2011

2010

H. F. Ding and G. Popescu, Opt. Exp. 18, 1569 (2010).
[CrossRef]

2006

2005

2004

2001

1995

M. Servin and F. Cuevas, J. Mod. Opt. 42, 1853 (1995).
[CrossRef]

1992

C. Joenathan and B. M. Khorana, J. Mod. Opt. 39, 2075 (1992).
[CrossRef]

1982

Bhaduri, B.

Carl, D.

Cuevas, F.

M. Servin and F. Cuevas, J. Mod. Opt. 42, 1853 (1995).
[CrossRef]

Dasari, R. R.

Debnath, S. K.

Ding, H.

Ding, H. F.

H. F. Ding and G. Popescu, Opt. Exp. 18, 1569 (2010).
[CrossRef]

Do, M.

Feld, M. S.

Gillette, M. U.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Ikeda, T.

Ina, H.

Joenathan, C.

C. Joenathan and B. M. Khorana, J. Mod. Opt. 39, 2075 (1992).
[CrossRef]

Kato, J.

Kemper, B.

Khorana, B. M.

C. Joenathan and B. M. Khorana, J. Mod. Opt. 39, 2075 (1992).
[CrossRef]

Kim, M. K.

Kobayashi, S.

Lo, C.-M.

Mann, C.

Millet, L. J.

Mir, M.

Mizuno, J.

Ohta, S.

Park, Y. K.

Patel, S.

Pham, H.

Popescu, G.

Rogers, J. A.

Servin, M.

M. Servin and F. Cuevas, J. Mod. Opt. 42, 1853 (1995).
[CrossRef]

Sobh, N.

Takeda, M.

Unarunotai, S.

von Bally, G.

Wang, Z.

Wernicke, G.

Yamaguchi, I.

Yu, L.

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Figures (3)

Fig. 1.
Fig. 1.

Derivative method for phase calculation: (a) original DPM image, (b) 1st order derivative of (a) w.r.t. x, (c) 2nd order derivative of (a) w.r.t. x, (d) the reconstructed unwrapped phase, (e) 3×3 average filtered phase of (d), (f) phase obtained by HT; the color bars show the phase in rad.

Fig. 2.
Fig. 2.

Quantitative phase imaging with wDPM setup: (a) Microbead immersed in oil; the color bar shows the height in μm, (b) Live Hela cells; the color bars show the phase in rad. The arrows indicate nucleoli.

Fig. 3.
Fig. 3.

Comparison between DM and SPS. Quantitative phase image of red blood cells processed from an interferogram obtained by iSLIM without filtering using: (a) the DM method, (b) SPS method; the color bars show the phase in rad; (c) Profile of the dashed lines in (a) and (b); (d) Profile of the same dashed lines after filtering the phase images using 3×3 average filtering.

Equations (11)

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I(x,y)=Ib(x,y)+γ(x,y)cos[ϕ(x,y)+kx],
k=2πsinθ/λ,
I(x,y)x=Ib(x,y)x+cos[ϕ(x,y)+kx]γ(x,y)xγ(x,y)sin[ϕ(x,y)+kx][ϕ(x,y)x+k].
Ibx0,γx0,φxk,
I=I(x,y)x=γksin[ϕ(x,y)+kx].
I=2I(x,y)x2=γk2cos[ϕ(x,y)+kx].
ϕ(x,y)=arg(I+ikI)kx.
ϕ(x,y)=tan1[kII]kx,
ϕ(x,y)=tan1[tan(kδx2)I2+I1I2I1]kx,
I1I3=(I3I2+I2I1)=(I2+I1),
I1+2I2I3=(I3I2)+(I2I1)=(I2I1).

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