Abstract

We present a dual-wavelength off-axis quasi-common-path digital holography for quantitative phase imaging using polarization-multiplexing in a single shot. Employing an off-axis nearly common-path configuration, our approach separates the two-wavelength information using a polarizing beam splitter, while modulates the orthogonal fringe directions for each wavelength using two retro-reflector mirrors, and thus generates a single multiplexed off-axis interferogram on a monochrome CCD camera. The information of a specimen, including phase and height, is reconstructed through a division algorithm for dual wavelengths with the help of a specimen-free multiplexed interferogram. The experimental results obtained on a square step target and a circular step target illustrate the validity and stability of our setup.

© 2017 Optical Society of America

1. Introduction

Digital holography (DH), also known as wide-filed interferometry, has attracted much attention from the research community as it can be used for non-destructive, high precision, full filed and especially quantitative phase measurements [1–4]. DH has been widely used to investigate a variety of unlabeled specimens, such as biological specimens, surface profile, and micro structures. In terms of setup, DH can be divided into a series of groups, including separated-path geometries [1, 2] or common-path geometries [4–8], on-axis geometries [1, 9, 10] or off-axis geometries [6–8]. Compared to the separated-path geometries, the common-path geometries provide simplicity, robustness and even compactness in the setup due to the same path between the reference and sample beams. On the other hand, the on-axis geometries can make full use of the space-bandwidth product of a CCD camera. But to eliminate the zero-order and conjugate image terms, phase-shifting algorithm [9–12] is applied, which penalizes the acquisition rate [1, 9] or the utilization of the field of view of the CCD camera [10–12]. To overcome this, the off-axis geometries filter out the unwanted image terms in the Fourier domain with a single shot [6–8], and then allow for much faster acquisition rates. So the off-axis common-path DHs are of growing interest in recent years. However, most of the off-axis common-path DHs just utilize a single wavelength [5–12], in which if a specimen is optically thicker than the illumination wavelength, its imaging phase is ambiguous and produces 2π discontinuities. A digital phase unwrapping algorithm [13, 14] can enable continuous phase retrieval. However, these algorithms are often computational intricate at the expense of retrieval time, and especially cannot identify high aspect-ratio phase discontinuities of over one wavelength. As a normal solution, dual-wavelength DH (DWDH) [15–22] is proposed to avoid the 2π discontinuities. This method records two interferograms with different wavelengths to extract each wrapped phase map separately, and then utilizes a subtraction procedure between the two wrapped phases to yield an unwrapped phase map with a large synthetic wavelength, which improves the unambiguous phase range. Combining the significant advantages of the off-axis common-path DH and DWDH presented above, the off-axis common-path DWDH has being received great scientific interest in recent years [20–22].

In 2014, Kim [20] et al. utilized a pinhole array to select a different diffraction order of a grating for each wavelength so that they can distinguish the dual-wavelength interferogram obtained in a single shot. However, to avoid the cross-talk between the two wavelengths, a smaller period of the interferogram is required at the cost of either spatial resolution or field of view. In 2016, Zhao [21] et al. employed a parallel glass plate to reflect two lasers from its front and back surfaces, and then create a lateral shear to obtain a multiplexed interferogram with the two-wavelength information. However, the size of the measured specimens must be smaller than the shear, and a cross-talk also exits between the two wavelengths. To reduce the cross talk, Shaked [22] et al. adopted a modified Michelson interferometer using transmission pinhole array to multiplex two wavelength information into one interferogram with orthogonal spatial frequencies. Their setup used a dichroic mirror to separate the two wavelengths and two mirrors to adjust each wavelength to create an orthogonal off-axis interference fringe direction. However, the illumination wavelengths are restricted by the commercial dichroic mirror.

Therefore, inspired by previous work [16–19, 23–25], we present an off-axis nearly common-path DWDH using polarization-multiplexing to yield a multiplexed interferogram with orthogonal spatial frequencies for each wavelength in a single shot. A division algorithm is also used to perform the dual-wavelength unwrapping. In terms of simplicity in procedure and setup, we would like to emphasize our advancement. Compared with [16–19], our method is more stable and compact due to the quasi common path. While compared with [22], our method may be difficult to multiplex more than two wavelengths, and slightly harder to align the angles between the sample and reference beams. However, our method can make the two wavelengths very close to each other, and optimize both the illumination wavelengths and synthetic wavelength to fit application requirements but not be limited by the commercial dichroic mirror. To some extent, our method can be more practical and compact in application.

2. Experimental setup

Figure 1 shows the proposed experimental setup. The two laser sources are a red laser with a wavelength of λ1 and a green laser with a wavelength of λ2. The red beam is linearly polarized by a polarizer P1 through 0° and the green beam is done by a polarizer P2 through 90°, both with respect to the horizontal axis. The two orthogonal polarized beams are combined into one beams by a beam splitter BS1 and then collimated and expanded by a collimator & expander (BE). After passing through a specimen S, the combined beam is Fourier-transformed by a lens L1, and then split into two copies using another beam splitter BS2. One copy, referred to as the reference beam, is low-pass filtered and reflected by a pinhole-mirror PM [24]. The other copy, referred to as the sample beam, is separated into two wavelength channels again using a polarizing beam splitter PBS. Each of the channels is reflected by retro-reflectors, RR1 and RR2, to yield a full multiplexed off-axis interferogram on a CCD camera [7, 23]. The two retro-reflectors are fixed perpendicular to each other [23] to create orthogonal Fourier-plane shifts between the two wavelengths. The three beams are merged again by BS2 and Fourier-transformed back to the CCD camera plane by a lens L2. To compensate chromatic aberration, all the lens are achromatic. In this case, two orthogonal off-axis interference fringe directions are created for each wavelength, and thus a single multiplexed off-axis interferogram for the two wavelengths can be acquired by the CCD camera in a single shot. Noted that each wavelength interferograms fringes can be independently adjust by RR1 and RR2 both in spatial frequency and orientation, respectively. But to minimize the cross-talk between the two wavelengths, the better choice is to enable orthogonal spatial frequencies orientation for each wavelength, which can ensure optimum overlaps of the image terms in the interferogram Fourier domain.

 figure: Fig. 1

Fig. 1 (a).Experimental setup: P1 and P2, polarizers; BS1 and BS2, beam-splitters; BE, beam expander; S, sample; L1 and L2, lenses; PBS, polarizing beam splitter; PM, pinhole mirror; RR1 and RR2, retro-reflector mirrors ;(b) and (c) three-dimensional positions of RR1 and RR2.

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3. Division reconstruction algorithm for dual wavelengths

Assuming that the two-wavelength beams illuminated the specimen are both uniform plane wave, and the multiplexed interferogram is an incoherent superposition of the interferograms λ1 and λ2, the intensity of the multiplexed interferogram can be then expressed as

I(x,y)=a12+a22+{0.5b1{exp[i(φ1+φbg1+2πfx1x+2πfy1y)]+exp[i(φ1+φbg1+2πfx1x+2πfy1y)]}+0.5b2{exp[i(φ2+φbg2+2πfx2x+2πfy2y)]+exp[i(φ2+φbg2+2πfx2x+2πfy2y)]}},
where ai is the zero-order term, bi is the local contrast of the fringes, φi is the phase distribution of the specimen, φbgi is the background phase aberration, fxi and fyi are the spatial frequencies in the x and y directions, and the subscripts of i = 1, 2 represent the corresponding parameters for λ1 and λ2, respectively.

To extract the specimen phase φi and remove the background phase aberration φbgi, a double exposure method [21] can be applied with the help of one offline prior acquisition of a multiplex interferogram without any specimen. However, this method requires to ensure the spatial frequencies accurately. Similar to the double exposure method, a division method [24, 25] was proposed by us to relieve the background phase aberration and spatial frequency errors, but it is only suitable for single-wavelength reconstruction. So we modify the division method to make it to fit dual-wavelength reconstruction as following.

After applying Fourier-transform operation, the zero-order term and the two couples of cross-correlation terms can be fully separated in the spectral domain. The real image terms for each wavelength can be chosen through band pass filters, and then transferred to two complex results using inverse Fourier-transform operation, which become

C1(x,y)=IFT{FT(I)*BPF1}=0.5b1{exp[i(φ1+φbg1+2πf1xx+2πf1yy)]},
C2(x,y)=IFT{FT(I)*BPF2}=0.5b2{exp[i(φ2+φbg2+2πf2xx+2πf2yy)]},
where FT represents the Fourier-transform operation, IFT represents the inverse Fourier-transform operation, and BPFi is a band pass filter for wavelength λi.

When there is no specimen in the position of S, Eqs. (2) and (3) can be rewritten as

C1'(x,y)=IFT{FT(I')*BPF1}=0.5b1{exp[i(φbg1+2πfx1x+2πfy1y)]},
C2'(x,y)=IFT{FT(I')*BPF2}=0.5b2{exp[i(φbg2+2πfx2x+2πfy2y)]},

After applying division operations, we can obtain

φ1(x,y)=tan1[C1(x,y)C1'(x,y)],
φ2(x,y)=tan1[C2(x,y)C2'(x,y)],

Equations (6) and (7) show that with the help of a multiplexed specimen-free interferogram, we can retrieve the specimen phases for each wavelength but remove the phase disturbance caused by the spatial frequency and background phase. Noted that we can prior record and analyze the specimen-free interferogram only once, and then use their results in the subsequent process.

According to the dual-wavelength unwrapping method [21, 22, 26], we can achieve

φs(x,y)={φ2(x,y)φ1(x,y);ifφ2(x,y)φ1(x,y)>0φ2(x,y)φ1(x,y)+2π;ifφ2(x,y)φ1(x,y)<0.

From Eq. (8), we can extract the height map h(x, y) of the specimen. But since our method operates in a transmission mode, in which the phase information associates with the height and the refractive index, the refractive index must be taken into consideration during the extracted process.

We start with the definition of the specimen phase, which can be expressed as

φi(x,y)=h(x,y)×2π×(ni1)λi=h(x,y)×2π×1λei,
where ni is the refractive index for wavelength λi, and λei = λi / (ni −1) is the corresponding equivalent wavelength.

As a result, we can obtain

h(x,y)=φs(x,y)2π×λe1λe2λe1λe2=φs(x,y)2π×λs.
where λs = λe1λe2 / (λe1λe2) is a synthetic equivalent wavelength, which allows the specimen to be retrieved without phase unwrapping in a larger unambiguous range.

4. Results and discussion

In order to illustrate our approach, the experimental setup is constructed by using a He-Ne laser with red wavelength of λ1 = 632.8 nm, a solid-state laser with green wavelength of λ2 = 532 nm, two lenses L1 and L2 with the same focal length of 200 mm, a pinhole-mirror PM with a pinhole diameter of 30 μm, and a monochrome CCD camera with pixel size 4.8 μm × 4.8 μm and 1280 × 1024 pixels.

The first experiment was carried out on a square step target made of fused silica, which has a refractive index of n1 = 1.457 for λ1 = 632.8 nm and n2 = 1.460 for λ2 = 532 nm. The height of the step target is provided by BRUKER Atomic Force Microscopy (AFM) and the result is about 2500 nm. In the case, a synthetic equivalent wavelength of λs = 7018.8 nm can be achieved, which is larger than the target height. Figure 2(a) shows the multiplexed interferogram without any specimen, and Fig. 2(b) shows the multiplexed interferogram with the square step target. When the two images are Fourier transformed, the resulting power spectrums are obtained as illustrated in Figs. 2(c) and 2(d), respectively. We can see that due to the orthogonal spatial frequencies, the zero-order term and the two pairs of cross-correlation terms can be fully separated with low cross-talk in the spectral domain. In other words, the real terms for each wavelength can be selected independently as marked with color circles in Figs. 2(c) and 2(d). Noted that since the two real terms have spectral widths proportional to the frequency band of the specimen profile, the area of these markers must be chosen as large as possible, but avoid the overlap between interference terms [17–21, 27], in which the higher frequency components of these terms can be achieved. Of course, such smoothed filtering maskers [20, 27] as Gaussian and Hamming can be used to avoid the occurrence of high-frequency fluctuations in the extracted images, and automatic spatial filtering approaches [28, 29] can be attempted to optimize the shape of real terms to improve the extracted quality. Using Eqs. (6)-(8), we can obtain the wrapped phase maps for each original wavelength as shown in Figs. 3(a) and 3(b), respectively, and the unwrapped phase map for the synthetic equivalent wavelength as shown in Fig. 3(c). Noted that the wrapped phase maps for each original wavelength should be reversed and matched to each other due to the image flipping introduced by the two retro-reflectors [23]. Figure 4 shows the comparison of 1D height profiles, which are yielded using Eqs. (9) and (10) by the phase maps indicated by the dash lines in Figs. 3(a)-3(c), respectively. Obviously, the conventional single-wavelength method cannot work well but the dual-wavelength method can in the condition of shaper jump on the specimen. The step height can be evaluated as 2590.9 nm from the difference of both averages [22] of the black line in Fig. 4. Although the experimental result is slightly larger than the nominal result, the two results still agree well with each other. Furthermore, the standard deviation is 16.8 nm for λ1, while 16.6 nm for λ2 and 172.1 nm for λs. As many others [21, 22, 26, 30] pointed out that the oscillations in the results for λs are mainly produced by the noise amplification using a synthetic wavelength, which is inherent to DWDH in general. But in fact, the increased noise level can be reduced by such noise-reduction methods as linear programming phase unwrapping [30], and the result is illustrated by the blue line denoted by λs′ in Fig. 4. Figure 5 illustrates the 3D height map for the square step target.

 figure: Fig. 2

Fig. 2 Multiplexed interferograms (a) without and (b) with the specimen; (c) power spectrum of (a); (d) power spectrum of (b).

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 figure: Fig. 3

Fig. 3 Reconstructed phase maps for (a) λ1, (b) λ2, and (c) λs, with the color bar indicates phase in rad.

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 figure: Fig. 4

Fig. 4 1D height profiles obtained from phase maps along dash lines marked in Figs. 3.

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 figure: Fig. 5

Fig. 5 An unwrapped 3D height map of the step target.

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To further access the feasibility of our approach, a circular step target made of fused silica was also measured. Figure 6(a) illustrates the multiplexed interferogram, and Fig. 6(b) illustrates the corresponding power spectrums. After applying the division reconstruction algorithm, we obtain the 3D height map of the circular step target, and the result is shown in Fig. 6(c). The step height of the circular step target is about 2026.3 nm, which also coincides with the measured result of 2000 nm from AFM.

 figure: Fig. 6

Fig. 6 Experimental results for the circular step target. (a) Multiplexed interferogram; (b) power spectrum; (c) 3D height map.

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To demonstrate the stability of our approach, 100 sequential measurements were also performed without any specimen at interval of half minute. The variances of the optical path difference (OPD) [24] are obtained at a randomly selected point for each wavelength, respectively, and the results are shown in Fig. 7. From the Fig. 7, we can calculate that the standard deviation is 3.54 nm for λ1, while 3.56 nm for λ2 and 32.54 nm for λs. These means that our approach can achieve a long-term stability even the noise level is increased due to the synthetic wavelength.

 figure: Fig. 7

Fig. 7 Stability test for the proposed method.

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5. Summary

In conclusion, we developed an off-axis quasi common-path DWDH using polarization-multiplexing to achieve a single interferogram acquisition. In contrast to the off-axis quasi-common-path DWDH in [22], our approach can enable two-wavelength single-shot imaging using a more practical and compact configuration. A division method for dual wavelengths is also presented to reconstruct the phase of the specimen but remove the phase disturbance caused by the spatial frequency and background phase. Such phase specimens as a square step target and a circular step target can be simply extracted using the division method. However, it should be noted that the two interferograms of specimen and free-specimen share the same gray scale levels of the camera. The amplitude modulation should be then taken into consideration in absorptive specimens, as reported in [31] and [32], which can be resolved from the real part of the complex results of Ci(x, y). However, in all our specimens with phase distribution, amplitude modulation can be negligible, which fits our approximation in the division form. In addition, as many others did [17–21], we used the same sized digital filters to select real spectral terms for red and green wavelengths. However, these may lead to some errors in the reconstructed results to some extent for the corresponding extent of spatial frequencies is different for each wavelength. In fact, the errors can be avoided by keeping the filter sizes for the two wavelengths in appropriate ratio. We hope that our approach provides a powerful tool for quantitative phase imaging of specimens thicker than the illumination wavelength.

Funding

National Natural Science Foundation of China (61775046, 61377009); Major National Scientific Instrument and Equipment Development Project of China (2013YQ290489); Fundamental Research Funds for the Central Universities.

References and links

1. X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50(10), 1431–1435 (2012).

2. Z. Wang, L. J. Millet, M. U. Gillette, and G. Popescu, “Jones phase microscopy of transparent and anisotropic samples,” Opt. Lett. 33(11), 1270–1272 (2008). [PubMed]  

3. J. C. Aguilar, “Measuring of temperatures of a candle flame using four multidirectional point-diffraction interferometers,” Opt. Eng. 52(10), 104103 (2013).

4. W. Zhao, L. Qiu, Y. Xiao, and J. Yang, “Laser differential confocal interference multi-parameter comprehensive measurement method and its system for spherical lens,” Opt. Express 24(20), 22813–22829 (2016). [PubMed]  

5. N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative-phase microscopy of live cell dynamics,” Opt. Lett. 34(6), 767–769 (2009). [PubMed]  

6. G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006). [PubMed]  

7. P. Girshovitz and N. T. Shaked, “Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy,” Opt. Express 21(5), 5701–5714 (2013). [PubMed]  

8. S. Rawat, S. Komatsu, A. Markman, A. Anand, and B. Javidi, “Compact and field-portable 3D printed shearing digital holographic microscope for automated cell identification,” Appl. Opt. 56(9), D127–D133 (2017). [PubMed]  

9. P. Gao, I. Harder, V. Nercissian, K. Mantel, and B. Yao, “Phase-shifting point-diffraction interferometry with common-path and in-line configuration for microscopy,” Opt. Lett. 35(5), 712–714 (2010). [PubMed]  

10. H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Parallel-quadrature on-axis phase-shifting common-path interferometer using a polarizing beam splitter,” Appl. Opt. 54(32), 9513–9517 (2015). [PubMed]  

11. B. Hao, M. Shan, M. Diao, Z. Zhong, and H. Ma, “Common-path interferometer with a tri-window,” Opt. Lett. 37(15), 3213–3215 (2012). [PubMed]  

12. H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Common path interferometer based on the modified Michelson configuration using a reflective grating,” Opt. Lasers Eng. 75, 1–4 (2015).

13. L. Ma, Y. Li, H. Wang, and H. Jin, “Fast algorithm for reliability-guided phase unwrapping in digital holographic microscopy,” Appl. Opt. 51(36), 8800–8807 (2012). [PubMed]  

14. H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and C. J. Moore, “Fast and robust three-dimensional best path phase unwrapping algorithm,” Appl. Opt. 46(26), 6623–6635 (2007). [PubMed]  

15. M. T. Rinehart, N. T. Shaked, N. J. Jenness, R. L. Clark, and A. Wax, “Simultaneous two-wavelength transmission quantitative phase microscopy with a color camera,” Opt. Lett. 35(15), 2612–2614 (2010). [PubMed]  

16. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15(12), 7231–7242 (2007). [PubMed]  

17. A. Khmaladze, M. Kim, and C. M. Lo, “Phase imaging of cells by simultaneous dual-wavelength reflection digital holography,” Opt. Express 16(15), 10900–10911 (2008). [PubMed]  

18. D. G. Abdelsalam, R. Magnusson, and D. Kim, “Single-shot, dual-wavelength digital holography based on polarizing separation,” Appl. Opt. 50(19), 3360–3368 (2011). [PubMed]  

19. Z. Wang, Y. Chen, and Z. Jiang, “Dual-wavelength digital holographic phase reconstruction based on a polarization-multiplexing configuration,” Chin. Opt. Lett. 14(1), 010008 (2016).

20. M. R. Jafarfard, S. Moon, B. Tayebi, and D. Y. Kim, “Dual-wavelength diffraction phase microscopy for simultaneous measurement of refractive index and thickness,” Opt. Lett. 39(10), 2908–2911 (2014). [PubMed]  

21. J. Di, Y. Li, M. Xie, J. Zhang, C. Ma, T. Xi, E. Li, and J. Zhao, “Dual-wavelength common-path digital holographic microscopy for quantitative phase imaging based on lateral shearing interferometry,” Appl. Opt. 55(26), 7287–7293 (2016). [PubMed]  

22. N. A. Turko and N. T. Shaked, “Simultaneous two-wavelength phase unwrapping using an external module for multiplexing off-axis holography,” Opt. Lett. 42(1), 73–76 (2017). [PubMed]  

23. P. Girshovitz and N. T. Shaked, “Doubling the field of view in off-axis low-coherence interferometric imaging,” Light Sci. Appl. 3, e151 (2014).

24. H. Bai, Z. Zhong, M. Shan, L. Liu, L. Guo, and Y. Zhang, “Interferometric phase microscopy using slightly-off-axis reflective point diffraction interferometer,” Opt. Lasers Eng. 90, 155–160 (2017).

25. B. Hao, M. Shan, Z. Zhi, M. Diao, Y. Wang, and Y. Zhang, “Parallel two-step spatial carrier phase-shifting interferometric phase microscopy with fast phase retrieval,” J. Opt. 17, 035602 (2015).

26. J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. 28(13), 1141–1143 (2003). [PubMed]  

27. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39(23), 4070–4075 (2000). [PubMed]  

28. J. Weng, J. Zhong, and C. Hu, “Automatic spatial filtering to obtain the virtual image term in digital holographic microscopy,” Appl. Opt. 49(2), 189–195 (2010). [PubMed]  

29. X. He, C. V. Nguyen, M. Pratap, Y. Zheng, Y. Wang, D. R. Nisbet, R. J. Williams, M. Rug, A. G. Maier, and W. M. Lee, “Automated Fourier space region-recognition filtering for off-axis digital holographic microscopy,” Biomed. Opt. Express 7(8), 3111–3123 (2016). [PubMed]  

30. Z. Wang, J. Jiao, W. Qu, F. Yang, H. Li, A. Tian, and A. Asundi, “Linear programming phase unwrapping for dual-wavelength digital holography,” Appl. Opt. 56(3), 424–433 (2017). [PubMed]  

31. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).

32. Z. Wang, L. J. Millet, M. U. Gillette, and G. Popescu, “Jones phase microscopy of transparent and anisotropic samples,” Opt. Lett. 33(11), 1270–1272 (2008). [PubMed]  

References

  • View by:

  1. X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50(10), 1431–1435 (2012).
  2. Z. Wang, L. J. Millet, M. U. Gillette, and G. Popescu, “Jones phase microscopy of transparent and anisotropic samples,” Opt. Lett. 33(11), 1270–1272 (2008).
    [PubMed]
  3. J. C. Aguilar, “Measuring of temperatures of a candle flame using four multidirectional point-diffraction interferometers,” Opt. Eng. 52(10), 104103 (2013).
  4. W. Zhao, L. Qiu, Y. Xiao, and J. Yang, “Laser differential confocal interference multi-parameter comprehensive measurement method and its system for spherical lens,” Opt. Express 24(20), 22813–22829 (2016).
    [PubMed]
  5. N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative-phase microscopy of live cell dynamics,” Opt. Lett. 34(6), 767–769 (2009).
    [PubMed]
  6. G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006).
    [PubMed]
  7. P. Girshovitz and N. T. Shaked, “Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy,” Opt. Express 21(5), 5701–5714 (2013).
    [PubMed]
  8. S. Rawat, S. Komatsu, A. Markman, A. Anand, and B. Javidi, “Compact and field-portable 3D printed shearing digital holographic microscope for automated cell identification,” Appl. Opt. 56(9), D127–D133 (2017).
    [PubMed]
  9. P. Gao, I. Harder, V. Nercissian, K. Mantel, and B. Yao, “Phase-shifting point-diffraction interferometry with common-path and in-line configuration for microscopy,” Opt. Lett. 35(5), 712–714 (2010).
    [PubMed]
  10. H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Parallel-quadrature on-axis phase-shifting common-path interferometer using a polarizing beam splitter,” Appl. Opt. 54(32), 9513–9517 (2015).
    [PubMed]
  11. B. Hao, M. Shan, M. Diao, Z. Zhong, and H. Ma, “Common-path interferometer with a tri-window,” Opt. Lett. 37(15), 3213–3215 (2012).
    [PubMed]
  12. H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Common path interferometer based on the modified Michelson configuration using a reflective grating,” Opt. Lasers Eng. 75, 1–4 (2015).
  13. L. Ma, Y. Li, H. Wang, and H. Jin, “Fast algorithm for reliability-guided phase unwrapping in digital holographic microscopy,” Appl. Opt. 51(36), 8800–8807 (2012).
    [PubMed]
  14. H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and C. J. Moore, “Fast and robust three-dimensional best path phase unwrapping algorithm,” Appl. Opt. 46(26), 6623–6635 (2007).
    [PubMed]
  15. M. T. Rinehart, N. T. Shaked, N. J. Jenness, R. L. Clark, and A. Wax, “Simultaneous two-wavelength transmission quantitative phase microscopy with a color camera,” Opt. Lett. 35(15), 2612–2614 (2010).
    [PubMed]
  16. J. Kühn, T. Colomb, F. Montfort, F. Charrière, Y. Emery, E. Cuche, P. Marquet, and C. Depeursinge, “Real-time dual-wavelength digital holographic microscopy with a single hologram acquisition,” Opt. Express 15(12), 7231–7242 (2007).
    [PubMed]
  17. A. Khmaladze, M. Kim, and C. M. Lo, “Phase imaging of cells by simultaneous dual-wavelength reflection digital holography,” Opt. Express 16(15), 10900–10911 (2008).
    [PubMed]
  18. D. G. Abdelsalam, R. Magnusson, and D. Kim, “Single-shot, dual-wavelength digital holography based on polarizing separation,” Appl. Opt. 50(19), 3360–3368 (2011).
    [PubMed]
  19. Z. Wang, Y. Chen, and Z. Jiang, “Dual-wavelength digital holographic phase reconstruction based on a polarization-multiplexing configuration,” Chin. Opt. Lett. 14(1), 010008 (2016).
  20. M. R. Jafarfard, S. Moon, B. Tayebi, and D. Y. Kim, “Dual-wavelength diffraction phase microscopy for simultaneous measurement of refractive index and thickness,” Opt. Lett. 39(10), 2908–2911 (2014).
    [PubMed]
  21. J. Di, Y. Li, M. Xie, J. Zhang, C. Ma, T. Xi, E. Li, and J. Zhao, “Dual-wavelength common-path digital holographic microscopy for quantitative phase imaging based on lateral shearing interferometry,” Appl. Opt. 55(26), 7287–7293 (2016).
    [PubMed]
  22. N. A. Turko and N. T. Shaked, “Simultaneous two-wavelength phase unwrapping using an external module for multiplexing off-axis holography,” Opt. Lett. 42(1), 73–76 (2017).
    [PubMed]
  23. P. Girshovitz and N. T. Shaked, “Doubling the field of view in off-axis low-coherence interferometric imaging,” Light Sci. Appl. 3, e151 (2014).
  24. H. Bai, Z. Zhong, M. Shan, L. Liu, L. Guo, and Y. Zhang, “Interferometric phase microscopy using slightly-off-axis reflective point diffraction interferometer,” Opt. Lasers Eng. 90, 155–160 (2017).
  25. B. Hao, M. Shan, Z. Zhi, M. Diao, Y. Wang, and Y. Zhang, “Parallel two-step spatial carrier phase-shifting interferometric phase microscopy with fast phase retrieval,” J. Opt. 17, 035602 (2015).
  26. J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. 28(13), 1141–1143 (2003).
    [PubMed]
  27. E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39(23), 4070–4075 (2000).
    [PubMed]
  28. J. Weng, J. Zhong, and C. Hu, “Automatic spatial filtering to obtain the virtual image term in digital holographic microscopy,” Appl. Opt. 49(2), 189–195 (2010).
    [PubMed]
  29. X. He, C. V. Nguyen, M. Pratap, Y. Zheng, Y. Wang, D. R. Nisbet, R. J. Williams, M. Rug, A. G. Maier, and W. M. Lee, “Automated Fourier space region-recognition filtering for off-axis digital holographic microscopy,” Biomed. Opt. Express 7(8), 3111–3123 (2016).
    [PubMed]
  30. Z. Wang, J. Jiao, W. Qu, F. Yang, H. Li, A. Tian, and A. Asundi, “Linear programming phase unwrapping for dual-wavelength digital holography,” Appl. Opt. 56(3), 424–433 (2017).
    [PubMed]
  31. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982).
  32. Z. Wang, L. J. Millet, M. U. Gillette, and G. Popescu, “Jones phase microscopy of transparent and anisotropic samples,” Opt. Lett. 33(11), 1270–1272 (2008).
    [PubMed]

2017 (4)

2016 (4)

2015 (3)

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Parallel-quadrature on-axis phase-shifting common-path interferometer using a polarizing beam splitter,” Appl. Opt. 54(32), 9513–9517 (2015).
[PubMed]

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Common path interferometer based on the modified Michelson configuration using a reflective grating,” Opt. Lasers Eng. 75, 1–4 (2015).

B. Hao, M. Shan, Z. Zhi, M. Diao, Y. Wang, and Y. Zhang, “Parallel two-step spatial carrier phase-shifting interferometric phase microscopy with fast phase retrieval,” J. Opt. 17, 035602 (2015).

2014 (2)

M. R. Jafarfard, S. Moon, B. Tayebi, and D. Y. Kim, “Dual-wavelength diffraction phase microscopy for simultaneous measurement of refractive index and thickness,” Opt. Lett. 39(10), 2908–2911 (2014).
[PubMed]

P. Girshovitz and N. T. Shaked, “Doubling the field of view in off-axis low-coherence interferometric imaging,” Light Sci. Appl. 3, e151 (2014).

2013 (2)

J. C. Aguilar, “Measuring of temperatures of a candle flame using four multidirectional point-diffraction interferometers,” Opt. Eng. 52(10), 104103 (2013).

P. Girshovitz and N. T. Shaked, “Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy,” Opt. Express 21(5), 5701–5714 (2013).
[PubMed]

2012 (3)

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50(10), 1431–1435 (2012).

L. Ma, Y. Li, H. Wang, and H. Jin, “Fast algorithm for reliability-guided phase unwrapping in digital holographic microscopy,” Appl. Opt. 51(36), 8800–8807 (2012).
[PubMed]

B. Hao, M. Shan, M. Diao, Z. Zhong, and H. Ma, “Common-path interferometer with a tri-window,” Opt. Lett. 37(15), 3213–3215 (2012).
[PubMed]

2011 (1)

2010 (3)

2009 (1)

2008 (3)

2007 (2)

2006 (1)

2003 (1)

2000 (1)

1982 (1)

Abdelsalam, D. G.

Abdul-Rahman, H. S.

Aguilar, J. C.

J. C. Aguilar, “Measuring of temperatures of a candle flame using four multidirectional point-diffraction interferometers,” Opt. Eng. 52(10), 104103 (2013).

Anand, A.

Asundi, A.

Bai, H.

H. Bai, Z. Zhong, M. Shan, L. Liu, L. Guo, and Y. Zhang, “Interferometric phase microscopy using slightly-off-axis reflective point diffraction interferometer,” Opt. Lasers Eng. 90, 155–160 (2017).

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Parallel-quadrature on-axis phase-shifting common-path interferometer using a polarizing beam splitter,” Appl. Opt. 54(32), 9513–9517 (2015).
[PubMed]

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Common path interferometer based on the modified Michelson configuration using a reflective grating,” Opt. Lasers Eng. 75, 1–4 (2015).

Burton, D. R.

Charrière, F.

Chen, J.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50(10), 1431–1435 (2012).

Chen, Y.

Clark, R. L.

Colomb, T.

Cuche, E.

Dakoff, A.

Dasari, R. R.

Depeursinge, C.

Di, J.

Diao, M.

B. Hao, M. Shan, Z. Zhi, M. Diao, Y. Wang, and Y. Zhang, “Parallel two-step spatial carrier phase-shifting interferometric phase microscopy with fast phase retrieval,” J. Opt. 17, 035602 (2015).

B. Hao, M. Shan, M. Diao, Z. Zhong, and H. Ma, “Common-path interferometer with a tri-window,” Opt. Lett. 37(15), 3213–3215 (2012).
[PubMed]

Emery, Y.

Feld, M. S.

Gao, P.

Gass, J.

Gdeisat, M. A.

Gillette, M. U.

Girshovitz, P.

P. Girshovitz and N. T. Shaked, “Doubling the field of view in off-axis low-coherence interferometric imaging,” Light Sci. Appl. 3, e151 (2014).

P. Girshovitz and N. T. Shaked, “Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy,” Opt. Express 21(5), 5701–5714 (2013).
[PubMed]

Guo, L.

H. Bai, Z. Zhong, M. Shan, L. Liu, L. Guo, and Y. Zhang, “Interferometric phase microscopy using slightly-off-axis reflective point diffraction interferometer,” Opt. Lasers Eng. 90, 155–160 (2017).

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Parallel-quadrature on-axis phase-shifting common-path interferometer using a polarizing beam splitter,” Appl. Opt. 54(32), 9513–9517 (2015).
[PubMed]

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Common path interferometer based on the modified Michelson configuration using a reflective grating,” Opt. Lasers Eng. 75, 1–4 (2015).

Hao, B.

B. Hao, M. Shan, Z. Zhi, M. Diao, Y. Wang, and Y. Zhang, “Parallel two-step spatial carrier phase-shifting interferometric phase microscopy with fast phase retrieval,” J. Opt. 17, 035602 (2015).

B. Hao, M. Shan, M. Diao, Z. Zhong, and H. Ma, “Common-path interferometer with a tri-window,” Opt. Lett. 37(15), 3213–3215 (2012).
[PubMed]

Harder, I.

He, X.

Hu, C.

Ikeda, T.

Ina, H.

Jafarfard, M. R.

Javidi, B.

Jenness, N. J.

Jiang, Z.

Jiao, J.

Jin, H.

Khmaladze, A.

Kim, D.

Kim, D. Y.

Kim, M.

Kim, M. K.

Kobayashi, S.

Komatsu, S.

Kühn, J.

Lalor, M. J.

Lee, W. M.

Li, E.

Li, H.

Li, Y.

Lilley, F.

Liu, L.

H. Bai, Z. Zhong, M. Shan, L. Liu, L. Guo, and Y. Zhang, “Interferometric phase microscopy using slightly-off-axis reflective point diffraction interferometer,” Opt. Lasers Eng. 90, 155–160 (2017).

Liu, S.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50(10), 1431–1435 (2012).

Lo, C. M.

Lu, X.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50(10), 1431–1435 (2012).

Ma, C.

Ma, H.

Ma, L.

Ma, Z.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50(10), 1431–1435 (2012).

Magnusson, R.

Maier, A. G.

Mantel, K.

Markman, A.

Marquet, P.

Millet, L. J.

Montfort, F.

Moon, S.

Moore, C. J.

Nercissian, V.

Nguyen, C. V.

Nisbet, D. R.

Popescu, G.

Pratap, M.

Qiu, L.

Qu, W.

Rawat, S.

Rinehart, M. T.

Rug, M.

Shaked, N. T.

Shan, M.

H. Bai, Z. Zhong, M. Shan, L. Liu, L. Guo, and Y. Zhang, “Interferometric phase microscopy using slightly-off-axis reflective point diffraction interferometer,” Opt. Lasers Eng. 90, 155–160 (2017).

B. Hao, M. Shan, Z. Zhi, M. Diao, Y. Wang, and Y. Zhang, “Parallel two-step spatial carrier phase-shifting interferometric phase microscopy with fast phase retrieval,” J. Opt. 17, 035602 (2015).

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Parallel-quadrature on-axis phase-shifting common-path interferometer using a polarizing beam splitter,” Appl. Opt. 54(32), 9513–9517 (2015).
[PubMed]

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Common path interferometer based on the modified Michelson configuration using a reflective grating,” Opt. Lasers Eng. 75, 1–4 (2015).

B. Hao, M. Shan, M. Diao, Z. Zhong, and H. Ma, “Common-path interferometer with a tri-window,” Opt. Lett. 37(15), 3213–3215 (2012).
[PubMed]

Takeda, M.

Tayebi, B.

Tian, A.

Turko, N. A.

Wang, H.

Wang, Y.

X. He, C. V. Nguyen, M. Pratap, Y. Zheng, Y. Wang, D. R. Nisbet, R. J. Williams, M. Rug, A. G. Maier, and W. M. Lee, “Automated Fourier space region-recognition filtering for off-axis digital holographic microscopy,” Biomed. Opt. Express 7(8), 3111–3123 (2016).
[PubMed]

B. Hao, M. Shan, Z. Zhi, M. Diao, Y. Wang, and Y. Zhang, “Parallel two-step spatial carrier phase-shifting interferometric phase microscopy with fast phase retrieval,” J. Opt. 17, 035602 (2015).

Wang, Z.

Wax, A.

Weng, J.

Williams, R. J.

Xi, T.

Xiao, Y.

Xie, M.

Yang, F.

Yang, J.

Yao, B.

Zhang, J.

Zhang, Y.

H. Bai, Z. Zhong, M. Shan, L. Liu, L. Guo, and Y. Zhang, “Interferometric phase microscopy using slightly-off-axis reflective point diffraction interferometer,” Opt. Lasers Eng. 90, 155–160 (2017).

B. Hao, M. Shan, Z. Zhi, M. Diao, Y. Wang, and Y. Zhang, “Parallel two-step spatial carrier phase-shifting interferometric phase microscopy with fast phase retrieval,” J. Opt. 17, 035602 (2015).

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Common path interferometer based on the modified Michelson configuration using a reflective grating,” Opt. Lasers Eng. 75, 1–4 (2015).

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Parallel-quadrature on-axis phase-shifting common-path interferometer using a polarizing beam splitter,” Appl. Opt. 54(32), 9513–9517 (2015).
[PubMed]

Zhang, Z.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50(10), 1431–1435 (2012).

Zhao, J.

Zhao, W.

Zheng, Y.

Zhi, Z.

B. Hao, M. Shan, Z. Zhi, M. Diao, Y. Wang, and Y. Zhang, “Parallel two-step spatial carrier phase-shifting interferometric phase microscopy with fast phase retrieval,” J. Opt. 17, 035602 (2015).

Zhong, J.

Zhong, L.

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50(10), 1431–1435 (2012).

Zhong, Z.

H. Bai, Z. Zhong, M. Shan, L. Liu, L. Guo, and Y. Zhang, “Interferometric phase microscopy using slightly-off-axis reflective point diffraction interferometer,” Opt. Lasers Eng. 90, 155–160 (2017).

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Parallel-quadrature on-axis phase-shifting common-path interferometer using a polarizing beam splitter,” Appl. Opt. 54(32), 9513–9517 (2015).
[PubMed]

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Common path interferometer based on the modified Michelson configuration using a reflective grating,” Opt. Lasers Eng. 75, 1–4 (2015).

B. Hao, M. Shan, M. Diao, Z. Zhong, and H. Ma, “Common-path interferometer with a tri-window,” Opt. Lett. 37(15), 3213–3215 (2012).
[PubMed]

Appl. Opt. (9)

S. Rawat, S. Komatsu, A. Markman, A. Anand, and B. Javidi, “Compact and field-portable 3D printed shearing digital holographic microscope for automated cell identification,” Appl. Opt. 56(9), D127–D133 (2017).
[PubMed]

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Parallel-quadrature on-axis phase-shifting common-path interferometer using a polarizing beam splitter,” Appl. Opt. 54(32), 9513–9517 (2015).
[PubMed]

L. Ma, Y. Li, H. Wang, and H. Jin, “Fast algorithm for reliability-guided phase unwrapping in digital holographic microscopy,” Appl. Opt. 51(36), 8800–8807 (2012).
[PubMed]

H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and C. J. Moore, “Fast and robust three-dimensional best path phase unwrapping algorithm,” Appl. Opt. 46(26), 6623–6635 (2007).
[PubMed]

D. G. Abdelsalam, R. Magnusson, and D. Kim, “Single-shot, dual-wavelength digital holography based on polarizing separation,” Appl. Opt. 50(19), 3360–3368 (2011).
[PubMed]

J. Di, Y. Li, M. Xie, J. Zhang, C. Ma, T. Xi, E. Li, and J. Zhao, “Dual-wavelength common-path digital holographic microscopy for quantitative phase imaging based on lateral shearing interferometry,” Appl. Opt. 55(26), 7287–7293 (2016).
[PubMed]

E. Cuche, P. Marquet, and C. Depeursinge, “Spatial filtering for zero-order and twin-image elimination in digital off-axis holography,” Appl. Opt. 39(23), 4070–4075 (2000).
[PubMed]

J. Weng, J. Zhong, and C. Hu, “Automatic spatial filtering to obtain the virtual image term in digital holographic microscopy,” Appl. Opt. 49(2), 189–195 (2010).
[PubMed]

Z. Wang, J. Jiao, W. Qu, F. Yang, H. Li, A. Tian, and A. Asundi, “Linear programming phase unwrapping for dual-wavelength digital holography,” Appl. Opt. 56(3), 424–433 (2017).
[PubMed]

Biomed. Opt. Express (1)

Chin. Opt. Lett. (1)

J. Opt. (1)

B. Hao, M. Shan, Z. Zhi, M. Diao, Y. Wang, and Y. Zhang, “Parallel two-step spatial carrier phase-shifting interferometric phase microscopy with fast phase retrieval,” J. Opt. 17, 035602 (2015).

J. Opt. Soc. Am. (1)

Light Sci. Appl. (1)

P. Girshovitz and N. T. Shaked, “Doubling the field of view in off-axis low-coherence interferometric imaging,” Light Sci. Appl. 3, e151 (2014).

Opt. Eng. (1)

J. C. Aguilar, “Measuring of temperatures of a candle flame using four multidirectional point-diffraction interferometers,” Opt. Eng. 52(10), 104103 (2013).

Opt. Express (4)

Opt. Lasers Eng. (3)

H. Bai, M. Shan, Z. Zhong, L. Guo, and Y. Zhang, “Common path interferometer based on the modified Michelson configuration using a reflective grating,” Opt. Lasers Eng. 75, 1–4 (2015).

X. Lu, J. Chen, S. Liu, Z. Ma, Z. Zhang, and L. Zhong, “3D profile reconstruction of biological sample by in-line image-plane phase-shifting digital microscopic holography,” Opt. Lasers Eng. 50(10), 1431–1435 (2012).

H. Bai, Z. Zhong, M. Shan, L. Liu, L. Guo, and Y. Zhang, “Interferometric phase microscopy using slightly-off-axis reflective point diffraction interferometer,” Opt. Lasers Eng. 90, 155–160 (2017).

Opt. Lett. (10)

J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π ambiguity by multiwavelength digital holography,” Opt. Lett. 28(13), 1141–1143 (2003).
[PubMed]

M. R. Jafarfard, S. Moon, B. Tayebi, and D. Y. Kim, “Dual-wavelength diffraction phase microscopy for simultaneous measurement of refractive index and thickness,” Opt. Lett. 39(10), 2908–2911 (2014).
[PubMed]

N. A. Turko and N. T. Shaked, “Simultaneous two-wavelength phase unwrapping using an external module for multiplexing off-axis holography,” Opt. Lett. 42(1), 73–76 (2017).
[PubMed]

Z. Wang, L. J. Millet, M. U. Gillette, and G. Popescu, “Jones phase microscopy of transparent and anisotropic samples,” Opt. Lett. 33(11), 1270–1272 (2008).
[PubMed]

Z. Wang, L. J. Millet, M. U. Gillette, and G. Popescu, “Jones phase microscopy of transparent and anisotropic samples,” Opt. Lett. 33(11), 1270–1272 (2008).
[PubMed]

P. Gao, I. Harder, V. Nercissian, K. Mantel, and B. Yao, “Phase-shifting point-diffraction interferometry with common-path and in-line configuration for microscopy,” Opt. Lett. 35(5), 712–714 (2010).
[PubMed]

N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative-phase microscopy of live cell dynamics,” Opt. Lett. 34(6), 767–769 (2009).
[PubMed]

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006).
[PubMed]

B. Hao, M. Shan, M. Diao, Z. Zhong, and H. Ma, “Common-path interferometer with a tri-window,” Opt. Lett. 37(15), 3213–3215 (2012).
[PubMed]

M. T. Rinehart, N. T. Shaked, N. J. Jenness, R. L. Clark, and A. Wax, “Simultaneous two-wavelength transmission quantitative phase microscopy with a color camera,” Opt. Lett. 35(15), 2612–2614 (2010).
[PubMed]

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Figures (7)

Fig. 1
Fig. 1 (a).Experimental setup: P1 and P2, polarizers; BS1 and BS2, beam-splitters; BE, beam expander; S, sample; L1 and L2, lenses; PBS, polarizing beam splitter; PM, pinhole mirror; RR1 and RR2, retro-reflector mirrors ;(b) and (c) three-dimensional positions of RR1 and RR2.
Fig. 2
Fig. 2 Multiplexed interferograms (a) without and (b) with the specimen; (c) power spectrum of (a); (d) power spectrum of (b).
Fig. 3
Fig. 3 Reconstructed phase maps for (a) λ1, (b) λ2, and (c) λs, with the color bar indicates phase in rad.
Fig. 4
Fig. 4 1D height profiles obtained from phase maps along dash lines marked in Figs. 3.
Fig. 5
Fig. 5 An unwrapped 3D height map of the step target.
Fig. 6
Fig. 6 Experimental results for the circular step target. (a) Multiplexed interferogram; (b) power spectrum; (c) 3D height map.
Fig. 7
Fig. 7 Stability test for the proposed method.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

I ( x , y ) = a 1 2 + a 2 2 + { 0.5 b 1 { exp [ i ( φ 1 + φ b g 1 + 2 π f x 1 x + 2 π f y 1 y ) ] + exp [ i ( φ 1 + φ b g 1 + 2 π f x 1 x + 2 π f y 1 y ) ] } + 0.5 b 2 { exp [ i ( φ 2 + φ b g 2 + 2 π f x 2 x + 2 π f y 2 y ) ] + exp [ i ( φ 2 + φ b g 2 + 2 π f x 2 x + 2 π f y 2 y ) ] } } ,
C 1 ( x , y ) = I F T { F T ( I ) * B P F 1 } = 0.5 b 1 { exp [ i ( φ 1 + φ b g 1 + 2 π f 1 x x + 2 π f 1 y y ) ] } ,
C 2 ( x , y ) = I F T { F T ( I ) * B P F 2 } = 0.5 b 2 { exp [ i ( φ 2 + φ b g 2 + 2 π f 2 x x + 2 π f 2 y y ) ] } ,
C 1 ' ( x , y ) = I F T { F T ( I ' ) * B P F 1 } = 0.5 b 1 { exp [ i ( φ b g 1 + 2 π f x 1 x + 2 π f y 1 y ) ] } ,
C 2 ' ( x , y ) = I F T { F T ( I ' ) * B P F 2 } = 0.5 b 2 { exp [ i ( φ b g 2 + 2 π f x 2 x + 2 π f y 2 y ) ] } ,
φ 1 ( x , y ) = tan 1 [ C 1 ( x , y ) C 1 ' ( x , y ) ] ,
φ 2 ( x , y ) = tan 1 [ C 2 ( x , y ) C 2 ' ( x , y ) ] ,
φ s ( x , y ) = { φ 2 ( x , y ) φ 1 ( x , y ) ; i f φ 2 ( x , y ) φ 1 ( x , y ) > 0 φ 2 ( x , y ) φ 1 ( x , y ) + 2 π ; i f φ 2 ( x , y ) φ 1 ( x , y ) < 0 .
φ i ( x , y ) = h ( x , y ) × 2 π × ( n i 1 ) λ i = h ( x , y ) × 2 π × 1 λ e i ,
h ( x , y ) = φ s ( x , y ) 2 π × λ e 1 λ e 2 λ e 1 λ e 2 = φ s ( x , y ) 2 π × λ s .

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