## On-chip differential interference contrast microscopy using lensless digital holography

Optics Express, Vol. 18, Issue 5, pp. 4717-4726 (2010)

http://dx.doi.org/10.1364/OE.18.004717

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### Abstract

We introduce the use of a birefringent crystal with lensless digital holography to create an on-chip differential interference contrast (DIC) microscope. Using an incoherent source with a large aperture, in-line holograms of micro-objects are created, which interact with a uniaxial crystal and an absorbing polarizer, encoding differential interference contrast information of the objects on the chip. Despite the fact that a unit fringe magnification and an incoherent source with a large aperture have been used, holographic digital processing of such holograms rapidly recovers the differential phase contrast image of the specimen over a large field-of-view of ~24 mm^{2}.

© 2010 OSA

## 1. Introduction

1. F. Zernike, “Phase-contrast, a new method for microscopic observation of transparent objects. Part II,” Physica **9**(10), 974–986 (1942). [CrossRef]

1. F. Zernike, “Phase-contrast, a new method for microscopic observation of transparent objects. Part II,” Physica **9**(10), 974–986 (1942). [CrossRef]

4. X. Cui, M. Lew, and C. Yang, “Quantitative differential interference contrast microscopy based on structured-aperture interference,” Appl. Phys. Lett. **93**(9), 091113 (2008). [CrossRef]

5. E. D. Barone-Nugent, A. Barty, and K. A. Nugent, “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. **206**(3), 194–203 (2002). [CrossRef] [PubMed]

^{2}. Unlike digital reconstruction based holographic DIC approaches discussed above, the use of a thin birefringent crystal physically creates differential interference holograms at the sensor plane that encode the spatial phase variation of the sample into amplitude oscillations. This modulation process can be physically controlled by varying the crystal thickness, independent of the spatial resolution of the holographic system. In addition, as we will further illustrate with experimental results, this DIC amplitude modulation with a sub-pixel physical shear distance leads to enhancement in contrast and sharpness of the reconstructed holographic images. Another important difference in the presented DIC approach is that it does not utilize any lenses, coherent sources such as lasers or any mechanical scanning.

12. G. Sirat and D. Psaltis, “Conoscopic holography,” Opt. Lett. **10**(1), 4–6 (1985). [CrossRef] [PubMed]

13. K. Buse and M. Luennemann, “3D imaging: wave front sensing utilizing a birefringent crystal,” Phys. Rev. Lett. **85**(16), 3385–3387 (2000). [CrossRef] [PubMed]

## 2. Lensless on-chip microscopy based on incoherent digital holography

*D*~ 100

*λ*– see Fig. 1 ) which creates a limited coherence diameter (

*R*

_{C}) at the object plane (such that

*R*

_{C}

^{2}<< FOV). In practice, the finite physical distance between the incoherent source and the aperture would create partial coherence at the aperture plane to effectively increase

*R*

_{C}at the object plane. However, this partial spatial coherence at the aperture plane is not a requirement for our recording geometry (Fig. 1). In other words, even if a perfectly incoherent field filled the large aperture, the free space propagation between the aperture and the object planes would create a sufficiently large spatial coherence diameter for each micro-object within the imaging field-of-view. The advantages of such a large incoherent aperture are several folds: (i) it permits significant reduction of the speckle noise; (ii) the undesired coherent cross-talk among micro-objects of the same FOV is greatly reduced; and (iii) the light throughput of the aperture is significantly increased making the alignment of the in-line holographic imaging system much simpler.

*F*) of >5-10 [14

14. W. Haddad, D. Cullen, H. Solem, J. Longworth, A. McPherson, K. Boyer, and C. Rhodes, “Fourier-transform holographic microscopy,” Appl. Opt. **31**(24), 4973–4978 (1992). [CrossRef] [PubMed]

18. J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Immersion digital in-line holographic microscopy,” Opt. Lett. **31**(9), 1211–1213 (2006). [CrossRef] [PubMed]

*F*≈1) by placing the sample plane much closer to the sensor array than to the incoherent source [i.e.,

*z*

_{1}>>

*z*

_{2}and

*F*= (

*z*

_{1}+

*z*

_{2})/

*z*

_{1}≈1, see Fig. 1(a)]. With this hologram recording geometry, the large aperture of the incoherent source now gets scaled at the sensor plane by a demagnification factor of

*M*=

*z*

_{1}/

*z*

_{2}, which is typically ~100, eliminating the limiting effect of the large incoherent aperture on spatial resolution. To be more precise, under spatially incoherent illumination as in Fig. 1, it can be theoretically shown that a de-magnified (by

*M*fold) version of the aperture function is convolving the holographic diffraction terms at the sensor array, and since in our recording geometry we utilize

*M*~100, the filtering effect of a large aperture function on spatial frequency content of the holographic diffraction terms is almost entirely removed. The same choice (

*M*>> 1 and

*F*≈ 1) also permits us to image a significantly larger FOV claiming the entire digital sensor area as our microscopic imaging FOV.

14. W. Haddad, D. Cullen, H. Solem, J. Longworth, A. McPherson, K. Boyer, and C. Rhodes, “Fourier-transform holographic microscopy,” Appl. Opt. **31**(24), 4973–4978 (1992). [CrossRef] [PubMed]

15. W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. **98**(20), 11301–11305 (2001). [CrossRef] [PubMed]

18. J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Immersion digital in-line holographic microscopy,” Opt. Lett. **31**(9), 1211–1213 (2006). [CrossRef] [PubMed]

*F*, which enables successful recording of fringes that carry high spatial frequencies (over a smaller sample FOV that is now reduced by ~

*F*

^{2}when compared to the sensor area). For instance, by using a high-index oil (

*n*= 1.5) to replace air, together with

*F*> 35, it is feasible to achieve sub-micron resolution at ~500 nm illumination with lensless digital in-line holography [18

18. J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Immersion digital in-line holographic microscopy,” Opt. Lett. **31**(9), 1211–1213 (2006). [CrossRef] [PubMed]

*F*~1 and a large incoherent aperture of ~50 µm, we manage to achieve sub-pixel spatial resolution (<1.5 μm with

*λ*~ 470 nm and a pixel size of 2.2 μm – see Suppl. Figures 5 -7 in Appendix) through iterative processing of the acquired holograms without any paraxial approximations.

## 3. Differential interference contrast (DIC) imaging using incoherent lensfree holography

*z*

_{2}(typically ~1 mm). To achieve differential interference contrast imaging, a thin birefringent crystal (e.g., ~180 μm thick quartz plate), whose optic axis is at 45° with respect to the propagation direction (

*z*-axis), is inserted underneath the object plane as shown in Figs. 1(a), 1(b). In the following analysis, we will only consider normal incidence to the birefringent crystal and ignore the angular spectrum of the complex field entering the crystal, which will be left as a topic to further expand in the next Section #4. As a result of the double-refraction phenomenon, as soon as the complex object wavefronts enter the crystal, they split into two components corresponding to the

*ordinary*and the

*extra-ordinary*waves, which have orthogonal polarizations. At the exit of the crystal, these two complex wavefronts propagate parallel to each other with a lateral shift (

*δ*), also known as the shear distance in conventional DIC microscopy. Since the effective coherence diameter at the object plane is much larger than the shear distance, these two waves are coherent to each other but they carry information of slightly different points of the object, which leads to the differential interference contrast operation. Two aligned polarizers (i.e., parallel or crossed linear polarizers) are used to create interference between these two orthogonal waves. The hologram as a result of this interference is sampled by the digital sensor array. The reconstructed image of this digital hologram, under appropriate imaging conditions, contains the differential phase contrast information of the sample.

*x*-

*z*plane, aligned at 45° with respect to the

*z*-axis (Fig. 1), it experiences double refraction as a result of which the two orthogonal polarization components are split by a small shear distance, i.e.,

*n*and

_{o}*n*are the ordinary and extra-ordinary indices of refraction, respectively, and

_{e}*t*is the thickness of the crystal plate. Without loss of generality, we will limit our derivations to positive birefringent crystals where

*n*>

_{e}*n*. After the crystal plate, the outgoing wave can be written as:

_{o}*z*=

*z*

_{1}defines the exit plane of the crystal,

*λ*is the wavelength of light, and

*OPD*is the optical path length difference between the ordinary and extraordinary waves, given by

*δ*, and their interference encodes the spatial phase variation of the sample into amplitude oscillations.

*x*-axis in the

*x*-

*y*plane [see Fig. 1(a)]. If the object is mainly a phase object, i.e.,

*z*=

*z*

_{2}) becomes:

*x*and

*x*-

*δ*) of the complex wavefronts. For achieving maximum differential phase contrast, the effect of the phase bias term (

*φ*) should be minimized. For this end, let us first consider

_{bias}*φ*= 2

_{bias}*m*π where

*m*is an integer and assume that a crossed-polarizer configuration (i.e.,

*ϕ*= 45°) is used. Under these hologram recording conditions and for small phase differences i.e., Δ

*φ*<<1 (cos(Δ

*φ*) ≈1 − Δ

*φ*

^{2}/2), the amplitude of the resulting complex wavefront can be written as: Equation (1) indicates that the detected amplitude at the sensor plane is linearly proportional to the differential phase information (Δ

*φ*) of the micro-object. Similarly, the same conclusion can also be reached with a

*parallel-polarizer configuration*(i.e.,

*ϕ*= −45°) when

*φ*= (2

_{bias}*m*+1)π. Therefore, crossed- and parallel-polarizer configurations can be made equivalent to each other (in terms of DIC performance) depending on the phase bias term.

*φ*is minimized. This phase bias, however, can be canceled by stacking two identical birefringent crystal plates at 90° with respect to each other. For such a double crystal configuration, the same optimum DIC operation can be achieved over a wide range of wavelengths. A minor disadvantage of this approach is an increase in the total crystal length, which then increases the shear distance by 2.

_{bias}## 4. Experimental results and discussions

^{2}. For the light source, we utilized a monochromator with a Xenon lamp (Cornerstone T260, Newport Corp.) with a spectral bandwidth (FWHM) of ~15-20 nm. The light from the monochromator was filtered by a 50 μm diameter pinhole, which was placed at ~10 cm above the sample surface. The objects were placed ~1 mm away from the active sensor area such that

*M*~100 and

*F*~1.

^{2}and the reconstructed DIC images at different areas within this FOV.

*C. elegans*samples as illustrated in Fig. 4 . In this figure, we also compared the reconstructed DIC images of the samples against regular holographic images that are obtained with the same setup [Fig. 1(a)], but this time

*without*the use of any polarizers or the birefringent crystal. This figure clearly shows the increased contrast for the fine features of the DIC images [Figs. 4(b), 4(e)] when compared to the regular lensfree images [Figs. 4(c), 4(f)] of the same specimen.

19. G. C. Sherman, “Application of the convolution theorem to Rayleigh’s integral formulas,” J. Opt. Soc. Am. **57**(4), 546–547 (1967). [CrossRef] [PubMed]

21. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. **3**(1), 27–29 (1978). [CrossRef] [PubMed]

*δ*and Δ

*φ*are sensitive to the incident angle (

_{bias}*θ*) of the fields that make up the object wavefront. Next, we would like to better understand this angular dependency of the DIC term, and its impact for image quality. For simplicity, we limit our discussions to the case where the optic axis of the crystal lies in the plane of incidence. This is a valid assumption since both

_{i}*δ*and Δ

*φ*are most sensitive to the incident angle in this direction. Under this assumption, both

_{bias}*δ*and the DC field intensity (

*I*~1−cos(Δ

_{DC}*φ*)) can be analytically expressed as a function of

_{bias}*θ*[22

_{i}22. M. Avendaño-Alejo and M. Rosete-Aguilar, “Optical path difference in a plane-parallel uniaxial plate,” J. Opt. Soc. Am. A **23**(4), 926–932 (2006). [CrossRef]

*θ*on the shear distance and the strength of the DC term for our hologram recording geometry. Since our holograms are effectively recorded with

_{i}*F*≈1, the DIC image distortion that is caused by such an angular dependency is relatively reduced which is an important reason why our DIC image quality remains quite well across the entire sensor FOV of ~24 mm

^{2}as also indicated in Fig. 3.

## 5. Conclusions

^{2}) constituting ~10 fold improvement over a conventional 10X objective lens. Despite these advantages, the finite pixel size of the sensor array limits our spatial resolution to be <~1.5 µm at ~470 nm illumination for a pixel size of 2.2µm.

## Acknowledgements

## References and Links

1. | F. Zernike, “Phase-contrast, a new method for microscopic observation of transparent objects. Part II,” Physica |

2. | G. Nomarski, “Differential microinterferometer with polarized light,” J. Phys. Radium |

3. | M. Pluta, |

4. | X. Cui, M. Lew, and C. Yang, “Quantitative differential interference contrast microscopy based on structured-aperture interference,” Appl. Phys. Lett. |

5. | E. D. Barone-Nugent, A. Barty, and K. A. Nugent, “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. |

6. | P. Ferraro, D. Alferi, S. De Nicola, L. De Petrocellis, A. Finizio, and G. Pierattini, “Quantitative phase-contrast microscopy by a lateral shear approach to digital holographic image reconstruction,” Opt. Lett. |

7. | G. Popescu, Y. K. Park, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Diffraction phase and fluorescence microscopy,” Opt. Express |

8. | N. Lue, W. Choi, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Quantitative phase imaging of live cells using fast Fourier phase microscopy,” Appl. Opt. |

9. | S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express |

10. | C. Mann, L. Yu, C. M. Lo, and M. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express |

11. | G. Popescu, “Quantitative phase imaging of nanoscale cell structure and dynamics,” Methods in Cell Biology, Edited by B. Jena (Elsevier, 2008) |

12. | G. Sirat and D. Psaltis, “Conoscopic holography,” Opt. Lett. |

13. | K. Buse and M. Luennemann, “3D imaging: wave front sensing utilizing a birefringent crystal,” Phys. Rev. Lett. |

14. | W. Haddad, D. Cullen, H. Solem, J. Longworth, A. McPherson, K. Boyer, and C. Rhodes, “Fourier-transform holographic microscopy,” Appl. Opt. |

15. | W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. |

16. | G. Pedrini and H. Tiziani, “Short-coherence digital microscopy by use of a lensless holographic imaging system,” Appl. Opt. |

17. | L. Repetto, E. Piano, and C. Pontiggia, “Lensless digital holographic microscope with light-emitting diode illumination,” Opt. Lett. |

18. | J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Immersion digital in-line holographic microscopy,” Opt. Lett. |

19. | G. C. Sherman, “Application of the convolution theorem to Rayleigh’s integral formulas,” J. Opt. Soc. Am. |

20. | G. Situ and J. T. Sheridan, “Holography: an interpretation from the phase-space point of view,” Opt. Lett. |

21. | J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. |

22. | M. Avendaño-Alejo and M. Rosete-Aguilar, “Optical path difference in a plane-parallel uniaxial plate,” J. Opt. Soc. Am. A |

**OCIS Codes**

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(180.3170) Microscopy : Interference microscopy

(090.1995) Holography : Digital holography

**ToC Category:**

Microscopy

**History**

Original Manuscript: January 11, 2010

Revised Manuscript: February 6, 2010

Manuscript Accepted: February 9, 2010

Published: February 22, 2010

**Virtual Issues**

Vol. 5, Iss. 6 *Virtual Journal for Biomedical Optics*

**Citation**

Chulwoo Oh, Serhan O. Isikman, Bahar Khademhosseinieh, and Aydogan Ozcan, "On-chip differential interference contrast microscopy using lensless digital holography," Opt. Express **18**, 4717-4726 (2010)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-5-4717

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### References

- F. Zernike, “Phase-contrast, a new method for microscopic observation of transparent objects. Part II,” Physica 9(10), 974–986 (1942). [CrossRef]
- G. Nomarski, “Differential microinterferometer with polarized light,” J. Phys. Radium 16, 9s–13s (1955).
- M. Pluta, Specialized Methods, Vol. 2 of Advanced light microscopy (Elsevier, New York, 1989), Chap. 7.
- X. Cui, M. Lew, and C. Yang, “Quantitative differential interference contrast microscopy based on structured-aperture interference,” Appl. Phys. Lett. 93(9), 091113 (2008). [CrossRef]
- E. D. Barone-Nugent, A. Barty, and K. A. Nugent, “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. 206(3), 194–203 (2002). [CrossRef] [PubMed]
- P. Ferraro, D. Alferi, S. De Nicola, L. De Petrocellis, A. Finizio, and G. Pierattini, “Quantitative phase-contrast microscopy by a lateral shear approach to digital holographic image reconstruction,” Opt. Lett. 31(10), 1405–1407 (2006). [CrossRef] [PubMed]
- G. Popescu, Y. K. Park, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Diffraction phase and fluorescence microscopy,” Opt. Express 14(18), 8263–8268 (2006). [CrossRef] [PubMed]
- N. Lue, W. Choi, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Quantitative phase imaging of live cells using fast Fourier phase microscopy,” Appl. Opt. 46(10), 1836–1842 (2007). [CrossRef] [PubMed]
- S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006). [CrossRef] [PubMed]
- C. Mann, L. Yu, C. M. Lo, and M. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13(22), 8693–8698 (2005). [CrossRef] [PubMed]
- G. Popescu, “Quantitative phase imaging of nanoscale cell structure and dynamics,” Methods in Cell Biology, Edited by B. Jena (Elsevier, 2008)
- G. Sirat and D. Psaltis, “Conoscopic holography,” Opt. Lett. 10(1), 4–6 (1985). [CrossRef] [PubMed]
- K. Buse and M. Luennemann, “3D imaging: wave front sensing utilizing a birefringent crystal,” Phys. Rev. Lett. 85(16), 3385–3387 (2000). [CrossRef] [PubMed]
- W. Haddad, D. Cullen, H. Solem, J. Longworth, A. McPherson, K. Boyer, and C. Rhodes, “Fourier-transform holographic microscopy,” Appl. Opt. 31(24), 4973–4978 (1992). [CrossRef] [PubMed]
- W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, “Digital in-line holography for biological applications,” Proc. Natl. Acad. Sci. U.S.A. 98(20), 11301–11305 (2001). [CrossRef] [PubMed]
- G. Pedrini and H. Tiziani, “Short-coherence digital microscopy by use of a lensless holographic imaging system,” Appl. Opt. 41(22), 4489–4496 (2002). [CrossRef] [PubMed]
- L. Repetto, E. Piano, and C. Pontiggia, “Lensless digital holographic microscope with light-emitting diode illumination,” Opt. Lett. 29(10), 1132–1134 (2004). [CrossRef] [PubMed]
- J. Garcia-Sucerquia, W. Xu, M. H. Jericho, and H. J. Kreuzer, “Immersion digital in-line holographic microscopy,” Opt. Lett. 31(9), 1211–1213 (2006). [CrossRef] [PubMed]
- G. C. Sherman, “Application of the convolution theorem to Rayleigh’s integral formulas,” J. Opt. Soc. Am. 57(4), 546–547 (1967). [CrossRef] [PubMed]
- G. Situ and J. T. Sheridan, “Holography: an interpretation from the phase-space point of view,” Opt. Lett. 32(24), 3492–3494 (2007). [CrossRef] [PubMed]
- J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3(1), 27–29 (1978). [CrossRef] [PubMed]
- M. Avendaño-Alejo and M. Rosete-Aguilar, “Optical path difference in a plane-parallel uniaxial plate,” J. Opt. Soc. Am. A 23(4), 926–932 (2006). [CrossRef]

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