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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 6, Iss. 4 — May. 4, 2011
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Transflective digital holographic microscopy and its use for probing plasmonic light beaming

Yongjun Lim, Seung-Yeol Lee, and Byoungho Lee  »View Author Affiliations


Optics Express, Vol. 19, Issue 6, pp. 5202-5212 (2011)
http://dx.doi.org/10.1364/OE.19.005202


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Abstract

We present a novel digital holographic microscopy technique termed transflective digital holographic microscopy in order to probe plasmonic beaming fields and to view their platform structures. Here, we borrow the term, ‘transflective’, a portmanteau meaning a blend of transmission and reflection according to the light-collecting condition, which is conventionally used in liquid crystal display systems. Incorporating the transmission type holographic microscopy with the reflection type, achieved by the utilization of polarization property of coherent light waves, we propose an application of the system to probing the beam path and its corresponding structure in plasmonic beaming phenomena.

© 2011 OSA

1. Introduction

2. Fundamental concepts

Complex wavefront reconstruction is computationally performed in digital holographic microscopy, and the requisite numerical reconstruction methods have been widely suggested. Unlike conventional transmission mode and reflection mode activating independently, our TDHM follows the following relationships which are used in the polarization imaging by the use of digital holographic microscopy [22

22. T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41(1), 27–37 (2002). [CrossRef] [PubMed]

24

24. T. Colomb, F. Durr, E. Cuche, P. Marquet, H. G. Limberger, R. P. Salathe, and C. Depeursinge, “Polarization microscopy by use of digital holography: application to optical-fiber birefringence measurements,” Appl. Opt. 44(21), 4461–4469 (2005). [CrossRef] [PubMed]

].
IH=|ΨR+ΨOT+ΨOR|2=|ΨR|2+|ΨOT|2+|ΨOR|2+ΨRΨOT*+ΨR*ΨOT+ΨOTΨOR*+ΨOT*ΨOR+ΨRΨOR*+ΨR*ΨOR,
(1)
where ΨR, ΨOTand ΨOR are respectively the reference wave, the object wave from the transmission mode and the object wave from the reflection mode.

If two object waves, ΨOTand ΨOR, are orthogonal to each other, the following relation is valid:
ΨOTΨOR=0,
(2)
which means two orthogonally polarized light do not interfere with each other. Accordingly, two terms indicating the interference between two object waves including the conjugate term of each object wave vanish as is shown below.

ΨOTΨOR+ΨOTΨOR=0.
(3)

Hence, Eq. (1) can be simply arranged as follows.
IH=|ΨR|2+|ΨOT|2+|ΨOR|2+ΨRΨOT+ΨRΨOT+ΨRΨOR+ΨRΨOR       =|ΨR|2+|ΨOT|2+|ΨOR|2+ΨR(ΨOT+ΨOR)+ΨR(ΨOT+ΨOR),
(4)
where IH denotes the intensity of the recorded hologram on the CCD. From the above Eq. (4), it can be concluded that the recorded hologram excludes the interference between two object waves, and the conventional procedure is adopted to reconstruct the hologram. After the hologram intensity is captured by the CCD, the wavefront of the objective wave is reconstructed by a numerical method. Though several methods have been suggested to suppress or to effectively efface the quadratic DC term, we adopt phase shifting interferometry [39

39. T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography,” Opt. Lett. 23(15), 1221–1223 (1998). [CrossRef]

43

43. J. Hahn, H. Kim, Y. Lim, E. Kim, and B. Lee, “Spatial phase-shifting interferometry with compensation of geometric errors based on genetic algorithm,” Chin. Opt. Lett. 7(12), 1113–1116 (2009). [CrossRef]

]. By referring to the previously shown methods in the polarization microscopy with phase-shifting interferometry configuration, Jones matrix formalism is applied to our numerical reconstruction relationships represented as follows.

ΨR=(Exexp(iϕx(x,y))Eyexp(iϕy(x,y))),
(5)
ΨOT=(0EOTexp[iϕOT(x,y)]),
(6)
ΨOR=(EORexp[iϕOR(x,y)]0).
(7)

Hence, the resultant interference intensity pattern recorded by the CCD is written as follows.
IH(x,y)=ER2+EOT2+EOR2+2Re{ExEORexp(ΔX)}+2Re{EyEOTexp(ΔY)},
(8)
where
ER2=Ex2+Ey2,
(9)
ΔX=ϕx(x,y)ϕOR(x,y),
(10)
and

ΔY=ϕy(x,y)ϕOT(x,y).
(11)

Here, we assume that Ex2=Ey2. Consequently, with the 4-step phase-shifting interferometer, the object wave can be derived from the four different images with relative phase shift of π/2in tandem, and the resultant object wave at the CCD plane, ΨS(x,y), is given as follows:
ΨS(x,y)=14ΨR*[IH1IH3+j(IH4IH2)],
(12)
where IHi (i=1, 2, 3, 4) means IH in Eq. (4) with relevant phase shifts in reference beam. By adopting Fresnel transformation, the resultant object wave at the image plane, ΨRE(u,v,z), is given as follows.

ΨRE(u,v,z)=ΨS(x,y)exp(jkz)exp[ik2z{(ux)2+(vy)2}]dxdy..
(13)

In addition, as we adopt off-axis geometry, the additional phase terms are added in Eqs. (10) and (11) and we apply an experimentally-detected reference wave rather than a digitally-given reference wave to Eq. (13). In frequency domain, we can arrange Eq. (13) as the following form while taking convolution algorithm into our considerations.
F.T.[ΨRE(u,v)]=F.T.[ΨS(x,y)]H(fx,fy),
(14)
where F.T. stands for Fourier transform. Numerical methods for retrieving the recorded wavefront are required as long as the above Fresnel integral formula, Eq. (13) is related, and we use the following reconstruction algorithm appropriate for relatively short distance range. If we regard UREand Uare respectively Fourier transform of ΨRE and ΨS, the following relationship can be adopted [6

6. F. Zhang, I. Yamaguchi, and L. P. Yaroslavsky, “Algorithm for reconstruction of digital holograms with adjustable magnification,” Opt. Lett. 29(14), 1668–1670 (2004). [CrossRef] [PubMed]

, 8

8. F. Zhang, G. Pedrini, and W. Osten, “Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution,” Opt. Lett. 31(11), 1633–1635 (2006). [CrossRef] [PubMed]

].
URE(fx,fy;s,t;z0)=m,n=U(fxmΔx,fynΔy;0)H(fxmΔx,fynΔy;s,t;z0)+m,n=U(fxmΔx,fynΔy;0)p,q=pm;qnH(fxpΔx,fyqΔy;s,t;z0),
(15)
where

H(fx,fy;s,t;d)=exp[i2π(fxs+fyt)]exp[i2πdλ(1λ2fx2λ2fy2)1/2].
(16)

3. Experiments

In Fig. 1
Fig. 1 Schematic diagram for the proposed TDHM.
, the schematic diagram for the proposed TDHM configuration is shown. As is shown in Fig. 1, the p-polarized light wave passing through the collimation optics configuration is firstly separated in two ways. One is the reference arm, and the other is the signal arm. At the beam splitter (B.S.) 2, the signal beam is split into the transmission-mode path and the reflection-mode path. And then, the p-polarized light illuminates the rear-side of the object at the transmission-mode path, and the s-polarized light used as a reflection light source is shown-up after passing through the half wave retarder placed in the reflection mode path. Hence, two orthogonally polarized light waves illuminate the rear side and the front side of the target object, respectively. In the reference arm, the circularly polarized light reaches the CCD after being reflected from the piezo-electric driven mirror. Consequently, two orthogonal linearly-polarized light waves and one circularly polarized light contribute to the resultant interference pattern which is to be captured by the CCD.

In our experiment, an Nd:YAG laser with a wavelength of 532 nm (Verdi, Coherent Corp.) is used as the light source. An XYZ-38 made by Piezosystem Jena is used as the piezo-electric driven stage for the phase shifter, and a SONY XCD-SX90 with 1280 (horizontal) × 960 (vertical) pixels is used as the CCD, each pixel size of which is 3.75 μm × 3.75 μm. Two SIGMA KOKI 65GR mechanical shutters are used to automatically block the signal waves depending on each activating-mode. In other words, the shutter 1 is open for the transmission mode, the shutter 2 is open for the reflection mode and both of them are open for the transflective mode. An Olympus BXFM is used for the microscopy, and a 100× LMPlanLN with numerical aperture of 0.85 is used as the microscope objective. The resultant field of view at the CCD plane is 24 μm(horizontal) × 18 μm(vertical). To experimentally verify our proposed TDHM, the conventional USAF target pattern is used, the minimum resolution of which is 228 lp/mm. According to the light-illumination mode, the detected object wavefronts are properly retrieved. In Fig. 2
Fig. 2 Experimental verification of TDHM using conventional USAF test target images. The amplitude image acquired by (a) the reflection mode, (b) the transmission mode, and (c) the transflective mode. The phase images obtained by (d) the reflection mode, (e) the transmission mode, and (f) the transflective mode.
, the retrieved images are shown according to each operating-mode. Figure 2(a), (b) and (c) are retrieved amplitude images of the transmission mode, reflection mode and transmission mode respectively, and Fig. 2(d), (e), and (f) are retrieved phase images of the transmission mode, reflection mode and transflective mode, respectively. As is shown by Fig. 2(c), the amplitude image acquired by the transflective mode contains the boundary line of the inscribed pattern. Even though unwanted phase aberration appears due to the small path-difference between two objective waves and the tilt of the target image, conventional methods can be used to compensate for these aberration-oriented problems. We use the negative lens in the reference arm before the beam splitter 4 as is seen in Fig. 1. As is seen in Fig. 2, our proposed concept is verified, and the transflective mode can provide both the transmitted and reflected wavefronts simultaneously. In Fig. 2(c), the amplitude image shows the distinct boundary line between the opaque area (surface of the USAF-1951 test target) and the transparent area. Due to the orthogonal property of two object waves, the retrieved amplitude image contains the optical information simultaneously given by the transmitted light (p-polarized) and the reflected light (s-polarized). Based on this fundamental experiment regarding our proposed TDHM, we use the TDHM to probe the optical far-field distribution of plasmonic light beaming phenomena and to view their platform structures in the following section.

4. Application for plasmonic light beaming phenomena

In Fig. 4
Fig. 4 Numerically calculated results for plasmonic light beaming depending on the number of inscribed slits in the Ag layer. The intensity distribution on the x-z plane when the number of slits is (a) 5, (b) 7, and (c) 9.
, the numerically calculated results are shown, and the number of slits inserted in the thin metal film in Fig. 4(a), (b) and (c) is 5, 7 and 9, respectively. As is seen in Fig. 4, the number of slits that are inserted in the silver layer affects the intensity distribution at the optical far-field regions. To identify these beam patterns and to view the difference between those constituting structures, our proposed TDHM is used. We use focused ion beam machining (Quanta 200 3D, FEI Corp.) to inscribe the narrow metal slit array structures after depositing a 500 nm Ag layer on the SiO2 substrate, and the SEM images of the fabricated structures are shown in Figs. 5(a), (b) and (c)
Fig. 5 (a), (b) and (c) are SEM images of the fabricated metal slit array structures. (d), (e) and (f) are retrieved surface images obtained by the reflection mode. (g), (h) and (i) are x-z plane images showing the intensity distributions of plasmonic light beaming detected by the transmission mode. (j), (k) and (l) are amplitude images concurrently showing the optical beaming and the corresponding structure, obtained by the transflective mode.
. As we are interested in optical field distributions and the images of the platforms structures, amplitude images are mainly retrieved as is shown in Figs. 5(d) through (l). Reconstructed images regarding the corresponding surface structure are given by the reflection mode, which are shown in Figs. 5(d), (e) and (f). Here, structures between each slit are not clearly shown because of the aliasing caused by the inherent diffraction limit of the system, i.e. the resolution limit of the microscope objective. However, it is expected that recently proposed concepts on improving resolution limits are expected to be adopted [47

47. C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143 (2002). [CrossRef]

49

49. M. Paturzo, F. Merola, S. Grilli, S. De Nicola, A. Finizio, and P. Ferraro, “Super-resolution in digital holography by a two-dimensional dynamic phase grating,” Opt. Express 16(21), 17107–17118 (2008). [CrossRef] [PubMed]

].

The beam-paths or the intensity distributions on the x-z plane acquired by the transmission-mode configuration are shown in Figs. 5(g), (h) and (i), respectively, and the retrieved images simultaneously showing the beams and the corresponding structures based on TDHM are shown in Figs. 5(j), (k) and (l). Figures 5(j) through (l) provide the optical information regarding the fabricated slit structures and optical field distributions centered around them at the same time. We clearly observe the generated beaming field emanating from the center of the fabricated metal slit array structures. This is the featuring property of our proposed TDHM in that two orthogonal waves can be retrieved at the same time. Due to this characteristic, we can identify that the generated beaming fields are distributed along the center of the fabricated slit array structures, while perceiving the boundary line between the fabricated structure and the surface of the silver film. In addition, we can observe that the generated plasmonic beaming field is different from one another and gradually increases according to the number of carved slits through our experimental results shown in Figs. 5(d) through (l). Compared to theoretical values, errors on fabrication such as surface damage caused by focused ion beam milling and roughness on the silver film during e-beam evaporation process mainly affect the radiation field at the exit region of each slit. Hence, the experimental results are not perfectly matched with those numerical ones. Additionally, as we use temporal phase shifting interferometry, errors such as intensity fluctuation of the light source, aberration of optics, unwanted multiple reflections of optics and vibration cause unwanted noises during holographic measurement process. Though we do not take into account those errors to improve numerical analysis results, we observe good agreement between numerical results and experimental results Figs. 5(g) through (i).

5. Conclusions and discussions

Acknowledgment

The authors wish to acknowledge the support of the National Research Foundation and the Ministry of Education, Science and Technology of Korea through the Creative Research Initiative Program (Active Plasmonics Application Systems).

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J. Hahn, H. Kim, S. W. Cho, and B. Lee, “Phase-shifting interferometry with genetic algorithm-based twin image noise elimination,” Appl. Opt. 47(22), 4068–4076 (2008). [CrossRef] [PubMed]

43.

J. Hahn, H. Kim, Y. Lim, E. Kim, and B. Lee, “Spatial phase-shifting interferometry with compensation of geometric errors based on genetic algorithm,” Chin. Opt. Lett. 7(12), 1113–1116 (2009). [CrossRef]

44.

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46.

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47.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143 (2002). [CrossRef]

48.

V. Mico, Z. Zalevsky, C. Ferreira, and J. García, “Superresolution digital holographic microscopy for three-dimensional samples,” Opt. Express 16(23), 19260–19270 (2008). [CrossRef]

49.

M. Paturzo, F. Merola, S. Grilli, S. De Nicola, A. Finizio, and P. Ferraro, “Super-resolution in digital holography by a two-dimensional dynamic phase grating,” Opt. Express 16(21), 17107–17118 (2008). [CrossRef] [PubMed]

OCIS Codes
(110.0180) Imaging systems : Microscopy
(090.1995) Holography : Digital holography

ToC Category:
Microscopy

History
Original Manuscript: November 17, 2010
Revised Manuscript: January 17, 2011
Manuscript Accepted: February 23, 2011
Published: March 4, 2011

Virtual Issues
Vol. 6, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Yongjun Lim, Seung-Yeol Lee, and Byoungho Lee, "Transflective digital holographic microscopy and its use for probing plasmonic light beaming," Opt. Express 19, 5202-5212 (2011)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-6-5202


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References

  1. R. Vanligten and H. Osterberg, “Holographic microscopy,” Nature 211(5046), 282–283 (1966). [CrossRef]
  2. U. Schnars and W. Juptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33(2), 179–181 (1994). [CrossRef] [PubMed]
  3. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24(5), 291–293 (1999). [CrossRef]
  4. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38(34), 6994–7001 (1999). [CrossRef]
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