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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 3 — Feb. 11, 2013
  • pp: 2890–2902

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Complex wavefront shaping for optimal depth-selective focusing in optical coherence tomography

Jaeduck Jang, Jaeguyn Lim, Hyeonseung Yu, Hyun Choi, Jinyong Ha, Jung-Hoon Park, Wang-Yuhl Oh, Wooyoung Jang, SeongDeok Lee, and YongKeun Park  »View Author Affiliations


Optics Express, Vol. 21, Issue 3, pp. 2890-2902 (2013)
http://dx.doi.org/10.1364/OE.21.002890


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Abstract

We report on an approach to exploit multiple light scattering by shaping the incident wavefront in optical coherence tomography (OCT). Most of the reflected signal from biological tissue consists of multiply scattered light, which is regarded as noise in OCT. A digital mirror device (DMD) is utilized to shape the incident wavefront such that the maximal energy is focused at a specific depth in a highly scattering sample using a coherence-gated reflectance signal as feedback. The proof-of-concept experiment demonstrates that this approach enhances depth-selective focusing in the presence of optical inhomogeneity, and thus extends the penetration depth in spectral domain-OCT (SD-OCT).

© 2013 OSA

1. Introduction

Optical coherence tomography (OCT) plays an important role in the diagnosis of medical problems [1

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

], including ophthalmology [2

N. Nassif, B. Cense, B. Hyle Park, S. H. Yun, T. C. Chen, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography,” Opt. Lett. 29(5), 480–482 (2004). [CrossRef] [PubMed]

] and cardiology [3

I. K. Jang, B. E. Bouma, D. H. Kang, S. J. Park, S. W. Park, K. B. Seung, K. B. Choi, M. Shishkov, K. Schlendorf, E. Pomerantsev, S. L. Houser, H. T. Aretz, and G. J. Tearney, “Visualization of coronary atherosclerotic plaques in patients using optical coherence tomography: comparison with intravascular ultrasound,” J. Am. Coll. Cardiol. 39(4), 604–609 (2002). [CrossRef] [PubMed]

], due to its non-invasive and in-vivo imaging capabilities. OCT is based on low-coherence interferometry where only the single-backscattered light in tissue is regarded as a signal [1

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

,4

M. Bashkansky and J. Reintjes, “Statistics and reduction of speckle in optical coherence tomography,” Opt. Lett. 25(8), 545–547 (2000). [CrossRef] [PubMed]

]. OCT systems typically provide penetration depths of 2–3 mm depending on the optical properties of the target sample. In ophthalmology, the tissue structures are relatively transparent (i.e. there is a low probability for multiple scattering events), and the OCT system can achieve high penetration depth. However, the penetration depth of OCT for other non-transparent, highly turbid tissues is seriously limited by the scattering properties of the tissue such as skin [5

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1205–1215 (1999). [CrossRef]

–7

J. G. Fujimoto, C. Pitris, S. A. Boppart, and M. E. Brezinski, “Optical coherence tomography: an emerging technology for biomedical imaging and optical biopsy,” Neoplasia 2(1/2), 9–25 (2000). [CrossRef] [PubMed]

]. Attempts to image highly scattering biological tissue such as skin have been impeded by limitations due to multiple light scattering. Light propagation through optically inhomogeneous media inevitably yields multiple scattering, and thus only a very small fraction of the measured OCT signal originates from single back scattering. This results in a low signal-to-noise ratio (SNR) and limited penetration depth in deep tissue imaging. Consequently, the penetration depth and sensitivity of current OCT techniques are limited by the turbidity of target samples. Simply increasing the system SNR cannot, however, solve the limited penetration depth in conventional OCT, since it will also amplify multiply scattered light.

One of the approaches for reducing multiple scattering in OCT is to use optical clearing agents [8

S. Proskurin and I. Meglinski, “Optical coherence tomography imaging depth enhancement by superficial skin optical clearing,” Laser Phys. Lett. 4(11), 824–826 (2007). [CrossRef]

]. The use of optical clearing agents such as glucose or glycerol temporally reduces the refractive index inhomogeneity in tissues. However, this approach requires long settling time after the addition of agents (~10 min) and is only effective at the superficial layers of the tissue structure. Other attempts include spatial and frequency compounding methods [4

M. Bashkansky and J. Reintjes, “Statistics and reduction of speckle in optical coherence tomography,” Opt. Lett. 25(8), 545–547 (2000). [CrossRef] [PubMed]

,9

A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography images using digital filtering,” J. Opt. Soc. Am. A 24(7), 1901–1910 (2007). [CrossRef] [PubMed]

–17

A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. Motaghiannezam, G. J. Tearney, and B. E. Bouma, “Angle-resolved optical coherence tomography with sequential angular selectivity for speckle reduction,” Opt. Express 15(10), 6200–6209 (2007). [CrossRef] [PubMed]

]. These methods acquire multiple uncorrelated OCT measurements using slightly translated beam paths or multiple wavelength sources but only suppress the background noise at a certain depth. Wavefront correction methods by means of adaptive optics have also been applied in OCT [18

B. Hermann, E. J. Fernández, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, P. M. Prieto, and P. Artal, “Adaptive-optics ultrahigh-resolution optical coherence tomography,” Opt. Lett. 29(18), 2142–2144 (2004). [CrossRef] [PubMed]

–20

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006). [CrossRef] [PubMed]

], especially in ophthalmology [21

M. Pircher and R. J. Zawadzki, “Combining adaptive optics with optical coherence tomography: Unveiling the cellular structure of the human retina in vivo,” Expert Rev. Ophthalmol. 2(6), 1019–1035 (2007). [CrossRef]

]. However, they only correct the optical distortions (aberrations), not multiple scattering. Optical distortions can be compensated by low order spatial modes, but the multiple scattering can only be corrected using the full spatial frequency bandwidth.

In this paper, we propose and experimentally demonstrate a novel approach to control multiple scattering in spectral domain-OCT (SD-OCT) to achieve deeper penetration into the sample. This is the first demonstration of the application of turbidity control to an OCT system. Our approach, wherein a specific impinging wavefront is optimized and applied by utilizing a digital micro-mirror device (DMD), controls multiple scattering and focuses light deep into tissue, which allows increased penetration depth and enhanced SNR. We first show that OCT signals at specific depths can be selectively enhanced or annihilated with controlled incident wavefronts. With this principle, we demonstrate that a conventional SD-OCT can enhance energy delivery to a target point deep inside turbid media with the presented extension for wavefront shaping, and therefore can extend the maximal depth penetration further than existing approaches such as a conventional SD-OCT with a Gaussian beam illumination or a spatial compounding method.

2. Complex wavefront shaping in OCT

In conventional OCT, deteriorating effects arising from multiple light scattering in turbid biological tissue include the loss of signal, decreased resolution, and limited depth of penetration. In homogenous media [Fig. 1(a)], incident light can be focused onto a single point and the signal obtained upon reflection mostly comprises of single back scattered light from an object, which then provides the depth information of the object with low-coherent interference. However, realistic biological samples are optically inhomogeneous and cause significant amounts of multiple light scattering events [Fig. 1(b)]. The incident beam is scattered and scrambled into multiple random paths, resulting in a speckle field instead of focused light. This multiple scattering limits effective energy delivery into deep tissue and the generation of a light focus. In our approach, we apply a specifically shaped wavefront so that a constructive focus is generated at a target depth inside turbid media [Fig. 1(c)]. The phase of the incident beam is tuned so that the different optical paths are in phase at the target position. This phase matching condition for temporally low-coherence light automatically fulfills conditions for effective coherence gating, enabling direct application into conventional OCT systems.

Fig. 1 Experimental scheme for scattering control in turbid media. (a) Focusing through homogeneous media. (b) Multiple scattering in turbid media results in different scattering paths, which is detrimental in both light delivery to a specific point as well as coherence gating. (c) By shaping the impinging wavefront, different scattering paths can be phase matched to allow focusing deeper into tissue while satisfying the coherence gating condition at the same time

In principle, we incorporate wavefront shaping focusing in complex media [22

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012). [CrossRef]

] with an OCT system. Recently, control over multiple scattering in turbid media has been demonstrated by spatially modulating the wavefront of incident light [22

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012). [CrossRef]

,23

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007). [CrossRef] [PubMed]

]. These works have realized several methods to control multiple scattering rather than to avoid it. Among them, J. Aulbach and associates have demonstrated that spatial wavefront shaping of a low-coherence laser gives both spatial and temporal control over the scattered light [24

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106(10), 103901 (2011). [CrossRef] [PubMed]

].

Employing wavefront shaping in a SD-OCT system, we can control multiply scattered optical paths to focus light to an object located at a specific depth inside the turbid sample in the presence of optical inhomogeneity. The incident beam is modulated by binary control (amplitude modulation) in a DMD [25

D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express 19(5), 4017–4029 (2011). [CrossRef] [PubMed]

,26

D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20(2), 1733–1740 (2012). [CrossRef] [PubMed]

]. Although the DMD works as a binary amplitude modulator, each pixel of the DMD can be thought of as a point source by the Huygens-Fresnel principle, which results in modulation of both the amplitude and phase of the wavefront as a function of distance from the DMD.

Light propagation through turbid media is described by a transmission matrix T. To incorporate wavefront shaping using a DMD, we use the Hadamard basis hi to construct the optimized incident wavefront. The transmitted field in the sample Em can then be represented as a linear combination of the N different independent Hadamard bases and their phase ϕi multiplied by the elements tmn of the transmission matrix:

Em= ∑ n=1N t mn hn e j ϕn
(1)

To establish an effective focus at a target point (the mth output channel), all independent contributing bases (channels) should be phase-matched [constructive interference, Fig. 1(c)]; that is, the phases of all N input bases should satisfy
ϕn=−∠ t mn+α
(2)
where α is an arbitrary constant. This optimal phase value for each basis pattern can be found by changing the phase full cycle (0-2π) during the optimization procedure. We consider a full phase control by translating the pattern hi(x,y), i.e., by the translation property of the Fourier transform (FT) in both the x- and y-directions:
hi(x− x0,y− y0) ↔ FT Hi(u,v) e −j2π x0u e −j2π y0v
(3)
where u, v are spatial frequencies along x- and y-directions, respectively, and Hi(u,v) is the Fourier transform of hi(x,y). At the optimized phase shift (a lateral shift in the DMD plane) that delivers the maximum energy to the target point, the scattered light from the target object will also be at its maximum. Since wavefront shaping in the spatial domain can control spatiotemporal information of the scattered field [24

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106(10), 103901 (2011). [CrossRef] [PubMed]

,27

J. H. Park, C. H. Park, H. Yu, Y. H. Cho, and Y. K. Park, “Active spectral filtering through turbid media,” Opt. Lett. 37(15), 3261–3263 (2012). [CrossRef] [PubMed]

,28

E. Small, O. Katz, Y. Guan, and Y. Silberberg, “Spectral control of broadband light through random media by wavefront shaping,” Opt. Lett. 37(16), 3429–3431 (2012). [CrossRef]

], a corrected spatiotemporal focus can be generated inside complex media. Our strategy for finding the optimized phase for each basis is to use coherent-gated back scattered intensity in an OCT system as feedback, since the coherence-gated back scattered intensity must be proportional to the modulus square of the transmitted field in the sample ~|Em|2. This means that one can find the optimal wavefront to establish a focus at a specific depth using a coherence-gated reflectance signal, if a scattering object exists at the target point. Recently, M. Cui and associates applied the wavefront modulation technique for focusing into deep tissue based on coherence and confocal gating [29

R. Fiolka, K. Si, and M. Cui, “Complex wavefront corrections for deep tissue focusing using low coherence backscattered light,” Opt. Express 20(15), 16532–16543 (2012). [CrossRef]

], where the coherent-gated back scattered intensity was successfully used as a feedback signal for finding the complex optimized wavefront.

3. Experiments and results

3.1 Experimental setup

Our experimental setup of the wavefront controllable SD-OCT system using a DMD is shown in Fig. 2.

Fig. 2 Optical setup for wavefront controlled SD-OCT. A DMD and diffraction grating (G1) with a 4-f system (L1-L2) are added to a conventional SD-OCT system for wavefront shaping and dispersion compensation. L1 and L2 are 40 mm and 35 mm achromatic lenses, respectively.

A broadband super-luminescent diode (SLD-52, Superlum Diodes, Ltd., Ireland) with a center wavelength of 1025 nm, a full width at half maximum (FWHM, ∆λ) of 110 nm, and output power of 9.7 mW, which can provide a theoretical axial resolution of 4.2 μm in air, is used as the illuminating light source. The beam passes through an optical circulator OC and then a collimator C. The collimated beam impinges onto the DMD (0.7″ XGA, 1024 × 768, Texas Instruments, United States) surface, which is utilized for wavefront modulation of the incident beam. The DMD consists of about 800k micro-mirrors; each mirror can be independently controlled and switched between two configurations: 12° and −12° for the on and off states at a 17 kHz frame rate, respectively. We chose the 4th order diffraction beam at a center wavelength of 1025 nm for maximum diffraction efficiency of the DMD, where the maximum spatial frequency of 400 lines/mm can be controlled by the DMD. For dispersion compensation, the wavefront shaped beam reflected from the DMD is projected onto a diffraction grating G1 (300 lines/mm, GR25-0310, Thorlabs, Unites States), which is placed after a 4-f telescopic lens system.

The shaped beam then goes to a conventional SD-OCT system. A beam splitter BS divides the beam into a sample and a reference arm. The beam for the sample arm is first steered by a two-dimensional galvano mirror GM (6210H, Cambridge Technology, Unites States) and then impinges onto a sample through an × 5 objective lens (LSM03-BB, Thorlabs, United states). The beam for the reference arm passes through a dispersion compensator (LSM03DC, Thorlabs, United States), and is reflected by a mirror, M3.

The interference signal from the reference and sample arms is collected by a single-mode fiber and recorded by a spectrometer for SD-OCT measurement. Although a large fraction of the reference light is lost in the SMF, the use of SMF has following advantages in our system: (1) the SMF works as a spatial filter and OCT signal on the optical axis will be effectively corrected and (2) modal dispersion, expected in using a multi-mode fiber, can be ignored. We defer all theoretical and background discussion of the SD-OCT to the published literature [30

A. F. Fercher, “Optical coherence tomography,” J. Biomed. Opt. 1(2), 157–173 (1996). [CrossRef] [PubMed]

,31

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003). [CrossRef]

]. The spectrometer consists of a collimator lens C (0.24 NA, F810APC-1310, Thorlabs, United States), a transmission grating G2 (1200 lines/mm, Wasatch Photonics, United States), an achromatic doublet lens (L4) (100 mm, Thorlabs, United States), and a InGaAs line CCD (SU1024, 1024 lines, 92 kHz frame rate, Sensors Unlimited Inc., Unites States). The imaging range of our system is measured as 1.5 mm in air. Although we tried to achieve minimal energy loss in the optical system and to illuminate target samples with the maximum energy, we had to consider the energy loss in the DMD. Specifically, we measured the energy loss of 6 dB from multiple diffractions from the DMD and an additional 50% power loss from the wavefront shaping using binary amplitude modulation. Such losses reduce the SNR and the overall image quality.

3.2 Sample preparation

To demonstrate the feasibility of the proposed approach, we prepared two different tissue phantoms. The first sample is a weakly scattering sample, which was used to test the principle and the validity of the present method. The conventional B-scan OCT images of the sample are shown in Fig. 3(a). The sample consists of five layers. A scattering layer is made of 10 μm dia. polystyrene (PS) beads (72986Model #, Sigma Aldrich, United States) embedded in poly-dimethylsiloxane (PDMS, Sylgard 184, Dow Corning, United States), producing ~150 μm thickness. To achieve uniform thickness and appropriate scattering properties, we spin-coated a mixture of PDMS, a curing agent, and a bead solution of 3 ml, 0.3 ml, and 2.5 ml, respectively, at a speed of 4000 rpm. Finally, the first phantom was prepared by stacking transparent Scotch tape (I), the beads in 5 layers of PDMS (II), non-transparent Scotch tape (III), and a cover glass slide (IV). The second sample was used to demonstrate extended penetration depth [Fig. 5(a)]. We sequentially stacked 10 μm dia. PS beads embedded in PDMS (I), transparent tape (II), a lens cleaning paper (MC-5, Thorlabs, United States) (III), and an infra-red card (VRC2D1, Thorlabs, United States) (IV). The PS beads in the PDMS layer were prepared in a similar fashion as the first sample with a slower spin coating speed (2500 rpm). The third sample we used was a dried leaf of cherry blossom Prunus serrulata which has strong light scattering properties [Fig. 6(a)].

Fig. 3 Experimental results. (a) B-scan image for the 1st phantom which consists of transparent tape (I), PDMS mixed with 10 μm PS beads (II), non-transparent tape (III), cover glass (IV), and non-transparent tape (V). (b) and (c) For the yellow dotted line in (a), the maximized and minimized A-scan signals corresponding to the optimized wavefront (patterns #1-250 for each depth #1-250), respectively. (d) The patterns optimized for each depth (A, B, and C). Only 50 × 50 pixels at the center of 150 × 150 patterns were shown for visualization purposes.

The scattering properties of each layer used in the phantoms were characterized. The transport mean free paths (MFP) lt were obtained by measuring the total transmission as a function of thickness [32

J. Gómez Rivas, R. Sprik, C. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” EPL (Europhys. Lett.) 48(1), 22–28 (1999). [CrossRef]

]. The anisotropy factor g was measured by the light scattering intensity as a function of scattering angle. The scattering MFP ls were then calculated from lt and g, lt = ls /(1-g). For the first sample, the values for the scattering mean free paths (MFP) were measured as ls = 49.2 ± 3.4 (lt = 639.5 ± 43.9 μm, g = 0.923) and ls = 8.6 ± 0.5 (lt = 94.4 ± 5.6 μm, g = 0.909) for layer II and III, respectively. For the second sample, the MFPs were measured as ls = 72.9 ± 5.0 (lt = 767.4 ± 52.7 μm, g = 0.905) and ls = 9.1 ± 0.6 (lt = 55.5 ± 10.3 μm, g = 0.815) for layer I and III, respectively. For, the third sample, the MFPs were measured as ls = 2.71 ± 0.35 (lt = 15.6 ± 2.01 μm, g = 0.826)

3.3 Depth-specific light delivery using wavefront shaping

To demonstrate the principle of the present method, we first measured the phantom in which multiple scattering layers were sandwiched. The overall structure of the phantom was visualized by a single B-scan measured in a conventional SD-OCT configuration [Fig. 3(a)].

In order to find the optimal wavefront that generates a focus with maximum energy at a certain depth, we utilized 500 independent Hadamard basis patterns. While each pattern was applied onto the DMD and laterally translated by a full cycle (one period; 2π phase shift in Fourier space) in both the x- and y-directions by 5 sampling steps per one period for each direction (total 25 lateral shifts for each pattern), the SD-OCT signals were recorded. From the recorded signal set, an optimal phase shift value for each basis ϕn was found from the lateral shift that gives the greatest reflectance at the target depth, which satisfies the condition in Eq. (2). Once the set of optimal phase values were obtained for delivering maximal energy to a focus at each depth, the optimized wavefront fm could be synthetized by linearly superimposing each basis pattern with its according optimal phase value:

fm= ∑ n=1N hnexp ( j ϕn), where ϕn=−∠ t mn+α
(4)

By utilizing this relation for each targeted depth m of the A-scan, the optimized pattern for the entire range of the A-scan is calculated. The calculation takes ~0.06 seconds on a typical desktop computer (Intel Core i5-2500K, 3.3 GHz) for each depth m. The superimposed pattern was then binarized by thresholding with respect to half of the entire number of basis patterns (N/2) [26

D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20(2), 1733–1740 (2012). [CrossRef] [PubMed]

]:
dm= { 1,  fm>N/2 0,  fm≤N/2
(5)
The OCT system then re-acquired the images for the same target positions with the set of wavefronts that were optimized to generate a corrected focus at the target depth. We note that the power of the incident beam for each basis patterns remains almost constant, since we have the same number of on and off pixels of the DMD. In addition, the ratios of on and off pixels of the DMD were unchanged (45.5 ± 0.2%) for the optimized patterns for delivering the optimal light to different positions.

The results are shown in Fig. 3. For the proof-of-principle demonstration, we optimized one A-line scan indicated with a yellow dash-line [Fig. 3(a)]. Figure 3(b) shows the entire set of A-scan signals obtained with the set of optimized wavefronts; each wavefront was optimally shaped such that it will generate a corrected focus at a certain depth. For example, pattern #105 was optimally shaped so that an optimized focus could be formed at a depth index #105. Thus, the diagonal elements of Fig. 3(b) represent the optimized SD-OCT signals with wavefront shaping. Overall, the three dominant scattering layers (#30, #105, and #210) clearly show major structures of the sample. It is clearly shown that each scattering layer gives a significantly enhanced the SD-OCT signal along the diagonal line, which shows that the wavefront shaped by the DMD successfully delivers more energy at specific depth of the sample. Representative optimized patterns are shown in Fig. 3(d). The letters ‘A’, ‘B’, and ‘C’ represents the optimized pattern for three dominant scattering layers (#30, #105, and #210). The optimized patterns are highly randomized with features in high spatial modes. There is almost no correlation between the optimized patterns, which indicates that the incident wavefront pattern exploits and controls multiple light scattering in the turbid sample—and thus these features are not aberrations.

Interestingly, the minimum SD-OCT signals can also be obtained using the same principle. The phase values for each basis can be found such that destructive interference is generated at the target depth. It can thus be readily understood as the wavefront shaping is a linear coherent process, as described in Eq. (2). The SD-OCT signals obtained with the optimized patterns give the minimum transmitted field in the sample at a specific depth, as shown in Fig. 3(c). Compared with the maximized result in Fig. 3(b), the same approach could be applied in a reverse manner, where the collected signal can be minimized at target depths. The SD-OCT signals were significantly decreased along the diagonal line. These results with both the maximum and minimum transmission field clearly demonstrate that the wavefront shaping in the OCT system indeed fully controls multiple scattering inside turbid media.

For a quantitative analysis, we compare the results with conventional SD-OCT systems including the spatial compounding method (Fig. 4). We obtained the A-line scan profiles, denoted as the yellow line in Fig. 3(a), with three different methods: (1) the wavefront shaping method proposed in this study, (2) SD-OCT measurements with a random pattern, and (3) the spatial compounding method. The SD-OCT signal obtained with the present method is indicated as a red line in Fig. 4. The incident wavefronts were selectively optimized for a specific depth, as described above. The red line is identical to the SD-OCT signals along the diagonal elements in Fig. 3(b). The conventional SD-OCT measurement (gray dotted line) was obtained by applying a random pattern (randomly chosen from the Hadamard basis patterns) onto the DMD with comparable illumination energy as with the optimized patterns. The SD-OCT signals obtained with the spatial compounding method (black line) were retrieved by incoherently averaging SD-OCT signals measured with 10 different illumination patterns (randomly chosen from orthogonal Hadamard basis patterns) written onto the DMD. All the measurements were carried out in the same sample with same optical instrumentation.

Fig. 4 Signal enhancement in wavefront controlled OCT signal; red lines in the figures represent the enhanced signal due to the optimized wavefront at single back-scattering positions indicated by A, B, and C. Black solid and dotted lines represent spatial compounding and single measurement using a Hadamard basis pattern.

The OCT signals show the locations of three dominant scattering layers, indicated with the letters ‘A’, ‘B’, and ‘C’. However, significant speckle noise is also seen in the conventional OCT measurement. As is well known, the OCT signals obtained using the compounding method (black line) effectively reduce speckle noise signals and provide reflectance signals for the sample locations that are comparable with those derived with the single OCT measurement. In contrast, the SD-OCT signal obtained with wavefront shaping clearly demonstrates considerable enhancement in signal levels at the target depths. For the three dominant scattering layers indicated as ‘A’, ‘B’, and ‘C’, the signals were enhanced by approximately 1.65, 1.72, and 1.73 times, respectively, in comparison with the OCT using spatial compounding. The speckle noise was also significantly reduced, comparable to the decrease obtained with the spatial compounding method.

3.4 Increase of penetration depth

To address whether our method can extend the penetration depth of the OCT signal, we employed a sample that exhibits more multiple scattering than the sample used in Section 3.4. The sample consists of a combination of weakly and strongly scattering layers with a thickness larger than the imaging range in a conventional OCT measurement mode [Fig. 5(a)]. The sample images along the indicated line [yellow line in Fig. 5(a)] were measured with three different methods: (1) the wavefront shaping method proposed in this study, (2) SD-OCT measurements with a random pattern, and (3) the spatial compounding method. The results are shown in Fig. 5(b). The OCT signals at a shallow depth [down to ~300 µm in Fig. 5(b)] were well restored with all three different methods.

Fig. 5 Experimental results. (a) B-scan image for the 2nd phantom, which consists of PDMS mixed with 10 μm dia. PS beads (I), transparent tape (II), lens cleaning paper (III), and IR card (IV). (b) Reconstructed OCT signals of dotted yellow lines in (a). (c) The maximized A-scan signals corresponding to optimized wavefront for the yellow dotted line in (a). Increase in penetration depth can be seen by the detection of lens cleaning tissue layers depicted by the blue arrow.

However, beyond the depth of 300 µm in this sample, the conventional OCT techniques (both single OCT measurement and spatial compounding methods) do not measure significant signals; the measured OCT signals show very low SNR. In contrast, the present method—OCT with wavefront shaping—measures significant signals at a depth of 310–350, as indicated by the blue arrow in Figs. 5(b)–5(c). This region corresponds to the lens cleaning tissue layer, consisting of multiple micro-meter sized fibers that give strong reflectance signals. The result demonstrates that the penetration depth of OCT systems in turbid media can be improved by using the present method.

To further study the improvement of the penetration depth, we imaged a highly turbid sample, a dried leaf of cherry blossom Prunus serrulata. The optical power of the sample arm is 0.6 mW after passing through the modulated DMD pattern. The A-scan measurements along the indicated line [yellow line in Fig. 6(a)] were measured with four different methods: (1) the wavefront shaping method, (2) the spatial compounding method, (3) conventional SD-OCT measurements with a Gaussian beam illumination (optical power, 0.6 mW), and (4) conventional SD-OCT measurements with a Gaussian beam illumination (higher optical power, 1.3mW). Here we used an × 10 objective lens (LSM02-BB, Thorlabs, United states) with a NA of 0.06 to control higher spatial frequency orders in wavefront shaping, whereas we used an objective lens with a NA of 0.03 for the results in Figs. 3–5. To show results for SD-OCT with a conventional Gaussian beam, we utilized a flip mirror to directly send a beam to the sample and bypass DMD, L1, L2, and G1 (Fig. 2). The results are shown in Figs. 6(b)–6(c). With wavefront controlled beams, the OCT signal amplitude and penetration depth are significantly superior than using a conventional Gaussian beam or the spatial compounding method. The proposed method—OCT with wavefront shaping—even showed better penetration depth compared to a conventional OCT using a Gaussian beam with an even higher illumination power. Figure 6(c) shows the entire set of A-scan signals obtained with the set of optimized wavefronts. It clearly shows that an optimally shaped wavefront delivers a significantly enhanced light energy to a certain depth and the depth of penetration is markedly improved. These results also indicate that the controlled wavefront does not merely correct an aberrated wavefront which can be caused by a randomly chosen Hadamard basis pattern or a topographical shape of a sample surface, but indeed controls multiply scattered light paths in highly scattering samples to generate an optimized focus at a specific depth.

Fig. 6 Experimental results. (a) B-scan image for the 3nd phantom, a dried leaf. (b) Reconstructed OCT signals of dotted yellow lines in (a). The values for laser power were measured at the sample plane. (c) The maximized A-scan signals corresponding to optimized wavefront for yellow the dotted line in (a). Increase in penetration depth can be seen by the detection of leaf layer in targeted depths, i.e. enhanced OCT signals along the main diagonal.

4. Discussions and conclusions

We demonstrate, for the first time to our knowledge, a wavefront shaping method in a SD-OCT system, which effectively controls multiple scattering inside turbid media so that optimized energy delivery is enabled at a specific target depth. A DMD device (1024 × 768 micro mirrors) is utilized for fast manipulation of the impinging wavefront. Independent bases based on Hadamard patterns are utilized and controlled by a full phase shift method. The coherence-gated reflected OCT signal is employed for feedback; the appropriate phase value that maximizes the back scattered signal from a target depth is found for each basis. The final optimized wavefront, constructed with a linear combination of all optimized input bases, maximizes energy transport at the target depth and automatically satisfies the coherence gating condition. The experimental results show clearly that the OCT signals at specific depths can be selectively enhanced or annihilated by applying an appropriate incident wavefronts (Figs. 3b-c). The optimized wavefront significantly increases the SNR of the OCT signal at deeper depths and also extends the penetration depth.

In addition, the enhanced OCT signals with optimized wavefronts correspond to reflection at the specific depth, not the result of multiple scattering in shallower layers producing accidentally the same path length. Conventional OCT measures a path length, and thus does not distinguish a signal which really has been reflected at the specified depth form the one from shallower layers producing accidentally the same path length due to multiple scattering. This is also related to the issue, why one can observe multiple speckle patterns in conventional OCT images, especially for highly turbid samples. Generating an optimized complex wavefront amounts to summing coherently all the spatial modes of the propagating light at a specific depth with zero relative phase while maintaining the same optical path length. This is because we optimize the illumination wavefront to generate a constructively enhanced reflected signal while maintaining coherence-gating the reflected signals at the specific optical path length. In addition, the reflected beam was collected with the relatively low NA objective lens and a single-mode optical fiber. Thus, single back scattering signal from a specific depth (optical path length more precisely) on the optical axis will be effectively collected, while multiply scattered light in shallower lasers may not be effectively collected by the low NA objective even though they might have the same optical path length. Therefore, single scattering object at the specific depth will be coherently and constructively enhanced with the optimization process, whereas other multiple scattered light paths occurring in shallower layers will be destructively averaged out as shown in Figs. 4 and 5(b).

Although we demonstrate the concept of complex wavefront shaping in SD-OCT geometry, there are many aspects that can be improved. Most importantly, we only demonstrate the control of the spatial wavefront for the impinging beam, which was sufficient to systematically control the transmission field to the target depth. However, the reflected beam from the target depth is not controlled, and thus only a significant fraction of the reflected beam was coupled in the optical fiber. It would be possible to control the reflected wavefront from the sample such that the maximal energy is delivered to the spectroscopy measurement part.

In principle, our complex amplitude control system should work irrespective of the signal intensity, since the key idea is based on the principle of coherent interference of multiple waves. However, our results show that the enhancement depends on signal strengths (Fig. 4). We speculate that this observation can be attributed to the system noise. Low SNR may prevent from measuring correct coherent-gated responses to illuminated basis patterns, and thus it will make it difficult to correctly calculate the right optimized pattern. In the future, controlling the wavefronts in both directions—coming to and reflected from the target depth—may increase the SNR and further enhance the performance.

In addition, we used 500 independent input bases for wavefront shaping. This number of bases was sufficient to demonstrate the principle of the method, yet the full number of controllable bases is even larger. The maximum number of independent optical modes for the transmission matrix of the turbid media is described as Nmax = 2πA/d2, where A is the illuminated surface area and d is the effective focal spot size [33

R. P. Feynman, Feynman Lectures on Physics. Volume 3: Quantum Mechanics edited by R. P. Feynman, R. B. Leighton, and M. Sands, eds. (Addison-Wesley, Reading, MA, 1965).

]. In the present experimental setup with a × 5 objective lens, for instance, the field of view at the sample plane is ~9.4 mm × 9.4 mm and the mean spot size is ~21 µm, which gives Nmax ~1,260,000.

The present technique of controlling the incident wavefront for OCT systems will be particularly useful in cases where OCT images are degraded due to inevitable multiple light scattering. The approach may inspire new approaches to control the wave interference in OCT techniques. Although we demonstrate the technique in a SD-OCT system, the methodology presented here can be easily adapted to different versions of OCT systems; it can be readily applied to time-domain OCT and swept-source OCT. Considering that the optical transmission matrices are sufficiently uncorrelated between different wavelengths [27

J. H. Park, C. H. Park, H. Yu, Y. H. Cho, and Y. K. Park, “Active spectral filtering through turbid media,” Opt. Lett. 37(15), 3261–3263 (2012). [CrossRef] [PubMed]

] and polarization [34

J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. K. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express 20(15), 17010–17016 (2012). [CrossRef]

], the present concept can also be adapted to spectroscopic and polarization-sensitive OCT [35

F. E. Robles, C. Wilson, G. Grant, and A. Wax, “Molecular imaging true-colour spectroscopic optical coherence tomography,” Nat. Photonics 5(12), 744–747 (2011). [CrossRef] [PubMed]

,36

W. Y. Oh, S. H. Yun, B. J. Vakoc, M. Shishkov, A. E. Desjardins, B. H. Park, J. F. de Boer, G. J. Tearney, and B. E. Bouma, “High-speed polarization sensitive optical frequency domain imaging with frequency multiplexing,” Opt. Express 16(2), 1096–1103 (2008). [CrossRef] [PubMed]

]. In addition, the current limit of the spatial resolution of OCT can be overcome by exploiting multiple light speckle fields [37

Y.-K. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17(15), 12285–12292 (2009). [CrossRef] [PubMed]

,38

I. Vellekoop, A. Lagendijk, and A. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 320–322 (2010). [CrossRef]

]. The concept of wavefront shaping in OCT can be fully exploited in direct experimental study and will lead to potential useful applications in medical diagnostic fields.

Acknowledgments

This work was mainly supported by the Samsung Advanced Institute of Technology and partially supported by KAIST, KAIST Institute for Optical Science and Technology, the Korean Ministry of Education, Science and Technology (MEST) grant No. 2009-0087691 (BRL) and National Research Foundation (NRF-2012R1A1A1009082). Y. K. P. acknowledges support from the TJ ChungAm Foundation.

References and Links

1.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

2.

N. Nassif, B. Cense, B. Hyle Park, S. H. Yun, T. C. Chen, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography,” Opt. Lett. 29(5), 480–482 (2004). [CrossRef] [PubMed]

3.

I. K. Jang, B. E. Bouma, D. H. Kang, S. J. Park, S. W. Park, K. B. Seung, K. B. Choi, M. Shishkov, K. Schlendorf, E. Pomerantsev, S. L. Houser, H. T. Aretz, and G. J. Tearney, “Visualization of coronary atherosclerotic plaques in patients using optical coherence tomography: comparison with intravascular ultrasound,” J. Am. Coll. Cardiol. 39(4), 604–609 (2002). [CrossRef] [PubMed]

4.

M. Bashkansky and J. Reintjes, “Statistics and reduction of speckle in optical coherence tomography,” Opt. Lett. 25(8), 545–547 (2000). [CrossRef] [PubMed]

5.

J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1205–1215 (1999). [CrossRef]

6.

B. Karamata, M. Laubscher, M. Leutenegger, S. Bourquin, T. Lasser, and P. Lambelet, “Multiple scattering in optical coherence tomography. I. Investigation and modeling,” J. Opt. Soc. Am. A 22(7), 1369–1379 (2005). [CrossRef] [PubMed]

7.

J. G. Fujimoto, C. Pitris, S. A. Boppart, and M. E. Brezinski, “Optical coherence tomography: an emerging technology for biomedical imaging and optical biopsy,” Neoplasia 2(1/2), 9–25 (2000). [CrossRef] [PubMed]

8.

S. Proskurin and I. Meglinski, “Optical coherence tomography imaging depth enhancement by superficial skin optical clearing,” Laser Phys. Lett. 4(11), 824–826 (2007). [CrossRef]

9.

A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography images using digital filtering,” J. Opt. Soc. Am. A 24(7), 1901–1910 (2007). [CrossRef] [PubMed]

10.

M. Hughes, M. Spring, and A. Podoleanu, “Speckle noise reduction in optical coherence tomography of paint layers,” Appl. Opt. 49(1), 99–107 (2010). [CrossRef] [PubMed]

11.

A. E. Desjardins, B. J. Vakoc, G. J. Tearney, and B. E. Bouma, “Speckle reduction in OCT using massively-parallel detection and frequency-domain ranging,” Opt. Express 14(11), 4736–4745 (2006). [CrossRef] [PubMed]

12.

M. Szkulmowski, I. Gorczynska, D. Szlag, M. Sylwestrzak, A. Kowalczyk, and M. Wojtkowski, “Efficient reduction of speckle noise in optical coherence tomography,” Opt. Express 20(2), 1337–1359 (2012). [CrossRef] [PubMed]

13.

N. Iftimia, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography by “path length encoded” angular compounding,” J. Biomed. Opt. 8(2), 260–263 (2003). [CrossRef] [PubMed]

14.

M. Pircher, E. Gotzinger, R. Leitgeb, A. F. Fercher, and C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003). [CrossRef] [PubMed]

15.

G. van Soest, M. Villiger, E. Regar, G. J. Tearney, B. E. Bouma, and A. F. W. van der Steen, “Frequency domain multiplexing for speckle reduction in optical coherence tomography,” J. Biomed. Opt. 17(7), 076018 (2012). [CrossRef] [PubMed]

16.

H. Wang and A. M. Rollins, “Speckle reduction in optical coherence tomography using angular compounding by B-scan Doppler-shift encoding,” J. Biomed. Opt. 14(3), 030512–030513 (2009). [CrossRef] [PubMed]

17.

A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. Motaghiannezam, G. J. Tearney, and B. E. Bouma, “Angle-resolved optical coherence tomography with sequential angular selectivity for speckle reduction,” Opt. Express 15(10), 6200–6209 (2007). [CrossRef] [PubMed]

18.

B. Hermann, E. J. Fernández, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, P. M. Prieto, and P. Artal, “Adaptive-optics ultrahigh-resolution optical coherence tomography,” Opt. Lett. 29(18), 2142–2144 (2004). [CrossRef] [PubMed]

19.

R. J. Zawadzki, S. M. Jones, S. S. Olivier, M. Zhao, B. A. Bower, J. A. Izatt, S. Choi, S. Laut, and J. S. Werner, “Adaptive-optics optical coherence tomography for high-resolution and high-speed 3D retinal in vivo imaging,” Opt. Express 13(21), 8532–8546 (2005). [CrossRef] [PubMed]

20.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006). [CrossRef] [PubMed]

21.

M. Pircher and R. J. Zawadzki, “Combining adaptive optics with optical coherence tomography: Unveiling the cellular structure of the human retina in vivo,” Expert Rev. Ophthalmol. 2(6), 1019–1035 (2007). [CrossRef]

22.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012). [CrossRef]

23.

I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32(16), 2309–2311 (2007). [CrossRef] [PubMed]

24.

J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett. 106(10), 103901 (2011). [CrossRef] [PubMed]

25.

D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express 19(5), 4017–4029 (2011). [CrossRef] [PubMed]

26.

D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express 20(2), 1733–1740 (2012). [CrossRef] [PubMed]

27.

J. H. Park, C. H. Park, H. Yu, Y. H. Cho, and Y. K. Park, “Active spectral filtering through turbid media,” Opt. Lett. 37(15), 3261–3263 (2012). [CrossRef] [PubMed]

28.

E. Small, O. Katz, Y. Guan, and Y. Silberberg, “Spectral control of broadband light through random media by wavefront shaping,” Opt. Lett. 37(16), 3429–3431 (2012). [CrossRef]

29.

R. Fiolka, K. Si, and M. Cui, “Complex wavefront corrections for deep tissue focusing using low coherence backscattered light,” Opt. Express 20(15), 16532–16543 (2012). [CrossRef]

30.

A. F. Fercher, “Optical coherence tomography,” J. Biomed. Opt. 1(2), 157–173 (1996). [CrossRef] [PubMed]

31.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003). [CrossRef]

32.

J. Gómez Rivas, R. Sprik, C. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” EPL (Europhys. Lett.) 48(1), 22–28 (1999). [CrossRef]

33.

R. P. Feynman, Feynman Lectures on Physics. Volume 3: Quantum Mechanics edited by R. P. Feynman, R. B. Leighton, and M. Sands, eds. (Addison-Wesley, Reading, MA, 1965).

34.

J. H. Park, C. Park, H. Yu, Y. H. Cho, and Y. K. Park, “Dynamic active wave plate using random nanoparticles,” Opt. Express 20(15), 17010–17016 (2012). [CrossRef]

35.

F. E. Robles, C. Wilson, G. Grant, and A. Wax, “Molecular imaging true-colour spectroscopic optical coherence tomography,” Nat. Photonics 5(12), 744–747 (2011). [CrossRef] [PubMed]

36.

W. Y. Oh, S. H. Yun, B. J. Vakoc, M. Shishkov, A. E. Desjardins, B. H. Park, J. F. de Boer, G. J. Tearney, and B. E. Bouma, “High-speed polarization sensitive optical frequency domain imaging with frequency multiplexing,” Opt. Express 16(2), 1096–1103 (2008). [CrossRef] [PubMed]

37.

Y.-K. Park, W. Choi, Z. Yaqoob, R. Dasari, K. Badizadegan, and M. S. Feld, “Speckle-field digital holographic microscopy,” Opt. Express 17(15), 12285–12292 (2009). [CrossRef] [PubMed]

38.

I. Vellekoop, A. Lagendijk, and A. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 320–322 (2010). [CrossRef]

OCIS Codes
(170.4500) Medical optics and biotechnology : Optical coherence tomography
(110.0113) Imaging systems : Imaging through turbid media
(110.1080) Imaging systems : Active or adaptive optics

ToC Category:
Imaging Systems

History
Original Manuscript: November 16, 2012
Revised Manuscript: January 10, 2013
Manuscript Accepted: January 21, 2013
Published: January 30, 2013

Virtual Issues
Vol. 8, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Jaeduck Jang, Jaeguyn Lim, Hyeonseung Yu, Hyun Choi, Jinyong Ha, Jung-Hoon Park, Wang-Yuhl Oh, Wooyoung Jang, SeongDeok Lee, and YongKeun Park, "Complex wavefront shaping for optimal depth-selective focusing in optical coherence tomography," Opt. Express 21, 2890-2902 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-2890


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References

  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254(5035), 1178–1181 (1991). [CrossRef] [PubMed]
  2. N. Nassif, B. Cense, B. Hyle Park, S. H. Yun, T. C. Chen, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography,” Opt. Lett.29(5), 480–482 (2004). [CrossRef] [PubMed]
  3. I. K. Jang, B. E. Bouma, D. H. Kang, S. J. Park, S. W. Park, K. B. Seung, K. B. Choi, M. Shishkov, K. Schlendorf, E. Pomerantsev, S. L. Houser, H. T. Aretz, and G. J. Tearney, “Visualization of coronary atherosclerotic plaques in patients using optical coherence tomography: comparison with intravascular ultrasound,” J. Am. Coll. Cardiol.39(4), 604–609 (2002). [CrossRef] [PubMed]
  4. M. Bashkansky and J. Reintjes, “Statistics and reduction of speckle in optical coherence tomography,” Opt. Lett.25(8), 545–547 (2000). [CrossRef] [PubMed]
  5. J. M. Schmitt, “Optical coherence tomography (OCT): a review,” IEEE J. Sel. Top. Quantum Electron.5(4), 1205–1215 (1999). [CrossRef]
  6. B. Karamata, M. Laubscher, M. Leutenegger, S. Bourquin, T. Lasser, and P. Lambelet, “Multiple scattering in optical coherence tomography. I. Investigation and modeling,” J. Opt. Soc. Am. A22(7), 1369–1379 (2005). [CrossRef] [PubMed]
  7. J. G. Fujimoto, C. Pitris, S. A. Boppart, and M. E. Brezinski, “Optical coherence tomography: an emerging technology for biomedical imaging and optical biopsy,” Neoplasia2(1/2), 9–25 (2000). [CrossRef] [PubMed]
  8. S. Proskurin and I. Meglinski, “Optical coherence tomography imaging depth enhancement by superficial skin optical clearing,” Laser Phys. Lett.4(11), 824–826 (2007). [CrossRef]
  9. A. Ozcan, A. Bilenca, A. E. Desjardins, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography images using digital filtering,” J. Opt. Soc. Am. A24(7), 1901–1910 (2007). [CrossRef] [PubMed]
  10. M. Hughes, M. Spring, and A. Podoleanu, “Speckle noise reduction in optical coherence tomography of paint layers,” Appl. Opt.49(1), 99–107 (2010). [CrossRef] [PubMed]
  11. A. E. Desjardins, B. J. Vakoc, G. J. Tearney, and B. E. Bouma, “Speckle reduction in OCT using massively-parallel detection and frequency-domain ranging,” Opt. Express14(11), 4736–4745 (2006). [CrossRef] [PubMed]
  12. M. Szkulmowski, I. Gorczynska, D. Szlag, M. Sylwestrzak, A. Kowalczyk, and M. Wojtkowski, “Efficient reduction of speckle noise in optical coherence tomography,” Opt. Express20(2), 1337–1359 (2012). [CrossRef] [PubMed]
  13. N. Iftimia, B. E. Bouma, and G. J. Tearney, “Speckle reduction in optical coherence tomography by “path length encoded” angular compounding,” J. Biomed. Opt.8(2), 260–263 (2003). [CrossRef] [PubMed]
  14. M. Pircher, E. Gotzinger, R. Leitgeb, A. F. Fercher, and C. K. Hitzenberger, “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt.8(3), 565–569 (2003). [CrossRef] [PubMed]
  15. G. van Soest, M. Villiger, E. Regar, G. J. Tearney, B. E. Bouma, and A. F. W. van der Steen, “Frequency domain multiplexing for speckle reduction in optical coherence tomography,” J. Biomed. Opt.17(7), 076018 (2012). [CrossRef] [PubMed]
  16. H. Wang and A. M. Rollins, “Speckle reduction in optical coherence tomography using angular compounding by B-scan Doppler-shift encoding,” J. Biomed. Opt.14(3), 030512–030513 (2009). [CrossRef] [PubMed]
  17. A. E. Desjardins, B. J. Vakoc, W. Y. Oh, S. M. Motaghiannezam, G. J. Tearney, and B. E. Bouma, “Angle-resolved optical coherence tomography with sequential angular selectivity for speckle reduction,” Opt. Express15(10), 6200–6209 (2007). [CrossRef] [PubMed]
  18. B. Hermann, E. J. Fernández, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, P. M. Prieto, and P. Artal, “Adaptive-optics ultrahigh-resolution optical coherence tomography,” Opt. Lett.29(18), 2142–2144 (2004). [CrossRef] [PubMed]
  19. R. J. Zawadzki, S. M. Jones, S. S. Olivier, M. Zhao, B. A. Bower, J. A. Izatt, S. Choi, S. Laut, and J. S. Werner, “Adaptive-optics optical coherence tomography for high-resolution and high-speed 3D retinal in vivo imaging,” Opt. Express13(21), 8532–8546 (2005). [CrossRef] [PubMed]
  20. M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A.103(46), 17137–17142 (2006). [CrossRef] [PubMed]
  21. M. Pircher and R. J. Zawadzki, “Combining adaptive optics with optical coherence tomography: Unveiling the cellular structure of the human retina in vivo,” Expert Rev. Ophthalmol.2(6), 1019–1035 (2007). [CrossRef]
  22. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics6(5), 283–292 (2012). [CrossRef]
  23. I. M. Vellekoop and A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett.32(16), 2309–2311 (2007). [CrossRef] [PubMed]
  24. J. Aulbach, B. Gjonaj, P. M. Johnson, A. P. Mosk, and A. Lagendijk, “Control of light transmission through opaque scattering media in space and time,” Phys. Rev. Lett.106(10), 103901 (2011). [CrossRef] [PubMed]
  25. D. Akbulut, T. J. Huisman, E. G. van Putten, W. L. Vos, and A. P. Mosk, “Focusing light through random photonic media by binary amplitude modulation,” Opt. Express19(5), 4017–4029 (2011). [CrossRef] [PubMed]
  26. D. B. Conkey, A. M. Caravaca-Aguirre, and R. Piestun, “High-speed scattering medium characterization with application to focusing light through turbid media,” Opt. Express20(2), 1733–1740 (2012). [CrossRef] [PubMed]
  27. J. H. Park, C. H. Park, H. Yu, Y. H. Cho, and Y. K. Park, “Active spectral filtering through turbid media,” Opt. Lett.37(15), 3261–3263 (2012). [CrossRef] [PubMed]
  28. E. Small, O. Katz, Y. Guan, and Y. Silberberg, “Spectral control of broadband light through random media by wavefront shaping,” Opt. Lett.37(16), 3429–3431 (2012). [CrossRef]
  29. R. Fiolka, K. Si, and M. Cui, “Complex wavefront corrections for deep tissue focusing using low coherence backscattered light,” Opt. Express20(15), 16532–16543 (2012). [CrossRef]
  30. A. F. Fercher, “Optical coherence tomography,” J. Biomed. Opt.1(2), 157–173 (1996). [CrossRef] [PubMed]
  31. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys.66(2), 239–303 (2003). [CrossRef]
  32. J. Gómez Rivas, R. Sprik, C. Soukoulis, K. Busch, and A. Lagendijk, “Optical transmission through strong scattering and highly polydisperse media,” EPL (Europhys. Lett.)48(1), 22–28 (1999). [CrossRef]
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