Parallel wavefront optimization method forfocusing light through

random scattering mediaMeng Cui

Janelia Farm Research Campus, Howard Hughes Medical Institute,Ashburn, Virginia 20147, USA (cuim@janelia.hhmi.org)

Received November 22, 2010; revised December 27, 2010; accepted February 8, 2011;posted February 15, 2011 (Doc. ID 138569); published March 9, 2011

A parallel wavefront optimization method is demonstrated experimentally to focus light through random scatteringmedia. The simultaneous modulation of multiple phase elements, each at a unique frequency, enables a paralleldetermination of the optimal wavefront. Compared to a pixel-by-pixel measurement, the reported parallel methoduses the target signal in a highly efficient way. With 441 phase elements, a high-quality focus was formed through aglass diffuser with a peak-to-background ratio of ∼270. The accuracy and repeatability of the system were testedthrough experiments. © 2011 Optical Society of AmericaOCIS codes: 110.0113, 110.1080, 110.7050.

Optical imaging is a powerful tool for biomedicalsciences. Research in the past decade has greatly ad-vanced spatial resolution [1] and imaging speed [2]. How-ever, the penetration depth in tissues is still very limited.For fluorescence imaging in deep tissues, two-photonmicroscopy is the most widely employed technique [3],which uses ballistic light to form a focus and is capableof providing high-resolution images through tissues sev-eral hundred micrometers thick [4]. At greater depth, theballistic component further decays and the out of focuscontribution becomes significant, causing an increasedbackground signal [5]. In addition, the accumulated aber-ration in the path of the ballistic component is nonnegli-gible [6,7], distorting the optical focus. Adaptive opticstechniques [6–8] have been applied to improve imagequality in two-photon microscopy. However, the im-provement in penetration depth is moderate. To furtherextend the penetration depth, methods that utilize notonly the ballistic light but also the scattered light forfocusing need to be explored. Despite the apparent ran-domness, scattering is a deterministic process. A prop-erly designed wavefront can propagate in a randomscattering medium and form a high-quality focus, awell-known effect in the research field of optical phaseconjugation [9–11]. Generally, there are two approachesto determine the correct wavefront. One approachrequires a direct measurement or recording of the scat-tered light field from the target, which can be achievedeither electronically using a wavefront sensor [12] or di-gital holography [13,14], or through nonlinear light–matter interactions [9]. The other approach measuresthe power of the target signal while optimizing the inputwavefront [15]. For deep-tissue fluorescence imaging ap-plications, the second approach has the advantage ofbeing able to use all the signals from the target, whilethe first approach can only utilize signals within a finitenumber of spatial modes and within a limited spectralbandwidth. Despite these advantages of the wavefrontoptimization method, the reported demonstrations wererather slow, in which one phase pixel was adjusted at onetime in the measurement. For in vivo applications, muchgreater speed is required. In this Letter, I report a new

method for focusing light through random scatteringmedia, in which the wavefront is determined in a parallelfashion. Compared to a pixel-by-pixel measurement, theparallel method uses the target signal highly efficiently.

The idea is based on the multidither coherent opticaladaptive technique (COAT) [16], a method developed atthe Hughes Research Laboratories in the 1970s for focus-ing a laser beam through air turbulence. The basic prin-ciple of the multidither COAT is shown in Fig. 1(a). Alaser beam is split into two beams by a beam splitter.One beam is transmitted through a phase modulator.Both beams are converted to diverging beams by con-cave lenses. At a distance, the two beams interfereand form spatial fringes. When the phase difference isshifted by the phase modulator, the interference fringeswill move. A target much smaller than the fringe spacingis used to sample the fringe intensity, which could be asmall detector, a strong scatterer, or a fluorophore. If thephase is modulated at a frequency f , the signal will alsohave a frequency component at f . The phase differencebetween the driving source and the detected signal isused as the error signal in a feedback loop for maxi-mizing the light intensity at the target. This schemecan be generalized to multiple beams. For example, an18-element COAT system has been demonstrated to com-pensate for air turbulence with an ∼1 kHz update rate[17], in which a relatively simple (18 degrees of freedom)phase profile was sufficient for the compensation.

In this Letter, I show through experiments that theprinciple of multidither COAT can also be applied to fo-cus light through a highly scattering medium, which re-quires a much greater number of degrees of freedom. In

Fig. 1. (Color online) (a) Schematic drawing of the multiditherCOAT in free space. (b) Schematic drawing of the parallelwavefront optimization in random scattering media.

870 OPTICS LETTERS / Vol. 36, No. 6 / March 15, 2011

0146-9592/11/060870-03$15.00/0 © 2011 Optical Society of America

the presence of a random scattering medium, the lightbeam is diffused and the trajectories are randomized,as shown in Fig. 1(b). With each beam incident on thescattering medium, there is an associated E field insidethe medium. When another phase-modulated beam is ap-plied, there will be an intensity modulation caused bytheir interference. Therefore, by modulating each phasecontrol element at a different rate, we can determine therequired wavefront in parallel through a Fourier trans-form of the detected signal.The experiment setup is shown in Fig. 2(a). A linearly

polarized laser (785 nm) was used in the experiment. Thelight intensity and polarization were controlled by a neu-tral density filter and a half-wave plate, respectively. Thebeam was expanded and directed toward a phase-onlyspatial light modulator (SLM) that was configured to pro-vide 441 (21 × 21) phase control elements and was con-jugate to the rear pupil plane of a 0:5NA 20× objectivelens. A 1:6mm thick glass diffuser was placed in frontof the objective to convert the output of the objective intoa random speckle that was imaged by a 0:9NA 60× ob-jective onto an 8 bit CCD camera.Although the idea of the experiment reported here is

based on the multidither COAT, the design and operationare both different. In the original COAT experiment, oneclosed-loop feedback system was used to control onephase element. The phase [ϕiðtÞ ¼ ϕi0 þ φi sinðωitÞ] wasoscillating over a small phase range (φi) at an angularfrequency ωi, and the feedback system gradually ad-justed the phase ϕi0 to its optimal value. In the experi-ment reported here, all the phase elements go througha 2π phase variation to maximize the oscillatory signal,and the phase variation is a linear function of time[ϕiðtÞ ¼ ωit], such that the interference between themodulated field and the reference field is a sinusoidalfunction of time. Each SLM phase element is modulatedat a unique frequency, and the correct phase value can bedetermined through a Fourier transform, as shown inFig. 2(b).In the COAT experiment, all the phase elements were

controlled by feedback loops. The oscillatory signal at

each modulation frequency was due to the interferencebetween the E field of the modulated element and thereference field that was the summation of the E fieldfrom all the rest of the elements. Therefore, the referencefield is not stationary. Because the Fourier transform isused in this experiment to determine the correct phasevalues for all the phase elements at once, a stationary re-ference field is required. In this experiment, all the phaseelements on the left half of the SLM were first modulated,while the right half was held at a constant value. After thephase on the left half was determined, the right half wasmodulated while the left half was maintained at the newlydetermined phase values. The reasons that such ascheme was chosen are twofold. First, interferometrymeasurements can provide a shot-noise-limited signal-to-noise ratio (SNR) under the condition that the shotnoise generated by the reference field is the dominantnoise component. Therefore, it is beneficial to keep alarge portion of the input light stationary and use it asthe reference field. Second, given a strong referencefield, all the rest of the phase elements should be modu-lated simultaneously for better efficiency. This point iseasy to see in the frequency domain. If only one phaseelement is modulated, there will be only one AC compo-nent in the frequency domain and the signals controlledby all the rest of the phase elements are in the DC com-ponent that does not contribute to the phase measure-ment. As more phase elements are modulated, there willbe more AC components contributing to the phase mea-surement. Mathematically, if the average optical powercontrolled by each phase element at the target is �P fora given modulation time t, the SNR for that modulatedpixel is

ffiffiffiffiffi

�Ptp

under the shot-noise-limited condition. Ifthe pixels are modulated one by one, it takes nt toachieve such an SNR (

ffiffiffiffiffi

�Ptp

) for n phase elements. Ifall the n phase elements are modulated simultaneously,it only takes time t to achieve the same SNR for all the nphase elements. Taking these two points into considera-tion, the experiment is designed to simultaneously mod-ulate half of the phase elements. In such a way, the signalis used efficiently for the phase measurement, and astrong reference field is provided by half of the phaseelements.

As an initial test, a 1:6mm thick 120 grit ground glassdiffuser (Edmund Optics, NT83-381) was used to ran-domly scatter the light before it reached the focal plane.The diffusing surface faced the 0:9NA objective lens. Thetransmitted light became a random speckle, as shown inFig. 3(a). A 450 nm × 450 nm area on the focal plane waschosen as the target, which corresponded to 8 × 8 pixelson the camera. The SLM frame was updated every 0:1 s,and 2048 frames were used in each measurement. The

Fig. 2. (Color online) (a) Experiment setup: ND, neutraldensity filter; λ=2, half-wave plate; Expand, beam expander;M, mirror; SLM, phase-only spatial light modulator; L1,0:5NA, 20× objective lens; L2, 0:9NA 60× objective lens; andCCD, CCD camera. (b) Schematic drawing of the operation ofthe parallel wavefront optimization method. Each phase ele-ment of the SLM was modulated at a different frequency.The detected target signal was Fourier transformed, and thephase values at the corresponding frequencies were displayedon the SLM to focus light onto the target.

Fig. 3. (Color online) (a) Observed random speckle with a flatphase profile displayed on the SLM. (b) Fourier transform de-termined phase pattern. (c) Observed focus profile with themeasured phase pattern displayed on the SLM. The inset showsthe magnified focus.

March 15, 2011 / Vol. 36, No. 6 / OPTICS LETTERS 871

441 (21 × 21) frequency components were uniformlydistributed between 2.68 and 4:82Hz. The minimum num-ber of samplings required for the 441 phase values is 882.Because of the limited bit depth of the 8 bit CCD camera,2048 samplings were used to achieve the optimal focusquality. The phase information was acquired from the441 frequency components and then displayed on theSLM, which is shown in Fig. 3(b). With the measuredphase profile displayed, a bright round focus was ob-served on the camera at the target position [Fig. 3(c)].The peak-to-background ratio, defined as the ratio ofthe peak intensity to the average intensity of the areaaround the focus, was measured at two different cameraexposure times to ensure that the weak background wasproperly measured, and the measured ratio was ∼270.The FWHM of the measured focus was 0:78� 0:01 μm.A deconvolution with the point spread function (PSF)of the 0:9NA imaging lens yielded a FWHM of 0:62�0:01 μm. The FWHM of the diffraction-limited PSF ofthe NA 0.5 objective is 0:84 μm. The fact that the opti-mized focus was smaller than the expected aberration-free focus was surprising, and yet it is a well-understoodeffect in optical phase conjugation and time reversal stu-dies [11,18]. The explanation is that scattering can widenthe NA of the optical system.To test if this method can correctly find the optimal

wavefront and to determine the repeatability of the mea-surements, the following experiments were implemen-ted. The glass diffuser was removed from the setup. Arandom phase pattern was displaced on the SLM, asshown in Fig. 4(a). The goal of the experiment was tosee if the method can correctly compensate for the addedphase pattern. With the random phase displayed on theSLM, the light on the focal plane became a randomspeckle, as shown in Fig. 4(b). After the wavefront opti-mization, a bright round focus was observed [Fig. 4(d)].The combined wavefront (random phase pattern plusmeasured phase pattern) is shown in Fig. 4(c). TheFWHM of the formed focus was 0:99� 0:1 μm. Deconvo-lution with the PSF of the 0:9NA objective yielded aFWHM of 0:87� 0:01 μm, which was close to the diffrac-tion-limited value of 0:84 μm. When a flat phase profile

[Fig. 4(e)] was displayed, the focus became slightlydistorted and the peak intensity was lower [Fig. 4(f)], sug-gesting that the optimization method compensated fornot only the added random phase pattern but also theaberration in the system. The experiments were re-peated, and the RMS phase profile difference betweentwo consecutive measurements was 0:38 rad or 47nmfor the 785 nm light used in the experiments.

In conclusion, a parallel wavefront optimization meth-od has demonstrated the ability to focus light throughhighly scattering media. Compared to a pixel-by-pixelmeasurement, the parallel method reported here usesthe target signal very efficiently. With 441 phase ele-ments, a peak-to-background ratio of ∼270 has beenobserved through a glass diffuser. In the reported experi-ment, an SLM was used for phase modulation and thephase profile was updated at 10Hz during the measure-ment. With a commercially available segmented deform-able mirror, the operation speed can be potentiallyincreased by ∼3 orders of magnitude, which would beideal for in vivo imaging applications.

The author thanks Na Ji, Eric Betzig, and MatsGustafsson for helpful discussions. The research is sup-ported by the Howard Hughes Medical Institute.

References

1. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S.Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, Science 313, 1642 (2006).

2. J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K.Stelzer, Science 305, 1007 (2004).

3. W. R. Zipfel, R. M. Williams, and W. W. Webb, Nat. Biotech-nol. 21, 1369 (2003).

4. B. A. Wilt, L. D. Burns, E. T. W. Ho, K. K. Ghosh, E. A.Mukamel, and M. J. Schnitzer, Annu. Rev. Neurosci. 32,435 (2009).

5. P. Theer and W. Denk, J. Opt. Soc. Am. A 23, 3139 (2006).6. N. Ji, D. E. Milkie, and E. Betzig, Nat. Meth. 7, 141 (2010).7. M. Rueckel, J. A. Mack-Bucher, and W. Denk, Proc. Natl.

Acad. Sci. USA 103, 17137 (2006).8. D. Debarre, E. J. Botcherby, T. Watanabe, S. Srinivas, M. J.

Booth, and T. Wilson, Opt. Lett. 34, 2495 (2009).9. A. Yariv and P. Yeh, IEEE J. Quantum Electron. 14,

650 (1978).10. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, Nat. Photon.

2, 110 (2008).11. M. Cui, E. J. McDowell, and C. H. Yang, Appl. Phys. Lett. 95,

123702 (2009).12. A. Roorda, F. Romero-Borja, W. J. Donnelly, H. Queener, T.

J. Hebert, and M. C. W. Campbell, Opt. Express 10,405 (2002).

13. M. Cui and C. Yang, Opt. Express 18, 3444 (2010).14. C. L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, Opt. Express

18, 12283 (2010).15. I. M. Vellekoop and A. P. Mosk, Opt. Lett. 32, 2309 (2007).16. W. B. Bridges, P. T. Brunner, S. P. Lazzara, N. Ta, T. R.

Omeara, Sanguine. Ja, and W. P. Brown, Appl. Opt. 13,291 (1974).

17. J. E. Pearson, W. B. Bridges, S. Hansen, T. A. Nussmeier,and M. E. Pedinoff, Appl. Opt. 15, 611 (1976).

18. A. Derode, P. Roux, and M. Fink, Phys. Rev. Lett. 75,4206 (1995).

Fig. 4. (Color online) (a) Added random phase pattern. (b) Ob-served speckle with the added random phase pattern displayedon the SLM. (c) The added random phase pattern plus themeasured phase pattern. (d) Observed focus profile with theadded random phase pattern plus the measured phase patterndisplayed on the SLM. (e) Flat phase used in (f). (f) Observedfocus profile with a flat phase displayed on the SLM. Insets,magnified focus.

872 OPTICS LETTERS / Vol. 36, No. 6 / March 15, 2011