Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Transmission-matrix-based point-spread-function engineering through a complex medium

Open Access Open Access

Abstract

PSF engineering is of utmost interest, in particular for microscopy, but remains mostly restricted to weakly scattering or transparent samples. We report a method to design at will the spatial profile of transmitted coherent light after propagation through a strongly scattering sample. We compute an operator based on the experimentally measured transmission matrix, obtained by numerically adding an arbitrary mask in the Fourier domain prior to focusing. We demonstrate the strength of the technique through several examples: propagating Bessel beams, thus generating foci smaller than the diffraction-limited speckle grain; donut beams; and helical beams. We characterize the three-dimensional profile of the achieved foci and analyze the fundamental limitations of the technique. Our approach generalizes Fourier optics concepts for random media and opens in particular interesting perspectives for super-resolution imaging through turbid media.

© 2017 Optical Society of America

1. INTRODUCTION

Generating a specific optical point-spread function (PSF) has been one of the cornerstones of modern microscopy. This is conventionally done by inserting a phase or amplitude mask in the Fourier plane of the imaging system. For instance, Durnin et al. generated Bessel beams using a spatial filter for beam shaping [1]. Nowadays, holographic methods using a spatial light modulator (SLM) are the most versatile [2,3]. These techniques allow flexible beam shaping in a wide range of applications such as super-resolution microscopy [4,5], 3D microscopy [6,7], optical tweezers [810], and particle trapping [11]. However, all these studies typically require high-quality optics and demand little or no sample aberrations.

Light propagation in materials with optical index heterogeneities is affected by scattering. In scattering materials such as white paint or biological tissue, multiple scattering is at the origin of an intricate interference light field at the output of the medium, also known as speckle pattern [12]. Although the size of a speckle grain is diffraction-limited, this complex interference figure is detrimental for all conventional imaging systems. Nonetheless, this scattering process is linear and deterministic and thus even strongly scattering materials can be described by a transmission matrix (TM) [13].

Wavefront-shaping techniques have recently emerged as a powerful technique for controlling the output field using SLMs or phase-conjugate mirrors [14]. SLMs provide up to several million degrees of freedom to design the input field at will, in order to control the propagation of light after the medium. Over the last decade, pioneering works have proven the capability to drastically increase light intensity at one or several output positions of a disordered system such as white paint [13,15], multimode fibers [16], or biological samples [17]. However, the resulting focal spots have sizes comparable to a speckle grain, and thus are diffraction-limited [18]. This limit can be improved by increasing the numerical aperture of the imaging system [19] or controlling the optical near field [20]. Nonetheless, the achieved focus still has the same size as a speckle grain.

Recently, Di Battista et al. [21] overcame this size limit by mechanically inserting an annular mask just after the scattering medium, prior to iteratively optimizing the focus intensity at a distance via wavefront shaping. Due to the filtering of the low spatial frequencies, the resulting speckle and optimized spot was narrower than the initial speckle. After removing the filter, the narrow spot—effectively a Bessel-like beam—remained intense, over a background speckle pattern wider than the focus.

Herein we report the first formulation, to our knowledge, of a TM-based operator with a controllable PSF that enables deterministic focusing after propagation through a multiply scattering medium. We build this new operator by numerically applying a well-chosen mask (that can be arbitrarily designed in amplitude and/or phase) in a virtual Fourier plane of the output modes of the experimentally measured transmission matrix. We then demonstrate experimentally that a focus with the corresponding PSF can be obtained after the medium by performing digital phase conjugation on this operator. To demonstrate the robustness and wide applicability of our technique, we generate and characterize a variety of useful PSFs. First, we generate a Bessel beam focus using an amplitude annulus mask and show that its central FWHM is narrower than the size of a speckle grain, therefore demonstrating deterministic sub-speckle focusing without mechanical masking as in [21]. We also demonstrate donut-mode generation with various topological charges and helical foci. Characterization of the axial properties of Bessel and helical PSFs shows the potential of the technique for 3D wave control and for subspeckle imaging, extending previous studies to 3D control of the focus with only a transverse measurement.

2. PRINCIPLE OF THE EXPERIMENT

A particular class of wavefront-shaping methods relies on the measurement of the optical transmission matrix (TM), denoted H in this paper, which contains the relationship between the input field and output field [22]. Its complex coefficients hXX connect the optical complex field at the output [X=(x,y) camera pixel coordinates] to the input field [X=(x,y) SLM pixel coordinates] by

EXout=XhXXEXin.

Experimentally, the TM is measured by displaying a set of input fields on the SLM and recording the corresponding output fields on the camera, and requires the medium to be stable during the whole measurement process (a few minutes in our case). The digital phase conjugation of the TM, H, where stands for the conjugate transpose, enables focusing at any output position [13] or scanning of the focus [23]. The resulting spot has a size given approximately by the spatial correlation of the output speckle, i.e., diffraction-limited [12,18]. It effectively sets to a common phase all contributions arriving at this position. However, it is possible to completely tune the phase and amplitude distribution of the k-vectors forming this focus, and therefore control at will the PSF.

In Fig. 1, we detail how we build a new operator based on the experimentally measured TM to generate an arbitrary mask and generate the corresponding PSF at the focus. We first numerically perform a two-dimensional spatial Fourier transform on the TM, noted F2D, of every output field. We define h^KX=F2D(hXX), where K=(kx,ky) is the wave vector associated with X. This numerical operation is equivalent to computing the TM in a Fourier plane of the output imaging plane. In order to generate a given PSF, we then multiply in the k-space the field in the pupil plane by mask M (amplitude and/or phase), corresponding to this PSF. We thus obtain a new numerically filtered coefficient in the Fourier domain:

h^KXfilt=h^KX×M(kx,ky).

 figure: Fig. 1.

Fig. 1. General principle for PSF engineering behind a scattering medium. Top: schematic of the experiment. A spatial light modulator (SLM) is placed on one side of a scattering medium to shape the incident light. The transmission matrix is first measured, and then a new operator is calculated. From this operator, we can generate the SLM pattern, enabling focusing with arbitrary PSF after transmission through the sample in the imaging plane. Boxes: details of each steps to reach arbitrary PSF focusing. ① The standard transmission matrix H characterizes the propagation of light in the scattering medium. ② The digital optical phase conjugation (DOPC) of H enables focusing in any position of the imaging plane, with a size limited by diffraction [13]. 2 To go beyond the previous approach, a numerical step can be added to control the PSF. With a prior numerical computation of the optical field in a virtual pupil with a Fourier transform operation, the corresponding new operator Hfilt is obtained by numerically applying an arbitrary mask onto that pupil. 3 The DOPC of Hfilt allows for focusing in the output plane after the medium, the shape of the focus being given by PSF (in this example a donut mode) defined by the Fourier transform of the arbitrary mask. As in [13], the complex focus stands over a speckle background.

Download Full Size | PPT Slide | PDF

We then return to the spatial domain XX by taking the inverse Fourier transform of h^KXfilt:

hXXfilt=F2D1(h^KXfilt).

The resulting operator Hfilt can now be used instead of H to perform focusing and scanning with the chosen PSF. We compute the complex input field using the phase conjugation of Hfilt [22], and we display its phase on the phase-only SLM to generate the corresponding PSF at the chosen position at the output of the scattering sample. As discussed in [22], the penalty of displaying only the phase information of the phase-conjugation solution is just a mild factor 2 in signal to noise, and does not compromise the shape of the PSF. Nonetheless, encoding phase and amplitude on the SLM is also possible [24].

3. EXPERIMENTAL DEMONSTRATION

Figure 2 sketches the experimental setup to measure the transmission matrix H, compute Hfilt, and generate and characterize the formed PSF in three dimensions. A cw laser (λ=800nm, MaiTai, Spectra Physics) is split between a reference and sample path. In the sample path, a phase-only SLM (LCOS-SLM, Hamamatsu X10468) subdivided in 64×64 macropixels is conjugated with the back focal plane of a microscope objective, which illuminates a scattering medium made of ZnO nanoparticles (thickness 100μm). Another microscope objective is used to image the transmitted speckle. The objective is placed onto a motorized stage (Thorlabs, Z825B) to scan the imaging plane axially. For the TM measurement, the output beam is recombined with the reference on a beam splitter and the hologram is recorded on a charge-coupled device (CCD) camera (Allied Vision, Manta G-046). The reference beam is blocked during focusing and PSF characterization.

 figure: Fig. 2.

Fig. 2. Experimental setup. A cw laser (λ=800nm) illuminates an SLM that modulates the wavefront of light before propagation through a multiple scattering medium (ZnO nanoparticles). Transmitted light is collected with another microscope objective, placed onto a motorized stage to scan the z axis. The output speckle pattern is recombined with a reference plane wave from the same laser, using a beam splitter (BS). One polarization state of the output field is selected with a polarizer (P) and imaged on a CCD camera. L, lens (focal distance 200 mm).

Download Full Size | PPT Slide | PDF

We first demonstrate the generation of a Bessel-like beam using an annular mask. The irradiance profile of the ideal beam is described by a zero-order Bessel function of the first kind, which propagates with an associated complex field J0(krr)exp(ikzz). The experimental result is represented in Fig. 3. The applied mask during the numerical filtering step is an annular amplitude mask with an inner ring size 58% of the pupil size (see Supplement 1 for details). This value has been found to be a good compromise between the loss in intensity at the output, the ability to detect the foci over the background speckle, and a significant narrowing of the FWHM of the central spot, as with a mechanical mask [21]. Using (Hfilt), we obtain in the imaging plane a Bessel-like focus standing over a background speckle. We compare its FWHM to a standard focus obtained with the standard TM H. In the same experimental conditions, the Bessel-like central lobe FWHM is 23% narrower than a standard speckle focus grain. Both intensity profiles are fitted to an ideal Bessel and Gaussian profile, respectively. The central lobe of a Bessel beam is surrounded by a decaying set of side-lobe rings. Each lobe carries approximately the same amount of energy as the central spot, whereas Gaussian beams contain 50% of their total energy within their FWHM [25]. Achieving a smaller FWHM than a diffraction-limited focus entails penalties such as loss of energy in the central peak (40% lower than a standard beam). Inherent to wavefront shaping in complex media techniques, the PSF is not perfect, but rather stands over a speckle pattern that remains in the background, with the peak to background ratio proportional to the number of input modes [15].

 figure: Fig. 3.

Fig. 3. Experimental sub-diffraction focusing with the propagation of Bessel-like beams. (a) The mask applied during computation of the effective focusing operator is an amplitude annulus having inner radius k1=0.58k0, with k0 the pupil width in k-space. (b) Comparison between standard (with H) and Bessel-like focusing [with Hfilt obtained using mask (a)]. Although standard focusing is brighter, the Bessel-like focusing has a narrower FWHM. (c) Intensity profile of both standard and Bessel-like focusing. Bessel-like focusing is narrower by 23% in FWHM.

Download Full Size | PPT Slide | PDF

In the generation of Bessel-like PSFs, an extra penalty is added due to the low transmission of the virtual annular mask, which steeply decreases the energy in the focus while the background remains the same (see Supplement 1 for a quantitative characterization of this effect). In order to detect the focus with sufficient SNR, a high number of degrees of freedom, i.e., SLM pixels, is required; here we used N=4096 input pixels. We therefore demonstrate sub-speckle focusing after propagation through a scattering medium, using a Bessel-like beam, without ever physically inserting a mask in the Fourier plane.

Since any arbitrary phase and/or amplitude mask can be computed and placed onto the virtual pupil field, we also demonstrate the generation of donut-shaped beams, which are closely related to single-ringed Laguerre–Gaussian beams (LG0m). The corresponding mask to be applied in the numerical filtering step is a spiral phase plate distribution presenting a continuous and gradual phase change from 0 to 2mπ around the optical axis, where m is to the integer number of 2π cycles in the pupil plane [26] and corresponds to a topological charge. The ring pattern dimensions increase with m. Experimental results of focusing (LG0m) beams, with m from 1 to 4, are presented in Fig. 4 using N=1024 SLM pixels. The transmittance M of the numerical phase mask in the Fourier domain applied during the numerical filtering step, as defined in Eq. (2) and illustrated in Fig. 4, reads

MDonut(k,θ)=circ(kk0)exp(imθ),
where k0 is the pupil size in k-space. Just as for the Bessel-like beam of Fig. 3, the focus stands over a background speckle pattern. When m increases, the intensity is distributed over a wider area in the imaging plane. Therefore, for a fixed number of SLM pixels used, the total energy in the targeted area is about the same but distributed over a bigger area, while the background speckle remains at the same average intensity.

 figure: Fig. 4.

Fig. 4. Generation of donut modes of various diameters after propagation through the scattering medium. Diameter increases with topological charge m from 1 to 4 (related to the corresponding Laguerre–Gauss beam LG0m). Applied masks in the pupil plane (left), intensity distribution retrieved with a CCD camera (center), and related intensity profile for each order (right).

Download Full Size | PPT Slide | PDF

Several beam profiles such as Bessel beams also have very interesting propagation properties along the z axis. Our setup enables the scan of the z axis thanks to a motorized stage under the collecting microscope objective. Experimentally, we can scan over a few Rayleigh ranges (zR=10μm) on both sides of the focal plane. In Fig. 5(a), yOz cross sections of Bessel-like beam obtained in the same conditions as in Fig. 3(a) are reported. As expected, we prove without ambiguity that the generated Bessel-like beam has a longer depth of focus during propagation along the z axis relative to standard Gaussian beams, for which the depth of focus is the Rayleigh length. Here, we observe experimentally that our Bessel-like beam has a depth of focus 1.7 times longer than the Gaussian focus.

 figure: Fig. 5.

Fig. 5. z axis properties of 3D beams. (a) The Bessel-like beam diverges more slowly than the Gaussian depth of focus, related to the Rayleigh range (zr) of the microscope objective. (b) Corresponding intensity profiles along the z axis of both standard and Bessel-like foci. (c) Phase mask applied in the pupil plane for double helix (DH) focusing. (d) Corresponding double helix beam along the z axis. z=0 corresponds to the focal plane axial position.

Download Full Size | PPT Slide | PDF

As a last example, we demonstrate the generation of double-helix point spread functions (DH-PSFs). This 3D design has two dominant lobes in the imaging plane, whose angular orientation rotates with the axial (z) position [5,7]. This profile is realized by applying a particular phase mask during the numerical filtering step leading to Hfilt, illustrated in Fig. 5(c), which reads [5]

MDH(k,θ)=circ(kk0)exp[iarg(j=MM(kexp(iθ)kjexp(iθj)))],
where M=(Nv1)/2, Nv=9 is the number of vortices, (kj,θj) is the position of the jth vortex, and k0 is the pupil size. A stack of images taken on both sides of the focal plane illustrates the rotation of the DH-PSF in Fig. 5(d). The pattern rotates approximately linearly with z, with a negative angle for negative z. The reference z=0 corresponds to the focal plane position. The DH rotates from 30° to +30° between 2zR and +2zR. This type of profiled PSF has been used for 3D localization with a single shot, where the rotation of the imaged spot is related to its depth [27].

4. DISCUSSION

We have demonstrated focusing with various PSFs, defined by arbitrary control of a mask in phase and amplitude in the virtual Fourier domain. It is to be noted that, as in all methods relying on focusing through a complex medium, the focus stands over a background speckle resulting from the incomplete phase conjugation [15], the signal to background of the focus increasing linearly with the number of segments controlled on the SLM. However, our technique goes well beyond spatial-shaping techniques, relying on intensity optimization in the imaging plane; namely, our approach allows for fine control of the focus shape, in amplitude and phase, that cannot simply be achieved using optimization approaches on the intensity. In the latter, the maximal intensity scales inversely with the number of target points [15] or the size of the focusing area, as in acousto-optic and photoacoustic techniques [28,29]. Similarly, in our approach, the maximal intensity in the PSF decreases with its complexity but the amount of energy in the PSF remains the same.

This PSF engineering method through complex media is also not limited to amplitude and phase modulation in the Fourier domain and could be, for instance, extended to an arbitrary polarization mask if measuring a polarization-resolved transmission matrix [30], or even to more complex spectrally dependent PSFs thanks to the spectral dependence of the speckle [31,32]. Moreover, the Fourier domain of the plane of interest may not be accessible in practice as in [21], where the amplitude mask was placed after the medium and the speckle observed at a distance. In contrast, our technique would work in any plane, even at the output surface of the medium. Furthermore, a single transmission matrix measurement can be used to focus at different positions and allows rapid switching between various PSFs, as the numerical filtering step and phase conjugation are realized a posteriori. Using a simple quadratic phase mask, the focusing plane can also be translated longitudinally at will.

On the downside, in order to perform an accurate spatial Fourier transform, the reference beam during the transmission matrix measurement needs to be a well-defined plane wave, which requires a reference arm with interferometric stability during the measurement process. Additionally, the resolution of the generated mask is related to the sampling in the Fourier domain and therefore depends mostly on the sampling in the imaging plane (on the CCD): generating an accurate mask requires sampling at least a few CCD pixels per speckle grain over an extended output spatial region of at least a few times the PSF size. Note that, however, the resolution of the mask is advantageously independent of the number and resolution of the SLM segments, which only affect the signal to background ratio of the focus after phase conjugation. Increasing the number of SLM segments involves a longer measurement time of the experimental transmission matrix, thus requiring increased stability of the scattering sample. In our implementation, a transmission matrix containing N=4096 input patterns can be measured in approximately 30 min, mainly limited by the refresh rate of the liquid crystal SLM, while the scattering sample is stable along a few hours. It is also worth pointing out that the signal to background ratio is crucially affected by the total transmission of the virtual mask (as pointed out by [21] for physical masks).

Finally, these presented results are strictly valid only in the regime of multiple scattered light. In this regime, the mixing between input degrees of freedom (pixels of the SLM) and output degrees of freedom (spatial [13], polarization [33], and spectrum [34]) is maximal, as illustrated by the fact that the transmission matrix can be shown to be well described by random matrix theory [13]. In a weaker scattering regime—for instance, for surface scattering or when the thickness of the medium is less than a few transport mean free paths (with a significant ballistic or forward scattering component)—the transmission matrix formalism is still valid so the PSF-shaping methodology is still applicable. However, due to imperfect mixing, the signal to noise ratio, resolution, fidelity, and achievable PSF may be degraded. For example, a thin scatterer might not allow for efficient amplitude modulation in the pupil plane.

5. CONCLUSION

In conclusion, we have reported the first formulation to our knowledge of an operator, built upon the experimental transmission matrix, that enables deterministic focusing of any arbitrary PSF after propagation through a multiply scattering sample. We have illustrated the strength of this technique by generating Bessel, “donut,” and double helix beams through a scattering sample with a simple use of this new operator, and characterized their transverse and longitudinal properties. The method can readily be extended to other complex media, from biological tissues to multimode fibers. The possibility of arbitrarily generating complex PSF through multiply scattering media opens up new opportunities in several fields, in particular for 3D and super-resolution microscopy as well as optical manipulation and trapping [35]. A particularly interesting extension would be to exploit more directly the high spectral diversity offered by multiply scattering media [31] to generate highly complex, spectrally varying PSFs that could have applications in coherent control or nanophotonics.

Funding

European Research Council (ERC) (278025); National Science Foundation (NSF) (1310487, 1611513).

Acknowledgment

The authors thank Andréane Bourges, Hugo Defienne, and Gaetan Gauthier for discussions. S.G. is a member of the Institut Universitaire de France. R.P. acknowledges NSF support.

 

See Supplement 1 for supporting content.

REFERENCES

1. J. Durnin, J. Miceli Jr., and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987). [CrossRef]  

2. A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200–227 (2016). [CrossRef]  

3. C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011). [CrossRef]  

4. K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006). [CrossRef]  

5. G. Grover, K. DeLuca, S. Quirin, J. DeLuca, and R. Piestun, “Super-resolution photon-efficient imaging by nanometric double-helix point spread function localization of emitters (spindle),” Opt. Express 20, 26681–26695 (2012). [CrossRef]  

6. T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011). [CrossRef]  

7. S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008). [CrossRef]  

8. D. Zhang and X.-C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett. 28, 740–742 (2003). [CrossRef]  

9. D. B. Conkey, R. P. Trivedi, S. R. P. Pavani, I. I. Smalyukh, and R. Piestun, “Three-dimensional parallel particle manipulation and tracking by integrating holographic optical tweezers and engineered point spread functions,” Opt. Express 19, 3835–3842 (2011). [CrossRef]  

10. E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13, 3777–3786 (2005). [CrossRef]  

11. K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011). [CrossRef]  

12. J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976). [CrossRef]  

13. S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010). [CrossRef]  

14. 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, 283–292 (2012). [CrossRef]  

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

16. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20, 10583–10590 (2012). [CrossRef]  

17. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008). [CrossRef]  

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

19. Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011). [CrossRef]  

20. J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013). [CrossRef]  

21. D. Di Battista, G. Zacharakis, and M. Leonetti, “Enhanced adaptive focusing through semi-transparent media,” Sci. Rep. 5, 17406 (2015). [CrossRef]  

22. S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011). [CrossRef]  

23. A. M. Caravaca-Aguirre, E. Niv, and R. Piestun, “High-speed phase modulation for multimode fiber endoscope,” in Imaging Systems and Applications (Optical Society of America, 2014), paper ITh3C–1.

24. E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, “Spatial amplitude and phase modulation using commercial twisted nematic LCDs,” Appl. Opt. 47, 2076–2081 (2008). [CrossRef]  

25. J. Durnin, J. H. Eberly, and J. J. Miceli, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13, 79–80 (1988). [CrossRef]  

26. D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11, 2747–2752 (2003). [CrossRef]  

27. S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009). [CrossRef]  

28. D. B. Conkey, A. M. Caravaca-Aguirre, J. D. Dove, H. Ju, T. W. Murray, and R. Piestun, “Super-resolution photoacoustic imaging through a scattering wall,” Nat. Commun. 6, 7902 (2015). [CrossRef]  

29. Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012). [CrossRef]  

30. S. Tripathi, R. Paxman, T. Bifano, and K. C. Toussaint, “Vector transmission matrix for the polarization behavior of light propagation in highly scattering media,” Opt. Express 20, 16067–16076 (2012). [CrossRef]  

31. M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016). [CrossRef]  

32. D. B. Conkey and R. Piestun, “Color image projection through a strongly scattering wall,” Opt. Express 20, 27312–27318 (2012). [CrossRef]  

33. Y. Guan, O. Katz, E. Small, J. Zhou, and Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37, 4663–4665 (2012). [CrossRef]  

34. D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015). [CrossRef]  

35. T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010). [CrossRef]  

References

  • View by:

  1. J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref]
  2. A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200–227 (2016).
    [Crossref]
  3. C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
    [Crossref]
  4. K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
    [Crossref]
  5. G. Grover, K. DeLuca, S. Quirin, J. DeLuca, and R. Piestun, “Super-resolution photon-efficient imaging by nanometric double-helix point spread function localization of emitters (spindle),” Opt. Express 20, 26681–26695 (2012).
    [Crossref]
  6. T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
    [Crossref]
  7. S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
    [Crossref]
  8. D. Zhang and X.-C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett. 28, 740–742 (2003).
    [Crossref]
  9. D. B. Conkey, R. P. Trivedi, S. R. P. Pavani, I. I. Smalyukh, and R. Piestun, “Three-dimensional parallel particle manipulation and tracking by integrating holographic optical tweezers and engineered point spread functions,” Opt. Express 19, 3835–3842 (2011).
    [Crossref]
  10. E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13, 3777–3786 (2005).
    [Crossref]
  11. K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
    [Crossref]
  12. J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145–1150 (1976).
    [Crossref]
  13. S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
    [Crossref]
  14. 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, 283–292 (2012).
    [Crossref]
  15. I. M. Vellekoop and A. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
    [Crossref]
  16. I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20, 10583–10590 (2012).
    [Crossref]
  17. Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
    [Crossref]
  18. I. Vellekoop, A. Lagendijk, and A. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
    [Crossref]
  19. Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
    [Crossref]
  20. J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
    [Crossref]
  21. D. Di Battista, G. Zacharakis, and M. Leonetti, “Enhanced adaptive focusing through semi-transparent media,” Sci. Rep. 5, 17406 (2015).
    [Crossref]
  22. S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
    [Crossref]
  23. A. M. Caravaca-Aguirre, E. Niv, and R. Piestun, “High-speed phase modulation for multimode fiber endoscope,” in Imaging Systems and Applications (Optical Society of America, 2014), paper ITh3C–1.
  24. E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, “Spatial amplitude and phase modulation using commercial twisted nematic LCDs,” Appl. Opt. 47, 2076–2081 (2008).
    [Crossref]
  25. J. Durnin, J. H. Eberly, and J. J. Miceli, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13, 79–80 (1988).
    [Crossref]
  26. D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11, 2747–2752 (2003).
    [Crossref]
  27. S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
    [Crossref]
  28. D. B. Conkey, A. M. Caravaca-Aguirre, J. D. Dove, H. Ju, T. W. Murray, and R. Piestun, “Super-resolution photoacoustic imaging through a scattering wall,” Nat. Commun. 6, 7902 (2015).
    [Crossref]
  29. Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
    [Crossref]
  30. S. Tripathi, R. Paxman, T. Bifano, and K. C. Toussaint, “Vector transmission matrix for the polarization behavior of light propagation in highly scattering media,” Opt. Express 20, 16067–16076 (2012).
    [Crossref]
  31. M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
    [Crossref]
  32. D. B. Conkey and R. Piestun, “Color image projection through a strongly scattering wall,” Opt. Express 20, 27312–27318 (2012).
    [Crossref]
  33. Y. Guan, O. Katz, E. Small, J. Zhou, and Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37, 4663–4665 (2012).
    [Crossref]
  34. D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
    [Crossref]
  35. T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
    [Crossref]

2016 (2)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photon. 8, 200–227 (2016).
[Crossref]

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

2015 (3)

D. B. Conkey, A. M. Caravaca-Aguirre, J. D. Dove, H. Ju, T. W. Murray, and R. Piestun, “Super-resolution photoacoustic imaging through a scattering wall,” Nat. Commun. 6, 7902 (2015).
[Crossref]

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref]

D. Di Battista, G. Zacharakis, and M. Leonetti, “Enhanced adaptive focusing through semi-transparent media,” Sci. Rep. 5, 17406 (2015).
[Crossref]

2013 (1)

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

2012 (7)

2011 (6)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

D. B. Conkey, R. P. Trivedi, S. R. P. Pavani, I. I. Smalyukh, and R. Piestun, “Three-dimensional parallel particle manipulation and tracking by integrating holographic optical tweezers and engineered point spread functions,” Opt. Express 19, 3835–3842 (2011).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[Crossref]

2010 (3)

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

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

2009 (1)

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref]

2008 (3)

2007 (1)

2006 (1)

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

2005 (1)

2003 (2)

1988 (1)

1987 (1)

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

1976 (1)

Andreoli, D.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref]

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Betzig, E.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Bifano, T.

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref]

Boccara, A.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Boccara, A. C.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[Crossref]

Caravaca-Aguirre, A. M.

D. B. Conkey, A. M. Caravaca-Aguirre, J. D. Dove, H. Ju, T. W. Murray, and R. Piestun, “Super-resolution photoacoustic imaging through a scattering wall,” Nat. Commun. 6, 7902 (2015).
[Crossref]

A. M. Caravaca-Aguirre, E. Niv, and R. Piestun, “High-speed phase modulation for multimode fiber endoscope,” in Imaging Systems and Applications (Optical Society of America, 2014), paper ITh3C–1.

Carminati, R.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Cho, Y.-H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Choi, W.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Choi, Y.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

Conkey, D. B.

Cooper, J.

Courtial, J.

Dasari, R. R.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Davidson, M. W.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Defienne, H.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

DeLuca, J.

DeLuca, K.

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

Di Battista, D.

D. Di Battista, G. Zacharakis, and M. Leonetti, “Enhanced adaptive focusing through semi-transparent media,” Sci. Rep. 5, 17406 (2015).
[Crossref]

DiMarzio, C. A.

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Dove, J. D.

D. B. Conkey, A. M. Caravaca-Aguirre, J. D. Dove, H. Ju, T. W. Murray, and R. Piestun, “Super-resolution photoacoustic imaging through a scattering wall,” Nat. Commun. 6, 7902 (2015).
[Crossref]

Dudley, A.

Durnin, J.

J. Durnin, J. H. Eberly, and J. J. Miceli, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13, 79–80 (1988).
[Crossref]

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Eberly, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Eberly, J. H.

Fang-Yen, C.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Farahi, S.

Feld, M. S.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[Crossref]

Fink, M.

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, 283–292 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Forbes, A.

Galbraith, C. G.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Galbraith, J. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Gan, X.

Ganic, D.

Gao, L.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Gigan, S.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Goodman, J. W.

Grésillon, S.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref]

Grover, G.

Gu, M.

Guan, Y.

Han, S.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Hell, S. W.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

Jahn, R.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Jordan, P.

Ju, H.

D. B. Conkey, A. M. Caravaca-Aguirre, J. D. Dove, H. Ju, T. W. Murray, and R. Piestun, “Super-resolution photoacoustic imaging through a scattering wall,” Nat. Commun. 6, 7902 (2015).
[Crossref]

Judkewitz, B.

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Kang, P.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Katz, O.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref]

Y. Guan, O. Katz, E. Small, J. Zhou, and Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37, 4663–4665 (2012).
[Crossref]

Ko, S. H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Lagendijk, A.

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, 283–292 (2012).
[Crossref]

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

Lee, K. J.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Leonetti, M.

D. Di Battista, G. Zacharakis, and M. Leonetti, “Enhanced adaptive focusing through semi-transparent media,” Sci. Rep. 5, 17406 (2015).
[Crossref]

Lerosey, G.

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, 283–292 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Liu, N.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref]

Lord, S. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref]

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Mazilu, M.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

McLaren, M.

Miceli, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Miceli, J. J.

Milkie, D. E.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Moerner, W.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref]

Moser, C.

Mosk, A.

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

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

Mosk, A. P.

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, 283–292 (2012).
[Crossref]

E. G. van Putten, I. M. Vellekoop, and A. P. Mosk, “Spatial amplitude and phase modulation using commercial twisted nematic LCDs,” Appl. Opt. 47, 2076–2081 (2008).
[Crossref]

Mounaix, M.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

Murray, T. W.

D. B. Conkey, A. M. Caravaca-Aguirre, J. D. Dove, H. Ju, T. W. Murray, and R. Piestun, “Super-resolution photoacoustic imaging through a scattering wall,” Nat. Commun. 6, 7902 (2015).
[Crossref]

Nam, K. T.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Niv, E.

A. M. Caravaca-Aguirre, E. Niv, and R. Piestun, “High-speed phase modulation for multimode fiber endoscope,” in Imaging Systems and Applications (Optical Society of America, 2014), paper ITh3C–1.

Padgett, M.

Papadopoulos, I. N.

Park, C.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Park, J.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Park, J.-H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Park, Y.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Pavani, S. R. P.

Paxman, R.

Piestun, R.

D. B. Conkey, A. M. Caravaca-Aguirre, J. D. Dove, H. Ju, T. W. Murray, and R. Piestun, “Super-resolution photoacoustic imaging through a scattering wall,” Nat. Commun. 6, 7902 (2015).
[Crossref]

D. B. Conkey and R. Piestun, “Color image projection through a strongly scattering wall,” Opt. Express 20, 27312–27318 (2012).
[Crossref]

G. Grover, K. DeLuca, S. Quirin, J. DeLuca, and R. Piestun, “Super-resolution photon-efficient imaging by nanometric double-helix point spread function localization of emitters (spindle),” Opt. Express 20, 26681–26695 (2012).
[Crossref]

D. B. Conkey, R. P. Trivedi, S. R. P. Pavani, I. I. Smalyukh, and R. Piestun, “Three-dimensional parallel particle manipulation and tracking by integrating holographic optical tweezers and engineered point spread functions,” Opt. Express 19, 3835–3842 (2011).
[Crossref]

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref]

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
[Crossref]

E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13, 3777–3786 (2005).
[Crossref]

A. M. Caravaca-Aguirre, E. Niv, and R. Piestun, “High-speed phase modulation for multimode fiber endoscope,” in Imaging Systems and Applications (Optical Society of America, 2014), paper ITh3C–1.

Planchon, T. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Popoff, S.

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Psaltis, D.

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20, 10583–10590 (2012).
[Crossref]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[Crossref]

Quirin, S.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Rizzoli, S. O.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

Schonbrun, E.

Shin, J.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Silberberg, Y.

Small, E.

Smalyukh, I. I.

Thompson, M. A.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref]

Toussaint, K. C.

Tripathi, S.

Trivedi, R. P.

Twieg, R. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref]

van Putten, E. G.

Vellekoop, I.

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

Vellekoop, I. M.

Volpe, G.

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref]

Wang, Y. M.

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Westphal, V.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

Willig, K. I.

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

Wulff, K. D.

Yang, C.

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[Crossref]

Yang, T. D.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

Yaqoob, Z.

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[Crossref]

Yu, H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Yuan, X.-C.

Zacharakis, G.

D. Di Battista, G. Zacharakis, and M. Leonetti, “Enhanced adaptive focusing through semi-transparent media,” Sci. Rep. 5, 17406 (2015).
[Crossref]

Zhang, D.

Zhou, J.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Laser Photon. Rev. (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Nat. Commun. (2)

D. B. Conkey, A. M. Caravaca-Aguirre, J. D. Dove, H. Ju, T. W. Murray, and R. Piestun, “Super-resolution photoacoustic imaging through a scattering wall,” Nat. Commun. 6, 7902 (2015).
[Crossref]

Y. M. Wang, B. Judkewitz, C. A. DiMarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref]

Nat. Methods (1)

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Nat. Photonics (6)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5, 335–342 (2011).
[Crossref]

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, 283–292 (2012).
[Crossref]

Z. Yaqoob, D. Psaltis, M. S. Feld, and C. Yang, “Optical phase conjugation for turbidity suppression in biological samples,” Nat. Photonics 2, 110–115 (2008).
[Crossref]

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

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[Crossref]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7, 454–458 (2013).
[Crossref]

Nature (1)

K. I. Willig, S. O. Rizzoli, V. Westphal, R. Jahn, and S. W. Hell, “STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis,” Nature 440, 935–939 (2006).
[Crossref]

New J. Phys. (1)

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Controlling light through optical disordered media: transmission matrix approach,” New J. Phys. 13, 123021 (2011).
[Crossref]

Opt. Express (8)

D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11, 2747–2752 (2003).
[Crossref]

I. N. Papadopoulos, S. Farahi, C. Moser, and D. Psaltis, “Focusing and scanning light through a multimode optical fiber using digital phase conjugation,” Opt. Express 20, 10583–10590 (2012).
[Crossref]

D. B. Conkey and R. Piestun, “Color image projection through a strongly scattering wall,” Opt. Express 20, 27312–27318 (2012).
[Crossref]

S. Tripathi, R. Paxman, T. Bifano, and K. C. Toussaint, “Vector transmission matrix for the polarization behavior of light propagation in highly scattering media,” Opt. Express 20, 16067–16076 (2012).
[Crossref]

G. Grover, K. DeLuca, S. Quirin, J. DeLuca, and R. Piestun, “Super-resolution photon-efficient imaging by nanometric double-helix point spread function localization of emitters (spindle),” Opt. Express 20, 26681–26695 (2012).
[Crossref]

S. R. P. Pavani and R. Piestun, “Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system,” Opt. Express 16, 22048–22057 (2008).
[Crossref]

D. B. Conkey, R. P. Trivedi, S. R. P. Pavani, I. I. Smalyukh, and R. Piestun, “Three-dimensional parallel particle manipulation and tracking by integrating holographic optical tweezers and engineered point spread functions,” Opt. Express 19, 3835–3842 (2011).
[Crossref]

E. Schonbrun, R. Piestun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13, 3777–3786 (2005).
[Crossref]

Opt. Lett. (4)

Phys. Rev. Lett. (4)

M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, “Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix,” Phys. Rev. Lett. 116, 253901 (2016).
[Crossref]

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[Crossref]

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and W. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. USA 106, 2995–2999 (2009).
[Crossref]

Sci. Rep. (2)

D. Di Battista, G. Zacharakis, and M. Leonetti, “Enhanced adaptive focusing through semi-transparent media,” Sci. Rep. 5, 17406 (2015).
[Crossref]

D. Andreoli, G. Volpe, S. Popoff, O. Katz, S. Grésillon, and S. Gigan, “Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix,” Sci. Rep. 5, 10347 (2015).
[Crossref]

Other (1)

A. M. Caravaca-Aguirre, E. Niv, and R. Piestun, “High-speed phase modulation for multimode fiber endoscope,” in Imaging Systems and Applications (Optical Society of America, 2014), paper ITh3C–1.

Supplementary Material (1)

NameDescription
Supplement 1: PDF (1157 KB)      Quantitative characterization of the generation of a Bessel-like beam.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. General principle for PSF engineering behind a scattering medium. Top: schematic of the experiment. A spatial light modulator (SLM) is placed on one side of a scattering medium to shape the incident light. The transmission matrix is first measured, and then a new operator is calculated. From this operator, we can generate the SLM pattern, enabling focusing with arbitrary PSF after transmission through the sample in the imaging plane. Boxes: details of each steps to reach arbitrary PSF focusing. ① The standard transmission matrix H characterizes the propagation of light in the scattering medium. ② The digital optical phase conjugation (DOPC) of H enables focusing in any position of the imaging plane, with a size limited by diffraction [13]. 2 To go beyond the previous approach, a numerical step can be added to control the PSF. With a prior numerical computation of the optical field in a virtual pupil with a Fourier transform operation, the corresponding new operator H filt is obtained by numerically applying an arbitrary mask onto that pupil. 3 The DOPC of H filt allows for focusing in the output plane after the medium, the shape of the focus being given by PSF (in this example a donut mode) defined by the Fourier transform of the arbitrary mask. As in [13], the complex focus stands over a speckle background.
Fig. 2.
Fig. 2. Experimental setup. A cw laser ( λ = 800 nm ) illuminates an SLM that modulates the wavefront of light before propagation through a multiple scattering medium (ZnO nanoparticles). Transmitted light is collected with another microscope objective, placed onto a motorized stage to scan the z axis. The output speckle pattern is recombined with a reference plane wave from the same laser, using a beam splitter (BS). One polarization state of the output field is selected with a polarizer ( P ) and imaged on a CCD camera. L , lens (focal distance 200 mm).
Fig. 3.
Fig. 3. Experimental sub-diffraction focusing with the propagation of Bessel-like beams. (a) The mask applied during computation of the effective focusing operator is an amplitude annulus having inner radius k 1 = 0.58 k 0 , with k 0 the pupil width in k -space. (b) Comparison between standard (with H ) and Bessel-like focusing [with H filt obtained using mask (a)]. Although standard focusing is brighter, the Bessel-like focusing has a narrower FWHM. (c) Intensity profile of both standard and Bessel-like focusing. Bessel-like focusing is narrower by 23% in FWHM.
Fig. 4.
Fig. 4. Generation of donut modes of various diameters after propagation through the scattering medium. Diameter increases with topological charge m from 1 to 4 (related to the corresponding Laguerre–Gauss beam LG 0 m ). Applied masks in the pupil plane (left), intensity distribution retrieved with a CCD camera (center), and related intensity profile for each order (right).
Fig. 5.
Fig. 5. z axis properties of 3D beams. (a) The Bessel-like beam diverges more slowly than the Gaussian depth of focus, related to the Rayleigh range ( z r ) of the microscope objective. (b) Corresponding intensity profiles along the z axis of both standard and Bessel-like foci. (c) Phase mask applied in the pupil plane for double helix (DH) focusing. (d) Corresponding double helix beam along the z axis. z = 0 corresponds to the focal plane axial position.

Equations (5)

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

E X out = X h X X E X in .
h ^ K X filt = h ^ K X × M ( k x , k y ) .
h X X filt = F 2 D 1 ( h ^ K X filt ) .
M Donut ( k , θ ) = circ ( k k 0 ) exp ( i m θ ) ,
M DH ( k , θ ) = circ ( k k 0 ) exp [ i arg ( j = M M ( k exp ( i θ ) k j exp ( i θ j ) ) ) ] ,

Metrics

Select as filters


Select Topics Cancel
© Copyright 2022 | Optica Publishing Group. All Rights Reserved