Abstract

In deep tissue photoacoustic imaging, the spatial resolution is inherently limited by acoustic diffraction. Moreover, as the ultrasound attenuation increases with frequency, resolution is often traded off for penetration depth. Here, we report on super-resolution photoacoustic imaging by use of multiple speckle illumination. Specifically, we demonstrate experimentally that the analysis of second-order fluctuations of the photoacoustic images enables the resolution of optically absorbing structures beyond the acoustic diffraction limit, with a resolution enhancement of about 1.4. In addition, deconvolution was implemented to fully exploit the highest spatial frequencies available and resulted in an effective resolution enhancement of at least 1.6 in the lateral direction. Our method introduces a new framework that could potentially lead to deep tissue photoacoustic imaging with subacoustic resolution.

© 2016 Optical Society of America

Light scattering prevents standard optical microscopes from obtaining well-resolved images deep inside biological tissues. In the past 20 years, photoacoustic (PA) imaging has been developed to overcome this limitation by imaging optical absorption deep inside strongly scattering tissue with the resolution of ultrasound imaging [1]. PA imaging relies on the unscattered ultrasonic waves emitted by absorbing structures under pulsed illumination via thermoelastic stress generation. It therefore provides images at depth in tissue with a spatial resolution limited by acoustic diffraction. Ultimately, the ultrasound resolution for biological soft tissue is limited by the attenuation of ultrasound, which typically increases linearly with frequency. As a result, the depth-to-resolution ratio of PA imaging at depth is around 200 in practice [1,2]. As an illustration, axial resolution down to 5 μm and lateral resolution down to 20 μm have been reached with high-frequency acoustic detectors at depth up to 5 mm [3].

In this Letter, we demonstrate that the conventional acoustic diffraction limit in PA imaging may be overcome by exploiting PA signal fluctuations, building on the super-resolution optical fluctuation imaging (SOFI) technique developed for fluorescence microscopy [4]. SOFI is based on the idea that a higher-order statistical analysis of temporal fluctuations caused by fluorescence blinking provides a way to resolve uncorrelated fluorophores within the same diffraction spot. In this work, we introduce multiple optical speckle illumination as a source of fluctuations for super-resolution PA imaging, inspired by the principle introduced in optics with SOFI [4] or from derived approaches using speckle illumination [5]. In PA imaging, multiple speckle illumination was initially introduced by our group as a means to palliate limited-view or high-pass filtering artifacts [6]. Here, we demonstrate that a second-order analysis of optical speckle-induced PA fluctuations also provides super-resolved PA images beyond the acoustic diffraction limit.

In this work, we consider PA images reconstructed from a set of PA signals measured with an ultrasound array. A conventional backprojection algorithm is used to reconstruct the images, and it is assumed that the reconstructed PA quantity A(r) may be written as a convolution:

A(r)=[μa(r)×I(r)]*h(r),
where h is the point spread function (PSF) corresponding to the conventional PA imaging process, μa is the distribution of optical absorption, and I is the optical intensity pattern [see Supplement 1, Section 1.A, for a detailed justification of Eq. (1)]. Let us now consider that the region of interest is successively illuminated by many different speckle patterns Ik(r) with mean I(r)=I0. The expression for the mean PA image, estimated from averaging the PA images obtained with many realizations Ik(r) of the speckle illumination, is
A(r)=I0×[μa(r)*h(r)],
and shows that the resolution of the reconstructed image A(r) is dictated by the spatial frequency content of h(r). Under the assumption that the optical speckle grain size is much smaller than that of h(r), the variance image σ2[A](r) for uncorrelated speckles is given by (see Supplement 1, Section 1.B)
σ2[A](r)μa2(r)*h2(r).
The variance image appears as the convolution of the squared object by the squared PSF, which has a higher frequency content than the PSF itself. As a result, the variance image is expected to have a higher resolution compared to the mean image.

Our objective was to demonstrate experimentally that the measurement of a two-dimensional (2D) variance image can provide a super-resolution PA image of the absorption distribution beyond the acoustic diffraction limit. The experimental setup used is shown in Fig. 1. The beam of a 5 ns pulsed laser (Continuum Surelite II-10, 532 nm wavelength, 10 Hz repetition rate) was focused on a ground glass diffuser (Thorlabs, 220 grit, no significant ballistic transmission). The scattered light illuminated 2D absorbing samples embedded in an agarose gel block. The samples were located 5 cm away from the diffuser, leading to a measured speckle grain size of 30μm. The absorbing samples were placed in the imaging plane of a linear ultrasound array (Vermon, 4 MHz center frequency, >60% bandwidth, 128 elements, 0.33 mm pitch) connected to an ultrasound scanner (Aixplorer, Supersonic Imagine, 128 channel simultaneous acquisition at 60 MS/s). Black polyethylene beads (Cospheric, 50 and 100 μm in diameter) were used to fabricate three absorbing samples with isotropic emitters. For each sample, a set of PA images was reconstructed for 100 uncorrelated speckle patterns obtained by rotating the diffuser. The mean and variance images were then computed on a per-pixel basis. As described in detail in Supplement 1, Section 2.B, special care was taken to reduce sources of fluctuations other than the multiple speckle illumination between PA acquisitions. For the image reconstruction, a time-domain backprojection algorithm was used (see Supplement 1, Section 2.C). Images were reconstructed on a grid of square pixels (25 μm side).

 

Fig. 1. Experimental setup. A 5 ns laser pulse is focused onto a rotating diffuser. Each resulting speckle pattern (scale bar 200 μm, speckle grain size 30μm) illuminates a collection of absorbing beads, generating ultrasound detected with a linear ultrasonic array.

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As a first demonstration of the resolution enhancement enabled by our approach, Fig. 2 shows the mean (conventional) PA image [Fig. 2(b)] and the variance image [Fig. 2(c)] obtained with a set of randomly distributed 100 μm diameter absorbing beads [Fig. 2(a)]. Whereas it is difficult if not impossible to unambiguously identify individual beads on the conventional PA image (which clearly shows overlapping of the individual contributions because of insufficient resolution) the variance image allows a clear identification of the contributions of each bead. The dimensions on the images of an isolated 100 μm bead (see Supplement 1, Section 3.C for the measurement method) were 340/414 μm in the lateral (x axis)/axial (z axis) directions on the mean image [inset in Fig. 2(b)] and 246/292 μm on the variance image [inset in Fig. 2(c)], much larger than the diameter of the bead. These images are therefore good approximations of the PSF h(r) and its square h2(r), and indicates a resolution enhancement factor of about 1.4 in both directions for the variance image as compared to the mean image. As shown in particular with the pair indicated by the arrow on Fig. 2(a), the variance image resembles the convolution of the sample with the squared PSF h2(r), as expected from absorbers distant from more than the speckle grain size and illuminated by multiple independent speckle realizations. The results shown in Fig. 2 are a direct illustration of the principle of SOFI applied to PA imaging with multiple speckle illumination.

 

Fig. 2. (a) Photograph of sample 1 (randomly positioned 100 μm diameter beads). (b) Mean PA image over 100 speckle realizations, mimicking uniform illumination. Inset: mean PA image of a single isolated bead. (c) Variance image over 100 speckle realizations. Inset: variance image of a single isolated bead. Scale bars: 300 μm.

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However, Figs. 2(b) and 2(c) also emphasize the bipolarity and anisotropy of the PSF commonly encountered in PA imaging, which do not have their counterpart in regular all-optical imaging. As a consequence, non-deconvolved PA images appear quite different from the original sample, as illustrated in both Figs. 2(b) and 2(c). Moreover, it is known that non-deconvolved images do generally not reflect the highest spatial frequency content available. It was, for instance, pointed out in the original SOFI paper that a simple deconvolution of a conventional optical image led to a resolution similar to that of the variance image [4].

To further demonstrate the performance of our approach, deconvolution was thus performed both to remove the peculiar side lobes of the PA PSF and to fully exploit the maximum available frequency content. Sample 2 was designed with pairs of 100 μm diameter beads precisely positioned along the z and x axes (see Supplement 1, Section 2.A), as illustrated in Fig. 3(a). Figures 3(b) and 3(c) show that none of the pairs could be resolved on either the mean or the variance image, in agreement with the PSF dimensions reported above, and therefore no obvious resolution enhancement can be seen from the comparison of the two images. In order to perform the deconvolution of the images shown in Fig. 3 from the knowledge of the PSF (for the mean image) and its square (for the variance image), estimates of the PSF h(r) were measured using isolated 50 μm diameter beads (see details in Supplement 1, Section 3). An inversion strategy that allows for accounting for the presence of noise in the measurement was carried out to perform the deconvolution. Retrieving μa2(r) from measurements of the variance image modeled as σ2[A]^(r)=h2(r)*μa2(r)+ε (with ε accounting for the experimental noise) was carried out by the minimization of the following constrained least-square functional:

J(x):=h2*xσ2[A]^2+αx2subject tox0,
with · being the Euclidian norm over the image space and α>0 being a regularization parameter. The constrained minimizer x^α provides a regularized solution to the deconvolution problem which, in turn, defines an estimation of the absorption distribution μaα^:=x^α (under the assumption of a uniform mean intensity distribution). For comparison, the exact same approach was applied to retrieve an estimation of μa from the measurement of the mean image. In practice, the minimization of the functional just shown required adjusting the regularization parameter α in order to obtain a fair resolution versus noise trade-off [7, Section 5.6], and choosing Niterations in the fast iterative soft thresholding algorithm (FISTA) numerical method used to perform the minimization (see Supplement 1, Sections 1.C and 2.D, for further details on the deconvolution). Deconvolved images are shown in Fig. 4. The deconvolved variance image was square-rooted to be proportional to the absorption distribution μaα^ in order to be comparable to the deconvolved mean images. The absorbers appear much sharper on the deconvolved variance image [Fig. 4(b)] as compared to the mean image [Fig. 4(a)]. Except for the upper pair (120 μm apart axially center to center, for which the beads are nearly touching), almost every pair is resolved on the deconvolved variance image. On the deconvolved mean image, only the axial pair separated by 200 μm is resolved. The effect of the PSF anisotropy is further illustrated with the deconvolved images shown in Fig. 5, obtained from sample 3 with 100 μm diameter beads distributed on a quarter circle (center-to-center distance of about 150 μm). Not a single bead can be resolved on the deconvolved mean image [Fig. 5(a)]. In contrast, the six beads can easily be distinguished on the deconvolved variance image [Fig. 5(b)]. The deconvolved images remain anisotropic, as the spatial extent of the PSF in the Fourier space is limited mostly by the temporal frequency bandwidth in the axial direction whereas it is additionally limited in the lateral direction by the detection aperture.

 

Fig. 3. (a) Photograph of sample 2. The distances between 100 μm diameter beads (center to center) were 120, 140, and 200 μm along the z direction (from top to bottom), and 250, 200, and 160 μm along the x direction (from left to right). The four 50 μm diameter beads used to estimate the PSF are also slightly visible (see Fig. S1 in Supplement 1). (b) Mean PA image over 100 speckle realizations, mimicking uniform illumination. (c) Square root of the variance image over 100 speckle realizations. Scale bars: 500 μm.

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Fig. 4. (a) Mean image deconvolved by the PSF; white dashed lines indicates the cross-sections. (b) Square root of the variance image deconvolved by the squared PSF. (c) Horizontal cross-sections: deconvolved mean image (blue) and square root of deconvolved variance image (red). (d) Vertical cross-sections: deconvolved mean image (blue) and square root of deconvolved variance image (red). Scale bars: 500 μm.

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Fig. 5. (a) Mean image deconvolved by the PSF. (b) Square root of the variance image deconvolved by the squared PSF; white dashed lines indicate the cross-section direction. (c) Photograph of sample 3. (d) Cross-sections. Blue curve, mean image; red curve, square root of variance image. Scale bars: 200 μm.

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Speckle-induced PA fluctuation imaging is an original method recently proposed by our group to enhance visibility in PA imaging [6]. In this study, we demonstrated that fluctuation imaging can also be used to overcome the ultrasound diffraction limit in PA tomography. We showed that this method can separate small absorbers unresolved under standard uniform illumination. This is, to the best of our knowledge, the first super-resolution PA imaging method which does not require optical focusing and therefore is applicable beyond the ballistic regime. Super-resolution PA microscopy was reported in previous studies, but it relied on light focusing and on nonlinear absorption mechanisms, a situation which cannot be translated to deep tissue PA imaging [8,9]. The common approach to obtain high resolution at depth in PA imaging was, to date, to improve the acoustic detection by employing higher frequencies and increasing the detection aperture. Here, we demonstrated that additional efforts can be deployed towards the illumination in order to induce fluctuations and separate discrete absorbers below the acoustic diffraction limit.

While variance images were shown to provide a resolution enhancement of about 1.4 in both directions as compared to the conventional mean image, deconvolution of the images was necessary to fully exploit the highest available spatial frequency content in each type of image given the available signal-to-noise ratio (SNR). Beads with centers 160 μm apart laterally (respectively 140 μm apart axially) were resolved on the deconvolved variances images, whereas the resolution of the variance image was about 250 μm laterally (respectively about 290 μm axially). The lateral pair 250 μm apart was not resolved in the deconvolved mean image while the lateral pair 160 μm apart was resolved on the deconvolved variance image, resulting in an effective resolution enhancement of at least 1.6—better than that observed on the images before deconvolution (see Supplement 1, Section 3.C on possible reasons for this effect). Deconvolution has already been considered in PA imaging as part of the reconstruction algorithm [10], and to compensate for smearing induced by the spatial impulse response of the finite-size detectors [11]. However, no super-resolution was yet demonstrated since there were no physical mechanisms extending the high spatial frequency information. Our approach goes beyond past works by considering fluctuations in PA images as signals that reveal higher spatial frequencies above the noise level. The deconvolution approach was implemented with absorbers of size similar to those of the absorbers used to measure the PSF. As an immediate drawback, deconvolution was unable to restore the actual size of the absorbers, which led the deconvolved image to reconstruct beads smaller than their real size. Nonetheless, this method showed a very good subacoustic resolution performance, which was the objective of our work. Although the beads were expected to be almost equally absorbing, a difference in the reconstructed amplitudes was noticed. The proposed method was therefore not shown to be quantitative, which could be attributed to the nonlinear deconvolution scheme. Further work should be carried out to investigate the possibility of retrieving quantitative absorption information.

Our proof-of-concept experiments were carried out at low medical ultrasound frequency to simplify the controlled fabrication of absorbing samples (see Supplement 1, Section 2.A). The speckle grain size of 30 μm was chosen so that the emitted ultrasound remained detectable given the bandwidth of our transducer, while being smaller but similar to the dimension of the absorbers to maximize the fluctuations. However, the approach could be scaled down using high-frequency detectors and could also be extended to 3D PA imaging. For speckle patterns generated deep in tissue (with lasers with a sufficient coherence length), the speckle grain size will be on the order of the optical wavelength. As a consequence, special care on the excitation and detection stability will be required in order to detect the PA fluctuations, which would be reduced in the case of speckle grain size much smaller than the size of the absorbers or the acoustic resolution [6].

In the past few years, several techniques combining shaped coherent illumination and PA imaging have been developed. These methods aim to focus light inside tissue, possibly with subacoustic resolution, which could also lead to super-resolved PA imaging [1214]. However, these methods require expensive hardware and tedious experimental procedures. We propose here a very simple imaging technique than does not require any costly equipment and nearly no optical alignment. For biological applications, even tissue-induced temporal decorrelation of speckle patterns could be exploited as a source of fluctuating illumination [15]. Alternatively, this super-resolution method can be extended to fluctuation of the absorption induced by blinking or switchable [16] contrast agents. As implemented in SOFI, the analysis of higher-order statistics is expected to provide higher-resolution enhancement for our PA technique. However, such analysis usually requires a very large number of acquisitions (several thousand) even for a sufficiently large SNR [4], and was beyond the scope of our proof-of-concept experiment.

Funding

Agence Nationale de la Recherche (ANR-10-LABX-24, ANR-10-IDEX-0001-02 PSL*); European Research Council (ERC) (278025); Fondation Pierre-Gilles de (FPGG) (031).

Acknowledgment

O. K. acknowledges the support of the Marie Curie Intra-European Fellowship. The authors thank Laurent Bourdieu and Jean-François Léger for their helpful assistance with the milling machine.

 

See Supplement 1 for supporting content.

REFERENCES

1. P. Beard, Interface Focus 1, 602 (2011). [CrossRef]  

2. L. V. Wang and S. Hu, Science 335, 1458 (2012). [CrossRef]  

3. M. Omar, D. Soliman, J. Gateau, and V. Ntziachristos, Opt. Lett. 39, 3911 (2014). [CrossRef]  

4. T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, Proc. Natl. Acad. Sci. U.S.A. 106, 22287 (2009). [CrossRef]  

5. J.-E. Oh, Y.-W. Cho, G. Scarcelli, and Y.-H. Kim, Opt. Lett. 38, 682 (2013). [CrossRef]  

6. J. Gateau, T. Chaigne, O. Katz, S. Gigan, and E. Bossy, Opt. Lett. 38, 5188 (2013). [CrossRef]  

7. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (CRC Press, 1998).

8. B. Rao, K. Maslov, A. Danielli, R. Chen, K. K. Shung, Q. Zhou, and L. V. Wang, Opt. Lett. 36, 1137 (2011). [CrossRef]  

9. L. Wang, C. Zhang, and L. V. Wang, Phys. Rev. Lett. 113, 174301 (2014). [CrossRef]  

10. C. Zhang, C. Li, and L. V. Wang, IEEE Photon. J. 2, 57 (2010). [CrossRef]  

11. H. Roitner, M. Haltmeier, R. Nuster, D. P. O’Leary, T. Berer, G. Paltauf, H. Grün, and P. Burgholzer, J. Biomed. Opt. 19, 056011 (2014). [CrossRef]  

12. T. Chaigne, O. Katz, A. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014). [CrossRef]  

13. A. M. Caravaca-Aguirre, D. B. Conkey, J. D. Dove, H. Ju, T. W. Murray, and R. Piestun, Opt. Express 21, 26671 (2013). [CrossRef]  

14. P. Lai, L. Wang, J. W. Tay, and L. V. Wang, Nat. Photonics 9, 126 (2015). [CrossRef]  

15. M. Jang, H. Ruan, I. M. Vellekoop, B. Judkewitz, E. Chung, and C. Yang, Biomed. Opt. Express 6, 72 (2015). [CrossRef]  

16. K. K. Ng, M. Shakiba, E. Huynh, R. A. Weersink, A. Roxin, B. C. Wilson, and G. Zheng, ACS Nano 8, 8363 (2014). [CrossRef]  

References

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  1. P. Beard, Interface Focus 1, 602 (2011).
    [Crossref]
  2. L. V. Wang and S. Hu, Science 335, 1458 (2012).
    [Crossref]
  3. M. Omar, D. Soliman, J. Gateau, and V. Ntziachristos, Opt. Lett. 39, 3911 (2014).
    [Crossref]
  4. T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, Proc. Natl. Acad. Sci. U.S.A. 106, 22287 (2009).
    [Crossref]
  5. J.-E. Oh, Y.-W. Cho, G. Scarcelli, and Y.-H. Kim, Opt. Lett. 38, 682 (2013).
    [Crossref]
  6. J. Gateau, T. Chaigne, O. Katz, S. Gigan, and E. Bossy, Opt. Lett. 38, 5188 (2013).
    [Crossref]
  7. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (CRC Press, 1998).
  8. B. Rao, K. Maslov, A. Danielli, R. Chen, K. K. Shung, Q. Zhou, and L. V. Wang, Opt. Lett. 36, 1137 (2011).
    [Crossref]
  9. L. Wang, C. Zhang, and L. V. Wang, Phys. Rev. Lett. 113, 174301 (2014).
    [Crossref]
  10. C. Zhang, C. Li, and L. V. Wang, IEEE Photon. J. 2, 57 (2010).
    [Crossref]
  11. H. Roitner, M. Haltmeier, R. Nuster, D. P. O’Leary, T. Berer, G. Paltauf, H. Grün, and P. Burgholzer, J. Biomed. Opt. 19, 056011 (2014).
    [Crossref]
  12. T. Chaigne, O. Katz, A. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
    [Crossref]
  13. A. M. Caravaca-Aguirre, D. B. Conkey, J. D. Dove, H. Ju, T. W. Murray, and R. Piestun, Opt. Express 21, 26671 (2013).
    [Crossref]
  14. P. Lai, L. Wang, J. W. Tay, and L. V. Wang, Nat. Photonics 9, 126 (2015).
    [Crossref]
  15. M. Jang, H. Ruan, I. M. Vellekoop, B. Judkewitz, E. Chung, and C. Yang, Biomed. Opt. Express 6, 72 (2015).
    [Crossref]
  16. K. K. Ng, M. Shakiba, E. Huynh, R. A. Weersink, A. Roxin, B. C. Wilson, and G. Zheng, ACS Nano 8, 8363 (2014).
    [Crossref]

2015 (2)

2014 (5)

K. K. Ng, M. Shakiba, E. Huynh, R. A. Weersink, A. Roxin, B. C. Wilson, and G. Zheng, ACS Nano 8, 8363 (2014).
[Crossref]

H. Roitner, M. Haltmeier, R. Nuster, D. P. O’Leary, T. Berer, G. Paltauf, H. Grün, and P. Burgholzer, J. Biomed. Opt. 19, 056011 (2014).
[Crossref]

T. Chaigne, O. Katz, A. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

M. Omar, D. Soliman, J. Gateau, and V. Ntziachristos, Opt. Lett. 39, 3911 (2014).
[Crossref]

L. Wang, C. Zhang, and L. V. Wang, Phys. Rev. Lett. 113, 174301 (2014).
[Crossref]

2013 (3)

2012 (1)

L. V. Wang and S. Hu, Science 335, 1458 (2012).
[Crossref]

2011 (2)

2010 (1)

C. Zhang, C. Li, and L. V. Wang, IEEE Photon. J. 2, 57 (2010).
[Crossref]

2009 (1)

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, Proc. Natl. Acad. Sci. U.S.A. 106, 22287 (2009).
[Crossref]

Beard, P.

P. Beard, Interface Focus 1, 602 (2011).
[Crossref]

Berer, T.

H. Roitner, M. Haltmeier, R. Nuster, D. P. O’Leary, T. Berer, G. Paltauf, H. Grün, and P. Burgholzer, J. Biomed. Opt. 19, 056011 (2014).
[Crossref]

Bertero, M.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (CRC Press, 1998).

Boccacci, P.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (CRC Press, 1998).

Boccara, A.

T. Chaigne, O. Katz, A. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

Bossy, E.

T. Chaigne, O. Katz, A. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

J. Gateau, T. Chaigne, O. Katz, S. Gigan, and E. Bossy, Opt. Lett. 38, 5188 (2013).
[Crossref]

Burgholzer, P.

H. Roitner, M. Haltmeier, R. Nuster, D. P. O’Leary, T. Berer, G. Paltauf, H. Grün, and P. Burgholzer, J. Biomed. Opt. 19, 056011 (2014).
[Crossref]

Caravaca-Aguirre, A. M.

Chaigne, T.

T. Chaigne, O. Katz, A. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

J. Gateau, T. Chaigne, O. Katz, S. Gigan, and E. Bossy, Opt. Lett. 38, 5188 (2013).
[Crossref]

Chen, R.

Cho, Y.-W.

Chung, E.

Colyer, R.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, Proc. Natl. Acad. Sci. U.S.A. 106, 22287 (2009).
[Crossref]

Conkey, D. B.

Danielli, A.

Dertinger, T.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, Proc. Natl. Acad. Sci. U.S.A. 106, 22287 (2009).
[Crossref]

Dove, J. D.

Enderlein, J.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, Proc. Natl. Acad. Sci. U.S.A. 106, 22287 (2009).
[Crossref]

Fink, M.

T. Chaigne, O. Katz, A. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

Gateau, J.

Gigan, S.

T. Chaigne, O. Katz, A. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

J. Gateau, T. Chaigne, O. Katz, S. Gigan, and E. Bossy, Opt. Lett. 38, 5188 (2013).
[Crossref]

Grün, H.

H. Roitner, M. Haltmeier, R. Nuster, D. P. O’Leary, T. Berer, G. Paltauf, H. Grün, and P. Burgholzer, J. Biomed. Opt. 19, 056011 (2014).
[Crossref]

Haltmeier, M.

H. Roitner, M. Haltmeier, R. Nuster, D. P. O’Leary, T. Berer, G. Paltauf, H. Grün, and P. Burgholzer, J. Biomed. Opt. 19, 056011 (2014).
[Crossref]

Hu, S.

L. V. Wang and S. Hu, Science 335, 1458 (2012).
[Crossref]

Huynh, E.

K. K. Ng, M. Shakiba, E. Huynh, R. A. Weersink, A. Roxin, B. C. Wilson, and G. Zheng, ACS Nano 8, 8363 (2014).
[Crossref]

Iyer, G.

T. Dertinger, R. Colyer, G. Iyer, S. Weiss, and J. Enderlein, Proc. Natl. Acad. Sci. U.S.A. 106, 22287 (2009).
[Crossref]

Jang, M.

Ju, H.

Judkewitz, B.

Katz, O.

T. Chaigne, O. Katz, A. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

J. Gateau, T. Chaigne, O. Katz, S. Gigan, and E. Bossy, Opt. Lett. 38, 5188 (2013).
[Crossref]

Kim, Y.-H.

Lai, P.

P. Lai, L. Wang, J. W. Tay, and L. V. Wang, Nat. Photonics 9, 126 (2015).
[Crossref]

Li, C.

C. Zhang, C. Li, and L. V. Wang, IEEE Photon. J. 2, 57 (2010).
[Crossref]

Maslov, K.

Murray, T. W.

Ng, K. K.

K. K. Ng, M. Shakiba, E. Huynh, R. A. Weersink, A. Roxin, B. C. Wilson, and G. Zheng, ACS Nano 8, 8363 (2014).
[Crossref]

Ntziachristos, V.

Nuster, R.

H. Roitner, M. Haltmeier, R. Nuster, D. P. O’Leary, T. Berer, G. Paltauf, H. Grün, and P. Burgholzer, J. Biomed. Opt. 19, 056011 (2014).
[Crossref]

O’Leary, D. P.

H. Roitner, M. Haltmeier, R. Nuster, D. P. O’Leary, T. Berer, G. Paltauf, H. Grün, and P. Burgholzer, J. Biomed. Opt. 19, 056011 (2014).
[Crossref]

Oh, J.-E.

Omar, M.

Paltauf, G.

H. Roitner, M. Haltmeier, R. Nuster, D. P. O’Leary, T. Berer, G. Paltauf, H. Grün, and P. Burgholzer, J. Biomed. Opt. 19, 056011 (2014).
[Crossref]

Piestun, R.

Rao, B.

Roitner, H.

H. Roitner, M. Haltmeier, R. Nuster, D. P. O’Leary, T. Berer, G. Paltauf, H. Grün, and P. Burgholzer, J. Biomed. Opt. 19, 056011 (2014).
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K. K. Ng, M. Shakiba, E. Huynh, R. A. Weersink, A. Roxin, B. C. Wilson, and G. Zheng, ACS Nano 8, 8363 (2014).
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Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1. Experimental setup. A 5 ns laser pulse is focused onto a rotating diffuser. Each resulting speckle pattern (scale bar 200 μm, speckle grain size 30 μm ) illuminates a collection of absorbing beads, generating ultrasound detected with a linear ultrasonic array.
Fig. 2.
Fig. 2. (a) Photograph of sample 1 (randomly positioned 100 μm diameter beads). (b) Mean PA image over 100 speckle realizations, mimicking uniform illumination. Inset: mean PA image of a single isolated bead. (c) Variance image over 100 speckle realizations. Inset: variance image of a single isolated bead. Scale bars: 300 μm.
Fig. 3.
Fig. 3. (a) Photograph of sample 2. The distances between 100 μm diameter beads (center to center) were 120, 140, and 200 μm along the z direction (from top to bottom), and 250, 200, and 160 μm along the x direction (from left to right). The four 50 μm diameter beads used to estimate the PSF are also slightly visible (see Fig. S1 in Supplement 1). (b) Mean PA image over 100 speckle realizations, mimicking uniform illumination. (c) Square root of the variance image over 100 speckle realizations. Scale bars: 500 μm.
Fig. 4.
Fig. 4. (a) Mean image deconvolved by the PSF; white dashed lines indicates the cross-sections. (b) Square root of the variance image deconvolved by the squared PSF. (c) Horizontal cross-sections: deconvolved mean image (blue) and square root of deconvolved variance image (red). (d) Vertical cross-sections: deconvolved mean image (blue) and square root of deconvolved variance image (red). Scale bars: 500 μm.
Fig. 5.
Fig. 5. (a) Mean image deconvolved by the PSF. (b) Square root of the variance image deconvolved by the squared PSF; white dashed lines indicate the cross-section direction. (c) Photograph of sample 3. (d) Cross-sections. Blue curve, mean image; red curve, square root of variance image. Scale bars: 200 μm.

Equations (4)

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A ( r ) = [ μ a ( r ) × I ( r ) ] * h ( r ) ,
A ( r ) = I 0 × [ μ a ( r ) * h ( r ) ] ,
σ 2 [ A ] ( r ) μ a 2 ( r ) * h 2 ( r ) .
J ( x ) : = h 2 * x σ 2 [ A ] ^ 2 + α x 2 subject to x 0 ,

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