Iterative optimization of time-gated reflectance for the efficient light energy delivery within scattering media

Seungwon Jeong; Dong-Young Kim; Ye-Ryoung Lee; Wonjun Choi; Wonshik Choi

doi:10.1364/OE.27.010936

1. Introduction

In optical imaging, sensing and light stimulation, objects of interest are often surrounded by complex media such as human skin and biological tissue. When light waves propagate in these media, they experience random diffusion due to the multiple light scattering induced by heterogeneous microscopic structures. Since light energy decreases with propagation depth and spreads laterally, only a small fraction of the incident energy is able to reach the object of interest. This issue has fundamentally limited the working depth of various non-invasive biophotonics techniques.

To reduce the detrimental effects of multiple scattering and increase the penetration depth of light waves, various efforts have been made in the context of wavefront shaping. The basic concept is to control the interference among scattered waves by the proper manipulation of the incident light wavefront. For example, spatial focusing of transmitted wave through a scattering layer was demonstrated at first [1,2], and both spatial and temporal focusing were implemented with the use of broadband light sources later on [3–5]. Instead of single point optimization, total transmission energy through scattering media was enhanced by coupling light energy to the transmission eigenchannels [6–8]. Although all these works have shown the effective way to exploit multiple light scattering, only the transmitted waves at the backside of the scattering medium could have been controlled. Previous studies dealing with the scattered waves inside the scattering medium required labeling agents [9], or the concepts were demonstrated only in the transmission geometry at which the applicability for in vivo studies has been limited.

Considering the geometry of in vivo applications, studies dealing with backscattered waves emerging from scattering media have been conducted. For instance, bright particles behind an aberrating layer were selectively focused by the injection of light to the eigenchannels of the steady-state backscattering matrix [10]. Eigenchannels with large singular values represent reflected complex fields where high-reflection particles were optimized. In principle, this method is equivalent to the iterative time-reversal operation of backscattered waves demonstrated in acoustics [11,12]. However, steady-state eigenchannels work only in a weakly scattering regime where multiple scattering is negligible. In the case of homogeneous scattering medium, light energy transmission through the medium was enhanced by the injection of steady-state reflection eigenchannels with low singular values [13]. Iterative wavefront shaping was also found to induce the enhancement of light energy transmission through a scattering medium by the attenuation of the intensity of the reflected wave from the medium [14]. However, the reduction of reflected energy by the steady-state eigenchannels is not effective for focusing energy to an embedded target.

The introduction of time-gated detection to reflection geometry has allowed wavefront shaping for light energy delivery be extended to a thick scattering medium [15,16]. In fact, similar approaches exploiting the combined use of the time-gated imaging and wavefront shaping were proposed earlier in the context of adaptive optics for enhancing the signal to noise ratio of imaging in the weakly scattering regime [17,18]. Recently, the selective focusing of multiple scattered waves to a deeply embedded target was achieved by the experimental realization of time-gated reflection eigenchannels with large singular values [16]. Time-gating mechanism can discriminate the waves having interacted with the embedded target object among the total reflected waves from deep scattering media, and high-reflection eigenchannel with specific arrival time can mainly affect the scattered waves from the target object. In our previous work, wavefront shaping of eigenchannels was implemented after the measurement of time-gated reflection matrix. Since the measured matrix contains the deterministic information of multiple scattered waves, eigenchannel acquisition from the measured matrix is ideal in terms of focusing efficiency. However, stable and static conditions are required during the matrix measurement, and these requirements undermine the applicability of the approach to dynamic samples.

Here, we propose an iterative feedback approach to efficiently focus light energy to a target object embedded within a scattering medium. Unlike the previous iterative optimization approach, which maximizes the total backscattering intensity, we selectively measure and enhance the intensity of the backscattered waves with the specific flight time. Reflection microscopy based on low-coherence and off-axis interferometry is used to record a complex field map of time-gated reflection and obtain the total intensity of the backscattered wave with the flight time associated with the target depth. From the self-interference of the randomly segmented incident wave, we optimized this total time-gated intensity. Our proposed method shows not only similar effect as previously demonstrated time-gated reflection eigenchannel, but also the potential to focus light energy to the target in dynamic condition.

2. Experimental setup

The schematic of the experimental setup for detecting the intensity of backscattered waves at a specific flight time is shown in Fig. 1(a). A Ti:Sapphire laser (central wavelength: 780 nm, pulse width ~60 fs) was used as the light source for femtosecond-scale time-gated measurement. A spatial light modulator (SLM, X10468-02, Hamamatsu) was installed at the conjugate plane of the sample plane to project patterned illumination to the sample (Fig. 1(b)). The illumination area on the sample plane was 40 × 40 µm², and the spatial frequency spectrum of the illumination pattern covered the angular range corresponding to the numerical aperture of 0.4. This set the effective number of orthogonal channels to about 1300.

Fig. 1 Iterative optimization of time-gated reflection signal. (a) Experimental schematic diagram. Ti:Sapphire laser (central wavelength: 780 nm, pulse width ~60 fs), BS1-4, Beamsplitters; SLM, Spatial light modulator; OL_R, Objective lens for reflection; OL_T, Objective lens for transmission; SM, Scanning mirror; DG, Diffraction grating;, Camera 1 for reflection measurement and Camera 2 for transmission measurement. SLM and camera plane are at the conjugated plane of sample plane, and 4-f lens relay was omitted in this scheme. (b) Representative phase in SLM. Part I (blue pixels) and II (red pixels) are randomly chosen at each iteration step. Color bar, phase in radians. (c) Experimental measurement of time-gated reflection intensity as a function of $Δ ϕ$ at the iteration steps of 5, 15, 45, 65, 100.

Download Full Size | PDF

Scanning mirror (SM) was used to control the length of the reference arm and select the time of flight of interest. Only the first-order diffracted wave from the diffraction grating (DG, Ronchi 72/mm, Edmund) was used for the reference wave to interfere with the sample wave at an angle in camera 1 plane (sCMOS, pco Edge 4.2) with its temporal pulse front parallel to the camera plane. By applying Hilbert transform to the recorded interferogram [19,20], we obtained the time-gated complex field map of the backscattered wave from the sample at the gating window set by the SM. We chose the flight time $t_{0}$ at which the reflection from the target was most probable. To identify $t_{0}$ , SM was scanned across a wide range and the total intensity of the time-gated complex field map, $I_{R} (t)$ was obtained (black curve in Fig. 2(a)). As a target sample, we embedded a thin 10 µm-diameter silver disc underneath a Poly-dimethylsiloxane (PDMS) layer in which 1 µm-diameter polystyrene particles were randomly distributed. The thickness of the silver disc was about 30 nm. The scattering and transport mean free paths of the PDMS layer were about 48.5 µm and 190 µm, respectively, and the silver disc was located at a depth of 240 µm. A prominent peak appeared at $t_{0}$ = 2.27 ps, which is almost equal to the flight time of the ballistic wave set by the depth of the silver disc and the average refractive index of the PDMS layer. This is mainly because the scattering layer has a large anisotropy factor, $g \approx 0.9$ . We also recorded the transmission image with camera 2 (CCD, LM135M, Lumenera) to directly monitor the light intensity at the silver disc target. The field of view of the transmission image was about 200 × 200 µm².

Fig. 2 Experimental result of time-gated reflection feedback. (a) Temporal reflection as feedback process. As the iteration number increases, the reflection of only the target time is increased. (b) The reflection enhancement $η_{r e}$ of each iteration step. (c) The transmission enhancement of target region $η$ of each iteration step. Blue straight lines in (b) and (c) are the enhancement of top eigenchannel from the measurement of time-gated reflection matrix. (d) Amplitude maps of time-gated reflection for initial random pattern (left) and optimized pattern (right). Scale bar, 10 µm. (e) Logarithmic map of transmission image for initial random pattern (left) and optimized pattern (right). Scale bar 40 µm. The inset shows the magnified map of the center region. Yellow dashed-circle indicates the region of the target. Each map in (d) and (e) is normalized by the maximum value of the optimized image.

Download Full Size | PDF

3. Optimization of the time-gated reflection intensity

To maximize the intensity of the reflected wave at the flight time $t_{0}$ , we first uploaded an arbitrary phase pattern on the SLM. We then randomly divided the SLM pixels into two parts, i.e. part I (blue pixels) and part II (red pixels) as shown in Fig. 1(b). We then added the overall phase $Δ ϕ$ only to the red pixels and recorded the total time-gated intensity $I_{R} (t = t_{0}) .$ As shown in Fig. 1(c), $I_{R} (t = t_{0})$ oscillated sinusoidally with respect to $Δ ϕ .$ For optimization, we measured the total intensity at three steps of $Δ ϕ,$ i.e. $Δ ϕ = 0, 2 π / 3, 4 π / 3,$ and extracted $Δ ϕ = Δ ϕ^{(1)}$ that would maximize the total intensity by using phase-shifting interferometry algorithm [21]. After adding $Δ ϕ^{(1)}$ to the red pixels, we measured the total time-gated intensity $I_{R}^{(1)} (t = t_{0}) .$ Then, a new random choice of parts I and II was made, and the same maximization operation was applied to find $Δ ϕ = Δ ϕ^{(2)}$ and $I_{R}^{(2)} (t = t_{0}) .$ We repeated the same procedure until the total intensity was saturated.

Figure 2(a) shows the time-dependent total reflection intensity $I_{R}^{(j)} (t)$ with the increase of the iteration number j. It was apparent that only the intensity at the selected time $t_{0}$ increased with the number of iterations. To quantify this enhancement of reflection intensity, we defined the reflection enhancement $η_{r e}$ as the ratio of $I_{R}^{(j)} (t = t_{0})$ to the initial $I_{R} (t = t_{0}) .$ Fig. 2(b) shows $η_{r e}$ as a function of j. $η_{r e}$ increased and gradually became saturated after 3000 iterations. The maximum enhancement factor reached almost 10. Figure 2(d) shows the amplitude maps of backscattered waves at $t_{0}$ before and after the optimization. We observed overall increase of reflection and more reflection enhancement near the position of the target after optimization.

During the feedback process, the transmission images were also recorded (Fig. 2(e)), and the total intensity $I_{T}^{(j)}$ at the target area indicated by the dashed circle in Fig. 2(e) was obtained. This intensity is proportional to the light intensity impinging on the target because the silver disc target used for the experiment has transmittance of 70%. Like the reflection enhancement factor, we defined the target enhancement factor $η$ as the intensity $I_{T}^{(j)}$ at the j^th iteration with respect to the initial intensity at the target. As shown in Fig. 2(c), $η$ was increased similarly to $η_{r e}$ and reached a maximum transmission enhancement factor of $η = 5.7$ . Figure 2(e) shows the intensity maps of the transmitted wave before and after the optimization. Note the distinctly bright spot at the position of the target, which is direct evidence that the wave was focused on the target.

3.1 Working principle of iterative feedback optimization of the time-gated intensity

In this section, the working principle on the iterative optimization of the time-gated reflectance is presented. As we reported earlier in the steady-state study [14], the optimization method used here enhances the contribution of eigenchannels with large eigenvalues. The main difference of this study is that it considers time-gated reflection eigenchannels instead of steady-state eigenchannels. The time-dependent interaction of light waves with a linear scattering medium can be described by the following relation:

E^{R} (t) = R (t) E^{i n},

where

E^{i n}

and

E^{R} (t)

represent incident and time-gated reflected complex fields, respectively.

R (t)

is the time-gated reflection matrix, which relates the complex field maps of reflected waves to a set of orthogonal modes at the input plane. As shown in our earlier study [14], the best way to maximize the total reflection at the selected flight time is to measure

R (t)

and find its eigenchannel with the largest eigenvalue by the singular value decomposition:

R (t) = U Σ V^{†} .

Here, $V$ and $U$ are unitary matrices whose column vectors correspond to time-gated reflection eigenchannels at the input and output planes, respectively. $Σ$ is a diagonal matrix with the diagonal elements $σ_{m}$ , which are called singular values. The physical meaning of singular values is the amplitude of reflection of each eigenchannels. The elements, $σ_{m}$ , in the $Σ$ are typically sorted in descending order with respect to m. For a given $σ_{m}$ , the m^th column vectors of $V$ and $U$ , $v_{m}$ and $u_{m}$ , are the corresponding eigenchannels at the specific time t at the input and output planes, respectively. The arbitrary incident wave is the superposition of the input eigenchannels and can be written as:

E^{i n} = \sum_{m = 1}^{N} c_{m} v_{m},

where N is the total number of eigenchannels and

c_{m}

is the complex coefficient of the input eigenchannel obtained by the inner product between

E^{i n}

and

v_{m}

. Every input eigenchannel contributes to the arbitrary incident wave, and the contributions are statistically equal for ensemble average. After the multiplication of

R (t)

on this incident wave, the reflected wave can be composed into the output eigenchannels as:

E^{R} (t) = \sum_{i = 1}^{N} c_{i} ​ σ_{i} ​ u_{i} .

In the reflected waves, the coefficient of each eigenchannel is weighted by the singular value, $σ_{m}$ , of the corresponding eigenchannels. Therefore, the contribution of the high-reflection eigenchannels is statistically larger than that of the low-reflection eigenchannels in reflected waves.

The main interest of the present study is to identify the eigenchannels with large eigenvalues without measuring the time-gated reflection matrix. For this purpose, we presented the iterative optimization of the total intensity at the specific flight time $t_{0}$ . In our experimental procedure, the incident wave was spatially decomposed into part I and part II on the SLM as shown in Fig. 1(b), and the two waves are incident at the same time as shown in Fig. 1(a). Each decomposed incident wave can be represented by the superposition of the input eigenchannels $v_{m}$ as follows:

\begin{array}{l} E^{i n} = E^{i n, I} + E^{i n, I I} \\ = \sum_{m = 1}^{N} [c_{m}^{I} v_{m} + c_{m}^{I I} v_{m}] . \end{array}

Here, $E^{i n, I}$ and $E^{i n, I I}$ are incident waves coming from the part I and part II on the SLM, respectively. $c_{m}^{I}$ and $c_{m}^{I I}$ are the complex coefficients of input eigenchannels obtained by the inner product between $E^{i n, I}$ and $v_{m}$ and between $E^{i n, I I}$ and $v_{m}$ , respectively. When we modulated the phase of the part II by $Δ ϕ$ in the incident wave, the modulated incident wave is written as:

\begin{array}{l} E^{i n} (Δ ϕ) = E^{i n, I} + e^{i Δ ϕ} E^{i n, I I} \\ = \sum_{m = 1}^{N} [c_{m}^{I} v_{m} + c_{m}^{I I} e^{i Δ ϕ} v_{m}] . \end{array}

In the same manner, the time-gated reflected wave, $E^{R} (t, Δ ϕ),$ is also decomposed into two parts as:

\begin{array}{l} E^{R} (t, Δ ϕ) = E^{R, I} (t) + E^{R, I I} (t) e^{i Δ ϕ} \\ = \sum_{m = 1}^{N} [c_{m}^{I} σ_{m} u_{m} + c_{m}^{I I} σ_{m} u_{m} e^{i Δ ϕ}], \end{array}

where

E^{R, I} (t)

and

E^{R, I I} (t)

are the time-gated reflected waves of

E^{i n, I}

and

E^{i n, I I}

, respectively. Since the eigenchannels are orthogonal, interference occurs only between eigenchannels of the same index. Therefore, the total intensity of the reflected wave is expressed as:

I^{R} (t, Δ ϕ) = {| E^{R} (t, Δ ϕ) |}^{2} = {\sum_{m = 1}^{N} τ_{m} | c_{m}^{I} + c_{m}^{I I} e^{i Δ ϕ} |}^{2},

where

τ_{m}

is the square of the singular value, such that

τ_{m} = σ_{m}^{2}

, and indicates the eigenvalue of the m^th eigenchannel. Since the intensity contributed by each eigenchannel takes a sinusoidal form as

Δ ϕ

is modulated from 0 to 2π, the total intensity of the time-gated reflected signal can be described as:

I^{R} (t, Δ ϕ) = A + B \cos (Δ ϕ + ϕ_{0}),

where

ϕ_{0}

is the phase determined by the random choice of part I and II in the SLM. The total intensity can be maximized by setting

Δ ϕ

as

- ϕ_{0}

. Since Eq. (6) is the summation with a weighting factor

τ_{m},

eigenchannels with large eigenvalues contribute preferentially to determining

ϕ_{0} .

As introduced in the previous steady-state regime study, this enables the maximization process to preferentially determine the phase of high-reflection eigenchannels. The increase of modulation contrast,

| B / A |,

is one of the direct experimental evidences that the iterative feedback optimization works since it indicates that the small number of eigenchannels dominantly contribute to the interference. For experimental verification, we recorded the contrast of

Δ ϕ

modulation from the coefficient of 3-step phase-shift at each iteration. The modulation contrast increased steeply from the beginning of the optimization process and converged to the maximum values (Fig. 3(a)), confirming that the input phase pattern converged to the input eigenchannels with large eigenvalues during the feedback operation.

Fig. 3 Comparison between time-gated eigenchannels and feedback results. (a) Contrast of modulation with $Δ ϕ$ at each iteration step. (b) The contribution of each eigenchannel to the incident wave before (blue) and after (red) the feedback process. Inset shows the contribution of top 10 channels. (c) The averaged contribution of the incident wave of the first 10 eigenchannels (red) and last 10 eigenchannels (blue) with respect to the number of iterations.

Download Full Size | PDF

3.2 Comparison between iterative optimization and time-gated eigenchannels

To obtain direct evidence that the iterative optimization of total backscattering intensity at a flight time $t_{0}$ converges to the time-gated eigenchannels with large eigenvalues, we experimentally recorded the time-gated reflection matrix $R (t)$ and coupled light to the eigenchannel with the largest eigenvalue (see experimental details in [16]). The measured reflection enhancement factor was 12.0 (blue line in Fig. 2(b)), which is slightly higher than the maximum $η_{r e}$ achieved by the iterative optimization. The discrepancy arose because iterative optimization did not converge to the eigenchannel with the largest eigenvalue, but to the superposition of eigenchannels with relatively large eigenvalues. Still, the feedback optimization could attain about 83% of the ideal reflectance. Similarly, the target enhancement factor $η$ of the feedback optimization was about 75% of that of the time-gated reflection eigenchannel.

We investigated the optimized wavefront in terms of time-gated reflection eigenchannels. We compared the contribution of each eigenchannel (Fig. 3(b)) determined by the square of cross-correlation between $E^{i n}$ and $v_{i}$ for both initial and optimized wavefronts. By the definition of contribution of eigenchannel in input pattern, the sum of total contribution is unity whether for initial or optimized patterns. However, while for the optimized solution (red curve in Fig. 3(b)) the contribution of specific eigenchannels with large eigenvalues was much higher than other eigenchannels, in the case of the initial random pattern each input eigenchannel contributed equally (blue curve in Fig. 3(b)).

In addition, we compared the contribution of eigenchannels with top 10 indices (high-reflection, red curve in Fig. 3(c)) and bottom 10 indices (low-reflection, blue curve in Fig. 3(c)) to input patterns at each iteration step. As the number of iteration steps increased, the contribution of the high-reflection eigenchannels increased while that of the low-reflection eigenchannels was decreased. These inspections of the optimized wavefront confirmed that the iterative optimization of time-gated reflection intensity indeed converged the input wavefront to the highly reflecting time-gated reflection eigenchannels.

3.3 Overcoming the sample drift

In our study, we could enhance light energy delivery to the embedded target by the iterative optimization of time-gated reflection intensity. Although the enhancement factor of the proposed method is slightly smaller than that of our previous study, unlike the previous study it does not require measurement of the time-gated reflection matrix to successfully find a similar solution. While the matrix measurement is the most effective way to find eigenchannels, it is highly susceptible to the sample perturbations typically occurring in biological and biomedical applications. In this respect, this feedback optimization approach has a practical value in some of the applications where sample drift is inevitable.

In this section, we investigated the performance of the feedback method in the presence of external perturbation during the iterative optimization process. We used a micromanipulator (Sutter Instruments, MP285) to move the target laterally four times with a step of 1 µm during whole feedback process (Fig. 4(a)). Whenever the sample stage shifted, $η_{r e}$ drastically dropped since the optimized solution was no longer effective due to the movement of the target. However, the feedback operation started to optimize the target signals, and $η_{r e}$ recovered quickly until the target was shifted again (Fig. 4(b)). We controlled the sample stage in same manner while measuring the time-gated reflection matrix and compared the enhancement factor of eigenchannel (blue solid line in Fig. 4(b)). The $η$ achieved by the two methods was also obtained and compared (Fig. 4(c)). Our proposed method can track the target and enhance the light energy whereas the matrix method becomes ineffective at delivering light energy to a moving target. In fact, the time required for 3000 iterations takes longer than the reflection matrix approach, which was about 20 min in the present study. However, reflection matrix approach can only be effective after the completion of the measurements while the iterative approach is working during the optimization process. This benefit of the iterative approach was demonstrated in Fig. 4.

Fig. 4 Light energy optimization to the target drifted in time. (a) Schematic of the sample preparation. Sample stage was shifted at a step of 1 µm laterally using a micromanipulator (not shown). The reflection enhancement $η_{r e}$ (b) and the target transmission enhancement $η$ (c) of each iteration step during the sample drift. The arrows indicate the times when the target was moved.

Download Full Size | PDF

4. Discussion

To conclude, we could enhance light energy delivery to a target deeply embedded behind about 1.2 transport mean free path-thick scattering layer using iterative feedback optimization of the time-gated reflection intensity. We proved that the optimized solution converges to the time-gated eigenchannels with large eigenvalues and demonstrated that the efficiency of light energy delivery can reach up to 80% of the ideal solution obtained by the matrix measurements. In addition, we demonstrated the quick recovery of light energy optimization to the target with external perturbation, where matrix measurement approach fails to work. Note that our study is the first proof-of-concept study demonstrating the effectiveness of feedback optimization of time-gated reflection intensity, so the system operation speed has not yet been optimized. In the present study, slow refresh rate (~10 Hz) of liquid-crystal based SLM is a limiting factor for operation speed. In addition, raw image acquisition, time-gated complex field calculation and optimal phase determination take significant time for each iteration step. Considering all these processes, the actual optimization rate of one iteration step was set to about 1.6 Hz, and the total feedback process took about 30 minutes for 3000 iterations.

The proposed method could be sped up by using a high-speed wavefront shaping device such as a digital micro-mirror device (DMD) or micro-electro-mechanical system (MEMS)-based SLM [22–24]. In addition, a field programmable gate array (FPGA) could be used to shorten data acquisition and image processing times [23,25]. Assuming the readout time is a few milliseconds for a few hundreds of lines of camera detection, the iteration rate of our method can be increased to about 100 Hz. Since the proposed approach requires the time-gated backscattering intensity, not the time-gated image, a single-pixel detector such as photodiode can be used along with high-speed gating such as Kerr gating [26]. Then, the iteration speed can reach those demonstrated in the point-optimization studies [22–24]. With further technical development, our proposed method has the potential to efficiently deliver light energy to targets embedded within a biological tissue where internal structures are dynamic. Future works may include in vivo applications of fast biomedical sensing or optical stimulation such as optogenetics [27] or laser therapy [28] for live animals.

Funding

Institute for Basic Science (IBS-R023-D1).

References

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

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

3. O. Katz, E. Small, Y. Bromberg, and Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5(6), 372–377 (2011). [CrossRef]

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(25), 253901 (2016). [CrossRef] [PubMed]

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

6. M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 581–585 (2012). [CrossRef]

7. R. Sarma, A. G. Yamilov, S. Petrenko, Y. Bromberg, and H. Cao, “Control of Energy Density inside a Disordered Medium by Coupling to Open or Closed Channels,” Phys. Rev. Lett. 117(8), 086803 (2016). [CrossRef] [PubMed]

8. C. W. Hsu, S. F. Liew, A. Goetschy, H. Cao, and A. D. Stone, “Correlation-enhanced control of wave focusing in disordered media,” Nat. Phys. 13(5), 497–502 (2017). [CrossRef]

9. R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9(9), 563–571 (2015). [CrossRef] [PubMed]

10. S. M. Popoff, A. Aubry, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, “Exploiting the time-reversal operator for adaptive optics, selective focusing, and scattering pattern analysis,” Phys. Rev. Lett. 107(26), 263901 (2011). [CrossRef] [PubMed]

11. C. Prada and M. Fink, “Eigenmodes of the Time-Reversal Operator - a Solution to Selective Focusing in Multiple-Target Media,” Wave Motion 20(2), 151–163 (1994). [CrossRef]

12. C. Prada, F. Wu, and M. Fink, “The Iterative Time-Reversal Mirror - a Solution to Self-Focusing in the Pulse Echo Mode,” J. Acoust. Soc. Am. 90(2), 1119–1129 (1991). [CrossRef]

13. M. Kim, W. Choi, C. Yoon, G. H. Kim, S. H. Kim, G. R. Yi, Q. H. Park, and W. Choi, “Exploring anti-reflection modes in disordered media,” Opt. Express 23(10), 12740–12749 (2015). [CrossRef] [PubMed]

14. W. Choi, M. Kim, D. Kim, C. Yoon, C. Fang-Yen, Q. H. Park, and W. Choi, “Preferential coupling of an incident wave to reflection eigenchannels of disordered media,” Sci. Rep. 5(1), 11393 (2015). [CrossRef] [PubMed]

15. Y. Choi, T. R. Hillman, W. Choi, N. Lue, R. R. Dasari, P. T. C. So, W. Choi, and Z. Yaqoob, “Measurement of the time-resolved reflection matrix for enhancing light energy delivery into a scattering medium,” Phys. Rev. Lett. 111(24), 243901 (2013). [CrossRef] [PubMed]

16. S. Jeong, Y. Lee, W. Choi, S. Kang, J. Hong, J. Park, Y. Lim, H. Park, and W. Choi, “Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering,” Nat. Photonics 12(5), 277–283 (2018). [CrossRef]

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

18. J. Jang, J. Lim, H. Yu, H. Choi, J. Ha, J. H. Park, W. Y. Oh, W. Jang, S. Lee, and Y. Park, “Complex wavefront shaping for optimal depth-selective focusing in optical coherence tomography,” Opt. Express 21(3), 2890–2902 (2013). [CrossRef] [PubMed]

19. Z. Yaqoob, T. Yamauchi, W. Choi, D. Fu, R. R. Dasari, and M. S. Feld, “Single-shot full-field reflection phase microscopy,” Opt. Express 19(8), 7587–7595 (2011). [CrossRef] [PubMed]

20. Y. Choi, T. D. Yang, K. J. Lee, and W. Choi, “Full-field and single-shot quantitative phase microscopy using dynamic speckle illumination,” Opt. Lett. 36(13), 2465–2467 (2011). [CrossRef] [PubMed]

21. P. S. Huang and S. Zhang, “Fast three-step phase-shifting algorithm,” Appl. Opt. 45(21), 5086–5091 (2006). [CrossRef] [PubMed]

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

23. B. Blochet, L. Bourdieu, and S. Gigan, “Focusing light through dynamical samples using fast continuous wavefront optimization,” Opt. Lett. 42(23), 4994–4997 (2017). [CrossRef] [PubMed]

24. A. S. Hemphill, Y. Shen, Y. Liu, and L. V. Wang, “High-speed single-shot optical focusing through dynamic scattering media with full-phase wavefront shaping,” Appl. Phys. Lett. 111(22), 221109 (2017). [CrossRef] [PubMed]

25. D. Wang, E. H. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, “Focusing through dynamic tissue with millisecond digital optical phase conjugation,” Optica 2(8), 728–735 (2015). [CrossRef] [PubMed]

26. W. Tan, Z. Zhou, A. Lin, J. Si, P. Zhan, B. Wu, and X. Hou, “High contrast ballistic imaging using femtosecond optical Kerr gate of tellurite glass,” Opt. Express 21(6), 7740–7747 (2013). [CrossRef] [PubMed]

27. A. M. Packer, B. Roska, and M. Häusser, “Targeting neurons and photons for optogenetics,” Nat. Neurosci. 16(7), 805–815 (2013). [CrossRef] [PubMed]

28. X. Huang, P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Gold nanoparticles: interesting optical properties and recent applications in cancer diagnostics and therapy,” Nanomedicine (Lond.) 2(5), 681–693 (2007). [CrossRef] [PubMed]

Iterative optimization of time-gated reflectance for the efficient light energy delivery within scattering media

Abstract

1. Introduction

2. Experimental setup

3. Optimization of the time-gated reflection intensity

3.1 Working principle of iterative feedback optimization of the time-gated intensity

3.2 Comparison between iterative optimization and time-gated eigenchannels

3.3 Overcoming the sample drift

4. Discussion

Funding

References

Cited By

Figures (4)

Equations (9)

Optics Express