Multiple feedback based wavefront shaping method to retrieve hidden signal

Turbid materials, including biological tissue or human skin, scatter light and create complex interference patterns, known as speckle. This prevents light from being focused inside biological materials or retrieving information from objects behind scattering media, posing a fundamental limitation to many information processing and visualization technologies. Biomedical applications, such as photodynamic therapy (PDT)¹ and optogenetics applications,² are either constraint to the outer layer of skin or become invasive through the insertion of an optical fiber.³ 

Wavefront shaping techniques using spatial light modulators (SLMs) have emerged as an attractive proposition to address these issues.^4,5 The SLM modulates the incident wavefront in order to focus light through a scattering medium,⁶ using methodologies based on phase conjugation,^7–9 feedback based optimization,^10,11 the transmission matrix,^12,13 or semi-definite programming¹⁴ approach. The objective of most studies is to demonstrate focusing through a scattering medium by utilizing speckle feedback, e.g., speckle correlations feedback¹⁵ rather than recovering signals/information hidden by a scattering medium. Nonlinear fluorescent signal has also been used as feedback to obtain diffraction-limited focusing through turbid samples.¹⁶ Approaches that employ only fluorescence feedback often require the initially detected fluorescence intensity to be greater than a threshold signal to noise ratio (SNR), and the resulting focus position is not predetermined or controlled.¹⁷ A shaped focus can be utilized to image masked objects with the help of memory effect, but this does not work for thick scattering samples.^18–20 However, different biomedical approaches require to assess the signal emitted by deeply buried sources to extract information. For example, in applications like noninvasive glucose measurement that utilizes fluorescence technology²¹ or fluorogenic probes that emit signal only in response to specific events,²² retrieval of the emitted fluorescent signal is very important. Various other methods, including an artificial neural network, are being developed to address it.^23,24 Controlling the target position and assaying the biological processes in a targeted way are also essential to identify the specific function of certain cells precisely.

In this paper, we present an approach that allows tracking, localization, and optimization of fluorescent signal emitted by objects hidden within and/or behind a scattering medium. Here, our goal is not to find a sharp focus in the speckle, instead we want to optimize the fluorescent signal in a region of interest. We combine the traditional principle of feedback scheme based wavefront shaping together with a switch function that utilizes both the speckle intensity and the masked signal. The feedback signals are characterized by two different detectors: the first measures the speckle intensity from the highly scattering medium, and the second detector monitors the signal generated by the hidden targets. The algorithm exploits the fact that modulating the incident wavefront to generate a focus in the speckle redirects the scattered input fields. These redirected light fields will simultaneously induce a response from objects hidden within or behind the scattering medium, thereby locating targets. Once the target signal is located or reaches the threshold intensity, the feedback mechanism now switches to use the signal from the hidden object and then proceeds to enhance or optimize it. Our method is not dependent on a high SNR or memory effect. This technique is a stride toward identifying and imaging hidden objects within highly scattering media. This approach will continue to improve biomedical imaging. More specifically, it can be an ideal biomedical tool for nondestructive, noninvasive diagnosis.

The algorithm is designed to find and probe a target deep inside a highly scattering medium. We start with the traditional iterative method utilizing a continuous sequential algorithm²⁵ but a switch function is added. The algorithm starts with finding the optimal wavefront for creating a focus at the detector that monitors the speckle intensity. The pixels of the SLM are subdivided into N groups of pixels, known as superpixels. The phase of each superpixel is iterated from 0 to $2π$ to find the phase that maximizes the feedback signal. These initial optimization processes are taken to generate a focus. The continuous variation due to the phase modulation can increase the signal from the hidden objects. After a predetermined number of iterations (n), e.g., at minimum the first row of superpixels must be optimized; the algorithm starts to “look” for this hidden signal and locates the buried target using the second detector. Once the signal from the target reaches the threshold intensity, the feedback signal is switched to come from the second detector. The algorithm now proceeds to enhance the signal from the target. The localization and enhancement of the target signal can be categorized into two cases:

• We predetermine the target position where fluorescence could be expected. The iterative algorithm is then started to generate a focus at the chosen location using the speckle as feedback. The algorithm switches feedback when the fluorescence detected is above a defined threshold and then proceeds to enhance the signal.

• The algorithm finds the signal: The iterative optimization is started to generate a focus at a random speckle point. The algorithm independently monitors the fluorescence signal from different targets. After modulating n number of superpixels with speckle feedback, the current fluorescence intensity (I_n) is compared to the initial fluorescence intensity (I_int). The hidden fluorescent source that is emitting maximum intensity at this point of the optimization process is located and chosen as the target. The algorithm now switches to use the fluorescence as feedback to enhance its signal (see Fig. 1).

For both of these cases, a seamless switch from the speckle to the fluorescence feedback is permitted, once the hidden signal's intensity at the target position [$Ifluo(target)$] attains a value of at least η times higher than the initial intensity [$Iint(target)$]: $Ifluo(target)≥η×Iint(target)$⁠, where $1.1≤η≤2$⁠. The switching parameter, η, is both sample and case dependent. If the value of η is too small, the algorithm will switch feedback before the target intensity, and $Ifluo(target)$ is sufficiently higher than the noise. In such a case, the algorithm will not converge. If η is too high, the algorithm will not switch its feedback, and the algorithm will proceed to generate a focus at the chosen speckle point.²⁶ Once the switching conditions are fulfilled, the algorithm proceeds to adjust the phases of the remaining superpixels to enhance the masked signal. The speckle is not used as the feedback for the remainder of the process and is only monitored. A focus spot in the speckle will also be obtained as a result of the optimization process. A pictorial representation of the process is shown in the supplementary material (Fig. S1).

The experimental optical setup is illustrated in Fig. 2. The light source is a continuous wave helium–neon laser (HeNe, $λ=632.8$ nm). The beam is expanded and incident on a phase-only SLM (Santec 200). The polarization of the incident beam is controlled by a half-wave plate (HWP) and sent to the SLM through a polarizing beam splitter (PBS). The reflected beam is transmitted through a 4f imaging system and focused on the sample by a microscope objective (MO1). A second microscopic objective (MO2) is used to collect the speckle and fluorescence from the sample. MO2 is fixed on a moving stage that allows it to move in the z direction (up and down) and collect light from samples of different thicknesses. A dichroic mirror (DM) splits the signals emanating from the sample. The speckle is detected by CAM1 (Thorlabs CS2100M) and the fluorescence by CAM2 (Andor Sona sCMOS). We use an additional longpass filter (⁠$λc=650$ nm) to ensure CAM2 only detects fluorescence.

Plain yogurt and pig skin are used as the scattering media, and the hidden objects are fluorescent microspheres (carboxylate-modified polystyrene beads, 0.04 μm diameter). The beads are excited at $λ=632.8$ nm and the emission peaks at λ = 720 nm. To prepare a 750 μm thick yogurt sample, we spread plain white yogurt on two microscope slides and sandwich the fluorescent beads between them. The pig skin sample is 2300 μm thick and is placed directly on a slide with the fluorescent beads randomly dispersed on the surface.

Starting with case (i), we choose a point $(xspeck,yspeck)$ in the speckle (CAM1) and define a target point $(xfluo,yfluo)$ in the fluorescence image (CAM2). The algorithm begins with optimizing the intensity at (x_speck, y_speck) using the feedback from CAM1 and keeps track of the fluorescence intensity at (x_fluo, y_fluo). The speckle pattern created by the yogurt sample [Fig. 3(a)] has dark patches due to the absorption of the beads. A point near the darker region in the speckle is chosen as $(xspeck,yspeck)$⁠, which is marked by the white rectangle.

Prior to the optimization process, the fluorescence emitted by the beads is negligible, as seen in Fig. 3(b). Once the switching condition [$Ifluo(target)≥η×Iint(target)$] is met during speckle optimization, the algorithm now switches to acquire its feedback signal from CAM2.

For this experiment, we set the switching parameter $η=1.16$⁠. The switching condition was met after optimizing only 16 superpixels [Fig. 3(c)]. As the feedback switched to CAM2, the intensity variations at (x_speck, y_speck) are no longer important as they do not affect the remainder of the optimization process. However, the speckle is still monitored by CAM1, and the optimization process generates a focus spot in the speckle, which is indicated by the blue rectangle in Fig. 3(d). As seen in Figs. 3(e) and 3(f), the fluorescence intensity at (x_fluo, y_fluo) increased significantly after optimization.

For case (ii), we only define the speckle point, $(xspeck,yspeck)$⁠. After optimizing the first row of superpixels with speckle feedback, the algorithm compares the initial and current fluorescence intensity for all the beads and chooses the one that exhibited the largest increase in the emitted fluorescence thus far as the target $(xfluo,yfluo)$⁠. Once the target is chosen, the speckle optimization continues until the feedback switching condition is met. For the data shown in Fig. 4, the top row (a)–(c) was obtained with plain yogurt as the scattering medium and the bottom row (d)–(f) with pig skin. For both samples, η was set to 1.5. In Figs. 4(a) and 4(d), it can be seen that before the optimization process, the fluorescence intensity is very low. After optimization, one can observe in Figs. 4(b) and 4(e) that the intensity at the targets chosen by the algorithm has increased significantly. Despite the pig skin being thicker by an order of magnitude, the algorithm switched feedbacks after optimizing approximately the same number of superpixels [Figs. 4(c) and 4(f)].

One of the benefits of case (ii) over case (i) is that the fluorescence optimization is to be successful even with higher values of η. Unlike case (i), no prior knowledge of expected fluorescence position is needed for case (ii); however, case (i) allows one to control the target position (supplementary material, Fig. S4).

Contrary to other wavefront shaping methods based on only fluorescence feedback that require higher SNR to begin the optimization process, this method is applicable even when there is no fluorescence detected initially. In addition, we consider linear fluorescence, which remains a key mechanism in biomedical applications, as it allows imaging or recording of various biological process.^27,28

While in most instances, the enhancement is proportional to the number of iterations,²⁹ it is not true for fluorescence optimization as increasing number of iterations will eventually result in photobleaching. Like most other wavefront shaping approaches, our method is limited by the time it requires to perform the optimization process, which can be reduced by using a faster SLM or a digital micromirror device (DMD). In our experimental demonstration, the fluorescent emission was collected in transmission geometry, but we expect the method to work with collecting fluorescence in reflection (supplementary material, Figs. S5 and S6). However, the enhancement factor obtained in reflection geometry will be smaller in comparison with the one in the transmission geometry. Since more scattered light will distort the fluorescence image even further, this can impose limitation on the localization of the fluorescent signal.

In summary, we have proposed a wavefront shaping method that allows for the tracking and enhancement of initially weak signal emitted by sources hidden behind highly scattering media. We have introduced in the algorithm a smart switching function that toggles between feedback signals. We have demonstrated two main scenarios to show the flexibility of our approach. In one case, the hidden target position is known, and in the other, the algorithm locates the position of the hidden object and identifies the target. Our optical method is simple, easy to implement, and flexible enough to be used in either transmission or in reflection. We believe this technique will assist in retrieving information from hidden objects inside or behind turbid media and is a stride toward the development of noninvasive optical tool for medical diagnosis.

See the supplementary material for more experimental details and results including the demonstration of the method in epi-detection geometry.