1 Introduction

Because of multiple scattering, the propagation of light in random media poses a fundamental problem in optical imaging technologies. The challenge becomes much more difficult when considering obtaining mesoscopic-level resolution in a scattering media. Most of the optical imaging methods still rely on the collection of ballistic light to construct the sample information, such as conventional microscopy imaging. They provide diffraction-limited resolution but image penetration is limited to a superficial level. This is because the amount of ballistic (or single scattering) light decreases exponentially with the penetration depth. At present, one method to overcome this is to take advantage of diffuse light reflected back from the layers deep inside the tissue, such as diffuse optical tomography, acousto-optic imaging, and photoacoustic imaging. But their resolutions are severely degraded because they rely on diffused light to form an image. In modern optical society, there are two techniques to discriminate single scattering light from the multiple scattering light for high-resolution imaging capacity. The first option is confocal grating technology, such as confocal microscopy [1] or two-photon microscopy [2,3,4], which spatially rejects unwanted multiple scattering light based on the spatial filter. Another option is the coherence grating method, such as optical coherence tomography [5, 6], which extracts single scattering light based on the path length they travel in tissue. The combining of these two gates together, optical coherence microscopy [7, 8], can be stronger than either gate individually, achieving greater image penetration in scattering medium without compromising the imaging resolution.

Either for optical imaging or focusing purpose, a lot of remarkable works have been done to break through the limitation caused by multiple scattering. The light manipulation method was proposed [9], known as wavefront shaping, to focus light through a highly scattering medium with the help of a spatial light modulator [10,11,12]. There have been many remarkable signs of progress such as the investigation of transmission matrix to describe the light propagation in a complex medium [13,14,15,16] and the presence of reflection matrix method to imaging through highly scattering tissue [17,18,19,20].

In this paper, we have demonstrated a reflection matrix OCT, which has the imaging ability of 15 times of the SMFP. At the same time, by using the lock-in detection instead of the four-step phase-shift method, the acquisition speed of each scanning point has been accelerated to 0.37 s. It is about ten times faster than the previous four-step phase-shift method (4.15 s for each scanning point). Then, we configured the sample arm to a transmitted mode for light focusing purposes. Based on a high-speed and high-sensitivity complex light field reconstruction technology, we realize the light focusing through the sample at the speed of ~113 ms.

2 Methods

2.1 Experimental Setup

The experimental setup to record the sample’s reflection matrix is depicted in Fig. 32.1. A femtosecond laser with center wavelength \(\lambda_{0} = 790\;{\text{nm}}\) and spectrum bandwidth \(\Delta \lambda = 90\;{\text{nm}}\) is first collimated and expanded by a pair of lenses. After passing through a beam splitter (BS1), the beam splits into the sample arm and reference arm.

Fig. 32.1
figure 1

Experimental setup for the measurement of RM

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In the reference arm, optical frequency is shifted to f0 + fr, where f0 is the center frequency of the laser and fr is the frequency difference of the two acousto-optic modulators (AOM). In our case, fr is 40 kHz. After passing through another pair of lenses and pinhole, BS2, PBS2, and a mirror, the reference light is then reflected back at BS3. In the sample arm, the phase of the beam is shaped by a spatial light modulator (PLUTO-2, HOLOEYE) operating at phase-only mode, and subsequently transmitted through the BS1 again. After passing through a PBS1 and a QWP oriented at 45°, it focuses onto the sample through a microscope objective (MO). In order to detect the phase of the sample, a piece of compensation glass has been used to match the dispersion introduced by the two AOMs in the reference arm. Finally, the interference signal will be detected by the lock-in camera. The benefit of using this type of camera is that it can directly output two components, in-phase (I) and quadrature (Q), to form the complex light field.

2.2 Time-Reversal Operation for Imaging Through Scattering Medium

In this setup, we apply a point-to-point scanning strategy to collect the sample information. For each scanning point, there will be a 2D matrix filled with complex light field information. Then, we reshape it into a 1D vector and fill it into one column of the RM. After finishing all the scanning and repeating this filling process, we achieve a huge matrix, the so-called reflection matrix. By using the singular value decomposition and time-reversal operation [21, 22], it is able to restore the imaging of the target beneath the scattering layer.

2.3 Wavefront Shaping for Focusing Light Through Scattering Medium

For light focusing purposes, we have changed the configuration of the sample arm into a transmitted mode, as shown in Fig. 32.2. Light from the first microscopy (M1) focused onto the front of the sample and the transmitted light would be collected by the second microscopy (M2).

Fig. 32.2
figure 2

Experimental setup for focusing light

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As shown in Fig. 32.3, it is the basis of our proposed high-speed wavefront method. In Fig. 32.3a, a plane wave incidents onto a scattering medium, the output beam forms a speckle pattern. Based on the fact that there always exists an optimal wavefront, by shaping the incident light to this wavefront, the transmitted light will become all in phase again. Equation (32.1) shows how to calculate this optimal wavefront:

$$O_{in} = E_{in} * E_{out}^{ - 1} * E_{in}$$
(32.1)
Fig. 32.3
figure 3

Principle of high-speed wavefront shaping

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3 Results and Discussion

3.1 Imaging at the Single Scattering Region

At this step, the imaging target is two beads attached to cover glass and there is no scattering layer (as shown in Fig. 32.4a). Figure 32.4b shows the distribution of singular values. We can see the singular values that have the first two corresponding to the imaging targets. Figure 32.4c is the microscopy image of the target for comparison purposes. Figure 32.4d–f shows the recovered images by using the first singular vector, second singular vector, and the first two singular vectors, respectively.

Fig. 32.4
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Imaging at the single scattering region

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3.2 Imaging at Multiple Scattering Regions

This time, we have inserted a high scattering layer, a piece of A4 paper sheet, between the microscopy and the cover glass (as shown in Fig. 32.5a). The thickness of the sheet is 97 μm and the SMFP is 6.4 μm, which means the optical thickness of the scattering layer is 15.2 SMFP. Figure 32.5b shows the distribution of singular values. We can see the singular values that have the first two corresponding to the imaging targets. Figure 32.5c–e shows the recovered images by using the first singular vector, second singular vector, and the first two singular vectors, respectively. Based on the above results, the RMOCT presents its ability to imaging ability through 15.2 SMFP.

Fig. 32.5
figure 5

Imaging at multiple scattering regions

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3.3 Imaging Through a Thick Biological Sample

We have home-made a highly scattering layer (0.8 mm thickness phantom) by adding 20 g titanium dioxide into a 100 g silicone rubber base. The imaging target this time is a polydimethylsiloxane (PDMS) material, which is soft and flexible. Figure 32.6a is the sample setup. We use a water immersion objective with a bigger numerical aperture this time. Figure 32.6b shows the distribution of singular values in decreasing order. Figure 32.6c is the microscopy imaging of the PDMS material. Figure 32.6d and e shows the recovered images by using the first 38 singular vectors at the situation without and with scattering later, respectively.

Fig. 32.6
figure 6

Imaging through a thick biological sample

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In order to show the power imaging ability of RMOCT, we use a commercial 1.3 μm swept-source OCT from Thorlabs Inc. to image the same sample. The results are shown in Fig. 32.7. Figure 32.7a is the imaging result of PDMS material without the scattering layer. We can see the boundaries are very clear. Figure 32.7b is the en-face imaging of the upper layer. Figure 32.7c is the imaging result of PDMS material beneath the scattering layer, and we can see the boundaries are blurry. Figure 32.7d is the en-face imaging of the upper layer of PDMS material. This time, the commercial OCT system lost the ability to recover the image.

Fig. 32.7
figure 7

Imaging results of a commercial 1.3 μm swept-source OCT

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3.4 High-Speed Wavefront Shaping

As for the light focusing experiment, the phase and amplitude before wavefront are all made of chaos. However, the phase and amplitude after wavefront have been shaped to a Gaussian-like distribution. The whole process only needs 133 ms.

4 Conclusions

In this paper, we have demonstrated a new type of OCT combined with reflection matrix measurement. The huge reflection matrix of the sample contains abundant information which describes the light propagation process within the sample. We have presented its amazing imaging power at deeper penetration depth, which is 15 times MSFP and two times the conventional OCT’s imaging depth. At the same time, we have shown a high-speed WFS method to focus light through a sample in ~133 ms. As a next step, we are now trying to apply WFS technology to OCT to realize deeper imaging depth.