1. Introduction

Forming a clear optical image through scattering media is one of the major technical challenges in the field of biomedical imaging. Intensive efforts have been made in recent years to address this problem and form non-distorted images through a scattering medium, including iterative wave front shaping [1–5], time reversal or phase conjugation [6–9], ultrasonic encoding [10–13], and transmission matrix measurement [14–18]. The first three methods rely on digitally modifying the incident wave front, to compensate the scattering effect and obtain a deterministic wave after the scattering medium. The correct incident wave front is measured by exhaustive searching algorithm in wave front shaping, or holographic recording using nonlinear [8, 9] or ultrasonic [10–13] beacons. In transmission matrix method, the scattering properties of the random medium are quantified and clear image could be retrieved through proper matrix operation.

A novel technique was demonstrated by Bertolotti et al [19] recently, which is based on scanning the speckle pattern produced by the scatterers across a fluorescence object and collecting the resulting fluorescence back through the scattering medium. We refer to this method as speckle scanning microscopy (SSM). As opposed to most other techniques that require information from both sides of the scatterers, in SSM, it is possible to image a fluorescence object behind the scatterers without accessing the back side of the scatterers. Moreover, no ultrasonic beacon is required in SSM, greatly simplifying the setup.

The concept of SSM was demonstrated in reference [19] by imaging a letter$\pi$in a dye doped polymer layer and a slice of the stem of C. majalis behind a ground glass diffuser. The successful imaging of ~1 mm big C. majalis was the very first step towards the application of SSM in bio-imaging. However, the C. majalis image only roughly revealed the shape of structures of hundreds of microns size; imaging of cellular level structures is more desirable in biological applications and it is demonstrated for the first time in this work. Additionally, the C. majalis image was obtained behind a ground glass diffuser rather than biological scatterers. In this paper, we applied SSM to image stained blood cells of a couple of microns in size, enclosed in chicken skin tissues.

Compared with a ground glass diffuser, chicken skin tissues lead to two major issues in SSM. First, SSM relies on the correlation of the speckle patterns, a phenomenon often termed the optical memory effect [20]. The speckle patterns generated behind tissues decorrelate much faster than behind the ground glass diffuser, limiting the scanning range of SSM. We investigated the influence of the scanning range numerically. Second, autofluorescence of the surrounding tissues poses a noticeable background and seriously impairs the quality of SSM. Hence, a transmission based configuration was adopted in the experiment, to minimize the influence from the surrounding tissues.

2. Theoretical analysis

The principle of SSM is illustrated in Fig. 1.A laser beam of diameter $W$illuminates on the first scattering medium of thickness$L_{\text{1}}$, and projects a speckle pattern $S$ on the sample plane after propagation over distance$d_1$. Rotating the beam by an angle $\theta$ causes the speckle pattern to slightly decorrelate and shift by $q$ in the two-dimensional sample plane, where$q=d_1\theta$. The correlation between the shifted and the original speckle patterns is regulated by the optical memory effect. The fluorescence excited by the speckle pattern in the sample $O$ propagates through distance $d_2$ and is scattered again by the second scattering medium of thickness$L_2$, after which the fluorescence signal is filtered and detected. An intensity map $I$can be generated by scanning the incident beam and plotting the detected fluorescence signal at each angle. The averaged autocorrelation $〈I\otimes I〉\left(q\right)$ of the measured intensity map can be expressed as [19] $〈I\otimes I〉\left(q\right)\text{=}〈\left[\left(O\otimes O\right)\ast \left(S\otimes S\right)\right]\left(q\right)〉$, where$\ast$ is the convolution operator, and $\otimes$ is the correlation operator. Laser speckles have a well-defined autocorrelation profile [21], which effectively becomes a delta function when the scanning step is larger than the mean speckle size. This renders $〈I\otimes I〉\left(q\right)$ approximately equal to the object autocorrelation $〈O\otimes O〉\left(q\right)$, from which it is possible to recover $O$ with a phase retrieval algorithm [22]. In practice, each particular realization of the speckle pattern introduces noise in$I\otimes I\left(q\right)$, and hence multiple instances of the autocorrelation should be averaged to suppress the random noise.

 

Fig. 1 Schematic diagram on the working principle of SSM.

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The approximation$〈I\otimes I〉\left(q\right)\text{=}〈O\otimes O〉\left(q\right)$relies on the correlation between speckle patterns while rotating the incident beam. This correlation decreases with the increase of the tilting angle. To ensure a good quality in SSM, the tilting angle should be limited within a range of significant speckle correlations. For subwavelength scatterers, Feng et al [20] gave an analytical solution to the optical memory effect, which can be expressed as $C\left(\theta \right)={\left(k\theta L_1\right)}^2/\sin h^2\left(k\theta L_1\right)$. The maximum tilting angle is defined as${\theta }_{\max }=2/k{L}_1$, beyond which the speckle correlation is less than 30%. In biological tissues, however, the scattering properties are more complicated, with contributions coming from both cellular level structures and subwavelength organelles [23]. The correlation curves as a function of incident angle were measured for a series of biological tissues and plotted in Fig. 2.The${\theta }_{\max }$for 50 μm thick tissues were around 3-8 mrad, which are much smaller than that of the ground glass used by Bertolotti. According to supplementary Fig. 3 of [19], the ground glass shows almost no decorrelation up to 17 mrad.

 

Fig. 2 Normalized correlation verses tilting angle for different tissues.

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The maximum scanning range in the object plane$2q_{\max }$ is determined by $d_1$and${\theta }_{\max }$, where$2q_{\max }=2d_1{\theta }_{\max }$. Given the small${\theta }_{\max }$, a large $d_1$ is required to achieve a reasonable$2q_{\max }$. At the same time, the physical resolution of SSM, determined by the mean speckle size, is $\lambda d_1/W$ [21], in the case of $W\ll d_1$. Therefore, a compromise is required between bigger scanning range and higher resolution.

The small ${\theta }_{\max }$ limits the maximum scanning range$2q_{\max }$, within which $〈I\otimes I〉\left(q\right)\text{=}〈O\otimes O〉\left(q\right)$ is roughly valid. In standard scanning microscopy, when the scanning range is small, one can simply move the sample around to cover the full range of the imaging target. However, in SSM, a problem shows up when the object is bigger than the scanning range. In this case, some parts of the object are illuminated by uncorrelated speckle patterns, yet the fluorescence from these parts is collected by the detector and contributes to the intensity map$I$. Intuitively, the fluorescence excited by uncorrelated speckle patterns would inevitably impair the approximation of$〈I\otimes I〉\left(q\right)\text{=}〈O\otimes O〉\left(q\right)$, and thus deteriorate the quality of SSM. We confirmed this intuition by numerical simulations.

Figure 3(a) shows an image of 8 fluorescent beads, arranged in an area of 128 × 128 μm². The memory effect was approximated by a linear combination of two uncorrelated speckle fields with different weighting, and the weighting values were chosen so that the calculated memory effect curve fitted the actual data measured in the experiment (Fig. 2 chicken skin 50 μm). ${\theta }_{\max }$was 8 mrad, and $d_1$ varied from 8 mm to 2 mm to control the scanning range $2q_{\max }$ from 128 μm to 32 μm. Figures 3(b)-3(d) show the simulation results when $2q_{\max }{\text{=}}_{}{\text{128}}_{}\mu \text{m}$, i.e. the size of the object equals the scanning range. Figure 3(b) is the calculated autocorrelation of the object, Fig. 3(c) is the averaged autocorrelation of 30 intensity maps, and Fig. 3(d) is a retrieved object from Fig. 3(c). Figure 3(d) faithfully recovers the object.

 

Fig. 3 (a) object to be imaged (128 × 128 μm²); (b)-(d): scanning range 128 μm, equals to the object size; (b) calculated autocorrelation of the object within the scanning range; (c) averaged autocorrelation of 30 intensity maps; (d) a retrieved object from (c); (e)-(g): scanning range 96 μm, equals to the parts within the red square of (a); (h)-(j): scanning range 64 μm, equals to the parts within the yellow square of (a); (k)-(m): scanning range 32 μm, equals to the parts within the white square of (a); (n) normalized error (between the reconstructed image and the parts of object within the scanning range) varies with scanning range

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However, the reconstruction quality deteriorates as scanning range $2q_{\max }$ decreases. Figures 3(e)-3(g) represent the simulation results when$2q_{\max }{\text{=}}_{}{\text{96}}_{}\mu \text{m}$. This scanning range equals to the area within the red square of Fig. 3(a). Fluorescence beads outside the red square introduce unwanted patterns in the averaged autocorrelation (Fig. 3(f)) and reconstructed image (Fig. 3(g)). This phenomenon becomes more prominent when $2q_{\max }$further decreases to 64 μm and 32 μm, and the corresponding results are presented in Figs. 3(h)-3(j) and Figs. 3(k)-3(m). Figure 3(n) plots the normalized error (between the reconstructed image and the parts of object within the scanning range) varies with the scanning range.

This phenomenon can be understood by considering the speckle pattern as a combination of several overlapping uncorrelated speckle fields spaced one memory range from each other in the space of incident angle. Each of these shifted speckle patterns is weighted with the corresponding memory coefficient and produces independently an autocorrelation. Since each autocorrelation is centered, the resulting autocorrelation of the measured intensity is a superposition of the autocorrelation of multiple partial objects. Therefore, an effect akin to “aliasing” occurs. Just as in aliasing, this part of the signal still contains potentially useful information about the object, but it appears as distortion and confuses the object retrieval algorithm. Based on this analysis, we conclude that for successful implementation of SSM, the object should be smaller than the maximum scanning range.

3. Experiments and results

Having understood the limited scanning range of biological tissues and its influence on SSM, we proceeded to design an experiment to demonstrate the application of SSM in the imaging of blood cells enclosed by chicken skin tissues. A laser beam of 488 nm wavelength was delivered to the sample through a pair of galvo mirrors for two-dimensional angular scanning. The scanning system was assisted by two pairs of conjugated 1:1 relay lenses such that the beam position remained unchanged while scanning its angle. The beam size at the entrance face of the sample was 2 mm. The sample consisting of Eosin-Y stained blood cells (see methods) was placed in-between two layers of chicken skin tissue with thickness $L_1=L_2={50}_{}\mu \text{m}$(Fig. 1). The chicken skin tissue was frozen using a cryostat, sliced to the desired thickness with a microtome, and mounted on a glass slide [24]. The scattering coefficient of the chicken skin tissue was measured to be ~45 mm⁻¹ at 488 nm. The distances between the blood sample to the first and second tissue layer was $d_1=4_{}\text{mm}$and $d_{\text{2}}=\text{0}{\text{.5}}_{}\text{mm}$, respectively. No additional medium other than air were used between the tissue layers and the blood sample. The mean speckle size projected on the blood sample was roughly 1 μm.

Given by the memory effect curve shown in Fig. 2, the maximum scanning range $2q_{\max }$ was roughly 64 μm. The angular scanning step was chosen as 0.12 mrad, corresponding to ~0.5 μm/step in the plane of the blood sample. The fluorescence signal, after propagating through the second layer of the scattering tissue, was collected by a microscope objective (50 × 0.7 NA) and filtered with a 483 nm notch filter (20 nm bandwidth) and a long pass filter cut at 532 nm. The combined rejection of the filters at the excitation wavelength exceeded an optical density of 14. An electron-multiplying charge-coupled device (EMCCD) was used as the detector in this demonstration for ease of alignment. The intensity captured by the entire EMCCD at one incident angle was summed up as one value, and an intensity map was generated by plotting different incident angles versus their corresponding intensity values. The integration time of each pixel was 0.05s, and a scanning of a 101 × 101pixels intensity map took ~8.5 minutes. In practice, a single-element photo-detector such as a photo-multiplying tube (PMT) or an avalanche photodiode (APD) could be used instead of EMCCD for higher speed and lower cost.

30 scanning intensity maps were acquired and their autocorrelations were averaged. For each scan, distinct non-overlapping incident angles were used to achieve uncorrelated central speckles. The averaged autocorrelation pattern was thresholded at ~5% of the autocorrelation peak, to remove the parts which change rapidly from one scan to the next, and further minimize the statistical noise. The image of the object was then retrieved by applying Fienup’s iterative phase retrieval algorithm. The optimum threshold value was usually determined by trial and error and it varied from sample to sample.

Figure 4(a) shows the wide field fluorescence image (with scattering media removed) of a white blood cell. Figure 4(b) is the calculated autocorrelation of Fig. 4(a), from which the phase retrieval algorithm is able to recover an image of the original object (Fig. 4(c)) with excellent fidelity. Shown in Fig. 4(d) is a typical two-dimensional fluorescence intensity map measured with the SSM. From 30 instances of such intensity map, the average autocorrelation was calculated, as displayed in Fig. 4(e). Figure 4(f) shows the reconstructed image of the original object from the average autocorrelation in Fig. 4(e). The recovered image Fig. 4(f) bears close resemblance to the original image, despite of some loss of fidelity due to statistics and optical noises. Nevertheless, the acuity of Fig. 4(f) is sufficient to clearly identify the white blood cell and measure its dimension and approximate shape. The pixel resolution of Figs. 4(d)-4(f) is 101 × 101 pixels, which corresponds to an actual scanning range of 50 × 50 μm². Note that the actual scanning range is smaller than the maximum scanning range of 64 × 64 μm² only because it is already big enough to image the cell with a dimension of ~10-15 μm. Objects with size up to 64 × 64 μm² could be imaged without problem under this experiment condition.

 

Fig. 4 (a) Wide field fluorescence image of a white blood cell; (b) calculated autocorrelation of (a); (c) reconstructed object from the calculated autocorrelation (b); (d) a typical two-dimensional fluorescence intensity map; (e) averaged autocorrelation of 30 intensity maps; (f) reconstructed image from the average autocorrelation (e). Scale bar: 10 μm.

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Figure 5 shows the result of another object containing two red blood cells (biconcave disks, 1 and 4) and two white blood cells (2 and 3). The dimension of the white blood cells was of ~10-15 μm, and the red blood cells were roughly ~6-8 μm in size. The total area of the 4 cells was around 50 × 50 μm². Other parameters remain the same as in Fig. 4. Both cell types are well reconstructed and readily distinguishable.

 

Fig. 5 (a) Wide field fluorescence image of two red blood cells and two white blood cells; (b) reconstructed image of the blood cells enclosed in chicken skin; scale bar: 10 μm

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4. Discussions

We discussed in section 2 about the limited memory effect range of biological tissues and its resulting challenge on SSM. Another challenge in bio-imaging comes from the autofluorescence of the surrounding tissues, which usually has a broad emission bandwidth that overlaps with the fluorescence signal from the object of interest and therefore cannot be eliminated easily. This autofluorescence from surrounding tissues usually introduces a remarkable background and its variation adds up to the noise level. Therefore, it is vital to minimize its influence.

This is the exact reason that we have collected the fluorescence signal in the transmission side (to the right of the tissue layer $L_2$ in Fig. 1) instead of in the epi side (to the left of the tissue layer $L_1$ in Fig. 1). In the configuration of epi collection, the chicken skin tissue was illuminated by unscrambled laser beam, and generated autofluorescence comparable with the signal intensity from the blood cells; whereas in the configuration of transmission collection, the illuminating beam was diffused and broadened by the time it reached the second scattering layer, and the resulting autofluorescence from the tissue was negligible compared with the signal from the blood cells. Based on the fluorescence intensity measured with the EMCCD, the signal from the stained cells was 19 times stronger than the autofluorescence background of the scattering tissues in transmission configuration whereas the ratio is ~1 in the epi configuration.

In SSM, what we call “signal” is not the total fluorescence intensity collected by the detector, but the fluctuation of fluorescence intensity when the speckles scan across the object. The total fluorescence is proportional to the number of speckles falling on the object, which is roughly$A_o/A_s$, where$A_s$ is the mean speckle area and$A_o$is the object area. The fluctuation relative to the mean value is then approximately${\left(A_s/A_o\right)}^{1/2}$. The total number of photons$N$received by the detector must ensure that the signal fluctuation exceeds the shot noise, i.e.$N>A_o/\left(\eta A_s\right)$, where $\eta$ is the detector quantum efficiency, and in a broader sense also includes the collection efficiency of the optics. Therefore, small objects, large speckle size and high quantum efficiency are beneficial to achieve a high signal to noise ratio.

SSM relies on the memory effect while tilting the incident beam. Our previous work [9] reveals that the memory effect can be extended into the third dimension: correlation exists when we change the curvature of the incident beam by adding a spherical phase factor. Additionally, the autocorrelation of 3D speckle could be approximated as a delta function before the speckle reaches far field. Therefore, it is possible to change the curvature of the incident beam by translating the collimating lens and achieve 3D scanning in SSM.

Finally, it is worth to point out that the current SSM configuration could be impractical in many biological applications, because of the required the gap between scattering layer and the objects. However, SSM is applicable, where a natural gap exists between the scattering layer and the structure of interest. One possible application could be visualizing the brain tissue under thinned cranium. Transmission-based scheme could also be an issue in in-vivo applications. Yet this could be avoided if standard protocol to minimize the autofluorescence from the scatterer is applicable [25]. Additionally, the transmission-based scheme could be useful in some cases, e.g. to determine structures enclosed in an egg-like shell.

5. Conclusion

We have studied the possibility of using SSM to image biological samples. We have found that the object of interest should be smaller than the maximum scanning range of the speckle patterns limited by the scattering property of the surrounding tissues. The autofluorescence from the surrounding tissue should be minimized, and using transmission collection is one of the possibilities. Within these frames, we demonstrated imaging of blood cells through chicken skin tissue using SSM. High quality images were obtained, where cell type and shape were clearly identifiable with decent fidelity and subcellular resolution. These results will inspire further research on advanced SSM methods and their bio-applications.

Method

500 µl of blood was extracted from the ring finger of the experimenter, and kept in an EDTA tube to prevent clotting. The tube was centrifuged at 2000 r/min for 10 min, and the supernatant was discarded. The rest of the blood was diluted with PBS at a ratio of 1:1, and centrifuged once more at 2000 r/min for 10 min. The supernatant was discarded again, and the buffy coat was harvested. The harvested blood contained a mixture of leukocytes (white blood cells), thrombocytes (platelets) and some remaining erythrocytes (red blood cells). A blood smear was prepared following the coverslip technique [26], fixed with methanol, and stained with Eosin-Y.