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Multiple guide stars optimization in conjugate adaptive optics for deep tissue imaging
Journal Pre-proof Multiple guide stars optimization in conjugate adaptive optics for deep tissue imaging Chenxue Wu, Jiajia Chen, Biwei Zhang, Yao Zheng, Xinpei Zhu, Ke Si, Wei Gong
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S0030-4018(19)31003-X https://doi.org/10.1016/j.optcom.2019.124891 OPTICS 124891
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Optics Communications
Received date : 12 August 2019 Revised date : 30 September 2019 Accepted date : 2 November 2019 Please cite this article as: C. Wu, J. Chen, B. Zhang et al., Multiple guide stars optimization in conjugate adaptive optics for deep tissue imaging, Optics Communications (2019), doi: https://doi.org/10.1016/j.optcom.2019.124891. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
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Multiple guide stars optimization in conjugate adaptive optics for deep tissue imaging
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CHENXUE WU,1,2 JIAJIA CHEN,2 BIWEI ZHANG,2 YAO ZHENG,1,2 XINPEI ZHU,1 KE SI1,2,3 AND WEI GONG,1,4 1
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State Key Laboratory of Modern Optical Instrumentation, Center for Neuroscience and Department of Neurobiology of the Second Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou 310058, China 2 College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China 3 [email protected] 4 weigong [email protected] Key words: Optical Microscopy; Adaptive Optics; Automatic Selection; Guide Stars; Imaging
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Abstract: Adaptive optics (AO) has been widely used in optical microscopy to recover high-resolution images in deep tissue. However, in conventional AO systems, the corrected field of view (FOV) of a single guide star is usually quite limited. Here we demonstrate a conjugate AO system based on automatic optimal multiple guide stars selection algorithm to achieve large effective corrected FOV with a small number of guide stars. For a random phase mask as the scattering medium, the effective correction coverage ratio can be increased to ~5.09 times than that in a conventional CAO system. For a mouse brain slice with 117 μm thickness, the effective corrected FOV is larger than that of conventional CAO system by a factor of ~2.58. Therefore, our method shows potentials in aberration correction with large FOV for deep tissue imaging.
1. Introduction Optical microscopy is one of the useful techniques to maintain high resolution in biological sciences [1, 2]. However, optical aberrations, which limit the imaging depth and signal-to-noise ratio of the system, often exist in living tissue [3]. The aberrations are mainly caused by the inhomogeneous distribution of refractive index and multiple scattering of the biological tissue, which need to be corrected especially for deep tissue imaging in biological sciences [4]. Adaptive optics (AO) is a valuable tool to compensate the aberrations, using a deformable mirror or a spatial light modulator (SLM) as the correction element [5-11]. There are two basic AO systems for the aberrations correction. One is the traditional pupil AO (PAO) correction system, where the correction element is placed in the conjugate plane of objective rear pupil [12]. The other one is the conjugate AO (CAO) correction system, where the correction element is conjugate to the scattering sample [13]. PAO system is only useful for spatially-invariant aberrations, such as the refractive index mismatch between cover glass and sample. But CAO system has the ability to correct the aberration varying with spatial positions [14]. Thus, compared with the conventional PAO system which limits the corrected field of view (FOV) to a small area around the center guide star (GS), the CAO system has the advantages of large corrected FOV thus improving the imaging speed [15, 16]. CAO system was introduced in astronomy first and then developed in the biology imaging for high resolution. To investigate the properties of CAO system, the refractive index profiles by ray tracing method have been proposed [14], and the relationship between the number of correction devices and the aberration correction was analyzed [15]. However, in many cases, only a single GS is used in the CAO system, which cannot meet
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the requirement of corrected FOV for morphological imaging and functional imaging. Thus, multiple GSs are applied in the CAO system to further increase the correction area and improve correction efficiency. A high-speed AO method in the CAO system with multiple GSs (CAOMG) is demonstrated to obtain high-speed imaging through scattering media [17]. For the CAOMG system, the distribution of the multiple GSs is of great concern, where optimal GSs can be used to further improve the correction performance. In this paper, an automatic optimal multiple GSs selection algorithm is introduced to get the distribution of the GSs and thus obtain large corrected FOV. The numerical results show that our method can greatly improve the correction efficiency through a layer of phase mask or a thick scattering medium. 2. Automatic optimal multiple GSs selection based on CAOMG system
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2.1 System design
Fig. 1. (a) Schematic diagram of the CAOMG system. L1, L2 and L3: lens; DM: dichroic mirror; X/Y-Galvo: X and Y axis Galvanometer Scanner; SL: scanning lens; SLM: spatial light modulator; TL: tube lens; Obj: objective; SM: scattering medium; O: object; BPF: band-pass filter; PH: pinhole; PMT: photomultiplier tube. (b) The diagram of available GSs and selection of optimal GSs. (c) The AO correction phase pattern with automatic optimal multiple GSs selection algorithm based on CAOMG correction system.
The schematic diagram of CAOMG system is shown in Fig.1 [14]. The beam from a continuous wave excitation laser ( = 630 nm ) is collimated and expanded through a pair of relay lens (L1 and L2). The beam is then scanned transversely by a pair of the X and Y galvanometers (X/Y-Galvo). A pair of relay lenses (Scanning lens and Tube lens, SL and TL) create an image of the galvo at the rear pupil plane of the imaging objective (Obj). The photomultiplier tube (PMT) together with the dichroic mirror (DM) is used to collect signal beam and form a confocal image. Here SLM, which is used for aberration correction, is placed in the middle of SL and TL. The SLM is approximately located at the conjugate plane of the scattering medium. Compared with conventional PAO system, where SLM is placed in the conjugation plane of the objective rear pupil, CAO system can correct the aberrations which vary with the spatial position. Therefore the corrected FOV is increased significantly [15, 16].
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2.2 Automatic optimal multiple GSs selection algorithm In the CAO system, compared with a single GS, multiple GSs can be used to further increase the correction region and improve the correction efficiency [17]. Then, the selection of GSs becomes the limit of the correction effect. However, in deep tissue imaging, the distribution of the GSs might be highly disordered. Therefore, to achieve the optimal distribution of the GSs, we develop an automatic optimal multiple GSs selection algorithm. In order to explain this algorithm, a slice of simulated random phase mask is used to mimic the scattering medium ( s L 4.40 , μs is the scattering coefficient, L is the thickness of scattering medium)
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and conjugate to SLM; a layer of fluorescent beads (4 μm diameter in average) is served as sample, which can be considered as the GS candidates. Thus, the scattering image of the fluorescent beads can be acquired through confocal imaging, which is shown in Fig. 2(a). The process of automatic multiple GSs selection algorithm is shown below. 2.2.1 Image Preprocessing Firstly, it is necessary to uniform the intensity distribution of the GS candidates (Fig. 2(b)). Secondly, we select the scattering beads with strong light intensity and then fit them with ellipse function. Thirdly, through comparing their long axes and short axes, the beads which are close to circular in shape are chosen as the available GSs (Fig. 2(c)). Finally, based on the available GSs acquired above, the automatic multiple GSs selection algorithm is applied to get the optimum GSs distribution for CAOMG (Fig. 2(d)). 2.2.2 Multiple GSs selection As shown in Fig. 2(g), for the purpose of getting the optimal GSs distribution (Fig. 2(d)), a GS among the candidates is randomly selected as the starting point. Next, a concentric ring is made which is centered at the starting GS. The inner radius r of the ring depends on the effective correction area with a single GS, which has been demonstrated in our previous work [17]. In other words, the inner radius r is the radius of the effective correction circle with a single GS. The outer radius is related to the inner radius r and requires minimum overlapping distance x among GSs. According to our previous work [17, 24], the minimum overlapping distance x is an experimental minimum distance between two selected GSs, which means that the whole FOV can be corrected effectively with fewest GSs. That is, the outer radius of the ring is 2r-x. To improve the correction efficiency, the new determined GS should be closed to the outer circle. Then, this process is repeated until there is no new determined GSs in the correction area. After that, the optimal GSs distribution can be obtained. To improve the efficiency of the automatic multiple GSs selection algorithm, the selection of the inner radius and the outer radius is quite essential. Based on our previous work, we can get that with a slice of random phase mask, the radius of effective correction area for a single GS is 62.5 μm [17]. Thus, for the automatic multiple GSs selection algorithm, the inner radius should be 62.5 μm, when the new determined GS is on the border of previous GS’s effective correction area. The maximal value of outer radius is 125 μm, where the correction areas of each GS are tangent. Here, we make the correction areas of each GS have overlapping parts to get a better correction effect, and then outer radius is set as 108.25 μm. 2.3 CAOMG correction process based on COAT with optimum GSs distribution In order to achieve the aberration compensation, coherent optical adaptive technique (COAT) is utilized to correct the aberrations in parallel, which has the advantages in correction speed and accuracy [18-20]. COAT was first developed for beam focusing through air turbulence by Hughes Research Laboratories in the 1970s [21] and then introduced to microscopy in 2011 [19]. In contrast to the traditional pixel-by-pixel correction methods, this optimization correction method can effectively correct the high-order aberrations, getting a faster correction and a better imaging performance. In COAT, the effective phase elements on SLM are randomly divided into two equal parts. At first, one part of the phase elements is modulated at different frequencies, and the other part remains constant as the reference. In each modulation time, the incident light is scanning
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through the position of the optimum GSs distribution on the focal plane. The intensities from all GSs are collected by PMT and then summarized as the feedback with time growing. By Fourier transform, the corrected phase value corresponding to the modulated phase elements can be calculated. Then, the previous modulated half are kept at the corrected phase value calculated, and the other half elements are modulated in the same way, whose corrected phase value can also be determined. In the end, the correction phase pattern on SLM is acquired. We simulated the method by angular spectrum theory [22, 23] in MATLAB. The numerical aperture of the objective is set to 0.1 for a better observation of the correction. The number of the effective phase elements is 16×16 on SLM, and the pixel number in each effective phase element is 16×16.
Fig. 2. The process of choosing the optimum GSs distribution. (a) The scattering image of the fluorescent beads. (b) Normalizing the intensity distribution. (c) Fitting the beads with ellipse function and choosing the beads close to circular in shape. (d) Getting the optimum GSs distribution for CAOMG system based on automatic GS selection algorithm. Two-dimensional distributions of Strehl ratio in a 250 μm 250 μm FOV with (e) a single GS, and (f) 10 GSs. (g) The diagram of getting the optimum GSs distribution. The blue solid circles in (d) are used to mark the corrected FOVs of each selected GS.
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For the random phase mask, after CAOMG correction process based on COAT with the optimum GSs distribution, the two-dimensional distributions of Strehl ratio are shown in Fig. 2(f). Strehl ratio is defined as the ratio between the maximum intensity of the focal spot with AO correction to that of the ideal focal spot. It can be seen that correction effects are achieved over a larger scale with our automatic multiple GSs selection algorithm than a single GS in the center.
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3. Results and Discussions
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3.1 Choosing of starting GS for automatic optimal multiple GSs selection algorithm Our previous work has discussed the method to select the starting GS [24]. It used to take all available GSs as the starting points to get their optimal GSs distributions, and then the one with the largest effective coverage ratio was chosen as the final distribution. The effective coverage ratio is defined as the proportion of the achieved effective correction coverage of the GSs distribution in the whole FOV. However, this way may limit the speed of aberration compensation. Here, we investigate the relationship between the choice of starting GS and correction effect. The scattering medium and sample are the same as that in section 2.2, and the number of all available GSs is 136. Besides, we use the number of required GSs and the effective coverage ratio as evaluating indicators for different starting GSs. The small number of required GSs means less time consumption; higher effective coverage ratio means better correction effect.
Fig. 3. Numbers of required GSs and effective coverage ratios with different starting GSs.
With different starting GSs, the number of required GSs and effective correction coverage ratio are shown in Fig. 3. It is illustrated that the number of required GSs is among 7 and 11, and the effective correction coverage ratio is all above 90%. It should be mentioned that there are little differences between time consumption and the correction effects for various starting GSs. Therefore, the selection of starting point is not important and we can select any of the available GS as the starting point. This proves from the side that this method has minor limitations. 3.2 Fluorescent imaging through a slice of the random phase mask To examine the imaging performance of CAOMG system based on automatic GSs selection algorithm, a slice of random phase mask is used to mimic the scattering medium and a layer of fluorescent beads is served as the sample, which has been illustrated in section 2.2. The images scanning through the whole two-dimensional on the focal plane are displayed in Fig. 4(a-d). Fig. 4(a) shows the ideal confocal fluorescent image without distortion. Fig. 4(b) illustrates the fluorescent image with scattering by a slice of the random phase mask. From the imaging results after correction, it is obvious that CAO system with a single GS can only compensate the aberrations around the central GS (Fig. 4(c)) and the corrected FOV is strongly limited. In contrast, in Fig. 4(d), there are 10 GSs used for AO correction, and the area of the corrected FOV is increased compared with a single GS. The effective coverage ratio is 0.9996 in CAOMG system, compared to 0.1963 with a single GS, which has increased about 5.09 times.
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The intensity profiles along line 1 and line 2 are demonstrated in Fig. 4(e) and (f), respectively. It can be noticed that CAO system with a single GS is a better choice for the center region (Fig .4(e)); while the automatic multiple GSs selection algorithm can be used to well compensate the phase aberrations in CAOMG system, whose corresponding corrected region can be extremely enlarged (Fig .4(f)).
Fig. 4. Imaging results of the fluorescent beads (4 μm diameter in average) through a slice of random phase mask (a) ideally, (b) with scattering, (c) after CAO correction with a single GS, (d) after CAOMG correction based on automatic GSs selection algorithm. Higher resolution images are also shown below. (e) The intensity profiles along the white dotted lines 1 in the (b-d). (f) The intensity profiles along the white dotted lines 2 in the (b-d).
3.3 Fluorescent imaging through the thick scattering medium To further verify the feasibility of the CAOMG system based on automatic multiple GSs selection algorithm in biological tissue, we used a mouse brain slice with a thickness of about 117 μm obtained from a two-photon microscope (OLYMPUS BX61WI-FV1200MPE, 10×) as the random scattering medium, as shown in Fig. 5(a). The brain slice consists of 24 layers (μs = 25.54 mm-1) whose average thickness is 4.88 μm. A single layer of fluorescent beads (4 μm diameter on average) is served as the object. Light propagation between the layers was computed via the Fourier shift theorem. The associated Fourier transforms were computed with FFT in MATLAB. We simulated the light scattering process by multiplying the electromagnetic field with the phase masks. The polarization effects and absorption were neglected. To further examine the correction effect on the focal plane, we load the correction phase patterns on SLM. The correction phase pattern after CAO with a single GS and multiple GSs are illustrated in Fig. 5(b1) and (b2). Then the illumination light scans laterally across the focal plane to acquire the two-dimensional fluorescent images, and the results are displayed in Fig. 5(c-f). Before correction, the fluorescent beads are obscure due to scattering caused by thick mouse brain tissue (Fig. 5(d)). The blue boxes in Fig. 5(d-f) demonstrate the center fluorescent distributions with scattering, CAO with a single GS and CAOMG based on automatic multiple GSs selection algorithm, respectively. It is obvious that in the central region, Fig. 5(e) shows a better
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correction effect. In the CAO correction system with a single GS, the only GS locates in the central area and the fluorescent beads around the GS can be clearly observed. This phenomenon is in accordance with the intensity profiles in Fig. 5(g), which describes the while dotted lines 1 in Fig. 5(d-f), respectively. The intensity improvement of CAO with a single GS is about 1.55 times larger than that of CAOMG.
Fig. 5. (a) One slice of the mouse brain tissue, whose thickness is set to 4.88 μm. The correction phase pattern (b1) after CAO with a single GS and (b2) after CAOMG based on automatic GSs selection algorithm. (c) Ideal imaging results of the fluorescent beads (4 μm diameter in average) without scattering. Imaging results of the fluorescent beads through thick mouse brain tissue (d) with scattering, (e) after CAO correction with a single GS, (f) after CAOMG correction based on automatic GSs selection algorithm. Higher resolution images of the yellow and blue boxes are also shown below. (g) Intensity profiles of the while dotted lines 1 in (d-f). (h) Intensity profiles of the while dotted lines 2 in (d-f).
What’s more, it can be noticed that the corrected FOV after CAOMG correction can cover a larger region than that with a single GS. CAOMG system achieves a better correction performance on the whole imaging area, and the fluorescent beads can still be seen in the yellow box in Fig. 5(f). For CAOMG correction, there are 148 GS candidates and 11 of them are chosen as the final GSs. The corrected FOV with CAOMG is extended to a diameter of about 183 μm, which is 2.58 times larger than CAO with a single GS (71 μm). Fig. 5(h) illustrates the intensity profiles of the while dotted lines 2 in Fig. 5(d-f), where the intensity improvement of CAOMG is extremely clear. It needs to be mentioned that for CAOMG method, the contribution of a certain GS to the correction phase value mainly depends on its intensity value. Thus, the intensity distribution after correction may be uneven in Fig. 5(f). The imaging results of the fluorescent beads through thick mouse brain tissue prove that high-resolution can be gotten over a larger corrected FOV in CAOMG system based on our algorithm.
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4. Conclusion In this article, we propose an automatic optimal multiple GSs selection algorithm in CAOMG system to improve the corrected FOV, using COAT for aberration correction. The aim of our
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work is to obtain larger corrected FOV of CAOMG system using fewer GSs, thus it will further improve the processing speed in deep tissue imaging. The results demonstrate that it is practical to make any available GSs as the starting point and implement the aberration correction procedure. Through a single layer of the phase mask, the effective coverage ratio can be increased to about 5.09 times than that in CAO system with a single GS. Through layers of the thick mouse brain tissue, we can also obtain high-resolution imaging and the corrected FOV is 2.58 times larger than CAO system with a single GS, correcting the aberrations quickly and improving the imaging performance effectively. It should be mentioned that this automatic multiple GSs selection algorithm can be applied to conventional AO systems with parallel process. In our CAOMG system, the time consumption of the wavefront correction is mainly depended on the COAT algorithm due to the low fresh rate of the spatial light modulator, which takes several minutes. In contrast, the automatic multiple GSs selection procedure only takes 2~5 seconds. The total correction time relates to the number of GSs. The required number of GSs is smaller, the total correction time is shorter. In the future, the selection of inner and outer radius for various biological tissues can be studied further. For instance, with a thick scattering medium, the area of effective correction with a single GS in CAO system may be smaller. Thus, the inner radius should be set smaller accordingly. To choose the optimal inner radius on unknown samples, we can first define a threshold of Strehl ratio where the point spread function is well corrected. Then, after correction based on a single GS, we can obtain the area that meets this threshold of Strehl ratio. Thus, the radius of this area is just the radius of the inner ring. And the overlapping parts over GSs can be changed to get a better correction effect, and then outer radius needs to be studied. In conclusion, our automatic optimal multiple GSs selection algorithm has potential applications in in vivo deep imaging for biomedical research. Funding
National Natural Science Foundation of China (31571110, 61735016, 81771877); Natural Science Foundation of Zhejiang Province of China (LZ17F050001), Zhejiang Lab (2018EB0ZX01), and the Fundamental Research Funds for the Central Universities.
Acknowledgments
We thank Sanhua Fang and Qiaoling Ding (Core Facilities of Zhejiang University Institute of Neuroscience for technical assistance) for guidance to imaging systems; Shuangshuang Liu and Junli Xuan (Imaging Facility, Core Facilities, Zhejiang University School of Medicine) for imaging technical assistance.
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Conference on Information Optics and Photonics (CIOP 2018) (SPIE, 2018), Vol. 10964, p. 4.
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S0030-4018(19)31003-X https://doi.org/10.1016/j.optcom.2019.124891 OPTICS 124891
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Optics Communications
Received date : 12 August 2019 Revised date : 30 September 2019 Accepted date : 2 November 2019 Please cite this article as: C. Wu, J. Chen, B. Zhang et al., Multiple guide stars optimization in conjugate adaptive optics for deep tissue imaging, Optics Communications (2019), doi: https://doi.org/10.1016/j.optcom.2019.124891. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
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Multiple guide stars optimization in conjugate adaptive optics for deep tissue imaging
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CHENXUE WU,1,2 JIAJIA CHEN,2 BIWEI ZHANG,2 YAO ZHENG,1,2 XINPEI ZHU,1 KE SI1,2,3 AND WEI GONG,1,4 1
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State Key Laboratory of Modern Optical Instrumentation, Center for Neuroscience and Department of Neurobiology of the Second Affiliated Hospital, Zhejiang University School of Medicine, Hangzhou 310058, China 2 College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China 3 [email protected] 4 weigong [email protected] Key words: Optical Microscopy; Adaptive Optics; Automatic Selection; Guide Stars; Imaging
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Abstract: Adaptive optics (AO) has been widely used in optical microscopy to recover high-resolution images in deep tissue. However, in conventional AO systems, the corrected field of view (FOV) of a single guide star is usually quite limited. Here we demonstrate a conjugate AO system based on automatic optimal multiple guide stars selection algorithm to achieve large effective corrected FOV with a small number of guide stars. For a random phase mask as the scattering medium, the effective correction coverage ratio can be increased to ~5.09 times than that in a conventional CAO system. For a mouse brain slice with 117 μm thickness, the effective corrected FOV is larger than that of conventional CAO system by a factor of ~2.58. Therefore, our method shows potentials in aberration correction with large FOV for deep tissue imaging.
1. Introduction Optical microscopy is one of the useful techniques to maintain high resolution in biological sciences [1, 2]. However, optical aberrations, which limit the imaging depth and signal-to-noise ratio of the system, often exist in living tissue [3]. The aberrations are mainly caused by the inhomogeneous distribution of refractive index and multiple scattering of the biological tissue, which need to be corrected especially for deep tissue imaging in biological sciences [4]. Adaptive optics (AO) is a valuable tool to compensate the aberrations, using a deformable mirror or a spatial light modulator (SLM) as the correction element [5-11]. There are two basic AO systems for the aberrations correction. One is the traditional pupil AO (PAO) correction system, where the correction element is placed in the conjugate plane of objective rear pupil [12]. The other one is the conjugate AO (CAO) correction system, where the correction element is conjugate to the scattering sample [13]. PAO system is only useful for spatially-invariant aberrations, such as the refractive index mismatch between cover glass and sample. But CAO system has the ability to correct the aberration varying with spatial positions [14]. Thus, compared with the conventional PAO system which limits the corrected field of view (FOV) to a small area around the center guide star (GS), the CAO system has the advantages of large corrected FOV thus improving the imaging speed [15, 16]. CAO system was introduced in astronomy first and then developed in the biology imaging for high resolution. To investigate the properties of CAO system, the refractive index profiles by ray tracing method have been proposed [14], and the relationship between the number of correction devices and the aberration correction was analyzed [15]. However, in many cases, only a single GS is used in the CAO system, which cannot meet
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the requirement of corrected FOV for morphological imaging and functional imaging. Thus, multiple GSs are applied in the CAO system to further increase the correction area and improve correction efficiency. A high-speed AO method in the CAO system with multiple GSs (CAOMG) is demonstrated to obtain high-speed imaging through scattering media [17]. For the CAOMG system, the distribution of the multiple GSs is of great concern, where optimal GSs can be used to further improve the correction performance. In this paper, an automatic optimal multiple GSs selection algorithm is introduced to get the distribution of the GSs and thus obtain large corrected FOV. The numerical results show that our method can greatly improve the correction efficiency through a layer of phase mask or a thick scattering medium. 2. Automatic optimal multiple GSs selection based on CAOMG system
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2.1 System design
Fig. 1. (a) Schematic diagram of the CAOMG system. L1, L2 and L3: lens; DM: dichroic mirror; X/Y-Galvo: X and Y axis Galvanometer Scanner; SL: scanning lens; SLM: spatial light modulator; TL: tube lens; Obj: objective; SM: scattering medium; O: object; BPF: band-pass filter; PH: pinhole; PMT: photomultiplier tube. (b) The diagram of available GSs and selection of optimal GSs. (c) The AO correction phase pattern with automatic optimal multiple GSs selection algorithm based on CAOMG correction system.
The schematic diagram of CAOMG system is shown in Fig.1 [14]. The beam from a continuous wave excitation laser ( = 630 nm ) is collimated and expanded through a pair of relay lens (L1 and L2). The beam is then scanned transversely by a pair of the X and Y galvanometers (X/Y-Galvo). A pair of relay lenses (Scanning lens and Tube lens, SL and TL) create an image of the galvo at the rear pupil plane of the imaging objective (Obj). The photomultiplier tube (PMT) together with the dichroic mirror (DM) is used to collect signal beam and form a confocal image. Here SLM, which is used for aberration correction, is placed in the middle of SL and TL. The SLM is approximately located at the conjugate plane of the scattering medium. Compared with conventional PAO system, where SLM is placed in the conjugation plane of the objective rear pupil, CAO system can correct the aberrations which vary with the spatial position. Therefore the corrected FOV is increased significantly [15, 16].
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2.2 Automatic optimal multiple GSs selection algorithm In the CAO system, compared with a single GS, multiple GSs can be used to further increase the correction region and improve the correction efficiency [17]. Then, the selection of GSs becomes the limit of the correction effect. However, in deep tissue imaging, the distribution of the GSs might be highly disordered. Therefore, to achieve the optimal distribution of the GSs, we develop an automatic optimal multiple GSs selection algorithm. In order to explain this algorithm, a slice of simulated random phase mask is used to mimic the scattering medium ( s L 4.40 , μs is the scattering coefficient, L is the thickness of scattering medium)
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and conjugate to SLM; a layer of fluorescent beads (4 μm diameter in average) is served as sample, which can be considered as the GS candidates. Thus, the scattering image of the fluorescent beads can be acquired through confocal imaging, which is shown in Fig. 2(a). The process of automatic multiple GSs selection algorithm is shown below. 2.2.1 Image Preprocessing Firstly, it is necessary to uniform the intensity distribution of the GS candidates (Fig. 2(b)). Secondly, we select the scattering beads with strong light intensity and then fit them with ellipse function. Thirdly, through comparing their long axes and short axes, the beads which are close to circular in shape are chosen as the available GSs (Fig. 2(c)). Finally, based on the available GSs acquired above, the automatic multiple GSs selection algorithm is applied to get the optimum GSs distribution for CAOMG (Fig. 2(d)). 2.2.2 Multiple GSs selection As shown in Fig. 2(g), for the purpose of getting the optimal GSs distribution (Fig. 2(d)), a GS among the candidates is randomly selected as the starting point. Next, a concentric ring is made which is centered at the starting GS. The inner radius r of the ring depends on the effective correction area with a single GS, which has been demonstrated in our previous work [17]. In other words, the inner radius r is the radius of the effective correction circle with a single GS. The outer radius is related to the inner radius r and requires minimum overlapping distance x among GSs. According to our previous work [17, 24], the minimum overlapping distance x is an experimental minimum distance between two selected GSs, which means that the whole FOV can be corrected effectively with fewest GSs. That is, the outer radius of the ring is 2r-x. To improve the correction efficiency, the new determined GS should be closed to the outer circle. Then, this process is repeated until there is no new determined GSs in the correction area. After that, the optimal GSs distribution can be obtained. To improve the efficiency of the automatic multiple GSs selection algorithm, the selection of the inner radius and the outer radius is quite essential. Based on our previous work, we can get that with a slice of random phase mask, the radius of effective correction area for a single GS is 62.5 μm [17]. Thus, for the automatic multiple GSs selection algorithm, the inner radius should be 62.5 μm, when the new determined GS is on the border of previous GS’s effective correction area. The maximal value of outer radius is 125 μm, where the correction areas of each GS are tangent. Here, we make the correction areas of each GS have overlapping parts to get a better correction effect, and then outer radius is set as 108.25 μm. 2.3 CAOMG correction process based on COAT with optimum GSs distribution In order to achieve the aberration compensation, coherent optical adaptive technique (COAT) is utilized to correct the aberrations in parallel, which has the advantages in correction speed and accuracy [18-20]. COAT was first developed for beam focusing through air turbulence by Hughes Research Laboratories in the 1970s [21] and then introduced to microscopy in 2011 [19]. In contrast to the traditional pixel-by-pixel correction methods, this optimization correction method can effectively correct the high-order aberrations, getting a faster correction and a better imaging performance. In COAT, the effective phase elements on SLM are randomly divided into two equal parts. At first, one part of the phase elements is modulated at different frequencies, and the other part remains constant as the reference. In each modulation time, the incident light is scanning
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through the position of the optimum GSs distribution on the focal plane. The intensities from all GSs are collected by PMT and then summarized as the feedback with time growing. By Fourier transform, the corrected phase value corresponding to the modulated phase elements can be calculated. Then, the previous modulated half are kept at the corrected phase value calculated, and the other half elements are modulated in the same way, whose corrected phase value can also be determined. In the end, the correction phase pattern on SLM is acquired. We simulated the method by angular spectrum theory [22, 23] in MATLAB. The numerical aperture of the objective is set to 0.1 for a better observation of the correction. The number of the effective phase elements is 16×16 on SLM, and the pixel number in each effective phase element is 16×16.
Fig. 2. The process of choosing the optimum GSs distribution. (a) The scattering image of the fluorescent beads. (b) Normalizing the intensity distribution. (c) Fitting the beads with ellipse function and choosing the beads close to circular in shape. (d) Getting the optimum GSs distribution for CAOMG system based on automatic GS selection algorithm. Two-dimensional distributions of Strehl ratio in a 250 μm 250 μm FOV with (e) a single GS, and (f) 10 GSs. (g) The diagram of getting the optimum GSs distribution. The blue solid circles in (d) are used to mark the corrected FOVs of each selected GS.
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For the random phase mask, after CAOMG correction process based on COAT with the optimum GSs distribution, the two-dimensional distributions of Strehl ratio are shown in Fig. 2(f). Strehl ratio is defined as the ratio between the maximum intensity of the focal spot with AO correction to that of the ideal focal spot. It can be seen that correction effects are achieved over a larger scale with our automatic multiple GSs selection algorithm than a single GS in the center.
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3. Results and Discussions
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3.1 Choosing of starting GS for automatic optimal multiple GSs selection algorithm Our previous work has discussed the method to select the starting GS [24]. It used to take all available GSs as the starting points to get their optimal GSs distributions, and then the one with the largest effective coverage ratio was chosen as the final distribution. The effective coverage ratio is defined as the proportion of the achieved effective correction coverage of the GSs distribution in the whole FOV. However, this way may limit the speed of aberration compensation. Here, we investigate the relationship between the choice of starting GS and correction effect. The scattering medium and sample are the same as that in section 2.2, and the number of all available GSs is 136. Besides, we use the number of required GSs and the effective coverage ratio as evaluating indicators for different starting GSs. The small number of required GSs means less time consumption; higher effective coverage ratio means better correction effect.
Fig. 3. Numbers of required GSs and effective coverage ratios with different starting GSs.
With different starting GSs, the number of required GSs and effective correction coverage ratio are shown in Fig. 3. It is illustrated that the number of required GSs is among 7 and 11, and the effective correction coverage ratio is all above 90%. It should be mentioned that there are little differences between time consumption and the correction effects for various starting GSs. Therefore, the selection of starting point is not important and we can select any of the available GS as the starting point. This proves from the side that this method has minor limitations. 3.2 Fluorescent imaging through a slice of the random phase mask To examine the imaging performance of CAOMG system based on automatic GSs selection algorithm, a slice of random phase mask is used to mimic the scattering medium and a layer of fluorescent beads is served as the sample, which has been illustrated in section 2.2. The images scanning through the whole two-dimensional on the focal plane are displayed in Fig. 4(a-d). Fig. 4(a) shows the ideal confocal fluorescent image without distortion. Fig. 4(b) illustrates the fluorescent image with scattering by a slice of the random phase mask. From the imaging results after correction, it is obvious that CAO system with a single GS can only compensate the aberrations around the central GS (Fig. 4(c)) and the corrected FOV is strongly limited. In contrast, in Fig. 4(d), there are 10 GSs used for AO correction, and the area of the corrected FOV is increased compared with a single GS. The effective coverage ratio is 0.9996 in CAOMG system, compared to 0.1963 with a single GS, which has increased about 5.09 times.
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The intensity profiles along line 1 and line 2 are demonstrated in Fig. 4(e) and (f), respectively. It can be noticed that CAO system with a single GS is a better choice for the center region (Fig .4(e)); while the automatic multiple GSs selection algorithm can be used to well compensate the phase aberrations in CAOMG system, whose corresponding corrected region can be extremely enlarged (Fig .4(f)).
Fig. 4. Imaging results of the fluorescent beads (4 μm diameter in average) through a slice of random phase mask (a) ideally, (b) with scattering, (c) after CAO correction with a single GS, (d) after CAOMG correction based on automatic GSs selection algorithm. Higher resolution images are also shown below. (e) The intensity profiles along the white dotted lines 1 in the (b-d). (f) The intensity profiles along the white dotted lines 2 in the (b-d).
3.3 Fluorescent imaging through the thick scattering medium To further verify the feasibility of the CAOMG system based on automatic multiple GSs selection algorithm in biological tissue, we used a mouse brain slice with a thickness of about 117 μm obtained from a two-photon microscope (OLYMPUS BX61WI-FV1200MPE, 10×) as the random scattering medium, as shown in Fig. 5(a). The brain slice consists of 24 layers (μs = 25.54 mm-1) whose average thickness is 4.88 μm. A single layer of fluorescent beads (4 μm diameter on average) is served as the object. Light propagation between the layers was computed via the Fourier shift theorem. The associated Fourier transforms were computed with FFT in MATLAB. We simulated the light scattering process by multiplying the electromagnetic field with the phase masks. The polarization effects and absorption were neglected. To further examine the correction effect on the focal plane, we load the correction phase patterns on SLM. The correction phase pattern after CAO with a single GS and multiple GSs are illustrated in Fig. 5(b1) and (b2). Then the illumination light scans laterally across the focal plane to acquire the two-dimensional fluorescent images, and the results are displayed in Fig. 5(c-f). Before correction, the fluorescent beads are obscure due to scattering caused by thick mouse brain tissue (Fig. 5(d)). The blue boxes in Fig. 5(d-f) demonstrate the center fluorescent distributions with scattering, CAO with a single GS and CAOMG based on automatic multiple GSs selection algorithm, respectively. It is obvious that in the central region, Fig. 5(e) shows a better
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correction effect. In the CAO correction system with a single GS, the only GS locates in the central area and the fluorescent beads around the GS can be clearly observed. This phenomenon is in accordance with the intensity profiles in Fig. 5(g), which describes the while dotted lines 1 in Fig. 5(d-f), respectively. The intensity improvement of CAO with a single GS is about 1.55 times larger than that of CAOMG.
Fig. 5. (a) One slice of the mouse brain tissue, whose thickness is set to 4.88 μm. The correction phase pattern (b1) after CAO with a single GS and (b2) after CAOMG based on automatic GSs selection algorithm. (c) Ideal imaging results of the fluorescent beads (4 μm diameter in average) without scattering. Imaging results of the fluorescent beads through thick mouse brain tissue (d) with scattering, (e) after CAO correction with a single GS, (f) after CAOMG correction based on automatic GSs selection algorithm. Higher resolution images of the yellow and blue boxes are also shown below. (g) Intensity profiles of the while dotted lines 1 in (d-f). (h) Intensity profiles of the while dotted lines 2 in (d-f).
What’s more, it can be noticed that the corrected FOV after CAOMG correction can cover a larger region than that with a single GS. CAOMG system achieves a better correction performance on the whole imaging area, and the fluorescent beads can still be seen in the yellow box in Fig. 5(f). For CAOMG correction, there are 148 GS candidates and 11 of them are chosen as the final GSs. The corrected FOV with CAOMG is extended to a diameter of about 183 μm, which is 2.58 times larger than CAO with a single GS (71 μm). Fig. 5(h) illustrates the intensity profiles of the while dotted lines 2 in Fig. 5(d-f), where the intensity improvement of CAOMG is extremely clear. It needs to be mentioned that for CAOMG method, the contribution of a certain GS to the correction phase value mainly depends on its intensity value. Thus, the intensity distribution after correction may be uneven in Fig. 5(f). The imaging results of the fluorescent beads through thick mouse brain tissue prove that high-resolution can be gotten over a larger corrected FOV in CAOMG system based on our algorithm.
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4. Conclusion In this article, we propose an automatic optimal multiple GSs selection algorithm in CAOMG system to improve the corrected FOV, using COAT for aberration correction. The aim of our
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work is to obtain larger corrected FOV of CAOMG system using fewer GSs, thus it will further improve the processing speed in deep tissue imaging. The results demonstrate that it is practical to make any available GSs as the starting point and implement the aberration correction procedure. Through a single layer of the phase mask, the effective coverage ratio can be increased to about 5.09 times than that in CAO system with a single GS. Through layers of the thick mouse brain tissue, we can also obtain high-resolution imaging and the corrected FOV is 2.58 times larger than CAO system with a single GS, correcting the aberrations quickly and improving the imaging performance effectively. It should be mentioned that this automatic multiple GSs selection algorithm can be applied to conventional AO systems with parallel process. In our CAOMG system, the time consumption of the wavefront correction is mainly depended on the COAT algorithm due to the low fresh rate of the spatial light modulator, which takes several minutes. In contrast, the automatic multiple GSs selection procedure only takes 2~5 seconds. The total correction time relates to the number of GSs. The required number of GSs is smaller, the total correction time is shorter. In the future, the selection of inner and outer radius for various biological tissues can be studied further. For instance, with a thick scattering medium, the area of effective correction with a single GS in CAO system may be smaller. Thus, the inner radius should be set smaller accordingly. To choose the optimal inner radius on unknown samples, we can first define a threshold of Strehl ratio where the point spread function is well corrected. Then, after correction based on a single GS, we can obtain the area that meets this threshold of Strehl ratio. Thus, the radius of this area is just the radius of the inner ring. And the overlapping parts over GSs can be changed to get a better correction effect, and then outer radius needs to be studied. In conclusion, our automatic optimal multiple GSs selection algorithm has potential applications in in vivo deep imaging for biomedical research. Funding
National Natural Science Foundation of China (31571110, 61735016, 81771877); Natural Science Foundation of Zhejiang Province of China (LZ17F050001), Zhejiang Lab (2018EB0ZX01), and the Fundamental Research Funds for the Central Universities.
Acknowledgments
We thank Sanhua Fang and Qiaoling Ding (Core Facilities of Zhejiang University Institute of Neuroscience for technical assistance) for guidance to imaging systems; Shuangshuang Liu and Junli Xuan (Imaging Facility, Core Facilities, Zhejiang University School of Medicine) for imaging technical assistance.
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