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Dynamic speckle illumination wide-field fluorescence microscopy with actively optical manipulation of rotational angles

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Abstract

We present a dynamic speckle illumination wide-field fluorescence microscopy (DSIWFM) combined with a line optical tweezers (LOTs) for rotational fluorescence sectioning imaging. In this method, large polystyrene fluorescent microspheres are stably trapped with LOTs, and precisely manipulated to rotate around a specific rotation axis. During the rotation process, multiple raw fluorescence images of trapped microspheres are obtained with dynamic speckle illumination. The root-mean-square (RMS) algorithm is used to extract the drastically changing fluorescent signals in the focal plane to obtain the fluorescence sectioning images of the samples at various angles. The influence of speckle granularity on the image quality of fluorescence sectioning images is experimentally analyzed. The rotational fluorescence sectioning images obtained by DSIWFM with LOTs could provide an alternative technique for applications of biomedical imaging.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

The laser scanning confocal fluorescence microscopy (LSCFM), combining the scanning of a focused laser beam and confocal detection, has become an important research tool for obtaining fluorescence sectioning images of the three-dimensional structure and the functional information of living cells and multi-cellular biological tissues [15]. However, a point-wise scanning system of the focused laser beam with a complex structure is required in a LSCFM system. Furthermore, the fluorescent molecules in the excitation volume of the focused beam are simultaneously excited, but only the fluorescent signals in the focal plane can be detected through a confocal pinhole, which results in the lower excitation efficiency. The DSIWFM is a quasi-confocal wide-field fluorescence microscopy with dynamic laser speckle illumination in the whole field of view to achieve fluorescence sectioning imaging [68]. The excited fluorescent signals with dynamic speckle illumination exhibit highly contrasted in the focal plane but blurred elsewhere [6]. Therefore, the randomly varying speckle patterns lead to more drastic changes of fluorescence images in the focal plane than that out-of-focus. By using the image extraction algorithm to process multiple raw fluorescence images, the disturbance of out-of-focus fluorescent signals can be effectively eliminated, and fluorescence sectioning images of the three-dimensional structure of samples can be obtained [9,10].

Usually, researchers can only conduct passive observations with a fluorescence microscopy, but cannot accurately and actively manipulate samples for repeatedly observing and studying on the interesting regions for a long time. The optical tweezers (OTs) have made it possible for researchers to capture and move biomolecules, organelles, and living cells in a non-contact manner without any disturbance on their life activities, and to observe them in the microscope [1114]. In traditional OTs, one laser beam is tightly focused by an objective with a high numerical aperture. The range of the optical potential well is limited to a small area near the focal point, which only allows the capture and manipulation of the smaller particles or single cell [14]. The LOTs, realized with the additional cylindrical lens, have a large trapping range, which are enable to simultaneously capture the multiple larger living cells or multicellular tissues, and precisely manipulate samples to achieve more complex movements, such as precise rotation and stretching [1519]. Recently, the traditional OTs had been combined with light sheet fluorescence microscopy to research the relation between structural and local mechanical properties in biological tissues [20]. But it is difficult for the stable capture and the precise manipulation of larger living cells or multicellular tissues with OTs.

In this paper, we present a DSIWFM with the actively optical manipulation of trapped samples’ rotational angles, in which a wide-field fluorescence microscopy with dynamic speckle illumination is combined with LOTs. In the system, the LOTs could be achieved with a laser beam passing through a cylindrical lens to precisely manipulate the stably trapped large samples to rotate around a specific axis in the focal plane. Another laser beam passes through a randomly moving diffuser to form a series of dynamically changing speckle patterns. These patterns are imaged onto the back aperture of an objective whose optical axis is perpendicular to the rotation axis. The excited fluorescent signals with the dynamical speckle illumination are collected by the objective. A serial of raw fluorescence images are recorded by a CMOS camera at the corresponding rotation angle. The drastically changing fluorescent signals in the focal plane can be extracted by using an image extraction algorithm. During the rotation of the trapped samples, the fluorescence sectioning images of the samples at different angles can be obtained. The system of DSIWFM with actively optical manipulation could be used as an effective tool for quickly obtaining the high spatial- and temporal-resolution fluorescence sectioning images of large living cells or multicellular biological tissues in situ without any contact and destruction, and allowing the long-time observation of their life activities. This method could make fully use of both the DSIWFM and actively optical manipulation technique to flexibly image the biological samples in solution, which proves to be a potential tool for analysis of the internal fine structures and evolution of mechanical responses of larger biological samples without any influence on the biological samples’ random movements during the long-time observation of their life activities.

2. Experimental setup

The structural schematic diagram of our experimental setup is shown in the Fig. 1. In the system, one near-infrared (NIR) laser beam from a continuous wave laser (Laser1, center wavelength: 1064 nm, maximal average output power: 1.5 W) is firstly shaped by a cylindrical lens (CyL) with the focal length of fCyL = 100 mm. After expended by two plano-convex lenses (L1 and L2) with focal lengths of f1 = 200 mm and f2 = 400 mm, the NIR laser beam is coupled into an objective (Obj1, Olympus, LMPlanFl, 20× / 0.4 NA) to form a linear optical trapping beam in the Obj1’s focal plane for the capture of samples in solution. The rotation of the LOTs is achieved by rotating the CyL mounted on a motorized precision rotational stage (adjustable rotational speed: 0-12000rpm, unidirectionally repeatability: 0.6° per step). By rotating the CyL around the optical axis, the rotational LOTs enable the trapped samples to be precisely manipulated to rotate in the focal plane around a specific rotational axis which is parallel to the Obj1’s optical axis. A dichroic mirror (DM1 transmission band: 600-750 nm, reflection band: 960-1100 nm) is used to reflect the NIR Laser1 and transmit the visible illumination light. After passing through a long-wavelength pass filter (F1, cut-off wavelength: 590 nm), the motion states of the manipulated samples are recorded with a CCD camera (Cam1, Olympus, DP72) under white light illumination. Meanwhile, the other continuous wave laser (Laser2, center wavelength: 532 nm, maximal average output power: 1 W) is expended by a pair of plano-convex lenses (L3 and L4) with focal lengths of f3 = 50 mm and f4 = 100 mm. After passing through a diffuser mounted on a line displacement stage (travelling range: 70 mm, resolution: 0.125 µm), the speckle patterns are imaged by another pair of plano-convex lenses (L5 and L6) with focal lengths of f5 = 200 mm and f6 = 500 mm in another objective’s (Obj2, Olympus LMPlanFl, 50× / 0.5 NA) back-focal plane. The full-field dynamic speckle illumination is implemented by transversely moving the diffuser perpendicular to the Obj2’s optical axis. The optical axis of the dynamic speckle illumination is perpendicular to that of LOTs from the Obj1. When the trapped samples are rotated to one angle, the excited fluorescent signals are collected by the Obj2, and reflected by a dichroic mirror (DM2 transmission band: 520-550 nm, reflection band: 570-700 nm). After passing through a band-pass filter (F2 central wavelength: 580 nm, passing bandwidth: 10 nm), one raw fluorescence image at the corresponding angular position is recorded by a CMOS camera (Cam2, ToupTek, ATR3CMOS26000KMA). At the position of each angle, a series of raw fluorescence images are sequentially recorded.

 figure: Fig. 1.

Fig. 1. Structural schematic diagram of the DSIWFM with active optical manipulation. laser1: CW 1064 nm laser; Laser2: CW 532 nm laser; CyL: cylindrical lens; DM1 and DM2: dichroic mirrors; L1 - L6: plano-convex lenses; TL1 and TL2: tube lenses; Obj1 and Obj2: objectives; F1: long-wavelength pass filter; F2: band-pass filter; Cam1: CCD camera; Cam2: CMOS camera.

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Each laser speckle pattern imaged in the objective’s (Obj2) back-focal plane forms a full-field illumination with a certain size and density in the entire field of view when the beam passes through various diffusers with different granularities to create laser speckle patterns. The granular fluorescence of almost the same size and density are thus excited by the speckle illumination where the size of the speckle grit is diffraction limited and roughly constant throughout the depth of field, and collected with the Obj2. If laser beam passes through a diffuser with smaller granularity, the sparser and larger granular fluorescence is formed. In contrast, the denser and smaller granular fluorescence is formed with a diffuser with bigger granularity. If the size of granular fluorescence is matched to the Obj2’s detective point spread function (PSFdet), the random variations in the intensity distributions of the granular speckle illumination can cause the most drastic change in the intensity of the fluorescent signals in the focal plane [6]. Therefore, the DSIWFM’s spatial resolution is determined by the diffuser’s granularity.

In each one of raw fluorescence images recorded by the Cam2 under the speckle illumination, the fluorescent signals arise from the fluorophores in granular speckle illuminated areas both inside and outside the Obj2’s focal plane. The contrast of the excited fluorescent signals inside the focal plane is higher than that of defocusing. When the Obj2’s PSFdet is matched to the size of the size of granular fluorescence, the random variations in the intensity distributions of the granular speckle illumination will cause more drastic changes in the intensity of the fluorescent signals in the focal plane than those out of the focal plane. Therefore, in order to obtain the fluorescence sectioning images of samples, a root-mean-square (RMS) image extraction algorithm is used to process the multiple raw fluorescence images under dynamical speckle illumination. The RMS images IRMS highlight the fluorescent signals arising from the focal plane to achieve fluorescence sectioning imaging. Here, the RMS image extraction algorithm is shown in the following equation [6]

$${I_{RMS}} = {\left\{ {\mathop \sum \limits_{i = 1}^N {{({{I_i} - {I_{i - 1}}} )}^2}/({2N} )} \right\}^{\frac{1}{2}}}$$
where N is the number of raw fluorescence images, Ii is the intensity of the ith raw fluorescence image recorded by the camera corresponding to different laser speckle patterns. From RMS image extraction algorithm, it can be seen that the number N of raw fluorescence images and the intensity distributions of a laser speckle pattern related to a diffuser’s granularity G are important factors affecting the imaging quality of the fluorescence sectioning images [21].

3. Experimental results and discussions

3.1 Experimental results of LOTs manipulation

In experiments, two polystyrene fluorescent microspheres (the excitation wavelength λEx = 540 nm and emission wavelength: λEm = 580 nm) with the same diameter of 20 µm in the deionized water are firstly trapped with the LOTs. In the focal plane of Obj1, the average power of the LOTs is about 120 mW. And then, the LOTs’ optical field is step-by-step rotated by rotating the CyL mounted on the motorized precision rotational stage. The trapped polystyrene fluorescent microspheres are precisely manipulated to rotate counterclockwise by 180° around the center of rotation where locates the microsphere marked No. I (microsphere I). Under the white light illumination, the motion states of the polystyrene fluorescent microspheres at different angular positions are shown in the Fig. 2. The rotation angles α are 0°, 40°, 90°, 150° and 180°, respectively. The experimental results show that the stable capture and precise control of rotation angles of large-size samples in solution can be achieved with LOTs.

 figure: Fig. 2.

Fig. 2. The motion states of two polystyrene fluorescent microspheres are trapped and manipulated with the LOTs at rotational angles of 0°, 40°, 90°, 150° and 180° corresponding to (a) to (e) respectively. (Scale bar: 10 µm)

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3.2 Experimental results of wide-field fluorescence with LOTs manipulation

The fluorescence images of two polystyrene fluorescent microspheres trapped with the LOTs are recorded with a wide-field fluorescence microscope at the corresponding angular positions, as shown in the Fig. 3. The exposure time of the camera is 5 ms. As the No. II polystyrene fluorescent (microsphere II) is manipulated with the LOTs to rotate counterclockwise around the microsphere I from 0° to 180°, the microsphere II leaves and goes back to the imaging focal plane of the wide-field fluorescence microscope. The excited fluorescent signals coming from the inside and outside of the focal plane are recorded by the camera of the wide-field fluorescence microscope. Therefore, the fluorescence sectioning imaging cannot be achieved.

 figure: Fig. 3.

Fig. 3. The wide-field fluorescence images of two polystyrene fluorescent microspheres at rotation angles of at rotational angles of 0°, 40°, 90°, 150° and 180° corresponding to (a) to (e) respectively. (Scale bar: 10 µm)

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3.3 Experimental results of DSIWFM with actively optical manipulation

The 532 nm laser beam passing through one diffuser with the granularity G = 200 is used to generate the laser speckle illumination in the full-field of objective. In the focal plane of Obj2, the average power of the 532 nm laser speckle illumination is about 100 mW. The polystyrene fluorescent microspheres are excited with the dynamic speckle by moving the diffuser transversely. The two trapped polystyrene fluorescent microspheres are precisely manipulated to rotate to an angle by the LOTs. At each angular position, the number of raw fluorescence images N = 60 are recorded by the CMOS camera with an exposure time of 5 ms per image. By sequentially rotating samples, the fluorescence sectioning images of the polystyrene fluorescent microspheres at the each corresponding angular position are obtained by using the RMS image extraction algorithm to process the 60 raw fluorescence images. The experimental results are shown in Fig. 4. SubFigs. 4(a) 1-5 show each one of sixty raw fluorescence images of samples at corresponding angular positions of α = 0°, 40°, 90°, 150° and 180°, respectively. The fluorescent signals of raw fluorescence images comes from the fluorescent molecules inside and outside the focal plane, whose intensities dynamically change with the dynamic speckle illumination. The RMS images of samples have been obtained according to Eq. (1), as shown in Fig. 4 (b). The normalized intensity profiles of fluorescent signals corresponding to the locations identified by the blue dashed line and red solid line in Fig. 4(a) and (b) are shown in the Fig. 4(c).

 figure: Fig. 4.

Fig. 4. (a) Raw fluorescence images with speckle illumination; (b) fluorescence sectioning images in RMS image extraction algorithm of two microspheres; (c) the intensity profiles along central axis of two microspheres in the wide-field fluorescence images (WF, black dash-dotted line), raw speckled images (DSI, blue dashed line) and fluorescence sectioning images (RMS, red solid line) at angles of 0°, 40°, 90°, 150° and 180° corresponding to number 1 to number 5 respectively with N = 60 and G = 200. (Scale bar: 10 µm)

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The experimental results show that, when the microsphere II is rotated 40° around the microsphere I as shown in Fig. 2(b), an RMS image is obtained by the RMS image extraction algorithm, as shown in Fig. 4(b)-2. Since the intensity of fluorescent signals inside the focal plane changes more drastically than that of the defocused fluorescent signals, the disturbance of defocused fluorescent signals can be effectively eliminated. Thus, the intensity profiles of fluorescent signals at the corresponding position in Fig. 4(c)-2 indicate that the width of the fluorescence intensity profile under wide-field illumination is much wider than that of RMS images based on dynamic speckle illumination. The experimental results demonstrate that the disturbance of defocus fluorescent signals can be effectively eliminated with RMS image extraction algorithm, and the fluorescence sectioning imaging can be achieved.

In RMS images of Fig. 4(b), a dark area appears in the center of the microspheres. At the corresponding position in the Fig. 4(c), the intensity of fluorescent signals near the center of the fluorescent microspheres is lower than that at the edge. This is because, in the illuminated area, speckle grits are sparse but large in size, when one laser beam passes through a diffuser with smaller granularity of G = 200. When the diffuser is moved to change the illumination speckle’s intensity distribution, the central area of the sample has been always illuminated by the sparse speckle grits larger than PSFdet, and the intensity variations of the excited fluorescent signals in the center are also smaller than those near the edge. Therefore, when the raw fluorescence images are processed with the RMS image extraction algorithm, the intensities of the fluorescent signals at the center of the samples decrease in the case of smaller granularity.

According to the above experimental results, the granularity related to the size of the laser speckle spots has a large influence on the imaging quality of the fluorescence sectioning images. In order to investigate the influence of speckle spots’ size on the imaging quality, the Laser2 respectively passes through the diffusers with G = 600 and 1500 to generate laser speckles of various granularities in the same experimental conditions. The experimental results of raw speckled images (one of sixty images at each angle), fluorescence sectioning images and intensity profiles along central axis of microspheres of wide-field fluorescence images, raw speckled images and fluorescence sectioning images at various angular positions for granularities G = 600 and 1500 are shown in Fig. 5(a-c) and 6(a-c), respectively.

 figure: Fig. 5.

Fig. 5. (a) Raw fluorescence images with speckle illumination; (b) fluorescence sectioning images in RMS image extraction algorithm of two microspheres; (c) the intensity profiles along central axis of two microspheres in the wide-field fluorescence images (WF, black dash-dotted line), raw speckled images (DSI, blue dashed line) and fluorescence sectioning images (RMS, red solid line) at angles of 0°, 40°, 90°, 150° and 180° corresponding to number 1 to number 5 respectively with N = 60 and G = 600. (Scale bar: 10µm)

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The experimental results show that the fluorescence sectioning imaging at corresponding angular position can be achieved under dynamical speckle illumination with G = 600 and 1500, during the polystyrene fluorescent microspheres are rotated with the LOTs. It is obvious to see that the fluorescence sectioning images obtained with the laser passing through the diffuser with G = 600 in Fig. 5(b) have better image quality than those obtained with G = 200 and 1500 in Figs. 4(b), and 6(b). Furthermore, every RMS image in Fig. 6(b) displays the similar dark area at the center of polystyrene fluorescent microspheres as in Fig. 4(b). The intensity profiles of fluorescent signals along central axis of two microspheres in Fig. 6(c) illustrates that the intensity of fluorescent signals at the corresponding position is depressed. And the intensity of fluorescent signals near the center of the polystyrene fluorescent microspheres are lower than that at the edge. This is because, in the same size illuminated area, the dense small speckle grits illuminate sample, when one laser beam passes through a diffuser with larger granularity of G = 1500. Under such dynamic speckle illumination, the fluorophores near the sample’s center have always been excited by the dense speckle grits smaller than PSFdet. The intensity variations of the excited fluorescent signals are also smaller than those near the edge. In RMS images, the intensity of the fluorescent signals at the center of the sample is thus reduced. Therefore, in order to obtain better image quality with dynamic speckle illumination, it is necessary to select a diffuser with an appropriate granularity.

 figure: Fig. 6.

Fig. 6. (a) Raw fluorescence images with speckle illumination; (b) fluorescence sectioning images in RMS image extraction algorithm of two microspheres; (c) the intensity profiles along central axis of two microspheres in the wide-field fluorescence images (WF, black dash-dotted line), raw speckled images (DSI, blue dashed line) and fluorescence sectioning images (RMS, red solid line) at angles of 0°, 40°, 90°, 150° and 180° corresponding to number 1 to number 5 respectively with N = 60 and G = 1500. (Scale bar: 10 µm)

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3.4 Experimental results of DSIWFM with a diffuser G = 600

In order to measure the spatial resolution and sectioning imaging depth of the DSIWFM, a glass slide USAF 1951 fluorescence resolution target is used as sample. The 532 nm laser beam passing through one diffuser with the granularity G = 600 is used to generate the dynamic laser speckle illumination in the full-field of objective. The imaging areas correspond to 6-3 to 6-5 of USAF1951 (80.6-102.0 lp/mm). Through vertically adjusting objective’s imaging focal plane, 60 raw fluorescence images are obtained with the CMOS camera at the imaging depths of 0, 40 and 80 µm, and then processed with the RMS image extraction algorithm. The experimental results are shown in Fig. 7.

 figure: Fig. 7.

Fig. 7. (a) Raw fluorescence images with speckle illumination; (b) fluorescence sectioning images in RMS image extraction algorithm of the USAF 1951 glass slide fluorescence resolution target; (c) the intensity profiles along the white line in raw fluorescence images (DSI, blue dashed line) and fluorescence sectioning images (RMS, red solid line) at sectioning imaging depths of 0, 40 and 80 µm corresponding to number 1 to number 3 respectively with N = 60 and G = 600. (Scale bar: 10 µm).

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The Fig. 7(a) shows one of sixty raw fluorescence images of sample at three different depths of 0, 40 and 80 µm corresponding to number 1 to number 3, respectively. The RMS images are shown in Fig. 7 (b). The normalized intensity profiles of fluorescent signals corresponding to the locations identified by the white line in Fig. 7(a) and (b) are shown in the Fig. 7(c). The experimental results show that, because the intensity of fluorescent signals inside the focal plane changes more drastically than that of the defocused fluorescent signals, the disturbance of defocused fluorescent signals can be effectively eliminated, and the fluorescence sectioning imaging with high resolution and contrast can be achieved with the RMS image extraction algorithm.

4. Conclusion

In this paper, the LOTs are combined with the DSIWFM to stably capture and precisely manipulate the large samples in a non-contact manner for obtaining the fluorescence sectioning images of samples at each corresponding angular position. In system, one NIR laser beam is shaped by a cylindrical lens to form a line optical trapping beam in an objective’s focal plane. The polystyrene fluorescent microspheres in water are stably captured and precisely manipulated with the LOTs to rotate around a rotational axis. Another laser beam passes through a diffuser to generate the speckle pattern, which is imaged in the other objective’s back-focal plane to illuminate samples. The two objectives’ optical axes are perpendicular to each other. When the trapped samples are forced to rotate an angle, multiple raw fluorescence images under the dynamic speckle illumination are recorded. By using the RMS image extraction algorithm to separate the fluorescent signals from inside and outside the focal plane, the fluorescence sectioning images at each corresponding angle are obtained. The influence of speckle granularity on the imaging quality of the fluorescence sectioning images are experimentally analyzed by using diffusers with different granularities. The experimental results show that the better image quality of fluorescence sectioning image could be obtained by using a diffuser with the appropriate granularity. With this method, researchers can transform passive observation with fluorescence microscopy into active manipulation of larger living cells or multi-cellular tissues, and obtain the high-resolution fluorescence sectioning images of internal structure and morphology changes in situ during their life activities.

Funding

National Natural Science Foundation of China (61965008); Natural Science Foundation of Guangxi Province (AD21220086, 2022GXNSFAA035643, 2023GXNSFDA026040, 2023GXNSFBA026071); Scientific Research Project for Guangxi University (2020KY05022); Guangxi Key Laboratory (YQ21109, GD21103); Innovation Project of GUET Graduate Education (2023YCXS203, 2023YCNS196).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (7)

Fig. 1.
Fig. 1. Structural schematic diagram of the DSIWFM with active optical manipulation. laser1: CW 1064 nm laser; Laser2: CW 532 nm laser; CyL: cylindrical lens; DM1 and DM2: dichroic mirrors; L1 - L6: plano-convex lenses; TL1 and TL2: tube lenses; Obj1 and Obj2: objectives; F1: long-wavelength pass filter; F2: band-pass filter; Cam1: CCD camera; Cam2: CMOS camera.
Fig. 2.
Fig. 2. The motion states of two polystyrene fluorescent microspheres are trapped and manipulated with the LOTs at rotational angles of 0°, 40°, 90°, 150° and 180° corresponding to (a) to (e) respectively. (Scale bar: 10 µm)
Fig. 3.
Fig. 3. The wide-field fluorescence images of two polystyrene fluorescent microspheres at rotation angles of at rotational angles of 0°, 40°, 90°, 150° and 180° corresponding to (a) to (e) respectively. (Scale bar: 10 µm)
Fig. 4.
Fig. 4. (a) Raw fluorescence images with speckle illumination; (b) fluorescence sectioning images in RMS image extraction algorithm of two microspheres; (c) the intensity profiles along central axis of two microspheres in the wide-field fluorescence images (WF, black dash-dotted line), raw speckled images (DSI, blue dashed line) and fluorescence sectioning images (RMS, red solid line) at angles of 0°, 40°, 90°, 150° and 180° corresponding to number 1 to number 5 respectively with N = 60 and G = 200. (Scale bar: 10 µm)
Fig. 5.
Fig. 5. (a) Raw fluorescence images with speckle illumination; (b) fluorescence sectioning images in RMS image extraction algorithm of two microspheres; (c) the intensity profiles along central axis of two microspheres in the wide-field fluorescence images (WF, black dash-dotted line), raw speckled images (DSI, blue dashed line) and fluorescence sectioning images (RMS, red solid line) at angles of 0°, 40°, 90°, 150° and 180° corresponding to number 1 to number 5 respectively with N = 60 and G = 600. (Scale bar: 10µm)
Fig. 6.
Fig. 6. (a) Raw fluorescence images with speckle illumination; (b) fluorescence sectioning images in RMS image extraction algorithm of two microspheres; (c) the intensity profiles along central axis of two microspheres in the wide-field fluorescence images (WF, black dash-dotted line), raw speckled images (DSI, blue dashed line) and fluorescence sectioning images (RMS, red solid line) at angles of 0°, 40°, 90°, 150° and 180° corresponding to number 1 to number 5 respectively with N = 60 and G = 1500. (Scale bar: 10 µm)
Fig. 7.
Fig. 7. (a) Raw fluorescence images with speckle illumination; (b) fluorescence sectioning images in RMS image extraction algorithm of the USAF 1951 glass slide fluorescence resolution target; (c) the intensity profiles along the white line in raw fluorescence images (DSI, blue dashed line) and fluorescence sectioning images (RMS, red solid line) at sectioning imaging depths of 0, 40 and 80 µm corresponding to number 1 to number 3 respectively with N = 60 and G = 600. (Scale bar: 10 µm).

Equations (1)

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I R M S = { i = 1 N ( I i I i 1 ) 2 / ( 2 N ) } 1 2
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