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Highly focused beam generated with a height tuned micro-optical structure for high contrast microscopic imaging

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Abstract

Light sheet illumination technology improves the signal-to-noise ratio, resolution, and reduces scattered backgrounds for biological microscopic detection system. Here, we developed a novel micro-optical structure to produce a focused and uniform beam for the enhancement of imaging contrast. The beam intensity and working distance can be modified by adjusting the height and period of the structure. Our experiments successfully recorded structured light illumination, demonstrating the ability of the structure to capture high-contrast imaging data. We compared the light fields generated with and without the structure to assess the imaging quality, revealing a maximum 4.78-fold improvement in the signal-to-noise ratio. This work provides a potential method for high-resolution and high-contrast light sheet fluorescence microscopic detection.

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

1. Introduction

The quality of microscopic imaging is crucial, especially in terms of contrast. A high level of contrast can effectively reduce noise and enhance the signal, thereby improving the overall imaging quality. Enhanced image contrast can be achieved by employing a limiting aperture [1], which facilitates fluorescence acquisition specifically in the focal plane. But this approach needs multiple irradiations for three-dimensional (3D) imaging, thereby imposing limitations on continuous imaging time and exacerbating issues of photobleaching [2]. Another approach involves utilizing a high numerical aperture objective, but the large size of the objective and the limited working distance can restrict the compactness of the imaging system [3]. Optical coherence tomography (OCT) [4,5] is a non-invasive imaging technique for cross-sectional imaging of biological tissues and materials [6]. Li et al. developed a dual-focus fiber-optic probe that extends the depth of focus in high-resolution endoscopic optical coherence tomography. However, there remain problems of complex system and high cost [7].

Light-sheet fluorescence microscopy (LSFM) is a technique that utilizes separate excitation and detection light paths to generate high-contrast images of fluorescent samples [811]. By generating thin light planes for optical sectioning, the excitation light path enables precise imaging of samples [12,13]. LSFM provides rapid image acquisition, minimal phototoxicity and photodamage, superior signal-to-noise ratio (SNR), and excellent 3D spatial resolution [1418]. However, when LSFM utilizes dynamic scanning to generate virtual light sheets, it often creates a significant axial paraflap, which can induce out-of-focus background excitation and affect resolution. Recently, Eric Betzig’s group proposed a two-dimensional (2D) lattice of thin light sheets that can balance the thickness and vertical length of the light sheet to reduce the energy of the paraflap and improve the resolution [1921]. Non-diffracting Bessel beams particularly those generated using the axicon method proposed by Mcleod J. H. in 1954 [22], can produce virtual light sheets of submicron thickness to facilitate imaging but may suffer from fabrication errors [19,23,24]. Zhai et al. proposed a method using computer-generated holograms (CGHs) and simulated with a spatial light modulator (SLM) [25]. By adjusting the CGHs, the type and parameters of the axicon can be easily modified, allowing for the dynamic generation of adjustable axes without machining errors to suit different applications [6]. However, there is still a lack of effective analysis to explain the impacts of the micro-optical structure on the function of the illumination light field, especially centered on the background noise reduction and the improvement of SNR with a height-tuned structure [6,17,26], which limits the large-scale application.

Here, we present a novel height-tuned micro-optical structure (HTMOS) capable of producing lattice light sheets, which can generate highly focused beams and enhance imaging contrast compared to traditional axicons. Through simulation and analysis of different structural cycles, we determine the optimal design and create a 2D array. Experimental results confirm the consistency between the recorded illumination of the lattice light sheet and the corresponding simulations. In addition, we compare the imaging quality of our in-house microscopic system using shaped and unshaped light fields, using polystyrene fluorescent microspheres and 293T cells as the image acquisition signal.

2. Structure and methods

2.1 Structure of HTMOS

Figure 1(a) illustrates the basic structure of optical glass triangular prisms. The central prism is marked as m = 1, while the symmetric structures on each side are assigned m-values of 2, 3, and so forth. The central rotational symmetry forms a 3D HTMOS structure (Figs. 1(b), (c), with m = 3 denoted as M3 structure). Figure 1(d) demonstrates the focusing capability of the isometric HTMOS structure, providing a detailed analysis of the central section. The right-angled triangular structures flanking the central isosceles triangle are designed with a height denoted as hm (m = 1, 2, 3,…). The symmetrical arrangement of these right triangles converges light. By extending the structure linearly with the same hm, the focal point of the light passing through the structure increases, and the effective working distance is extended. The working distance of the central structure can be determined by fixing its height h1 and applying the equation of the diffractive element design principle. The height of the central part of the structure is fixed and its working distance is set as the working distance of the whole structure.

 figure: Fig. 1.

Fig. 1. (a) The basic structure of optical glass triangular prisms. (b), (c) Schematic diagram of equal heights 3D structure and HTMOS. (d), (e) Schematic diagram of equal heights structure and HTMOS focusing ability, respectively.

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According to Snell’s law, the height design equation for the HTMOS component structures can be expressed as:

$${h_m} = \frac{\lambda }{{{n_1} - \sqrt {1 - {{\left( {\frac{\lambda }{\Lambda }} \right)}^2}} }} \approx \frac{\lambda }{{{n_1} - 1}}$$
where $\mit \lambda$ is the incident wavelength, $\Lambda$ is the structural period, and n1 is the refractive index of HTMOS. Each group of straight triangular prisms focuses the light, and the working distance falls within the range of the central triangular prism, achieving the desired focusing effect. $\alpha$m is the base angle, $\gamma$m denotes the refraction angle of light passing through the mth structure, $\beta$m is the angle between the outermost refracted ray and the base of the triangular prism, Zmax is the maximum working distance of the structure, and both $\Lambda$ and hm are at micron-meter scale. The HTMOS design equations are as follows:
$${h_m} = \Lambda \tan {\alpha _m}$$
$${Z_{\max }} = \Lambda \tan {\beta _m}$$
$${\gamma _m} = \arcsin ({n_1}\sin {\alpha _m})$$
$${\beta _m} = {\alpha _m} - {\gamma _m} + \frac{\pi }{2}$$

This transformation reduces stray light and sub-focusing, as shown in Fig. 1(b), and converges the light within the working range of the central structure. It extends the effective working distance and enhances the energy of the central focal spot, thereby improving the imaging quality of the structure.

2.2 Electromagnetic field simulation method

To determine the optimal value of m in the HTMOS, we used the 3D finite-difference time-domain (FDTD) method in Lumerical FDTD solution software. The HTMOS structure was illuminated with a light wavelength of 532 nm, propagating from the bottom towards the z-axis. With a refractive index of 1.5 and a period of $\Lambda$ = 5 µm, the height of HTMOS hm, was calculated using Eq. (1) and Eq. (2). The simulation size in xy plane was 35 µm $\times$ 35 µm, with a mesh accuracy of 0.2 µm in the x- and y-directions, and 0.1 µm in the z-direction. The electric field was monitored at the center of the structure using the absorbing boundary conditions of a perfectly matched layer (PML). The electric field intensity was normalized to 1 a.u., and the electromagnetic field distribution (E, H) was obtained through 3D-FDTD simulation at any location in the whole simulation area. Once the optimal m-value for a single structure is determined, a R$\times$R array can be created using a similar method to determine the optimal R-value of the array.

2.3 Light sheet microscopy illumination system design method

Figures 2(a) and (b) show the diagram and phase diagram of R$\times$R HTMOS array, respectively. To verify the structured light field generated by HTMOS and its application in illuminating fluorescent microspheres, an experimental setup is depicted in Fig. 2(c). A solid-state laser (MGL-III-532, Changchun New Industries Optoelectronics Tech. Co., Ltd) was served as the light source, with an attenuator placed behind it to adjust the intensity. The laser beam was extended and collimated through a spatial filter and a convex lens (L1, f = 15 cm). Then it was tailored by an aperture and converted into the beam of lattice light sheets using a SLM (Real Light, RL-SLMT1, 1024 $\times$ 512 pixels, 26 µm pixel pitch) with the phase mask of HTMOS. Linear polarizers were placed on both sides of the SLM to optimize modulation efficiency. The beam diameter was reduced to a quarter through a telescope system (L2, f = 20 cm and L3, f = 5 cm) to match the numerical aperture (NA) of microscope .

 figure: Fig. 2.

Fig. 2. (a), (b) R$\times$R HTMOS array diagram and phase diagram. (c) Set-up of the experiment system. The blue dashed rectangle represents light sheet microscopy of the light field detection system, the red dashed rectangle represents light sheet microscopy of the polystyrene fluorescent microspheres and 293T cells detection system.

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In our experiment, we converted the height distribution function of HTMOS into the corresponding phase mask and project it onto the SLM. Then the shaped beams were captured by a CCD camera. We used a translation stage combined with the CCD2 (1920 $\times$ 1200, pixel size 5.86 µm) to record the structured light field at different positions after HTMOS to verify the consistency of the experimental and simulated results.

2.4 Light sheet microscopy detection system design method

In the fluorescent microsphere experiments, a pair of lenses L2 (f = 20 cm) and L3 (f = 5 cm) were positioned 25 cm apart to adjust the size of the beam. And an aperture was added at the focal plane position between L2 and L3 to filter out the other diffraction orders. The microscopic objective O1 (10$\times$, NA = 0.25) directed the light beam into the sample chamber. Polystyrene fluorescent microspheres and 293T cells were imaged to evaluate the imaging quality of the light sheet detection system. 0.01 mg/mL polystyrene fluorescent microspheres (diameter: 1 µm, excitation center wavelength: 540 nm, emission center wavelength: 580 nm) immobilized by solid agar. The excitation wavelength of 293T cells transfected with pEGFP-N1 plasmid was 488 nm and the emission wavelength was 507nm.

The signal collection device was placed perpendicular to the illumination light path. The light field information was firstly magnified by microscope objective O2 (4$\times$, NA = 0.13), and then the illuminated laser light was filtered by a long-pass filter with a cut-off wavelength of 565 nm to isolate the incident laser light for the polystyrene fluorescents. For the 293T cells, the experimental system in Fig. 2(c) utilizes a 488 nm laser for illumination, with the remaining configuration unchanged. A BP525 bandpass filter was employed to isolate the incident laser (488 nm) with a central wavelength of 525 nm and a half-width of 20 nm (525$\times$20 nm). Finally, the signal was collected by a CCD1 (2048 $\times$ 2048, pixel size of 5.5 µm).

2.5 Preparation of polystyrene fluorescent microspheres

The sample preparation process is as follows: (1) Weigh an appropriate amount of agar powder and pure water, and mix them in a beaker with a concentration percentage of 0.5 %. (2) Place the beaker containing the mixed solution and stir the solution evenly. (3) Take an appropriate amount of polystyrene fluorescent microspheres with a diameter of 1 µm and then the concentration of solution is uniformly dispersed as 0.01 mg/mL with ultrasonic oscillation. (4) Remove the beaker from the ultrasonic cleaning box, place it into the electric incubator, set the heating temperature at 100 $^{\circ }\textrm {C}$, and heat it until the agar powder is completely melted. (5) When cooling to about 40 $^{\circ }\textrm {C}$, use a pipette to inject the solution into the cuvette. After the stabilization of the surroundings with the polystyrene fluorescent microspheres, the sample preparation is completed.

2.6 Preparation of 293T cells

The sample preparation process is outlined as follows: (1) 293T cells are seeded in six-well plates one day in advance. (2) The original medium is removed from the cells two hours prior to transfection and replaced with fresh complete medium. (3) 2 µg of pEGFP-N1 plasmid DNA is diluted with 50 µL of serum-free diluent and thoroughly mixed to create a DNA dilution. (4) 4 µL of transfection reagent is added to the DNA dilution, and the mixture is allowed to stand for 10-15 minutes at room temperature to complete the transfection complex configuration. (5) The cells are then cultured for 24-48 hours to complete the preparation.

3. Results and discussion

3.1 Electromagnetic field simulation directly generated by HTMOS

The 3D FDTD simulation results (Figs. 3(a)-(e)) show the focusing intensities of the five types of HTMOS in xz plane. Expanding the structure leads to a continuous focusing region, and resulting in a significant increase at the maximum intensity. Figure 3(f)-(j) show the focus intensity along x-axis in xy plane, and (l) is the comparisons of light intensity distribution curves for five structures at y = 0 along x-axis (range from -10 µm to 10 µm) in xy plane. It shows good symmetry, which means that it can be useful for light sheet imaging.

Figure 3(k) presents a comparison of the peak intensities, demonstrating a significant increase from m = 1 to m = 3 with the expansion of the structure size. The maximum intensity is obtained when m = 3 and remains stable thereafter. Figure 3(m) illustrates the light intensity distribution curves for the five structures at x = 0 in xz plane. The structures with m = 1 and m = 2 exhibit lower maximum focusing intensities compared to those with m $\geq$ 3. For m $\geq$ 4, a small peak emerges near the peak of the focusing intensity, which is caused by the fact that when m-value increases, the mutation points at the structural junction of HTMOS (a refraction diffraction hybrid type lens) also increase, resulting in stray light. The structure with m = 3 demonstrates the highest focusing ability and the strongest light homogenization effect.

 figure: Fig. 3.

Fig. 3. (a)–(e) The electric field intensity distribution of the beam in xz plane with m = 1, 2, 3, 4, 5, respectively. (f)-(j) Focus intensity along x-axis in xy plane with m = 1, 2, 3, 4, 5, respectively. (k) Comparison of five HTMOS peak intensities. (l) The comparisons of light intensity distribution curves for five structures at y = 0 along x-axis in xy plane. (m) The comparisons of light intensity distribution curves for five structures at x = 0 in xz plane.

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Spatial imaging of fluorescent microspheres plays a crucial role in assessing the performance of the microscopic system. However, weak fluorescence signals emitted by microspheres located in the central region of a Gaussian beam can introduce defocusing noise and degrade the overall imaging quality. To address this issue, our in-house microscopic detection system employs phase masks to modulate the incident Gaussian beam, resulting in a more uniform beam. This modulation technique effectively reduces noise surrounding the microspheres and enhances the SNR.

Figures 4(a)–(f) depict the uniform light ability of a single structure, with different HTMOS structures. A comparison of the noise and SNR along z-axis of the intensity profile is shown in Figs. 4(g) and (h). The phase masks of the structures modulates the incident Gaussian beam into a more uniform beam, which greatly reduces the observed noise value around the fluorescent microsphere and significantly improves the SNR. The SNR is defined as the ratio of the maximum signal to the average value of the noise signal:

$${\rm{SNR}} = \frac{{{S_{\max }}}}{{{N_{avg}}}}$$

 figure: Fig. 4.

Fig. 4. (a)–(f) The imaging comparisons of same polystyrene fluorescent microsphere (a) without HTMOS and (b)–(f) with HTMOS structure in xz plane. (g) The comparison of intensity profile curves along z-axis. (h) Histograms of SNR results for five HTMOS.

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The noise value decreased from 35.71 to approximately 7.50 when a phase mask was added. Additionally, the SNR improved from 5.37 to higher values (11.10, 10.92, 16.64, 9.29, 15.48) with the addition of phase masks with different HTMOS structures. It is particularly noteworthy that when m = 3, the imaging SNR of HTMOS structure is increased by 2.06 times.

In summary, HTMOS effectively homogenizes light, increases focal spot intensity, and improves imaging contrast. The optimal HTMOS structure with m = 3 can be implemented in a R$\times$R array format to achieve 3D illumination and capture superior data and high-quality images.

The HTMOS with m = 3 is arranged in R $\times$ R arrays (Fig. 2(b)), with R-values set from 1 to 5. The electromagnetic field distributions of the five HTMOS arrays are obtained through 3D-FDTD simulation, using the same analytical method as the HTMOS.

According to Rayleigh criterion, the lateral resolution of the system is:

$$\sigma = \frac{{0.61\lambda }}{{NA}}$$
where $\lambda$ = 0.532 µm is the wavelength of the incident light, and NA = 0.13 is the numerical aperture of the microscope objective [27]. As a result, the system provides a theoretical lateral resolution of about 2.5 µm. The axial resolution can be calculated as:
$${R_{axial}} = 2{\omega _0} = \frac{\lambda }{{\pi \theta }} = 2\frac{{n\lambda }}{{\pi NA}}$$
where $\omega$0 is the beam waist, f is the focal length of the microscope objective, D is the diameter, and n = 1.33 is the refractive index. As a result, the theoretical axial resolution of the system is around 3.5 µm.

Figures 5(a)–(e) display the focusing intensity of the arrays in xz plane. The white curve represents the variation of optical field intensity along z-direction on the centerline in xz plane. The full width at half maximum (FWHM), a distance where the beam energy exceeds a half of the peak intensity, are obtained to be 3.32 µm, 3.23 µm, 3.14 µm, 3.27 µm, and 3.27 µm for the five arrays, respectively. Notably, the HTMOS arrays with a R-value of 3 exhibit the smallest FWHM, which means the highest resolution. This is consistent with the theoretical values obtained in Eq. (8).

 figure: Fig. 5.

Fig. 5. (a)–(e) The electric field intensity distribution of the beam in xz plane with R = 1, 2, 3, 4, 5, respectively. (f)–(j) The intensity curve at the focal plane position.

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Figures 5(f)–(j) illustrate the intensity distribution of the centerline of the extracted focal plane. The maximum intensities are 744.49a.u., 750.61a.u., 773.18a.u., 763.01a.u., and 761.64a.u., respectively. These values demonstrate the pattern of an initial increase followed by a decrease, with the maximum intensity occurring at a R value of 3 in the array.

3.2 Light sheet microscopy illumination system

In order to confirm the consistency between experimental and simulated beams, the field intensity distributions of the focal xy plane and the pre-focal xy plane are extracted. Figures 6(a)–(e) display the simulated intensity distribution at the focal plane for the five array configurations, and Figs. 6(k)–(o) present the corresponding experimental results. Additionally, Figs. 6(f)–(j) depict the simulated intensity distribution at the pre-focal plane, and Figs. 6(p)–(t) show the corresponding experimental results. All optical patterns indicate ideal array distributions, providing good evidence for the agreement between experimental and simulated results. All findings reveal that the HTMOS arrays are well-suited for lattice light sheet illumination.

 figure: Fig. 6.

Fig. 6. The (a)-(j) simulation and (k)-(t) experimental results of field intensity distribution in xy plane. (a)-(e), (k)-(o) are on the focal plane and (f)-(j), (p)-(t) are on the pre-focal plane.

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3.3 Light sheet microscopy detection system

Figure 7(a) presents the results of the fluorescence microsphere imaging experiment without the use of the HTMOS array phase mask, while Figs. 7(b)–(f) illustrate the results for HTMOS arrays of 1$\times$1 to 5$\times$5 configurations. The phase mask of the structure effectively transforms the incident Gaussian beam into a more uniform beam, leading to a significant reduction in observed noise and a notable improvement in the SNR around the fluorescent microspheres. Figure 7(h) demonstrates that the noise level decreases from 35.71 to 7.15 with the presence of phase mask. Furthermore, by incorporating phase masks with different HTMOS array configurations, the SNR increases from 5.37 a.u. (without a phase mask) to higher values (16.64, 15.97, 25.67, 22.17, and 22.32 a.u.). Notably, the HTMOS array structure with a R-value of 3 enhances the SNR by 4.78 times. In addition, in Fig. 7(g), the FWHM without HTMOS phase mask is 4.82 µm, and the FWHM with HTMOS phase mask is 3.97 µm, 3.41 µm, 3.26 µm, 3.31 µm, and 3.31 µm from 1$\times$1 to 5$\times$5, respectively. The experimental results are consistent with the theoretical results of Eq. (8), and the resolution is increased by 1.46 times.

Figures 8(a)-(d) depict the findings of the experiment conducted on a biological sample of 293T cells. Figure 8(a) shows the observation under an inverted commercial microscope with numerous cells stacked on top of each other, which makes it difficult to distinguish individual cells. Figures 8(b) and (c) present the experimental outcomes of our in-house light sheet system without and with HTMOS phase mask, respectively, which can clearly observe individual cells with a higher resolution. Thus the internal information of the cells in Fig. 8(c) is more clear, while it is difficult to discern in Fig. 8(b) due to the presence of stray light. To quantitatively analyze the impact of the HTMOS phase mask on the improvement of image quality, we calculated the normalized intensity along the yellow line marked in the image. As depicted in Fig. 8(d), the SNR of the cells images obtained with HTMOS phase mask is approximately 4.3 times higher than that without the HTMOS phase mask, which is consistent with the results of the polystyrene fluorescent microspheres experiment.

 figure: Fig. 7.

Fig. 7. The imaging comparisons of same polystyrene fluorescent microsphere (a) without HTMOS array and (b)–(f) with HTMOS array (R = 1, 2, 3, 4, 5) in xz plane; (g) The curve of polystyrene fluorescent microspheres along z-axis illuminated without and with HTMOS array. (h) The comparison chart of the imaging, noise and SNR.

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 figure: Fig. 8.

Fig. 8. The imaging comparison in 293T cells. (a) Image results under inverted commercial microscope (20$\times$ objective); Experimental results in light sheet microscopy detection system (b) without HTMOS phase mask and (c) with HTMOS phase mask. (d) The profile comparison along the yellow line marked in the (b) and (c) with an illumination of the Gaussian and HTMOS.

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4. Conclusion

In conclusion, we propose a height-tuned micro-optical structure to effectively converge continuous beams generated by traditional axicon lenses. Through FDTD simulations and microscopic imaging experiments, we demonstrate that HTMOS significantly enhances the maximum intensity of the focal spot, reduces stray light and improves imaging contrast. Notably, the HTMOS structure with m = 3 exhibits the strongest focusing ability, resulting in a 3.09-fold increase of the SNR and a reduction of the scattering background compared to those without HTMOS phase mask. Furthermore, by constructing a R$\times$R array with a m = 3 HTMOS, it is found that the HTMOS array with R = 3 produces the highest light intensity. Experimental results validate the simulations, showing that the most significant SNR enhancement of 4.78 times compared to those without HTMOS phase mask and 1.54 times compared to the optimal m = 3 HTMOS structure. The array structure surpasses the non-array configuration in terms of light intensity enhancement and SNR improvement, making it well-suited for lattice light sheet illumination. All of the findings reveal the potential applications in optical imaging and micro-optical devices.

Funding

Natural Science Foundation of Tianjin Municipality (18JCZDJC38200); Fundamental Research Funds for the Central Universities (63201178).

Acknowledgments

The research was funded by Natural Science Foundation of Tianjin City (No. 18JCZDJC38200) and the Fundamental Research Funds for the Central Universities, Nankai University (No. 63201178).

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.

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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 (8)

Fig. 1.
Fig. 1. (a) The basic structure of optical glass triangular prisms. (b), (c) Schematic diagram of equal heights 3D structure and HTMOS. (d), (e) Schematic diagram of equal heights structure and HTMOS focusing ability, respectively.
Fig. 2.
Fig. 2. (a), (b) R$\times$R HTMOS array diagram and phase diagram. (c) Set-up of the experiment system. The blue dashed rectangle represents light sheet microscopy of the light field detection system, the red dashed rectangle represents light sheet microscopy of the polystyrene fluorescent microspheres and 293T cells detection system.
Fig. 3.
Fig. 3. (a)–(e) The electric field intensity distribution of the beam in xz plane with m = 1, 2, 3, 4, 5, respectively. (f)-(j) Focus intensity along x-axis in xy plane with m = 1, 2, 3, 4, 5, respectively. (k) Comparison of five HTMOS peak intensities. (l) The comparisons of light intensity distribution curves for five structures at y = 0 along x-axis in xy plane. (m) The comparisons of light intensity distribution curves for five structures at x = 0 in xz plane.
Fig. 4.
Fig. 4. (a)–(f) The imaging comparisons of same polystyrene fluorescent microsphere (a) without HTMOS and (b)–(f) with HTMOS structure in xz plane. (g) The comparison of intensity profile curves along z-axis. (h) Histograms of SNR results for five HTMOS.
Fig. 5.
Fig. 5. (a)–(e) The electric field intensity distribution of the beam in xz plane with R = 1, 2, 3, 4, 5, respectively. (f)–(j) The intensity curve at the focal plane position.
Fig. 6.
Fig. 6. The (a)-(j) simulation and (k)-(t) experimental results of field intensity distribution in xy plane. (a)-(e), (k)-(o) are on the focal plane and (f)-(j), (p)-(t) are on the pre-focal plane.
Fig. 7.
Fig. 7. The imaging comparisons of same polystyrene fluorescent microsphere (a) without HTMOS array and (b)–(f) with HTMOS array (R = 1, 2, 3, 4, 5) in xz plane; (g) The curve of polystyrene fluorescent microspheres along z-axis illuminated without and with HTMOS array. (h) The comparison chart of the imaging, noise and SNR.
Fig. 8.
Fig. 8. The imaging comparison in 293T cells. (a) Image results under inverted commercial microscope (20$\times$ objective); Experimental results in light sheet microscopy detection system (b) without HTMOS phase mask and (c) with HTMOS phase mask. (d) The profile comparison along the yellow line marked in the (b) and (c) with an illumination of the Gaussian and HTMOS.

Equations (8)

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h m = λ n 1 1 ( λ Λ ) 2 λ n 1 1
h m = Λ tan α m
Z max = Λ tan β m
γ m = arcsin ( n 1 sin α m )
β m = α m γ m + π 2
S N R = S max N a v g
σ = 0.61 λ N A
R a x i a l = 2 ω 0 = λ π θ = 2 n λ π N A
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