3D microscope image acquisition method based on zoom objective

Rong-Ying Yuan; Xiao-Li Ma; Yi Zheng; Zhao Jiang; Xin Wang; Chao Liu; Chao Liu; Qiong-Hua Wang; Qiong-Hua Wang

doi:10.1364/OE.487720

1. Introduction

The microscope is a vital precision instrument and it plays an essential role in medical treatment [1,2], scientific research [3,4], geological archaeology [5], micro-nano manufacturing [6,7], and so on. Compared with most traditional microscopes that can only be used to observe slices, a three-dimensional (3D) microscope that can obtain more information about specimens [8] has broader application potential and has become a research hotspot of microscopes. For example, confocal microscope [9–11], near-field scanning optical microscopes [12,13], and light-sheet microscope [14–17] have the capability to obtain 3D information and perform 3D modeling of the specimen. However, the 3D imaging results of most microscopes are still displayed in two dimensions, which is not conducive to making the obtained 3D information more realistic and intuitive to the observer. Therefore, there is an urgent need for a microscopic method that can be used for 3D displays.

To meet the requirements of the 3D display, the microscope should have the ability to obtain depth information and parallax information of the specimen. According to the characteristics of microscopic imaging, the depth of field of most microscopes is too small to obtain the entire depth information of a specimen. Several methods for extended depth of field (EDOF) of the microscope have been reported, such as wavefront encoding [18,19], phase pupil masking [20], and axial scanning [21,22]. Among these, axial scanning is the simplest and most commonly used method. The means of implementation of axial scanning without mechanical movement include the use of a deformable mirror [23], a liquid crystal lens [24,25], and a liquid lens [26–28]. In particular, liquid lenses can be used to realize fast axial scanning by varying the focal length of the lenses, which is considered one of the most promising methods for EDOF in microscopy. Moreover, liquid lenses can realize the function of correcting aberrations [29,30] and continuous optical zoom [31–33]. Although these microscopes have a large depth of field, they can still only capture a 2D image of the specimen without parallax information, and cannot be used for 3D display.

In terms of parallax information acquisition, the light field microscope [34–40] based on a microlens array can obtain parallax information of the specimen through a single shot and generate the elemental image array for 3D display. In the display, the lens element is used to modulate the light emitted by the corresponding image pixel, and the 3D information of the specimen is recovered. However, the depth information obtained by a light field microscope is not sufficient for a thicker specimen. In conclusion, a microscope system that can acquire 3D information is of great value.

In this paper, we propose a 3D microscope acquisition method based on the zoom objective. The zoom objective based on liquid lenses can achieve the EDOF imaging to acquire clear depth information of the specimen by adjusting the voltage. An arc shooting mount is designed to accurately rotate the objective to acquire the parallax information of the specimen. The parallax synthesis image is generated for 3D display. A 3D display screen is used to display the parallax synthesis image, and the results show that the 3D features of the specimen are restored. The proposed method has promising applications in industrial inspection, microbial observation, medical surgery, and so on.

2. Design of 3D microscope image acquisition

Figure 1 briefly shows the main process of the proposed method for obtaining the 3D image. We adopt the arc shooting method to shoot the specimen from different angles, and the zoom objectives are placed on the same arc centered at the intersection of the optical axes. The shooting field of each zoom objective intersects to form a circular area, and the scene located in this circular area can be photographed by the zoom objective, as shown in Fig. 1(a). In order to pursue high resolution, the depth of field of the objective lens is too small to obtain the complete depth information of the specimen, and the acquired image is blurred. So, the first process is to acquire the depth information of the specimen. The proposed zoom objective has the function of fast axial scanning, which can obtain high-resolution images of the specimen in different depth planes. The EDOF image is obtained by fusing focused images of different depths, which contain all the depth information of the specimen, as shown in Fig. 1(b). Then the process is repeated at each viewpoint to obtain the parallax images with complete depth information. The parallax synthesis image of the specimen can be obtained through the synthesis image generation algorithm [41,42], as shown in Fig. 1(c). Finally, the parallax synthesis image is displayed on a 3D display screen to achieve the 3D imaging of the specimen. And the zoom objective also has the function of continuous optical magnification variation, which can obtain a series of continuously optically magnified 3D images of the specimen, as shown in Fig. 1(d).

Fig. 1. Process of the 3D microscope image acquisition method. (a) Shooting. (b) Depth information acquisition. (c) Parallax information acquisition. (d) 3D display.

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2.1 Design and simulation of the zoom objective

To acquire complete depth information of the specimen, an objective with a large depth of field is required. However, the depth of field is inversely proportional to the resolution. To achieve a large depth of field, the method used in this paper is aimed to extend the depth of field by fusing images of different depths. To obtain a better fusion effect, a high degree of uniformity in magnification, sharpness, and resolution is required for each depth image obtained from the microscope scan.

The zoom objective consists of multiple lenses, as shown in Fig. 2(a). The light emitted from the object is modulated by passing through the refractive surface of each lens. According to the ray tracing of geometrical optics, the focal length f and back working distance l_F of the objective is related to the focal length and position of each lens:

(1)$$\tan {U_k} = \frac{{{h_1}}}{{{f_1}}} + \frac{{{h_2}}}{{{f_2}}} + \ldots + \frac{{{h_k}}}{{{f_k}}} = \sum\limits_1^k {\frac{h}{f}}$$

(2)$$f = \frac{{{h_1}}}{{\tan {U_k}}}$$

(3)$${l_F} = \frac{{{h_k}}}{{\tan {U_k}}}$$

where U is the angle between the light and the optical axis after it passes through the refraction surface of the lens, h is the incident height, and the subscript is the sequence number of the lens.

Fig. 2. (a) Components of the zoom objective and (b) optical structure of the liquid lens.

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According to the similar triangle relation, the imaging magnification β of the zoom objective can be expressed as follows:

(4)$$\beta = {\beta _1}{\beta _2}\ldots {\beta _k} ={-} \frac{{{f_1}{f_2}\ldots {f_k}}}{{{x_1}{x_2}\ldots {x_k}}} ={-} \frac{f}{x}$$

where x is object distance.

To acquire more optimized optical imaging, we analyze the aberrations of the zoom objective. The optical resolution σ of the zoom objective can be expressed as:

(5)$$\sigma \textrm{ = }\frac{{0.61\lambda }}{{NA}}$$

where NA is the numerical aperture of the zoom objective, and λ is the wavelength of incident light. Eq. (5) is the highest resolution that can be achieved, and due to the existence of aberration, the resolution of the image is lower than that indicated by Eq. (5). The existence of aberrations in microscopic systems can be described by wave aberration theory, as shown in Eq. (6):

(6)$$\begin{array}{c} W(x,y,{x_0}) = {a_1}({x^2} + {y^2}) + {a_2}x{x_0} + {b_1}{({x^2} + {y^2})^2} + {b_2}x{x_0}({x^2} + {y^2})\\ + {b_3}{x^2}{x_0}^2 + {b_4}{x_0}^2({x^2} + {y^2}) + {b_5}x{x_0}^3 + \cdots \end{array}$$

where (x, y) is the coordinates related to aperture, ${x_0}$ is the object height, ${a_1}({x^2} + {y^2})$ is the axial defocusing term, ${a_2}x{x_0}$ is the vertical defocusing term, ${b_1}$, ${b_2}$, ${b_3}$, ${b_4}$ and ${b_5}$ are the five primary aberrations. Because the zoom objective is a small-field optical system, aberrations related to the aperture are mainly considered: spherical aberration $\delta {L^{\prime}_\textrm{k}}$ and sinusoidal aberration $S{C_\textrm{k}}^\prime$, which can be expressed as:

(7)$$\delta {L_\textrm{k}}^\prime ={-} \frac{1}{{2{n_k}{u_k}{{^\prime }^2}}}\sum\limits_1^k {{S_\textrm{{I} }}}$$

(8)$$S{C_\textrm{k}}^\prime ={-} \frac{1}{{2J}}\sum\limits_1^k {{S_\textrm{{II} }}}$$

where u’ is the angle between the paraxial light and the optical axis after it passes through the refraction surface of the lens, and J is the Laplace invariant. $\sum\limits_1^k {{S_\textrm{{I} }}}$ is the primary spherical aberration coefficient, and $\sum\limits_1^k {{S_\textrm{{II} }}}$ is the primary aberration coefficient, and they are determined by the curved surface radius, position, and incident height of the lens. n is the refractive indices of the medium before and after the refraction surface of the lens.

The traditional zoom optical systems and axial scanning microscopes change the object distance and magnification by varying the distance between the solid lenses. In this work, we achieve an adaptive zoom without any mechanical movement using liquid lenses driven by electrowetting. The liquid lens consists of two liquids, as shown in Fig. 2(b). The contact angle of the liquid-liquid surface can be varied by applying a voltage. According to the Young-Lippmann equation [43], the relationship between contact angle θ and applied voltage V can be expressed as follows

(9)$$\cos \theta = \cos {\theta _0} + \frac{{\varepsilon {V^2}}}{{2\gamma d}}$$

where θ₀ and γ are the initial contact angle and interfacial tension of the liquid-liquid interface, and ε and d are the dielectric constant and thickness of the dielectric layer, respectively. The liquid lens can be regarded as a glued lens, and the focal length f_ll can be expressed as:

(10)$${f_{ll}} = \frac{R}{{{n_1} - {n_2}}}$$

where n₁ and n₂ are the refractive indices of the two liquids, respectively, and R is the curvature radius of the liquid-liquid interface. According to the geometric relationship, the aperture radius a and R of the liquid lens meet Eq. (11):

(11)$$\cos \theta = \frac{a}{R}$$

Thus, the focal length of the liquid lens can be changed by varying the driving voltage V:

(12)$${f_{ll}} = \frac{a}{{({n_2} - {n_1})(\cos {\theta _0} + \frac{{\varepsilon {V^2}}}{{2\gamma d}})}}$$

Combined with the above analysis, the zoom objective based on liquid lenses can not only realize the change of focal length and magnification of the microscope, but also eliminate the aberration of the zoom objective through multi-curvature optimized design, and these changes can be controlled by the driving voltage of the liquid lens. The relationship between them can be simplified as:

(13)$$f = {f_1}({R_1},{R_2}\ldots \ldots {R_k}) = {g_1}({V_1},{V_2}\ldots \ldots {V_k})$$

(14)$$\beta = {f_2}({R_1},{R_2}\ldots \ldots {R_k}) = {g_2}({V_1},{V_2}\ldots \ldots {V_k})$$

(15)$$RMS = {f_3}({R_1},{R_2}\ldots \ldots {R_k}) = {g_3}({V_1},{V_2}\ldots \ldots {V_k})$$

where RMS is the root mean square. Focal length, magnification, and RMS are functions of the voltage of the liquid lens. RMS is generally used to evaluate image quality.

Based on the above analysis, we design a prototype liquid lens-based zoom objective. The schematic diagram of this objective lens is shown in Fig. 3(a). The zoom objective consists of a front group, a zoom group, and a back group. The front group is a double-glued lens. The zoom group consists of four liquid lenses, and the back group consists of three glass lenses. The liquid lens is from Corning Inc. model Arctic-58N0, with an effective aperture of 5.8 mm. The focal length of the liquid lens varies with the voltage, which results in changes in the working distance and magnification of the zoom objective, as shown in Figs. 3(a)–3(d). The four liquid lenses provide four variables that increase the freedom to tune the objective and allow for dynamic correction of spherical aberration during magnification variations and axial scanning, which ensure that the objective always performs at high resolution.

Fig. 3. Structure of the zoom objective. (a)-(b) Changing the working distance. (c)-(d) Changing the magnification.

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We used the commercial software OpticStudio to simulate and optimize the zoom objective at different magnifications and different working distances. We added specific operands to ensure consistent resolution at different working distances and the same magnification. The simulation results of the modulation transfer function (MTF) at magnifications from 5× to 10× are shown in Fig. 4. The wavelengths are 486 nm, 587 nm, and 656 nm. The working distance is from 4 mm to 6 mm. The simulation results show that none of the spatial frequencies are below 300lp/mm (MTF > 0.3) during the working distance variation of the objective. It indicates that the scanning depth of the zoom objective at different magnifications is no less than 2 mm while maintaining high image resolution.

Fig. 4. MTF of the zoom objective. (a) Magnification 5×, working distance 4 mm. (b) Magnification 5×, working distance 6 mm. (c) Magnification 10×, working distance 4 mm. (d) Magnification 10×, working distance 6 mm.

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We change the radius of curvature of each liquid lens (r₁, r₂, r₃, r₄) to obtain the magnification and working distance of the zoom objective. Each lens can be voltage controlled individually. We obtain the voltage applied to each liquid lens at different magnifications and different depths based on the solution optimized for the curvature of the liquid lens in OpticStudio. Then the resolution target is used to calibrate the voltages with a consistent resolution as a reference. Figure 5 shows the voltages corresponding to each liquid lens for the objective scan of 2 mm depth at 5× and 10×, respectively.

Fig. 5. Voltages applied to each liquid lens at different magnifications. (a) Magnification 5×. (b) Magnification 10×.

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2.2 Design of parallax information acquisition

For the obtained parallax images to contain all the information needed for parallax synthesis image in the 3D display, it is necessary to determine the number of zoom objectives, shooting angles, and the distance between the objectives. To describe the position of the objective and the specimen, a coordinate system X_OY_OZ_O of the shooting space is established with the position of the central viewpoint as the origin. The coordinate system X_SY_SZ_S of the display space is established at the center of the display screen, as shown in Fig. 6. The zoom objectives are placed on the same arc centered at the intersection of the optical axes. All zoom objectives are evenly arranged to take the specimen from different directions to record the parallax information of the specimen, and then the parallax synthesis image is obtained, as shown in Fig. 6(a). The liquid crystal display screen is placed on the back focal plane of the lenticular lens array. The obtained parallax synthesis image is displayed. According to the optical path reversibility principle, the lenticular lens array gathers and restores the light emitted by all the pixels of the parallax synthesis image to reconstruct the 3D image of the specimen [44]. The 3D display reproduction process is shown in Fig. 6(b).

Fig. 6. Relationship between parallax image shooting space and 3D display space. (a) Parallax image shooting space. (b) 3D display space.

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The left and right neighboring viewpoints of the central axis are set as Objective-L1 and Objective-R1, and the spacing is b. According to the principle of binocular parallax [45], the coordinates of the image point A’ on Objective-L1 and Objective-R1 are satisfied by Eqs. (16)–(17), when the specimen is displayed after any point A(x_O, y_O, z_O) has been shouted.

(16)$${x_{\textrm{Sr}}} = \frac{{Mf[({x_\textrm{O}} - \frac{b}{2})\cos \alpha + {z_\textrm{O}}\sin \alpha ]}}{{{z_\textrm{O}}\cos \alpha - ({x_\textrm{O}} - \frac{b}{2})\sin \alpha }}$$

(17)$${x_{\textrm{Sl}}} = \frac{{Mf[({x_\textrm{O}} + \frac{b}{2})\cos \alpha - {z_\textrm{O}}\sin \alpha ]}}{{{z_\textrm{O}}\cos \alpha + ({x_\textrm{O}} + \frac{b}{2})\sin \alpha }}$$

where M is the magnification of the CCD imaging surface to the display screen surface, f is the focal length of the objective, x_Sr and x_Sl are the abscissae of the A’, and 2α is the convergence angle of adjacent viewpoints.

Figure 6(b) shows a schematic diagram of a 3D display based on the lenticular lens array, where any image pixel in the parallax synthesis image should contain all the parallax information for that specimen point. The 3D viewpoint m should be calculated as follows:

(18)$$m = \textrm{ceil}(\frac{p}{w})$$

where p is the effective pitch of each lenticular lens, w is the width of each sub-pixel, and the function ceil() means to take the integer up. The number of zoom objectives is equal to the number of viewpoints. The liquid crystal display screen is located at the focal plane of the lenticular lens array. The image pixel and the lenticular lens array have the same pitch and correspond to one-to-one. According to the geometric principle, they satisfy the equation:

(19)$$\frac{p}{{{f_{\textrm{LLA}}}}} = \frac{Q}{D}$$

where D is the viewing distance, f_LLA is the focal length of the lenticular lens array, and Q is the width of a complete viewing area at the viewing distance.

3. Experiment results

The experiment setup of the proposed 3D microscopic image acquisition method is shown in Fig. 7(a). The main components consist of a computer, a CCD camera, a zoom objective, an arc shooting mount, and a 3D display screen. The computer regulates voltage signals to control the focal length of the liquid lens and performs image processing and transmission. A CCD camera (resolution 3840 × 2160) is used to capture and transmit images. Figure 7(b) shows the fabricated zoom objective. To obtain parallax images, we designed an arc shooting mount and developed the control software to precisely deflect the zoom objective lens to match the 3D display parameters, as shown in Fig. 7(c). The deflection accuracy of the device is 0.005°. The 3D display screen consists of a liquid crystal display screen (resolution 3840 × 2160, sub-pixel ∼53 µm) and a lenticular lens array with a pitch of 423 µm, so the number of viewpoints of the 3D display is 8.

Fig. 7. (a) Experiment setup of the proposed 3D microscope image acquisition method, (b) zoom objective, and (c) arc shooting mount.

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3.1 Experiments of the zoom objective

The magnification of the zoom objective is measured to be continuously variable from 5× to 10×. The working distance of each magnification can be adjusted between 4 mm and 6 mm. The resolution of the zoom objective is measured using the resolution test chart (GCG-020602). Figure 8 shows the resolution target images captured and modulation curves of normalized intensity at different magnifications and different depths, respectively. At the magnification of 5×, element #6 of the resolution target Group-7 can be captured clearly, indicating that the resolution can reach 228.1lp/mm. At magnifications of 10×, element #2 of the resolution target Group-8 can be captured clearly, indicating that the resolution is 287.4lp/mm. The experimental results demonstrate that the fabricated objective can maintain good resolution during operation.

Fig. 8. Captured images of the resolution target and modulation curves of normalized intensity. WD: working distance.

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We select an untreated ant as a specimen. Since the specimen is opaque, we use dark field microscopy to shoot in this experiment. The Abbe condenser in Figure 7(a) is replaced with a dark field Abbe condenser. By inputting a preset voltage and adjusting the working distance of the objective, the local part of the ant is scanned axially from bottom to top to obtain the focused images at different depths. Figure 9(a) shows six focused images at different depths obtained when the magnification is 5×. These images are fused by the Laplace pyramid image fusion algorithm to obtain images with EDOF, and the fusion results are shown in Fig. 9(b). The thickness of the specimen is measured to be 1.2 mm. Depth information is converted to the pseudo-color image, as shown in Fig. 9(c).

Fig. 9. (a) Focused images at different depths, (b) composite EDOF image, and (c) pseudo-color image for depth information. The scale bar in the picture is 100 µm.

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3.2 Experimental verification of 3D image acquisition

To obtain the parallax images of the specimen with depth information, we use arc shooting to obtain depth-focused images at each viewpoint and obtain the EDOF images in that direction. To better demonstrate the capability of this zoom objective lens, we list the results obtained at four different magnifications from 5×, 6.7×, 7.8×, and 10×. When the magnification is 5× and 6.7×, we set the deflection angle to 0.03°. When the magnification is 7.8× and 10×, we set the deflection angle to 0.02°. Figure 10(a) shows the partial parallax images from the different viewpoints and the parallax synthesis images at the magnification of 5× and the magnification of 10×, respectively.

Fig. 10. Parallax images and parallax synthesis images. (a) Magnifications 5×. (b) Magnifications 10×. The scale bars in these pictures are 100 µm.

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Visualization 1 clearly shows the 3D display of the specimen with magnifications of 5×, 6.7×, 7.8× and 10×. Figure 11 shows the display results for magnifications of 5×, 6.7×, 7.8×, and 10× viewed in the left and right viewing areas, respectively. By comparison, we find that the details of the specimen viewed in different viewing areas are different. For example, the distance between the abdomen and the leg joints of the ant is significantly larger from the right viewpoint than from the left viewpoint. It indicates that this method increases not only the depth information of the observed specimen but also the more comprehensive positional information of the observed specimen.

Fig. 11. 3D display of the opaque specimen. The scale bars in these pictures are 100 µm (see Visualization 1).

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To better demonstrate the superiority and application of the proposed method, a specimen consisting of a luffa pollen slice overlapped with a pollen germination slice is used for imaging and display. Visualization 2 shows the viewing results at different magnifications. We can perceive the depth information between the luffa pollen and the pollen germination. Figure 12 shows the viewing results from the left and right viewing areas. From the experimental results, the position relation between the luffa pollen and the pollen germination can be clearly viewed. Moreover, the detail of the specimen becomes sharper as the magnification of the objective increases. It indicates that this method can provide complete depth information, positional information, and detailed information of the specimen compared to the traditional single microscope observation.

Fig. 12. 3D display of the sliced specimen. The scale bars in these pictures are 100 µm (see Visualization 2).

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4. Conclusions

In this paper, we propose a 3D microscope acquisition method based on a zoom objective. Based on the proposed method, 3D microscopic images of thick specimens with continuous optical magnification are achieved. A zoom objective based on the liquid lenses can obtain clear depth information of the specimen. The parallax information of the specimen is acquired by the zoom objective attached to an arc shooting mount. A 3D display screen is used to display the parallax synthesis images. The experimental results show that the obtained parallax synthesis image can accurately and efficiently restore the 3D features of the specimen. In this way, the complete depth information and the comprehensive positional information of the specimen are displayed. The proposed method has promising applications in industrial detection, microbial observation, medical surgery, and so on.

Funding

Beijing Municipal Natural Science Foundation (4222069); National Natural Science Foundation of China (61927809, 62175006); Science, Technology and Innovation Commission of Shenzhen Municipality (JCYJ20220818100413030).

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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3D microscope image acquisition method based on zoom objective

Abstract

1. Introduction

2. Design of 3D microscope image acquisition

2.1 Design and simulation of the zoom objective

2.2 Design of parallax information acquisition

3. Experiment results

3.1 Experiments of the zoom objective

3.2 Experimental verification of 3D image acquisition

4. Conclusions

Funding

Disclosures

Data availability

References

Supplementary Material (2)

Data availability

Cited By

Figures (12)

Equations (19)

Optics Express

Name	Description
Visualization 1	3D display of the opaque specimen
Visualization 2	3D display of the sliced specimen