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Abstract
The working distance of the high numerical aperture visible video microscope is extremely short, which greatly limits its application scenarios. To solve this problem, this paper proposes an unobstructed design method of double-sided telecentric microscope with high numerical aperture and long working distance. First, aiming at the obstruction problem of the image-side telecentric catadioptric microscope objective, the structure of the catadioptric optical system is improved. Then, the aspheric design method based on the best aberration compensation is analyzed theoretically to better correct the primary aberration of the high-numerical aperture microscope objective. Finally, a double-sided telecentric microscope optical system with a numerical aperture (NA) of 0.8 and a working distance of 10.0 mm was designed, which is composed of a spherical reflector, a beam splitter plate, a collimating lens group, and an image-side telecentric eyepiece optical system. The design results show that the imaging resolution of this high numerical aperture video microscope is as high as 0.42 µm, and the microscope has a magnification of about 220× for the image with 1080P (1920 × 1080 pixels) resolution. This double-sided telecentric microscope has the advantages of a large field of view, compact structure, good stray light suppression ability, and manufacturability, and has high practical value in the field of high-precision measurement and detection.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The objective and eyepiece of the video microscope magnify the observed object twice and then image it on a photodetector so that one can obtain information about the internal structure of the object more clearly [1,2]. This video microscopy imaging technology can replace the observer's eyes and realize the transformation from human vision to machine vision, qualitative detection to quantitative detection. It also could realize real-time dynamic recording. This technology can greatly improve efficiency, and overcome the uncertainty of human detection, which is suitable for long-time microscopic observation and is not easily fatigued [3–5]. With the continuous development of science and technology and the advent of the information age, high-resolution large field-of-view video microscopy has become a research hotspot, and it plays a pivotal role in scientific fields such as biology, medicine, astronomy, and materials science [6–8].
As the working distance of the high-numerical aperture microscope increases, the aperture of the objective optical system will increase dramatically, which greatly increases the difficulty of aberration correction [9,10]. In 2015, Xue et al. [11] optimized an apochromatic objective with numerical aperture (NA) of 0.75 by reasonably distributing the optical power and selecting the material, which was designed with a transmission structure. Its magnification is 20×, and the thickness of the cover glass is 0.17 mm, while the working distance is only 0.6 mm. In 2018, Yu et al. [12] studied a broad-spectrum, high numerical aperture flat-field apochromatic objective for cancer mutation detection, which has a spectral band of 450 nm∼800 nm and a NA of 0.95, but its working distance is only 0.21 mm. Shanghai optical instrument factory developed 10XB-PC metallographic microscope [13], there are three product models with NA of 0.4, 0.55, and 0.9, and their corresponding working distances are 10.6 mm, 5.1 mm, and 4 mm, respectively.
In the design of optical systems for lithographic lenses, Matsuyama et al. [14] pointed out that the optical system usually needs to use aspheric surfaces if the NA exceeds 0.75; the system has to use the image-side immersion technique if the NA exceeds 0.95; and if the NA exceeds 1.1, the system has to incorporate a reflector to form a fold-and-reverse structure, otherwise, the aperture of the system will increase dramatically. Currently, there are two main structural forms of high-NA projection lithography lenses [15]: the coaxial two-reflector optical system and the off-axis three-reflector optical system. The Ref. [14] provides two optical systems for ultra-high numerical aperture lithography lenses, one is a coaxial two-reflector lithography lens with a NA of 1.35, which uses a total of 19 aspherical surfaces in its optical system and has an image-side working distance of 3.1 mm. the other is an off-axis triple-reflector lithography lens with a NA of 1.30, which uses two planar mirrors and one concave mirror in its optical system and has an image-side working distance of 3.1 mm.
In summary, it can be seen that the working distance of the high-numerical aperture microscope is too short, which greatly limits its application scenarios. To solve this problem, this paper proposes an unobstructed design method of double-sided telecentric microscope with high numerical aperture and long working distance. We adopted the catadioptric secondary imaging optical structure based on the optical splitter plate to eliminate the obstruction, and combined with the method of correcting the primary aberration of the aspheric surface at the best position, and then designed an object-side telecentric microscope objective with a working distance of 10 mm, and a NA of 0.8. After that, we designed the matching image-side telecentric eyepiece optical system. Finally, we combined these two optical systems into a whole, and obtained a long working distance double-sided telecentric video microscope optical system, which possesses a magnification of 21.6×, a resolution of 0.42 µm, and a total length of 290 mm.
2. Design principle of unobstructed microscopic objective
2.1 Design principle of the catadioptric microscope objective
The video microscopes have various structural design types [16–18], which can be divided into transmission objectives and folding objectives according to the structure type of the objective. The folding objective can be divided into coaxial two-reflection objective and off-axis multi-reflection objective. Compared with the transmission objective, the working distance of the folding objective optical system is easier to increase. Since the optical system of reflexive objective is usually a secondary imaging structure, the larger aberration produced by the increase of the working distance of the optical system can be compensated by the secondary imaging group. Compared with the coaxial reflective objective lens, the off-axis reflective objective lens is more difficult to install. Therefore, this paper adopts the coaxial two-reflector structure for the design of the long working distance microscope objective.
The imaging principle of the long working distance refractive microscope objective is shown in Fig. 1. The light emitted from the object point A on the optical axis is reflected by a spherical mirror at point B, then reflected by a plane mirror at point C and imaged at point A′, finally collimated by the lens group 1, and the outgoing light is a parallel beam. From Fig. 1, it can be seen that the objective aperture angle of the microscope is $\theta $, and the incident height on the plane mirror is:
where $- {l_1}$ is the distance between the object point A and the plane mirror in the direction of the optical axis, which can be used to represent the working distance of the microscope.
From Eq. (1), it can be seen that the larger the working distance of the folding microscope, the smaller the effective reflective area of the plane mirror, that is, the larger the blocking. In addition, to reduce the radius of the center opening of the spherical reflector, so that the object point A can just image at the intersection of the spherical mirror and the optical axis. At this point, we can obtain Eq. (2) according to the object-image relationship of the spherical mirror.
where $\textrm{ - }{l_2}$ is the distance between the image point A′ in the direction along the optical axis and the plane mirror.And the vertical axis magnification of the microscope objective on the primary imaging plane is:
The image-side aperture angle θ′ on the primary imaging plane of the microscope objective is:
The role of lens group 1 is to collimate the primary imaging beam, the focal length of lens group 1 is f1, then the focal length of the microscope objective is:
To achieve mutual matching of the pupil of the objective and the eyepiece, the pupil diameter of the microscopic objective should be equal in size to the pupil diameter of the image-side telecentric eyepiece, whose pupil diameter is D1.
At this point, when the focal length of the image-side telecentric microscope eyepiece is f2, the imaging magnification of the whole video microscope can be calculated according to Eq. (7).
Through the above analysis, it can be seen that when the vertical axis magnification, NA and working distance of the microscope optical system are determined, the structural parameters of the whole system can be completely determined by l2 and f1.
2.2 Unobstructed design and aberration correction
As can be seen from Fig. 1, only when the radius of the center aperture of the plane mirror is greater than Δh, the imaging light from object point A will not be blocked. However, when the imaging light is reflected by the spherical mirror to the plane mirror, there will be light leakage in the center of the plane mirror, thus reducing the object-side NA of the microscope objective and reducing the resolution of the microscope objective. According to Eq. (1), the longer the working distance of the microscope objective, the larger the radius of the center aperture of the mirror, which is extremely detrimental to the resolution of the microscope. In addition, the plane mirror needs to have a certain mechanical thickness to meet the requirements of the structural installation, which will further reduce the working distance of the microscope objective.
In response to the above problems, we have improved the design method of the refractive microscope objective, the imaging principle is shown in Fig. 2. The surface 1 of the spectroscopic plate is coated with semi-transmissive and semi-reflective film so that the imaging light can both enter the optical system normally and be reflected, and the surface 2 of the spectroscopic plate is highly transmissive to the imaging light. The final light intensity into the imaging surface of the optical system is reduced to 25% of the original, but increasing the lighting intensity can solve the problem of brightness. Here, the use of the spectroscopic plate can avoid the generation of blocking, but also can effectively ensure that the microscope objective has sufficient working distance (the mechanical structure of the spectroscopic plate does not occupy the working distance of the microscope objective). This is an advantage that other refractive or reflective structures do not have [19–21]. As can be seen from Fig. 2, the entire microscope objective only has an aperture at the center of the spherical mirror, and its aperture radius is very small because the image height at the primary image plane is very small.
The incidence height of the first near-axis ray on the optical surface of a high-numerical aperture microscope is very large so the spectroscopic plate and the spherical mirror in Fig. 2 produce a large spherical aberration. The primary spherical aberration produced by the optical surface can be expressed as [22]:
where h is the incident height of the first near-axis ray on the optical surface, n is the refractive index of the optical material, i and i′ denote the incidence angle and exit angle of the ray, respectively, and u is the aperture angle of the first near-axis ray.From Eq. (8), it can be seen that the larger the working distance of the microscope objective, the greater the incident height of the first near-axis light on the spectroscopic plate, which results in greater spherical aberration of the spectroscopic plate. Therefore, for a high-numerical aperture microscope objective, how to effectively compensate the spherical aberration of the optical system becomes extremely important.
Even aspherical lenses have more design freedom and offer unique advantages in the aberration correction of optical systems [23]. Even aspheric surfaces are easy to process, employ mature technology, and are widely used. Therefore, in this paper, even aspheric surfaces are used to correct the spherical aberration of the high-numerical aperture microscope objective. The equation for an even aspheric surface is Eq. (9):
When the aspheric surface coincides with the aperture stop of the optical system, the additional primary aberration produced by the aspheric surface compared to the spherical surface can be calculated in Eqs. (10). According to Eqs. (10), it can be seen that the aspheric surface can only produce additional spherical aberration, so we can only correct the spherical aberration.
When the aspheric surface does not coincide with the aperture stop of the optical system, the additional primary aberration produced by the aspheric surface is Eq. (11) [24]. According to Eqs. (10) and (11), it is clear that the aspheric surface has no corrective effect on the primary field curvature of the optical system, regardless of where the aspheric lens is located.
In general, the axis-aberration contribution of the aspherical lens is most if it is put near the aperture stop, so it can be used to correct the aperture-related aberration; when the aspherical lens is placed far from the aperture stop position, it can be used to correct the field-of-view-related aberration. However, the spherical aberration of the high-numerical aperture microscope objective is mainly caused by the large aperture, and considering the correction of primary coma, primary dispersion, and primary distortion, this paper proposes to place the even-order aspherical lens near the aperture stop.
3. Optical system design of double-sided telecentric microscope
3.1 Design index
To increase the imaging field of the high-resolution microscope, a full-frame detector with a large imaging area (the diagonal length is 43.28 mm) was selected in this paper. The object-side resolution of the microscope optical system can be calculated according to Eq. (12). When the NA is 0.8 and the central wavelength is 0.55 µm, the microscope resolution is 0.42 µm.
where λ is the operating central wavelength of the microscope optical system.The suitable detector pixel size p can be obtained according to Eq. (13). When the microscope magnification is 21.6× and the resolution is 0.42 µm, the detector pixel size should be 9.1µm × 9.1 µm (0.42 × 21.6 = 9.072 µm). Therefore, in order to make full use of the limiting resolution of the microscope, the pixel size of the detector selected in this paper is 5µm × 5 µm. The magnification of a microscope consists of both optical magnification and digital magnification. The optical magnification of the microscope optical system is 21.6×, the digital magnification is approximately 11× (Convert full-frame digital image to 1080P image), therefore the total magnification of the microscope is about 220×. The design specifications of the double-sided telecentric microscope are shown in Table 1.
Table 1. Design index of the double-sided telecentric microscope
3.2 Objective lens design
The objective lens of a microscope usually adopts the idea of reverse design, so the high numerical aperture micro-objective lens needs to be testing by a backward tracing of light. But it will exist the ray tracing overflow question due to the aberrations. To solve this problem, this paper adopts the idea of forward design. In forward design, an ideal eyepiece is added behind the microscope objective to make the replacement.
Firstly, a spectroscopic plate and a spherical mirror are used to design the primary lens group of the microscopic objective. Due to the few design variables, its hard to optimize the working distance and the aberration correction simultaneously. We view the working distance as the more important issue.
The final designed primary lens group is shown in Fig. 3. The working distance of this optical system is 10.0 mm, the thickness of the spectrophotometer plate is 13.0 mm, the curvature radius of the mirror is -45.5 mm, and the numerical aperture NA of the object-side is 0.8.
In the primary lens group of the microscopic objective, the primary aberrations generated by each optical surface are shown in Fig. 4. The left surfaces of the spectrophotometer plate are the first and fifth optical surfaces, the right surfaces are the second, fourth, and sixth optical surfaces, and the spherical mirror is the third optical surface. As can be seen from Fig. 4, the first, second, third, and fourth optical surfaces produce very large spherical aberrations, while other primary aberrations are very small. Therefore, it can be seen that there is a large residual spherical aberration in the primary imaging group of the microscopic objective, which needs to be compensated by lens group 1.
The ideal eyepiece was put behind the objective lens, and lens group 1 of the microscopic objective lens was designed with the idea of forward design. Using the aberration correction method proposed in Section 2.2, an aspherical surface is designed near the objective aperture stop to correct the spherical aberration generated by the large-diameter optical system. The layout of the designed microscope objective optical system is shown in Fig. 5. The focal length of the objective optical system is -21.9 mm, and the microscopic objective optical system is an object-side telecentric structure with a total length of 200 mm and a maximum diameter of 115 mm. To reduce the number of aspheric surfaces used and the cost of the system, the optimal aspheric surface was found through the optimization of optical design software. Finally, it was determined that the right surface of the lens nearest to the left of the aperture stop was designed as an even aspheric surface. Finally, only a sixth-order even aspheric surface was used in the whole system.
The microscopic objective collimates the imaging points on the object surface into a beam of parallel light. The better the wavefront of the parallel beam, the better the imaging quality of the microscopic objective. Figure 6(a)-(d) shows the wavefront view of the microscopic objective. As can be seen from Fig. 6, the wavefront PV value of the imaging point in the normalized field of view 0.71 is less than 0.16 waves, and the wavefront PV value of the full field of view is less than 0.40 waves. The residual aberration of the microscope objective is small and the imaging quality of the optical system is good.
The MTF curve of the microscopical objective is shown in Fig. 7. As can be seen from Fig. 7 that the MTF of the microscope objective at the Nyquist frequency of 1200 lp/mm is close to the diffraction limit.
3.3 Eyepiece and overall synthetic design
The eyepiece optical system must be matched with the objective optical system for combination, so the location and size of the exit pupil of the eyepiece optical system must be the same as that of the objective optical system [25–27]. The ideal eyepiece optical system is replaced by an objective optical system that can be processed in practice. The eyepiece optical system is designed according to the entry pupil aperture, entry pupil position, focal length and image height of the eyepiece optical system. The layout of the designed eyepiece optical system is shown in Fig. 8. The focal length of the eyepiece optical system is 475 mm, the diameter of the entry pupil is 40 mm, the distance between the entry pupil and the first lens is 35 mm, and the total length of the system is 340 mm. The eyepiece optical system is an image-side telecentric structure, and five lenses are used.
After the combination of the designed microscopic objective lens and eyepiece, the double-sided telecentric video microscope was finally obtained, as shown in Fig. 9. To reduce the total length of the optical system, two planar mirrors were used to fold the optical path, and the size of the folded optical system was 290mm × 165mm × 115 mm.
3.4 Microscopic image quality evaluation
The image quality should be evaluated by the MTF, as shown in Fig. 10. From this figure, we can see that the modulation transfer functions of the center field of view and the edge field of view of the optical system at the Nyquist frequency of 50lp/mm are greater than 0.45 and 0.3, respectively, indicating excellent imaging quality of the optical system.
The spot diagram of the optical system of the high numerical aperture video microscope is shown in Fig. 11. The black circle represents the diffraction limit of the imaging spot diagram of the optical system, and the spot diagrams of all of the FOVs are close to the diffraction limit.
The distortion curve of the optical system of the high-numerical aperture microscope is shown in Fig. 12. The maximum distortion of the optical system is less than 0.12%.
3.5 Tolerance analysis
The requirement in aberration control of a high numerical microscope optical system is usually strict, and very small machining and assembling errors may cause a great deterioration in image quality. Therefore, we need to reasonably select multiple compensators to improve the imaging performance of the microscope and reduce the tolerance sensitivity of the optical system [10,22]. Here, we choose the longitudinal movement of the object plane, the image plane, and the triplet which is behind the primary image plane to compensate for the aberration. The tolerance distribution of the microscope optical system is shown in Table 2, and the current machining and assembly technology is fully capable of meeting the requirements in Table 2.
Table 2. Tolerance distribution
After Monte Carlo analysis, the average MTF distribution law of the double-sided telecentric microscope optical system is shown in Fig. 13. According to Fig. 13, in the Monte Carlo simulation, 50% of the systems have an average MTF greater than 0.19 at 50 lp/mm.
4. Stray light analysis
The stray light in the optical system is mainly caused by the surface of optical elements to the light after many times in reflection and refraction in the image plane to form a higher brightness spot—the ghost image. In the double-sided telecentric microscope optical system designed in this paper, the existence of optical plate leads 50% of the light to form the stray light, which is more likely to form a ghost image on the image plane after reflection and transmission of the optical element surface, so we must analyze the influence of the stray light in the microscope optical system.
In the analysis of stray light of the double-sided telecentric microscope optical system, the front surface of the optical plate is set as semi-inverse and semi-transparent, the transmittance of the rear surface is set as 98%, and the transmittance of other optical elements’ light passing surfaces is set as 98%. The reflectivity of the object plane is set as R = 0. A point light source was set on the object plane of the microscope optical system. The light emitted from the point light source filled the entire entrance pupil of the optical system, and the Total flux was set to 1 Watt. Finally, the stray light analysis software TracePro was used for ray tracing. Figure 14 is the illuminance distribution on the image plane after ray tracing. It can be seen that the stray light illuminance generated by object points contained in the field of view on the image plane is far less than the illumination of the imaging points, and the stray light illuminance generated by object points outside the field of view on the image plane is very small, and there is no spot with abnormal brightness appears.
In the optical system, the point source transmittance (PST: the ratio of the irradiance generated by the external field source on the image surface to the irradiance at the entrance pupil) is mainly used as the evaluation index to evaluate the suppression ability of the stray light [28]. To better obtain the stray light suppression ability of the microscope optical system, we conduct stray light tracing on the object points inside and outside the field of view on the object plane, and we obtain the PST curve is shown in Fig. 15 (Only points with a height of 0-35 mm are shown in Fig. 15). The two PST curves in Fig. 15 represent the ability to suppress stray light in the microscope when the reflectivity of the object plane is R = 0 and R = 4%, respectively. From this figure, we can find that the PST value outside the field of view of the microscope is reduced to below 3.5 × 10−3, and there is no mutation value, which means that the reflected light from the object plane and the optical elements in the optical system won’t produce the ghost image, and the stray light suppression ability of the microscope is well enough in meeting the requirements of engineering application.
5. Conclusion
The working distance of traditional high-resolution and large field-of-view video microscopes is difficult to increase, which greatly limits the application scenarios of video microscopes. To solve this problem, a design method of double-sided telecentric microscope with high numerical aperture and long working distance is proposed. We adopted a catadioptric secondary imaging structure to compress the aperture of the optical system and proposed an aspheric design method based on the best aberration compensation to better correct the primary aberration of the high-numerical aperture microscope objective. To eliminate the obstruction of the catadioptric optical system, the catadioptric structure was improved. Then, a double-sided telecentric video microscope optical system with a working distance of 10.0 mm and a numerical aperture NA of 0.8 is designed. The optical system uses two flat mirrors to fold the optical path. The structure size of the compact design is 290mm × 165mm × 115 mm. The resolution of the visible video microscope optical system is up to 0.42 µm, and the image quality is close to the diffraction limit. The microscope has a magnification of about 220× for the image with 1080P resolution. Finally, we conducted tolerance analysis and stray light analysis, the simulation analysis results showed that the double-sided telecentric microscope system has high manufacturability and good stray light suppression ability. This microscope system has wide application value in the fields of chip, aerospace, materials, chemistry, medicine and other scientific fields.
Funding
Natural Science Foundation of Sichuan Province (2023NSFSC0491, 2023NSFSC1308); Cutting-edge Distribution Program of Institute of Optics and Electronics Chinese Academy Sciences (C21K003); Instrument Development of Chinese Academy of Sciences (YJKYYQ20200060).
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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