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Design method of dual-band synchronous zoom microscope optical system based on coaxial Kohler illumination

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Abstract

The intrinsic properties of the observed object are closely related to its spectral information, to extend the imaging spectral range of a continuous zoom microscope to obtain more detailed intrinsic properties of the object, this paper proposes a design method of dual-band simultaneous zoom microscope optical system based on the coaxial Koehler uniform illumination. First, the imaging principle of the dual-band simultaneous zoom microscope optical system is theoretically analyzed, and we propose to split the front fixed group of the zoom system into a collimation lens group and a converging lens group to realize the compact design of the system. Then, two different rear fixed groups are used to correct the residual aberration, and a method for solving the initial structure of the dual-band simultaneous zoom microscope optical system is proposed. Finally, a dual-band synchronous zoom microscope optical system is designed using the method proposed in this paper. The design results show that the imaging magnification of the visible (VIS) band is −0.4 to −4.0, the simultaneous imaging magnification ranges are −0.4 to −0.8 in the VIS and short-wave infrared (SWIR) bands, and the magnification difference of its simultaneous zoom imaging is less than 1.25%. In addition, the system has the advantages of good imaging quality, clever design of coaxial illumination, and compact structure, thus verifying the feasibility of the design method.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Microscope optical systems are mainly categorized into fixed magnification microscope optical systems, multi-position zoom microscope optical systems, and continuous zoom microscope optical systems [14]. Compared with the multi-position zoom microscope optical system, the continuous zoom microscope optical system is continuously adjustable between certain two imaging magnifications, which makes it more widely used [57]. For example, fluorescence microscopes in the visible (VIS) band can only achieve imaging of living cells and thin tissues, while fluorescence microscopes in the short-wave infrared (SWIR) band are capable of achieving greater imaging depth with high imaging time resolution. However, with the in-depth study of spectral informatics, it has been found that the intrinsic feature information of an object is closely related to its imaged spectral information [8,9]. Therefore, to obtain more detailed information about the essential features of an object, multi-band zoom microscope imaging systems have become an inevitable development trend. Multi-band continuous zoom microscope imaging systems have a wide range of applications in many fields such as biomedical research, aerospace manufacturing, and chip manufacturing [1014].

At present, with the continuous improvement of the design theory of the zoom optical system, there are numerous design methods for single-band zoom imaging systems [1517], but the research on dual-band zoom imaging systems has stagnated due to the difficulty of chromatic aberration correction. Dual-band zoom imaging systems can be roughly classified into two types: the first one utilizes focus tunable lenses (FTL) to achieve zoom [1820], and the second one utilizes moving lens elements to achieve zoom [21,22]. For the FTL zoom imaging system, Li et al. [18] designed a double-sided telecentric zoom microscope optical system with an imaging magnification range of −0.8 to −1.6 using four focus tunable lenses and a motion stop, which realized only single-band zoom imaging. Lee et al. [19] used a dozen lenses and two focus tunable lenses to design a single-band medical laparoscopic zoom microscope optical system with no motion elements. The zoom ratio of this optical system is 4×. Li et al. [20] designed a dual-band shared-aperture zoom imaging system using two focus tunable lenses in each band, which only extended the imaging spectrum to the near-infrared band due to the restricted imaging spectral range of the liquid lenses, and the zoom ratio of the dual-band optical system is 4×. Based on the zoom imaging system with motion lens group element compensation, Wu et al. [21] designed a 20× zoom optical system using a positive group compensation structure and combined with the principle of wide-band complex achromatic aberration, and the imaging bands of the system covered the VIS and near-infrared bands; Chang et al. [22] used three motion groups of elements to design a confocal-planar dual-band zoom imaging system, which had a zoom ratio of 10×, and the imaging bands are 480-680 nm and 800-900 nm. Although there have been many relevant studies, none of the above imaging systems has the function of coaxial uniform illumination. From the above analysis, it can be seen that the optical system based on the liquid lens design has the disadvantages of small magnification ratio and restricted imaging spectrum of the liquid lens, while the optical system based on the motion element design has the disadvantages of difficult composition of the coaxial illumination optical path and narrow imaging spectral range.

To address the above problems, this paper proposes a design method for a dual-band synchronous zoom microscope optical system based on coaxial Koehler uniform illumination. We propose to split the front fixed group of the zoom system into a collimation lens group and a converging lens group to realize the compact design of the system and introduce beam-splitting prisms in the two groups to realize the coaxial Koehler uniform illumination by sharing the front fixed group, thus avoiding the influence of the lens group movement on the uniform illumination beam. Then we propose to use two post-fixed groups with the same magnification but different aberration contributions to correct the residual aberration of the dual-band zoom optical system. In the design of the optical system, the imaging quality of the VIS band is ensured first, and then the rear fixed group is replaced to compensate for the imaging quality of the SWIR band. The dual-band synchronous zoom microscope optical system designed using this method has zoom ratios of 10× and 2× in the VIS and SWIR bands, respectively. The difference in imaging magnification of the dual-band synchronous zoom imaging system was less than 1.25% when the imaging magnification range was −0.4 to −0.8.

2. Imaging principle of dual-band synchronous zoom microscope

The imaging principle of the dual-band synchronous zoom microscope optical system based on coaxial Kohler uniform illumination is shown in Fig. 1 [23]. The whole optical system consists of six parts: the front fixed group, the zoom group, the compensation group, the beam splitting prism 2, the rear fixed group 1, and the rear fixed group 2. To realize the Kohler coaxial uniform illumination and ensure that the overall structure of the microscope is compact, we propose to split the front fixed group into one collimating lens group and one converging lens group and add a beam splitting prism 1 in these two groups, the beam splitting prism l is used for uniform illumination. In the process of microscope zoom, the imaging channel and the illumination channel share the collimating lens group and the beam splitting prism 1. The imaging rays of the two wavelength bands are split in the beam splitting prism 2 and then imaged on the focal plane 1 and the focal plane 2 through the rear fixed group 1 and the rear fixed group 2, respectively. The positions of the object plane, the front fixed group, the beam splitting prism 2, the rear fixed group 1, the rear fixed group 2, and the image plane 1 are always kept constant during the continuous zoom imaging process of the dual-band synchronous zoom microscope. The theoretical analysis of the imaging principle of the dual-band synchronous zoom microscope optical system based on coaxial Kohler uniform illumination will be presented below.

 figure: Fig. 1.

Fig. 1. Imaging principle diagram of dual-band synchronous zoom microscope.

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According to Fig. 1, it can be seen that point A on the object plane is imaged at point B after passing through the front fixed group, then imaged at point D after the zoom group and the compensation group, and finally imaged at point F on the focal plane 1 after passing through the beam splitting prism 2 and the rear fixed group 1. During the synchronous continuous zoom process of the dual-band microscope, the magnification of the rear fixed group 1 and rear fixed group 2 should meet the Eq. (1) to ensure the magnification of the two channels is equal.

$${\beta _{41}} = {\beta _{42}} = {\beta _4}$$
The rays from object point A are collimated by the collimating lens group of the front fixed group first, and then imaging at point B through the beam splitting prism 1 and converging lens group. The focal length of the collimating lens group and converging lens group is:
$$\left\{ {\begin{array}{l} {{f_{11}}^{\prime} ={-} {l_1}}\\ {{f_{12}}^{\prime} = l_1^{\prime}} \end{array}} \right.$$
where l1 denotes the working distance of the microscope and ${l_1}^{\prime}$ denotes the image distance of the converging lens group.

To realize imaging without vignetting, the side length of the beam splitting prism 1 needs to satisfy Eq. (3). In addition, the interval t between the collimating lens group and the converging lens group should satisfy t > s.

$$s > - 2{l_1} \times \tan (\theta )$$
In the process of continuous zoom imaging, the distance between the object point B of the zoom group and the image point E of the beam splitting prism 2 will remain constant no matter how the relative positions of the zoom group and the compensation group change, which is represented by Eq. (4).
$$\overline {\textrm{BE}} = ({{l_3}^{\prime} - {l_3}} )- ({{l_2} - {l_2}^{\prime}} )\textrm{ + }\overline {\textrm{DE}} \textrm{ = }{l_3}^{\prime} - {l_3}\textrm{ + }{l_2}^{\prime} - {l_2}\textrm{ + }\overline {\textrm{DE}}$$
where ${l_2}$ and ${l_2}^{\prime}$ denote the object distance and image distance of the zoom group, respectively. ${l_3}$ and ${l_3}^{\prime}$ denote the object distance and image distance of the compensation group, respectively.

The thickness of the beam splitting prism 2 is p and the refractive index is n. When the incidence angle of the incident rays on the beam splitting prism is U, the distance between the object point D and the image point E is:

$$\overline {\textrm{DE}} \textrm{ = }p\left( {1 - \frac{{\cos U}}{{\sqrt {{n^2} - {{\sin }^2}U} }}} \right)$$
To simplify Eq. (5), only the case of imaging in the paraxial region, which means U = 0, is considered here, then Eq. (4) can be reduced to:
$$\overline {\textrm{BE}} = {l_2}^{\prime} + {l_3}^{\prime} - {l_2} - {l_3}\textrm{ + }p\left( {1 - \frac{1}{n}} \right)$$
The relationship between the focal length ${f^{\prime}}$, object distance l, image distance ${l^{\prime}}$, and magnification β of an optical system is:
$$\left\{ {\begin{array}{l} {l = \frac{{1 - \beta }}{\beta }{f^{\prime}}}\\ {{l^{\prime}} = ({1 - \beta } ){f^{\prime}}} \end{array}} \right.$$
Substituting Eq. (7) into Eq. (6), we can obtain:
$$\overline {\textrm{BE}} = 2({{f_2}^{\prime} + {f_3}^{\prime}} )- {f_2}^{\prime}\left( {{\beta_2} + \frac{1}{{{\beta_2}}}} \right) - {f_3}^{\prime}\left( {{\beta_3} + \frac{1}{{{\beta_3}}}} \right) + p\left( {1 - \frac{1}{n}} \right)$$
where β2 and β3 are the magnification of the zoom and compensation groups, respectively.

Since the distance from point B to point E is a constant, the magnification relation for the optical system of a continuous zoom microscope can be obtained as:

$$2({{f_2}^{\prime} + {f_3}^{\prime}} )- {f_2}^{\prime}\left( {{\beta_2} + \frac{1}{{{\beta_2}}}} \right) - {f_3}^{\prime}\left( {{\beta_3} + \frac{1}{{{\beta_3}}}} \right) + p\left( {1 - \frac{1}{n}} \right) = \textrm{Constant}$$
The Eq. (9) can be simplified as the thickness and refractive index of the beam splitting prism are fixed:
$$2({{f_2}^{\prime} + {f_3}^{\prime}} )- {f_2}^{\prime}\left( {{\beta_2} + \frac{1}{{{\beta_2}}}} \right) - {f_3}^{\prime}\left( {{\beta_3} + \frac{1}{{{\beta_3}}}} \right) = \textrm{Constant}$$
According to the Eq. (10), when the continuous zoom microscope is located in the minimum magnification, the zoom group and the compensation group correspond to the magnification of (${\beta _{2s}}$, ${\beta _{3s}}$); when the continuous zoom microscope is located in the maximum magnification, the zoom group and the compensation group correspond to the magnification of (${\beta _{2l}}$, ${\beta _{3l}}$). Based on the above relationship, we can deduce Eq. (11).
$$\;\;\;{f_2}^{\prime}\left( {{\beta_{2s}} + \frac{1}{{{\beta_{2s}}}}} \right) + {f_3}^{\prime}\left( {{\beta_{3s}} + \frac{1}{{{\beta_{3s}}}}} \right) = {f_2}^{\prime}\left( {{\beta_{2l}} + \frac{1}{{{\beta_{2l}}}}} \right) + {f_3}^{\prime}\left( {{\beta_{3l}} + \frac{1}{{{\beta_{3l}}}}} \right)$$
The magnification ratio of a continuous zoom microscope optical system is the ratio of the maximum magnification to the minimum magnification.
$$\Gamma = \frac{{{\beta _l}}}{{{\beta _s}}}\textrm{ = }\frac{{{\beta _1} \times {\beta _{2l}} \times {\beta _{3l}} \times {\beta _4}}}{{{\beta _1} \times {\beta _{2s}} \times {\beta _{2s}} \times {\beta _4}}} = \frac{{{\beta _{2l}} \times {\beta _{3l}}}}{{{\beta _{2s}} \times {\beta _{2s}}}}$$
$$\left\{ {\begin{array}{c} {{\beta_1}\textrm{ = }\frac{{{f_{12}}^{\prime}}}{{{f_{11}}^{\prime}}}}\\ {{\beta_4}\textrm{ = }\frac{{l_4^{\prime}}}{{{l_4}}}} \end{array}} \right.$$
where β1 and β4 are the magnification of the front fixed lens group and the rear fixed lens group, respectively, ${l_4}$ and ${l_4}^{\prime}$ denote the object and image distances of the rear fixed lens group, respectively.

When the magnification of each group of the continuous zoom microscope optical system at the minimum magnification is determined, the interval between groups at the minimum magnification is:

$$\left\{ {\begin{array}{l} {{d_{12s}} = {f_{12}}^{\prime} - {l_{2s}} = {f_{12}}^{\prime} - \frac{{1 - {\beta_{2s}}}}{{{\beta_{2s}}}}{f_2}^{\prime}}\\ {{d_{23s}} ={-} {l_{3s}} + {l_{2s}}^{\prime} ={-} \frac{{1 - {\beta_{3s}}}}{{{\beta_{3s}}}}{f_3}^{\prime} + ({1 - {\beta_{2s}}} ){f_2}^{\prime}}\\ {{d_{34s}} = {l_{3s}}^{\prime} - {l_4} + \overline {\textrm{DE}} = ({1 - {\beta_{3s}}} ){f_3}^{\prime} - \frac{{1 - {\beta_4}}}{{{\beta_4}}}{f_4}^{\prime} + p\left( {1 - \frac{1}{n}} \right)}\\ {{d_{4f}} = {l_4}^{\prime} = ({1 - {\beta_4}} ){f_4}^{\prime}} \end{array}} \right.$$
where ${d_{12s}}$, ${d_{23s}}$, ${d_{34s}}$, and ${d_{4f}}$ are denote the distance between the front fixed group and the magnification group, the distance between the magnification group and the compensation group, the distance between the compensation group and the rear fixed group, and the distance between the rear fixed group and the image plane of the microscope at the minimum magnification, respectively. In addition, the interval between the compensation group and the rear fixed group must be greater than the thickness of the beam splitting prism 2, i.e., ${d_{34s}} > p$.

Based on the geometric relationship in Fig. 3 and Eq. (8), the total length L of the dual-band simultaneous zoom microscope can be obtained.

$$\begin{array}{l} L = {f_{11}}^{\prime} + {f_{12}}^{\prime}\textrm{ + }t + \overline {\textrm{BE}} - ({{l_4} - {l_4}^{\prime}} )\\ \;\;\;\textrm{ = }\;{f_{11}}^{\prime} + {f_{12}}^{\prime}\textrm{ + }t + 2({{f_2}^{\prime} + {f_3}^{\prime} + {f_4}^{\prime}} )- \left( {{\beta_{2s}} + \frac{1}{{{\beta_{2s}}}}} \right){f_2}^{\prime}\\ \;\;\;\;\;\; - \left( {{\beta_{3s}} + \frac{1}{{{\beta_{3s}}}}} \right){f_3}^{\prime} - \left( {{\beta_{4s}} + \frac{1}{{{\beta_{4s}}}}} \right){f_4}^{\prime} + p\left( {1 - \frac{1}{n}} \right) \end{array}$$

3. Initial structure calculation method

3.1 Design index

In this paper, the 1/2-inch sensor IMX990-AABA-C developed by Sony is used, which responds to the spectral band from 400 nm to 1700nm, with a pixel count of 1280 × 1024 pixels and the pixel size is 5 µm × 5 µm. The dual-band simultaneous zoom microscope has a working distance of 70 mm, the magnification ratio of the VIS band is 10×, and the magnification ratio of the SWIR band is 2×. The overall design specifications of the dual-band synchronous zoom microscope are shown in Table 1. The magnitude of the object-side resolution of the microscope optical system can be calculated according to Eq. (16).

$$\sigma = \frac{{0.61\lambda }}{{NA}}$$
where NA and λ denote the numerical aperture of the object and the working wavelength of the microscope optical system, respectively.

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Table 1. Design index of the dual-band synchronous zoom microscope

3.2 Initial structural calculation

The initial structure parameters of the dual-band simultaneous zoom microscope optical system can be solved as the following steps:

  • Step 1: According to Eq. (2), the focal length f11′ of the collimating lens group in the front fixed group is 70 mm. The material of beam splitting prism 1 and beam splitting prism 2 is selected as H-K9L, and their edge lengths are set. Thus, the refractive indices and edge lengths of beam splitting prism 1 and 2 are a set of known parameters.
  • Step 2: The minimum magnification (${\beta _s}$=-0.4), the maximum magnification (${\beta _l}$=-4.0) and the total length (L = 300 mm) of the zoom microscope optical system are known parameters. When the zoom microscope is located at the minimum magnification, the distance between the front fixed group and the zoom group is minimized. Therefore, the parameter ${d_{12s}}$ needs to be assumed to be known, and we can obtain Eq. (17).
    $$\left\{ {\begin{array}{l} \begin{array}{l} L = {f_{11}}^{\prime} + {f_{12}}^{\prime}\textrm{ + }t + 2({{f_2}^{\prime} + {f_3}^{\prime} + {f_4}^{\prime}} )- \left( {{\beta_{2s}} + \frac{1}{{{\beta_{2s}}}}} \right){f_2}^{\prime}\\ \;\;\;\;\;\; - \left( {{\beta_{3s}} + \frac{1}{{{\beta_{3s}}}}} \right){f_3}^{\prime} - \left( {{\beta_{4s}} + \frac{1}{{{\beta_{4s}}}}} \right){f_4}^{\prime} + p\left( {1 - \frac{1}{n}} \right) \end{array}\\ {{\beta_s} = \frac{{{f_{12}}^{\prime}}}{{{f_{11}}^{\prime}}} \times {\beta_{2s}} \times {\beta_{3s}} \times {\beta_{4s}}}\\ {{d_{12s}} = {f_{12}}^{\prime} - \frac{{1 - {\beta_{2s}}}}{{{\beta_{2s}}}}{f_2}^{\prime}}\\ {({1 - {\beta_{3s}}} ){f_3}^{\prime} + p\left( {1 - \frac{1}{n}} \right) - \frac{{1 - {\beta_{4s}}}}{{{\beta_{4s}}}}{f_4}^{\prime} > p} \end{array}} \right.$$
  • Step 3: The set of Eq. (17) has seven variables and four equations. Firstly, we assume the focal length of the converging lens group and the magnification of the rear fixed group, then calculate the focal lengths of the remaining three lens groups and the magnification of the zoom group and the compensation group at the small magnification. The unknown parameters calculated with different parameter settings will vary and are only used here as a set of trial solutions.
  • Step 4: Calculate ${d_{12s}}$, ${d_{23s}}$, ${d_{34s}}$, and ${d_{4f}}$ according to Eqs. (14).
  • Step 5: Based on Eqs. (18) and (19), the magnification of the zoom group and the compensation group at the large magnification can be calculated.
    $$\begin{array}{l} L = {f_{11}}^{\prime} + {f_{12}}^{\prime}\textrm{ + }t + 2({{f_2}^{\prime} + {f_3}^{\prime} + {f_4}^{\prime}} )- \left( {{\beta_{2l}} + \frac{1}{{{\beta_{2l}}}}} \right){f_2}^{\prime}\\ \;\;\;\;\;\; - \left( {{\beta_{3l}} + \frac{1}{{{\beta_{3l}}}}} \right){f_3}^{\prime} - \left( {{\beta_{4l}} + \frac{1}{{{\beta_{4l}}}}} \right){f_4}^{\prime} + p\left( {1 - \frac{1}{n}} \right) \end{array}$$
    $${\beta _l} = \frac{{{f_{12}}^{\prime}}}{{{f_{11}}^{\prime}}} \times {\beta _{2l}} \times {\beta _{3l}} \times {\beta _4}$$
  • Step 6: Then we can calculate the distance between each group at large magnification according to Eq. (20).
    $$\left\{ {\begin{array}{l} {{d_{12l}} = {f_{12}}^{\prime} - {l_{2l}} = {f_{12}}^{\prime} - \frac{{1 - {\beta_{2l}}}}{{{\beta_{2l}}}}{f_2}^{\prime}}\\ {{d_{23l}} ={-} \frac{{1 - {\beta_{3l}}}}{{{\beta_{3l}}}}{f_3}^{\prime} + ({1 - {\beta_{2l}}} ){f_2}^{\prime}}\\ {{d_{34l}} = ({1 - {\beta_{3l}}} ){f_3}^{\prime} - \frac{{1 - {\beta_4}}}{{{\beta_4}}}{f_4}^{\prime} + p\left( {1 - \frac{1}{n}} \right)} \end{array}} \right.$$
  • Step 7: Bring all the parameters calculated above into the optical design software Zemax and establish an evaluation merit function for optimization to ensure that the zoom optical system does not have inflection point during the zoom process. If there is an inflection point, we need to return to the second step for recalculation (To avoid the occurrence of inflection points, we can refer to the method in reference 17). After meeting the requirements, we set the optical system aperture stop position and numerical aperture (NA), again for parameter optimization. In this optimization process, we try to ensure that the F-number of each group is greater than 1 to reduce the pressure of each group on aberration correction.
The initial structure of the dual-band simultaneous zoom microscope optical system is solved according to the above seven steps. In this paper, the materials of the beam splitting prism are all selected as H-K9L (n = 1.52), the edge length of the beam splitting prism 1 is s = 38 mm, and the edge length of the beam splitting prism 2 is p = 12.4 mm. The minimum magnification of the microscope optical system is ${\beta _s}$=-0.4, the maximum magnification is ${\beta _l}$=-4.0, the working distance −l1 = f11′=70 mm, the total length is L = 300 mm. After several solutions and optimization, we get the focal lengths of each group in the dual-band zoom microscope optical system, as shown in Table 2.

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Table 2. Focal length of the four groups in the initial structure

When the magnification of the microscope optical system is at −0.4, −1.2, and −4.0, respectively, the spacing between the groups is shown in Table 3.

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Table 3. Spacing between the four groups

The ideal structural model of the dual-band synchronous zoom microscope optical system is shown in Fig. 2. The total length of the optical system is 230 mm, and the position of the aperture stope is located at the compensation group. The aperture stope moves in synchronization with the compensation group during continuous zooming, and the aperture stope has an aperture of 7.5 mm and remains constant. The distance between the collimating and converging lens groups in the front fixed group and the first beam splitting prism is 10 mm and 3 mm, respectively.

 figure: Fig. 2.

Fig. 2. Ideal model diagram of the zoom microscope.

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As can be seen from Fig. 2, the zoom group gradually moves away from the front fixed group, and the compensation group gradually moves closer to the front fixed group during the continuous change of the magnification of the optical system from −0.4 to −4.0. There is no inflection point in the motion trajectories of the two motion group elements during zooming.

4. Design of dual-band synchronous zoom microscope

4.1 Optical system design

Then we substituted these ideal lenses into real lenses, and first ensure the imaging quality of the 10× VIS zoom optical system on the focal plane 2. At this time, when the magnifications are −0.4, −1.5, and −4.0, respectively, the residual aberrations of the SWIR band on the focal plane 2 is shown in Fig. 3. From Fig. 3, we can see that the residual aberrations of the SWIR band are different at the three magnifications. The main aberration at the magnification of −0.4 is the axial color and the coma, the main aberration at the magnification of −1.5 is the axial color, and the main aberration at the magnification of −4.0 is the axial color and the spherical. Therefore, as the imaging magnification increases, the most severe aberration change in the SWIR band is axial color, followed by spherical aberration, and the maximum residual aberration is axial color. However, the aberration that can be corrected by the rear fixed group 1 is a fixed value, so aberration compensation can only be applied to a small magnification segment (zoom range approximately 2×). Thus the zoom range of the SWIR band is sacrificial to ensure the large zoom range of the VIS band, which is more important in this dual-band zoom optical system.

 figure: Fig. 3.

Fig. 3. Residual aberrations of the SWIR band on the focal plane 2

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Finally, we use a rear fixed group 1 (β41=β42=β4) to replace the rear fixed group 2, and use the method of back working distance compensation to correct the residual aberrations in the SWIR band with a magnification range of −0.4 to −0.8. The final structure of the dual-band synchronous zoom microscope optical system is shown in Fig. 4. The full length of the dual-band microscope optical system is 250 mm, and the side lengths of the two beam splitting prisms are 38 mm and 12 mm, respectively. When the working wavelength is VIS band, the position of the visible imaging surface will remain fixed through the relative motion of the zoom group and the compensation group; when the working wavelength is SWIR band, the position of the SWIR imaging surface will move along the direction of the optical axis through the relative motion of the zoom group and the compensation group. When the magnification of the SWIR microscope is changed from −0.4 to −0.8, the image distance of the SWIR optical system is increased by 0.45 mm.

 figure: Fig. 4.

Fig. 4. Structure diagram of the dual-band zoom microscope.

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The structural parameters of the dual-band synchronous zoom microscope optical system are shown in Fig. 5. The materials used for the lenses in the zoom optical system are CDGM glass materials.

 figure: Fig. 5.

Fig. 5. Structural parameter diagram of the dual-band synchronous zoom microscope.

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4.2 Image quality evaluation

The object-side resolution of the dual-band synchronous zoom microscope is closely related to both the working wavelength and imaging magnification of the optical system. For the continuous zoom microscope designed in this paper, when the working wavelength is VIS and the magnification is −4.0, the zoom microscope has the highest object-side resolution, and the Nyquist frequency of the optical system is the lowest at this time; when the magnification is −0.4, the zoom microscope has the smallest object-side resolution, and the Nyquist frequency of the optical system is the highest at this time.

The imaging resolution of the dual-band synchronous zoom microscope designed in this paper is shown in Table 4. When the working band is VIS and the magnification of the microscope optical system is −0.4, the object-side resolution is 12.0 µm, which corresponds to a Nyquist frequency of 100 lp/mm; when the magnification of the optical system is −4.0, the object-side resolution is 2.1 µm, which corresponds to a Nyquist frequency of 60 lp/mm; when the working band is SWIR and the magnification of the microscope optical system is −0.4, the object-side resolution is 25.0 µm, which corresponds to a Nyquist frequency of 60 lp/mm. When the working wavelength is SWIR and the magnification of the microscope optical system is −0.4, the objective resolution is 25.0 µm, and the corresponding Nyquist frequency of the optical system is 50 lp/mm; when the magnification of the optical system is −0.8, the object-side resolution is 12.5 µm, and the corresponding Nyquist frequency of the optical system is 50 lp/mm.

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Table 4. Object-side resolution of the zoom microscope

The Modulation transfer function (MTF) curves of the dual-band synchronous zoom microscope at the VIS band are shown in Fig. 6(a)-(c), it can be seen that the average MTF of the full field of view of the optical system at 100 lp/mm are all greater than 0.36 when the magnification of the zoom microscope is −0.4, and the average MTF of the full field of view of the optical system at 85 lp/mm are all greater than 0.37 when the magnification of the zoom microscope is −1.2, and the average MTF of the full field of view of the optical system at 60 lp/mm are all greater than 0.23 when the magnification of the zoom microscope is −4.0. The MTF curves of the dual-band zoom microscope at SWIR band are shown in Figs. 6(d)-(f), it can be seen that when the magnification of the zoom microscope is −0.4, −0.6, and −0.8, the average MTF of the full field of view of the optical system at 50 lp/mm is greater than 0.30.

 figure: Fig. 6.

Fig. 6. MTF curves of the dual-band zoom microscope.

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The spot diagrams of the dual-band synchronous zoom microscope at the VIS band are shown in Figs. 7(a)-(c), it can be seen that the RMS of the diffuse spot imaged by the optical system increases with the increase of the magnification of the microscope, which is closely related to the diffraction limit of the microscope (the corresponding Nyquist frequencies of the optical system are different for different magnifications), but the amount of change basically does not affect the imaging quality. The spot diagrams in the SWIR band are shown in Figs. 7(d)-(f), it can be seen that the RMS of the diffuse spot in the center field of view is less than 8.7 µm when the magnification of the microscope is at −0.4, −0.6, and −0.8, respectively, and that the RMS of the edge field of view is larger than that of the center field of view, but it does not have much effect on the imaging quality.

 figure: Fig. 7.

Fig. 7. Spot diagram of the dual-band zoom microscope.

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The distortion curve of the dual-band synchronous zoom microscope optical system is shown in Fig. 8, it can be seen that the distortion of the optical system is less than 0.08%, and the lower optical distortion provides the necessary guarantee for high-precision microscopic measurement.

 figure: Fig. 8.

Fig. 8. Distortion curves of the dual-band zoom microscope.

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5. Coaxial lighting design and overall analysis

5.1 Optical system design of coaxial Kohler illumination

To fully illuminate the field of view of the object side of the zoom microscope, the radius of the illumination spot must be larger than the maximum imaging object height of the zoom microscope during the design of the uniform illumination optical system. In the process of continuous zoom imaging, the maximum imaging object height of the microscope is 10.0 mm, so the radius of the uniform illumination spot is designed to be 11.0 mm in this paper, to fully cover the entire imaging surface. The diameter of the illumination light source is 6 mm.

The illumination uniformity of the critical illumination mode is mainly dependent on the uniformity of the illumination source itself, however, the illumination uniformity of the Kohler illumination mode is superior to that of critical illumination, with illumination uniformity typically better than 98% [24]. In addition, the uniformity of Kohler illumination is independent of the uniformity of the illumination source itself. Therefore, the Kohler uniform illumination method is selected in this paper. The design of the coaxial uniform illumination optical system is carried out according to the principle of Kohler illumination, and the reverse design method is used in the design process. The specific design steps are as follows:

  • Step 1: First, the entrance pupil is designed to be at the object plane of the microscope optical system, and the optical system is uniformly illuminated to share the beam splitting prism 1 and the collimating lens group in the front fixed group of the zoom microscope, and the light rays exiting from the beam splitting prism 1 are imaged for the first time.
  • Step 2: Then, the design of the secondary imaging optical system is carried out. In the process of the secondary imaging optical system design, the ideal lens is used first, then the aperture stop is set on the ideal lens and the evaluation function is used to constrain the entrance pupil to the object plane of the microscope, and the ideal lens is replaced by a real lens while the position of the entrance pupil is optimized.
  • Step 3: Finally, the entire uniform illumination optical system is subjected to reverse light tracing and the illumination uniformity is evaluated using Tracepro software.
The above three steps are used to design the coaxial Koehler uniform illumination optical system, and the final design structure of the uniform illumination optical system is shown in Fig. 9. To make the whole system more compact, a reflector is used to fold the optical path, and the total length of the folded optical system is 112 mm, the width is 64 mm, the height is 38 mm, and the rear intercept is 15.0 mm.

 figure: Fig. 9.

Fig. 9. Optical system of coaxial Kohler uniform illumination.

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5.2 Overall optical path synthesis design

The overall optical path of the dual-band simultaneous zoom microscope based on coaxial Koehler uniform illumination is shown in Fig. 10, the illumination spot radius of the uniform illumination optical system is larger than the maximum object height imaged by the zoom microscope. In addition, the dual-band microscope always maintains the advantage of uniform illumination on the object plane throughout the continuous zoom process.

 figure: Fig. 10.

Fig. 10. Overall optical path diagram of the dual-band zoom microscope.

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5.3 Tolerance analysis

Tolerance analysis is one of the important analysis links before the manufacturing and assembly of the optical system. The manufacturing difficulty of the zoom microscope head can be quickly and effectively assessed using the tolerance analysis function in the optical design software [25]. Comprehensively considering the tolerance sensitivity of each optical lens at small magnification, medium magnification, and large magnification, the tolerance allocation of the dual-band zoom microscope optical system is finally determined as shown in Table 5.

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Table 5. Tolerance distribution table of the zoom microscope

The MTF Monte Carlo analysis of the dual-band zoom microscope optical systems using the tolerances assigned in Table 5 is shown in Fig. 11(a). When the magnification of the microscope is −0.4, −1.2 and −4.0, the MTFs of the 50% systems at the respective Nyquist frequencies are 0.26, 0.26, and 0.15, respectively. When the working band is SWIR, the distribution pattern of MTFs of the optical system of the microscope at 50 lp/mm is shown in Fig. 11(b). When the magnification of the zoom microscope is −0.4 and −0.8, 50% of the systems have MTFs of 0.29 and 0.25 at their respective Nyquist frequencies, respectively.

 figure: Fig. 11.

Fig. 11. Probability diagram of Monte Carlo analysis.

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5.4 Zoom curve analysis

The optical system of a zoom microscope achieves continuous zoom by moving the relative positions of the zoom group and the compensation group along the optical axis direction, and the cam is the key element that ensures the continuous movement of the zoom group and the compensation group in a certain fixed relationship along the optical axis direction, so the cam curve must be analyzed [23].

We fit the motion curves of the zoom group elements in the dual-band synchronous zoom optical system, and the relative motion relationship curves between the zoom group and the compensation group are shown in Fig. 12. The red curve represents the motion law of the zoom group and the compensation group in the continuous zooming process of the VIS band, and the blue curve represents the motion law of the zoom group and the compensation group in the continuous zooming process of the SWIR band. As can be seen from Fig. 12, the dual-band microscope optical system has the same cam curve when the magnification range of the microscope optical system is −0.4 to −0.8.

 figure: Fig. 12.

Fig. 12. Zoom curve fitting diagram.

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The distribution of the imaging magnification difference of the dual-band microscope optical system during the process of synchronous zoom is shown in Fig. 13. When the imaging magnification range of the microscope is −0.4 to −0.8, the difference in imaging magnification of the dual-band microscope optical system is less than 0.006, i.e., the difference in imaging magnification of the dual-band microscope optical system during simultaneous zooming is less than 1.25%.

 figure: Fig. 13.

Fig. 13. Magnification difference curve of the dual-band zoom microscope.

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6. Conclusion

To solve the problem of expanding the imaging spectral range of the zoom microscope optical system based on coaxial uniform illumination, this paper proposes a design method for a dual-band synchronous zoom microscope optical system based on Kohler coaxial uniform illumination. First, we propose to split the front fixed group of the mechanically compensated zoom microscope optical system into two lens groups, the front group is used for light collimation, the rear group converges the collimated light, and a beam splitting prism is added to realize the coaxial illumination and imaging, which not only reduces the aperture of the optical elements in the front fixed group, but also significantly compresses the coaxial Kohler illumination optical system by sharing the lens group. Then, we proposed to correct the residual aberration of the dual-band by employing two rear fixed lens groups with the same magnification but different aberration contributions, which will provide guarantees for high-precision fusion of dual band images. Finally, based on the imaging principle of the dual-band synchronous zoom microscope optical system, a method is proposed to solve for the initial structure, and a dual-band synchronous zoom microscope optical system is designed based on the method, which has a zoom magnification range of −0.4 to −4.0 and −0.4 to −0.8 in the VIS band and SWIR band, respectively. The magnification difference in synchronous zoom imaging is less than 1.25%, and the maximum resolution is 2.1 µm in the VIS band and 12.5 µm in the SWIR band, respectively. The synchronous zoom microscope system has a broad application prospect in aerospace, chip manufacturing and biomedical research.

Funding

Natural Science Foundation of Sichuan Province (2023NSFSC0491, 2023NSFSC1308).

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 (13)

Fig. 1.
Fig. 1. Imaging principle diagram of dual-band synchronous zoom microscope.
Fig. 2.
Fig. 2. Ideal model diagram of the zoom microscope.
Fig. 3.
Fig. 3. Residual aberrations of the SWIR band on the focal plane 2
Fig. 4.
Fig. 4. Structure diagram of the dual-band zoom microscope.
Fig. 5.
Fig. 5. Structural parameter diagram of the dual-band synchronous zoom microscope.
Fig. 6.
Fig. 6. MTF curves of the dual-band zoom microscope.
Fig. 7.
Fig. 7. Spot diagram of the dual-band zoom microscope.
Fig. 8.
Fig. 8. Distortion curves of the dual-band zoom microscope.
Fig. 9.
Fig. 9. Optical system of coaxial Kohler uniform illumination.
Fig. 10.
Fig. 10. Overall optical path diagram of the dual-band zoom microscope.
Fig. 11.
Fig. 11. Probability diagram of Monte Carlo analysis.
Fig. 12.
Fig. 12. Zoom curve fitting diagram.
Fig. 13.
Fig. 13. Magnification difference curve of the dual-band zoom microscope.

Tables (5)

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Table 1. Design index of the dual-band synchronous zoom microscope

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Table 2. Focal length of the four groups in the initial structure

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Table 3. Spacing between the four groups

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Table 4. Object-side resolution of the zoom microscope

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Table 5. Tolerance distribution table of the zoom microscope

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

β 41 = β 42 = β 4
{ f 11 = l 1 f 12 = l 1
s > 2 l 1 × tan ( θ )
BE ¯ = ( l 3 l 3 ) ( l 2 l 2 )  +  DE ¯  =  l 3 l 3  +  l 2 l 2  +  DE ¯
DE ¯  =  p ( 1 cos U n 2 sin 2 U )
BE ¯ = l 2 + l 3 l 2 l 3  +  p ( 1 1 n )
{ l = 1 β β f l = ( 1 β ) f
BE ¯ = 2 ( f 2 + f 3 ) f 2 ( β 2 + 1 β 2 ) f 3 ( β 3 + 1 β 3 ) + p ( 1 1 n )
2 ( f 2 + f 3 ) f 2 ( β 2 + 1 β 2 ) f 3 ( β 3 + 1 β 3 ) + p ( 1 1 n ) = Constant
2 ( f 2 + f 3 ) f 2 ( β 2 + 1 β 2 ) f 3 ( β 3 + 1 β 3 ) = Constant
f 2 ( β 2 s + 1 β 2 s ) + f 3 ( β 3 s + 1 β 3 s ) = f 2 ( β 2 l + 1 β 2 l ) + f 3 ( β 3 l + 1 β 3 l )
Γ = β l β s  =  β 1 × β 2 l × β 3 l × β 4 β 1 × β 2 s × β 2 s × β 4 = β 2 l × β 3 l β 2 s × β 2 s
{ β 1  =  f 12 f 11 β 4  =  l 4 l 4
{ d 12 s = f 12 l 2 s = f 12 1 β 2 s β 2 s f 2 d 23 s = l 3 s + l 2 s = 1 β 3 s β 3 s f 3 + ( 1 β 2 s ) f 2 d 34 s = l 3 s l 4 + DE ¯ = ( 1 β 3 s ) f 3 1 β 4 β 4 f 4 + p ( 1 1 n ) d 4 f = l 4 = ( 1 β 4 ) f 4
L = f 11 + f 12  +  t + BE ¯ ( l 4 l 4 )  =  f 11 + f 12  +  t + 2 ( f 2 + f 3 + f 4 ) ( β 2 s + 1 β 2 s ) f 2 ( β 3 s + 1 β 3 s ) f 3 ( β 4 s + 1 β 4 s ) f 4 + p ( 1 1 n )
σ = 0.61 λ N A
{ L = f 11 + f 12  +  t + 2 ( f 2 + f 3 + f 4 ) ( β 2 s + 1 β 2 s ) f 2 ( β 3 s + 1 β 3 s ) f 3 ( β 4 s + 1 β 4 s ) f 4 + p ( 1 1 n ) β s = f 12 f 11 × β 2 s × β 3 s × β 4 s d 12 s = f 12 1 β 2 s β 2 s f 2 ( 1 β 3 s ) f 3 + p ( 1 1 n ) 1 β 4 s β 4 s f 4 > p
L = f 11 + f 12  +  t + 2 ( f 2 + f 3 + f 4 ) ( β 2 l + 1 β 2 l ) f 2 ( β 3 l + 1 β 3 l ) f 3 ( β 4 l + 1 β 4 l ) f 4 + p ( 1 1 n )
β l = f 12 f 11 × β 2 l × β 3 l × β 4
{ d 12 l = f 12 l 2 l = f 12 1 β 2 l β 2 l f 2 d 23 l = 1 β 3 l β 3 l f 3 + ( 1 β 2 l ) f 2 d 34 l = ( 1 β 3 l ) f 3 1 β 4 β 4 f 4 + p ( 1 1 n )
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