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Abstract
A large relative aperture is essential to improve the spatial resolution of zoom systems. To overcome the limitations of the existing off-axis reflective mechanical zoom system with a low zoom rate and a small relative aperture, this paper proposes a non-axis movement method for increasing the degrees of freedom. On the basis of nodal aberration theory, passive eccentricity is changed into active eccentricity to achieve wave aberration balance in the multiple structures of the zoom imaging system. An off-axis aspherical four-mirror non-axial mechanical zoom optical system is designed and fabricated. The prototype has been successfully processed and assembled with the help of computer-aided alignment technology. The prototype’s F-number is 4 and zoom ratio is 4.57:1. Experimental results verify the feasibility of the proposed method.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the development of modern science and technology, the requirements of space optical imaging systems for target detection and identification have been increasing, directing the development of this kind of optical system toward variable focal lengths, large aperture, high resolution, and light weight [1,2]. Compared with refractive and refractive–reflective optical systems, reflective optical systems have obvious advantages, such as wide spectrum, high transmittance, absence of chromatic aberration, and large aperture [3–6]. Therefore, reflective zoom optical systems (RZOS) are widely used in optical remote sensing imaging, astronomical observation and other fields. Further, off-axis reflective optical systems (OROS) have a stronger application prospect than the coaxial structure due to their “no obstruction” advantage [7].
Many researchers have studied off-axis RZOS (ORZOS). Based on the zoom principle, ORZOS can be divided into two types: active zoom and mechanical zoom [8,9]. Off-axis reflective active zoom optical systems (ORAZOS) change their optical focal length by controlling the changes in the surface shape of the active optical elements [10,11] (e.g., deformable mirrors and spatial light modulators). On the basis of the “Schiefspiegler” approach, Heinrich [12] et al. designed an ORAZOS consisting of four mirrors with a triple zoom feature. The primary and fourth mirrors of this system are deformable mirrors, and three different zoom states can be achieved by changing the curvature of these two mirrors. Wang [13] et al. designed an ORAZOS with three mirrors, whose primary and tertiary mirrors are deformable mirrors and zoom ratio is 3:1. Cheng [14] et al. proposed an automatic optical design scheme for ORAZOS. In the proposed scheme, a system with 10× zoom capability is achieved through the focal length variable photoelectric element. The ORAZOS has a high response speed and a relatively small volume, but several limitations remain, such as high difficulty in fitting the surface profile of active optical elements, limited aperture, and high cost [15,16].
Off-axis reflective mechanical zoom optical systems (ORMZOS) achieve the focal length changes by controlling the movement of the mirrors. The surface parameters of the mirrors are used for aberration compensation, and eccentricity is mostly used for eliminating obscuration. ORMZOS is slower in response and larger in volume, but easier to control and less expensive than ORAZOS. Allen [17] et al. first designed an ORMZOS with three mirrors, whose zoom ratio is 2:1 and F-number varies in the range of 4 to 8. According to vector aberration theory, Zhang [18] et al. designed an off-axis three-mirror zoom imaging system with a 4× zoom ratio and a fixed pupil diameter of 37.5 mm. To improve the aberration correction capability, Xie [19] et al. designed an off-axis three-mirror zoom optical system based on freeform surface. Based on zoom principle and primary aberration theory, Cao [20] et al. designed a mechanically compensated off-axis four-mirror zoom optical system with three-gear zoom focal lengths of 300, 600, and 900 mm.
In existing ORMZOS, the pupil diameter is fixed or the relative aperture is small. Especially in the telephoto state, the relative aperture of this kind of system is extremely small, making the requirements of high-resolution imaging difficult to satisfy. When the relative aperture increases, the aberration of the system dramatically increases with it. To achieve high-resolution imaging, freeform surface [21–23] is used to correct the higher-order asymmetric aberrations of the system. However, the difficulty of processing and testing free-form mirrors greatly increases the difficulty and cost of developing such systems [24,25].
To increase the zoom ratio and relative aperture of ORMZOS and reduce the manufacturing costs, we first propose a non-axial zoom structure form in ORMZOS. On the basis of traditional optical design methods, we add eccentricity as the aberration compensation. That is, on the basis of nodal aberration theory, we increase the offset in the vertical direction (Y-axis direction) by using the offset feature of the aberration field center. By turning the passive eccentricity change into active eccentricity change, the freedom of the system is increased and the aberration correction capability is improved. To verify the feasibility of the proposed method, an off-axis aspheric four-mirror non-axial mechanical zoom imaging system with large relative aperture and zoom ratio is designed and machined. The experimental results show that the system has good imaging performance and can reach a zoom ratio of 4.57:1.
2. System design strategy
According to nodal aberration theory, when the mirrors are eccentric, no new aberrations are created. However, the center of the aberration field generated by each surface is no longer coaxial, and the aberration properties change. In the ORMZOS, before and after the mirror moves, the eccentricity vector (${\overrightarrow \sigma _i}$) of the aberration field on surface i changes, which is difficult to balance the aberrations among the structures with different focal lengths. Thus, as shown in Fig. 1, we propose a non-axial moving approach to replace the traditional axial moving approach, which means that the passive eccentricity caused by mirror movement is changed into active eccentricity, and the aberration field can be further compensated.
2.1 Zoom equation analysis of ORMZOS
As shown in Fig. 2, rays are reflected via four mirrors M1, M2, M3, M4 to the image plane. Based on Gaussian optics and matrix optics theory, the reflection matrix ${{\mathbf R}_i}$ and transfer matrix ${{\mathbf T}_{ji}}$ of mirror Mi in the jth structure are respectively expressed as follows:
Hence, the focal length fsysj of the system can be written as
During the zooming process, the image plane must remain stable and unchanged, so the distance between primary mirror M1 and the image plane should remain the same, which can be written as
2.2 Aberration analysis of non-axial ORMZOS
We define the initial data of the incident rays as ${A_{j1}} = (\begin{array}{{cc}} {{H_{j1}}}&{{U_{j1}})} \end{array}$, and the ray tracing data on surface i is shown as Eq. (4).
According to Eq. (4), we can obtain the chief ray heights ${y_{ji}}$, marginal ray heights ${h_{ji}}$ and aperture angle ${u_{ji}}$ and $u{^{\prime}_{ji}}$ on ${M_1},{M_2},{M_3},{M_4}$ in the optical system with the F number.
On the basis of Seidel aberration theory [26], the coefficient of spherical aberration ${S_{I,ji}}$, coma ${S_{II,ji}}$, astigmatism ${S_{III,ji}}$ and field curvature ${S_{IV,ji}}$ can be expressed as follows:
When the mirrors are eccentric, the wave aberration [27] ${W_j}$ in the jth structure of non-axial ORMZOS can be expressed as follows:
Based on the relation between Seidel aberration and wave aberration, the wave aberration can be calculated as:
Hence, the comprehensive evaluation function for the imaging performance of non-axial ORMZOS is expressed as
The imaging performance comprehensive evaluation function Q is a function expression of the optical parameters (${r_1},{r_2},{r_3},{r_4},{d_{j1}},{d_{j2}},{d_{j3}},{d_{j4}},{k_1},{k_2},{k_3},{k_4},{\sigma _{j1}},{\sigma _{j2}},{\sigma _{j3}},{\sigma _{j4}}$) in the system, which can be transformed into an optimization problem of the objective function and calculated by the optimization algorithm.
3. Optical design and analysis
3.1 Optical system design and simulation
An off-axis aspheric four-mirror non-axial mechanical zoom optical system is designed based on the theory in Section 2. Table 1 lists the specifications of the optical system. The system works in the band of 486–656 nm. The focal lengths of the system range from 100 mm to 450 mm and the F/# is 4. The layout of this system is shown in Fig. 3. The mirrors in the wide-angle structure are marked with blackness, while those marked with blueness are the secondary, tertiary, and fourth mirrors after zooming in the telephoto structure. These four mirrors in the zoom system are all high-order aspheric mirrors, and the position of the primary mirror is fixed. The focal length can be switched by moving the secondary, tertiary, and fourth mirrors before or after zooming while the position of the image plane is fixed. Table 2 lists the structural parameters of the optical system in different structures. Each mirror has different eccentricities in different structures, which can be used to assist in the correction of system aberrations.
Table 1. Specifications of the off-axis aspheric four-mirror non-axial mechanical zoom system
Table 2. Structural parameters of the optical system
In the design, real ray tracing data is also used to control the distance from a point to the straight line as shown in Fig. 4, to eliminate the obstruction of rays and surface interference between the two structures. However, the calculation of the marked point-to-line distances in the constraint requires the use of ray tracing data between the two structures. For example, we approximately decompose distance L9 as the difference between L1 and L1,9, where L1 represents the distance from a point to the line in a single structure (wide-angle structure) and L1,9 represents the difference of the rays in the local Y coordinates on the secondary mirror between the two structures. The constraints are not limited to those described above in this or other design tasks.
Fig. 4. Optimization constraints of obstruction in the zoom system. (a)wide-angle structure, (b)telephoto structure.
The optical system exhibits a good imaging performance. In the wide-angle and telephoto structures, the average modulation transfer functions (MTF) of the system in the full FOV reach 0.56 at 50 line pairs/mm (lp/mm) and 0.55 at 50 lp/mm, respectively. The MTF of the system under different sampling FOVs is shown in Fig. 5. In the wide-angle structure, the MTF values for each FOV are greater than 0.50 at 50 lp/mm. In the telephoto structure, the MTF values for each FOV are greater than 0.45 at 50 lp/mm.
Fig. 5. MTF of the off-axis aspheric four-mirror non-axial mechanical zoom system. (a)wide-angle structure, (b)telephoto structure.
3.2 Tolerance analysis
Tolerance analysis was performed to evaluate the feasibility of the practical machining and assembly of the optical system. The effects of slight fabrication and installation errors on the imaging quality of the system were investigated. The evaluation criterion was the average MTF at the Nyquist frequency. Compensation is the back intercept. The tolerance allocations for the designed system are listed in Table 3.
Table 3. Tolerance allocations results
Figure 6 shows the relationship between the image quality and cumulative probability under the proposed tolerance allocation. For the wide-angle structure, the MTF is eventually better than 0.2 at 50 lp/mm with a probability of 85%. For the telephoto structure, the MTF is eventually better than 0.2 at 50 lp/mm with a probability of 80%. These results indicate that the optical system has excellent instrumental feasibility.
Fig. 6. Wavefront differential tolerance analysis. (a) wide-angle structure, (b) telephoto structure.
4. Prototype and experiment
4.1 Optomechanical structure of the device
Figure 7 shows the optomechanical structure design for the off-axis aspheric four-mirror non-axial mechanical zoom system. According to the optical design scheme, the optomechanical structure of the system mainly includes a primary mirror subassembly (PMS), a secondary mirror subassembly (SMS), a tertiary mirror subassembly (TMS), a fourth mirror subassembly (FMS), a stop subassembly (SS), a displacement table subassembly (DTS), a focal plane subassembly (FPS), and a mounting substrate (MS). Using the modular design approach, each optical element was assembled into each subassembly separately, and each subassembly was integrated onto the MS. To adjust the position of each optical subassembly, the adjustment structure was designed to adjust the six degrees of freedom for rotation and displacement. For the DTS, three high-precision one-dimensional displacement table shelf products were used to drive the mirrors to move.
Fig. 7. Optomechanical structure for the off-axis aspheric four-mirror non-axial mechanical zoom system
4.2 Installation and assembly of the device
The mirrors were inspected using a ZYGO interferometer at a room temperature (23°C). As shown in Fig. 8, the PV and RMS values of the surface shape error in the primary mirror are 0.638 and 0.043 λ (λ=632.8 nm), respectively. The surface shape errors of the other mirrors are displayed in Table 4. The test results show that the surface shape errors of the mirrors are within the tolerance range and can meet the requirements for alignment.
Table 4. shape errors of the optical elements
The theodolite and the self-collimator were used for the preliminary installation and adjustment of the components. The mirrors were installed on the corresponding mirror subassemblies. The PMS was installed on the MS. The SMS, the TMS, and the FMS were installed on the DTS, and the DTS was installed on the MS.
In view of the characteristics of the ORMZOS designed in this study, the assembly is difficult because the telephoto and wide-angle structures affect each other and should be simultaneously considered. Thus, we used a computer-aided alignment technique developed for ORMZOS to achieve the high-precision assembly of the system. The eccentricity, tilt, and spacing of the secondary, tertiary, and fourth mirrors were taken as the misalignment to be solved, using the primary mirror as the alignment reference.
Three relative FOVs (i.e., (0, 0), (0, 1) and (0, -1)) were selected as the reference FOVs. The design residual aberrations of the three FOVs are shown in Table 5. Based on the measured wave aberrations in these three fields, the misalignments were solved. After six rounds of adjustment, the final wave aberrations of the three FOVs in the wide-angle structure are shown in Fig. 9, and the final wave aberrations of the three reference FOVs of the telephoto structure are shown in Fig. 10. The RMS values of the wave aberration in each FOV for the wide-angle structure are 0.083λ, 0.141λ, and 0.109λ (λ = 632.8 nm), and those of the wave aberration in each FOV for the telephoto structure are 0.173λ, 0.273λ, and 0.149λ (λ = 632.8 nm), respectively. The measurement results show that the wave aberration of each FOV in both the telephoto and wide-angle structures of the optical system are near the design values.
Fig. 9. Wave aberration of wide-angle structure after assembly. (a) (0, 0), (b) (0, 1), (c) (0, -1).
Fig. 10. Wave aberration of telephoto structure after assembly. (a) (0, 0), (b) (0, 1), (c) (0, -1).
Table 5. The design residual aberrations of the system
4.3 Experiment
The resolution of the optical system was used to measure the imaging performance. To test the system’s imaging performance, we built the experimental setup as shown in Fig. 11. All the optical instruments were mounted on an isolated optical table platform. An optical-resolution target (1951 USAF) was placed in the focal plane of a parallel light tube. The device was placed in the image space of the parallel light tube. Light from the light source hit the target, passed through the parallel light tube, entered the device, and eventually converged on the detector.
The angular resolution of the parallel optical tube in the image space is equal to the angular resolution of the non-axial OARZOS in the object space. Using this relationship, the spatial resolution of the non-axial OARZOS can be calculated when the unit image in the resolution plate pattern is resolved. Figure 12 shows the imaging results of the resolution target. For the target, the image heights of line 1 in Group 0 are 35 pixels and 160 pixels in the wide-angle and telephoto structures, respectively. Thus, the zoom ratio is measured to be 4.57:1. In addition, line 1 in Group 4 can be clearly distinguished in the telephoto structure, and line 6 in Group 1 can be clearly distinguished in the wide-angle structure. In 1951 USAF, the resolutions of line 6 in Group 1 and line 1 in Group 4 are 3.56 lp/mm and 16 lp/mm, respectively. Hence, the results indicate that the image resolutions of the system reach 53 lp/mm and 52 lp/mm in the wide-angle and telephoto structures, respectively.
Fig. 12. The images of resolution target. (a) wide-angle structure, (b) telephoto structure, (c) zoom-up image in (a), (d) zoom-up image in (b).
5. Conclusion
In this study, a non-axial ORMZOS design strategy was developed based on nodal aberration theory. The eccentricity change can increase the freedom of the system and contribute to the aberration compensation. An off-axis aspheric four-mirror non-axial mechanical zoom optical system was designed and successfully assembled. The experimental results show a good imaging performance with a zoom ratio of 4.57:1, verifying the feasibility of the proposed method in increasing the zoom ratio and the relative aperture and reducing the manufacturing cost.
However, some limitations remain. During the design process, continuous adjustments of the mirror decenter are required to compensate for the aberration and eliminate the obstruction of rays and surface interference. In different structures, the aperture region used by each mirror has a different aperture eccentricity, resulting in the large volume of the system. In addition, the mechanical zoom mode that relies on motor movement decreased the zoom speed of the system. These shortcomings may limit the application of the proposed system.
Funding
Key Laboratory of Optical System Advanced Manufacturing Technology, Chinese Academy of Sciences (2022KLOMT02-01).
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.
Supplemental document
See Supplement 1 for supporting content.
Reference
1. V. Corbacho, V H. Kuiper, and E. Gill, “Review on thermal and mechanical challenges in the development of deployable space optics,” J. Astron. Telesc. Instrum. Syst. 6(01), 1 (2020). [CrossRef]
2. M. Metwally, T. M. Bazan, and F. Eltohamy, “Design of very high-resolution satellite telescopes. Part 1: Optical system design,” IEEE Trans. Aerosp. Electron. Syst. 56(2), 1202–1208 (2020). [CrossRef]
3. A. Lightsey P, C. Atkinson, M. Clampin, and D. Feinberg L, “James Webb Space Telescope: large deployable cryogenic telescope in space,” Opt. Eng 51(1), 011003 (2012). [CrossRef]
4. K. Richter, D. Mader, K. Seidl, and G. Maas H, “Development of a geometric model for an all-reflective camera system,” ISPRS journal of photogrammetry and remote sensing 86, 41–51 (2013). [CrossRef]
5. V. I. Batshev and S. V. Bodrov, “A compact three-mirror astronomical objective,” Instrum. Exp. Tech. 59(4), 557–561 (2016). [CrossRef]
6. N. T. Ersumo, C. Yalcin, N. Antipa, N. Pegard, L. Waller, D. Lopez, and R. Muller, “A micromirror array with annular partitioning for high-speed random-access axial focusing,” Light: Sci. Appl. 9(1), 183 (2020). [CrossRef]
7. Z. Mi, Z. Li, and X. Zhang, “Construction of a compact off-axis three-mirror reflective system,” Appl. Opt. 61(9), 2424–2431 (2022). [CrossRef]
8. Benlan Shen, Jun Chang, Jiao Ouyang, Lifei Zhang, and Aman Wei, “Design of reflective active zoom systems with four mirrors,” Proc. SPIE 8557, 85571C (2012). [CrossRef]
9. A. Mann, “Infrared zoom lenses in the 1980s and beyond,” Opt. Eng 31(5), 1064–1071 (1992). [CrossRef]
10. M. Jungwirth, V. Wick D, and L. Dereniak E, “Theory and tradespace analysis of a reflective axial adaptive optical zoom system,” Opt. Eng 51(8), 083001-1 (2012). [CrossRef]
11. Y.-H. Huang, H.-C. Wei, W.-Y. Hsu, Y.-C. Cheng, and G.-D. J. Su, “Optical zoom camera module using two poly-dimethylsiloxane deformable mirrors,” Appl. Opt. 53(29), H248–H256 (2014). [CrossRef]
12. H. Grüger, “All-reflective optical power zoom objectives,” SPIE 9580, 95800H (2015). [CrossRef]
13. X. Wang, J. Chang, B. Shen, W. Zha, Y. Niu, and K. Zhang, “Design of an all-reflective active zoom system,” Optik 127(3), 1022–1026 (2016). [CrossRef]
14. X. Cheng, H. Ye, and Q. Hao, “Synthetic system design method for off-axis stabilized zoom systems with a high zoom ratio,” Opt. Express 29(7), 10592–10612 (2021). [CrossRef]
15. H. T. Cao, A. Brooks, S. W. S. Ng, D. Ottaway, A. Perreca, J. W. Richardson, A. Chaderjian, and P. J. Veitch, “High dynamic range thermally actuated bimorph mirror for gravitational wave detectors,” Appl. Opt. 59(9), 2784–2790 (2020). [CrossRef]
16. T. Peng, C. Dai, J. Lou, Y. Cui, B. Tao, and J. Ma, “A low-cost deformable lens for correction of low-order aberrations,” Opt. Commun. 460, 125209 (2020). [CrossRef]
17. A. Mann and R. Barry Johnson, “Design and analysis of a compact, wide filed, unobscured zoom mirror system,” SPIE 3129, 97–107 (1997). [CrossRef]
18. T. Zhang, Y. Wang, and J. Chang, “Design of unobscured reflective zoom system with three mirrors,” Chin. Opt. Lett. 8(7), 701–705 (2010). [CrossRef]
19. G. Xie, J. Chang, K. Zhang, J. Zhou, and Y. Niu, “Off-axis three-mirror reflective zoom system based on freeform surface,” Front. Optoelectron. 9(4), 609–615 (2016). [CrossRef]
20. Yiqing Cao, “Design of off-axis all-reflective three-gear zoom optical system with long focal length,” Laser & Optoelectronics Progress. 1–13 (2022). https://kns.cnki.net/kcms/detail/31.1690.tn.20220212.1751.018.html.
21. Y. Zhang, X. Wang, Z. Su, H. Pan, X. Chen, and W. Zhang, “Freeform optical surface design in an off-axis reflective imaging system by a double seed curve extension algorithm,” Appl. Opt. 60(4), 942–948 (2021). [CrossRef]
22. X. Liu and J. Zhu, “Automatic design method of starting points of freeform off-axis reflective imaging systems of small volume,” Opt. Express 30(5), 7954–7967 (2022). [CrossRef]
23. D. Cheng, C. Xu, T. Yang, and Y. Wang, “Off-axis reflective imaging system design with a conicoid-based freeform surface,” Opt. Express 30(6), 9590–9603 (2022). [CrossRef]
24. N. Takaki, J. C. Papa, A. Bauer, and J. P. Rolland, “Off-axis conics as base surfaces for freeform optics enable null testability,” Opt. Express 28(8), 10859–10872 (2020). [CrossRef]
25. D. G. Utrera, D. Aguirre-Aguirre, M. I. Rodríguez Rodríguez, and R. Diaz Uribe, “Null-screen testing of the complementary freeform surfaces of an adjustable focus lens,” Opt. Express 29(14), 21698–21710 (2021). [CrossRef]
26. Z. Qu, X. Zhong, K. Zhang, L. Li, and Y. Wang, “Automatic initial configuration in off-axis reflective optical system design using combined nodal and Seidel aberration,” Appl. Opt. 61(13), 3630–3640 (2022). [CrossRef]
27. K. P. Thompson, T. Schmid, O. Cakmakci, and J. P. Rolland, “Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry,” J. Opt. Soc. Am. A 26(6), 1503–1517 (2009). [CrossRef]
