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Abstract
In order to realize the miniaturization of the dual-band system, the monolithic compressed folding imaging lens (CFIL) is designed for infrared/laser dual-band in this paper. The relationship among the back focal length, field of view, pupil diameter, and central obscuration of the CFIL are derived. The design method of the dual-band CFIL is given, and the stray light of the CFIL can be suppressed by the double-layer hood structure. According to the design method of the CFIL, the infrared/laser dual-band can be applied by a monolithic optical element. The design results show that the minimum MTF for all fields of view in the infrared band is greater than 0.125 at 42lp/mm, the spot uniformity in the laser band is greater than 90%, and the total system length is only 0.305 times the focal length. After tolerance analysis, the MTF of CFIL is greater than 0.1, and the spot diagram is less than 880µm. The working temperature of the system is -20∼50°C, and the compensation distance is given. After stray light optimization, The point source transmittance (PST) value in the infrared band is reduced by 2 to 4 orders of magnitude, and the PST value in the laser band is reduced by 1 to 5 orders of magnitude. Compared with the traditional coaxial reflective system, the infrared/laser dual-band CFIL has only one lens, and the optical structure is compact. It provides a new idea for the integration and miniaturization of the multi-band system.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the diversification of recognized objects, complex background environment and intelligent countermeasures, the system is required to accurately identify targets and adapt to complex environments. Compared with conventional single-band imaging optical systems, dual-band or multi-band systems can detect different characteristics of a target and merge the obtained information, and further, the target identification accuracy can be improved significantly. However, dual-band system is usually of two optical paths with different waveband detectors, so the number of optical components and system size is too large to be miniaturized. If a common optical path is used, the selection of optical material is limited to achieve dual-band chromatic aberration correction, resulting in a complex system structure. Therefore, the multi-band detection system with a simple structure is still pressing.
Single-element imaging technologies include metalens and diffractive computational imaging. Metalenses have the advantages of thin volume, compact structure, and large numerical aperture [1–4], but metalens cannot achieve high diffraction efficiency at wide-band, and the object detection distance is limited. It also has serious chromatic aberration [5–7], so the high image quality cannot be achieved. In addition, the microstructure processing of metalens is difficult, so it cannot be applied in practical engineering. Diffractive computational imaging combines diffractive optical elements with computational imaging to achieve high performance while reducing the thickness of the imaging system [8–10]. However, the diffraction efficiency of the diffractive optical elements is low in wide-band, so the energy dispersion of the non-design order on the image plane leads to a decrease in contrast. Similar to metalens, the chromatic aberration in wide-band will affect the image quality [11,12].
In the past ten years, many dual-band optical systems based on catadioptric structures have been designed. This system uses a primary mirror and a secondary mirror to fold the optical path, incorporating a lens group and a dichroic beam splitter to achieve dual-band high quality imaging [13–15]. However, the volume that can be reduced by catadioptric structures is limited, and the assembly of the system is posed a huge challenge by the complex structure. The CFIL provides a solution to reduce the volume of the system by folding the optical path [16,17]. The system is produced by multiple concentric rings reflective surfaces on the front and rear surfaces of the substrate, and the entire system can realize dual-band system imaging with only one lens. When the light enters the element through the annular aperture, the transmitted light path is reflected by the annular reflective surfaces and focus on the image plane in the component center [18–20], the total length and volume of the system are greatly reduced. With the development of manufacturing technologies such as compression molding [21] and single-point diamond turning [22,23], the high-precision processing of the CFIL can be achieved [24]. Since the CFIL is integrated into one material, and the reflective annular surfaces are closely arranged, the imaging quality of the system is easily affected by stray light.
In this paper, we present demonstrate a monolithic infrared/laser dual-band CFIL. In section 2, the design method of infrared/laser dual-band CFIL and the theory of stray light elimination design are studied. In section 3, a monolithic infrared/laser dual-band CFIL is designed, and the stray light suppression structure is designed and analyzed. This system realizes the monolithic and miniaturization of the infrared/laser dual-band system, and provides a new idea for the design of dual-band CFIL.
2. Design method of monolithic dual-band CFIL and stray light suppression
2.1 Monolithic infrared/laser dual-band CFIL design method
The light splitting structure is critical for the dual-band system, it determines the size of the system. If the design of the dual-band CFIL is to be realized, the optimal splitting mode needs to be selected according to its optical path structure. Figure 1 shows a paraxial model lens with a focal length of $f^{\prime}$. Figure 2 (a), Fig. 2 (b), and Fig. 2 (c) depict three types of beam splitting for a CFIL with paraxial reflection. The light splitting methods shown in Fig. 2(a) and Fig. 2(b) lead to a longer total system length, and the optical path in Fig. 2(b) will be blocked by the external structure of the detector. The light splitting method in Fig. 2 (c) is the best choice among the three light splitting methods, because the reduced volume and reasonable space allocation can be achieved.
For CFIL, central obscuration depends on the second reflective surface. We use the geometric structure in Fig. 1 and Fig. 2 (c) to find the relationship between the central obscuration diameter and various parameters in the system. In Fig. 1, $f^{\prime}$ is the focal length of the system, and N is the number of light folds, which is also the reflection number of the CFIL, L is the back focal length of the optical system. The total length T of the folded system can be expressed as:
It can be seen from the Eq. (1) that longer system lengths have longer focal lengths, so the optical path with a long focal length needs more reflections to ensure the optical path folding effect. A large focal length band with more reflection times has a greater impact on the system structure, so the band with a large focal length is mainly used in parameter analysis. In Fig. 2(c), d is the central obstruction diameter, ${a_1}$ is the difference between the outer radius of the first annular reflective surface and the central obstruction radius, ${a_2}$ is the difference between the outer radius of the first annular reflective surface and the radius of the image plane. According to the relationship between the parameters, the Eq. (2) is obtained:
which, where FOV is the field of view. Substituting Eq. (3) and Eq. (4) into Eq. (2) gives:Furthermore, Eq. (6) of the obscuration ratio α can be obtained through the obscuration ratio equation $\mathrm{\alpha } = \frac{d}{D}$:
If the mirrors are closely arranged and there is no overlap, the relationship between the system parameters should satisfy the Eq. (5). In Fig. 3, the geometric relationship curves of the CFIL are shown, where the purple, red, and blue curves represent field-of-view angles of 5°, 10°, and 15°, in respectively. In Fig. 3(a), the relationship curve between the back focal length L and the central obscuration diameter d is shown. When the back focal length increases, the central obscuration diameter also increases linearly, so the smallest possible back focal length is selected in the design. In Fig. 3(b), the relationship curve between the entrance pupil diameter D and the obscuration ratio is shown. It can be analyzed from the curve that under the same entrance pupil diameter, central obscuration increases as FOV increases. In addition, the pupil diameter decreases as the obscuration ratio decreases at the same FOV. When the diameter of the entrance pupil is less than 60 mm, the obstruction ratio decreases greatly. Conversely, the magnitude of change in the obscuration ratio is slow when the entrance pupil diameter is greater than 60 mm.
Fig. 3. The geometric relationship curve of the CFIL (a) back focal length and central obscuration diameter (b) entrance pupil diameter and obscuration ratio
The increase in the central obscuration diameter will affect the modulation transfer function (MTF) of the system. To compare with the circular aperture system, the expression of defining the effective aperture diameter for the annular aperture is:
where ${D_{eff}}$ is the equivalent optical diameter, D is the outer diameter and α is the obscuration ratio.2.2 Stray light suppression method of CFIL
Compared with the traditional coaxial reflective optical system, the special structure of the CFIL contains multiple compactly arranged annular reflectors, so that stray light can enter the detector more easily. In the usage of the CFIL, if there is a strong light source like the sun in the external environment, the image will be covered by severe stray light.
E. J. Tremblay et al. used a honeycomb baffle to suppress stray light in an ultra-thin imaging system [16]. Although the honeycomb baffle is small and can effectively block stray light, this structure also blocks imaging beams, which affects the incident energy of the system. The design of the single-layer hood cannot block the imaging light, but the stray light can be suppressed only if the length is sufficient, so a new hood structure needs to be considered. Based on the structural characteristics of the annular incident surface of the CFIL and the distribution of stray light, a double-layer hood structure is designed.
In Fig. 4, a schematic diagram of the CFIL hood is shown. The frustum cone structure with double layers is adopted, and its cone angle is the same as the field of view of the system. In the analysis of the CFIL, it was found that the stray light conditions of the infrared and laser light paths are different, so the angle and location of the stray light are also different in the infrared and laser light paths. The spot stray light paths for the infrared system and laser system are shown in Fig. 5. One of the important principles of stray light suppression is that no stray light spots can be formed, but the obvious spots can be formed when the light path is similar to Fig. 5. If the light spot with a small angle is suppressed by the hood, the light spot with a large angle will also be suppressed, so it is necessary to find the angle with the smallest stray light spot. These two angles are shown as θ1 and θ2 in Fig. 5, where θ1 is the stray light characteristic angle for long focal length band, θ2 is the stray light characteristic angle for short focal length band.
Fig. 5. Infrared and laser light path spot stray light path diagram (a) long focal length band (b) short focal length band
When the system does not have a stray light suppression structure, the stray light path is analyzed. The angle of the first appearance of stray spots can be obtained by the PST data, and this angle is the stray light characteristic angle. According to the analysis of the stray light path diagram under the stray light characteristic angle, the data of θ1 and θ2 are obtained. This data can be used to calculate the shade structure.
Based on the relationship between the stray light path in the long focal length band and the outer light shield, Eq. (8) and Eq. (9) can be calculated for the critical conditions:
where D1 is the diameter of the bottom surface of the outer hood, D is the diameter of the entrance pupil, θ1 is the stray light characteristic angle, and L1 is the length of the outer hood. Based on Eq. (8) and Eq. (9), the Eq. (10) of the outer hood length is derived as follows:Similarly, based on the relationship between the stray light path in the short focal length band and the inner hood, Eq. (11) and Eq. (12) can be calculated for the critical conditions:
where D2 is the diameter of the bottom surface of the outer hood, D is the diameter of the entrance pupil, θ2 is the stray light characteristic angle, and L2 is the length of the outer hood. Based on Eq. (11) and Eq. (12), the Eq. (13) of the inner hood length is derived as follows:In Fig. 6, the blue curve is the relationship between the outer hood and the field of view, the red curve is the relationship between the inner hood and the field of view. When the field of view is less than 20°, the slope of the inner hood length curve changes slowly and linearly. The length of the outer hood shows a non-linear change, and the slope of the curve increases with the increase of the field of view. This means that the length of the outer hood increases significantly as the FOV increases.
3. System simulation and stray light suppression
3.1 Simulation of monolithic infrared/laser dual-band CFIL
According to the design method of the CFIL in Section 2, the monolithic infrared/laser dual-band CFIL is designed with the design specifications in Table 1. In this design example, the four-reflective structure is selected because the four-reflective structure has better light collection efficiency and smaller diameter than the six-reflective or eight-reflective structures [18].
Table 1. Design specifications of the compression-folding imaging system
According to the optical path structure analyzed in the Section 2.1, the focal length of the infrared system is 56 mm, and the focal length of the laser system is 40 mm. For the splitting surface, the imaging beam in the infrared band is reflected, and the laser band is transmitted. The initial entrance pupil diameter is 66 mm, the initial back focal length is 8 mm, the number of reflections is 4. Substituting the parameters into Eq. (5) results in a central obscuration diameter of 54.65 mm. The IRG24 infrared glass is used as the substrate material, which has excellent transmittance in both the infrared and laser bands [25]. Compared to conventional infrared materials, IRG24 infrared glass has lower dispersion characteristics and a smaller thermo-optic coefficient, and it can be processed by single-point diamond turning technology. Based on the above analysis and calculation, the initial structure of infrared/laser dual-band CFIL with four reflections is constructed. The first reflective surface has the main focal power of the system, and the aberrations of the system are corrected by the other surfaces. Finally, the air between the reflective surfaces is replaced by the substrate material IRG24, and the initial model of the CFIL can be obtained. All surfaces in the initial model of the system are spherical. In order to correct the monochromatic aberration of the system, the spherical surfaces need to be changed to aspherical surfaces. The incident surface, reflective surface, beam splitting surface, and emitting surface in the system are the even aspheric surface type, the expansion can be written as (14):
where z is the vector height of the even-order aspheric surface, K is the conic coefficient, y is the radial height, R is the radius, and A, B, and C are the fourth, sixth, and eighth term coefficients, respectively. Lens data of CFIL are shown in Table 2. In Fig. 7, the system layout of the optimized CFIL is shown. The optimized monolithic infrared/laser dual-band CFIL has an entrance pupil diameter of 66 mm, a total length of 16.5 mm, a ratio of thickness to focal length of 0.305, and an obscuration ratio of 0.751. In Fig. 8, the simulation model of the monolithic infrared/laser dual-band CFIL is shown, where the cyan part is the transmission region, the silver part is the reflection region, the red part is the splitting region, and the black is the absorption region. In Fig. 9(a), the MTF curves for the infrared system is shown. When the spatial frequency is 42lp/mm, the minimum MTF for all fields of view is greater than 0.125 which close to the diffraction limit. In Fig. 9(b), the spot diagram of the laser system is shown. It can be seen that the maximum value of the spot radius is 860µm, the minimum value is 802µm, and spot consistency is greater than 90%.Table 2. Lens data of CFIL
3.2 Tolerance analysis and thermal analysis
The CFIL is processed on both sides of the same base material, and the processing error of the element directly affects the imaging quality. The tolerances of the CFIL include the spacing between the various annulus surfaces, the eccentricity and tilt of each annulus surface, the annulus aspheric surface error, and the surface decenter and tilt errors of the components. The distance between the component and the detector is used as the tolerance compensation. The tolerance setting of the system is shown in Table 3.
Table 3. Tolerance of CFIL
According to the data in Table 3, the influence of tolerance on imaging quality is analyzed. The MTF is used as the standard for systematic evaluation of imaging quality, and the analysis results are obtained in Table 4. It can be seen from Table 4 that the MTF value in the tangential direction is greater than 0.102, and the MTF value in the sagittal direction is greater than 0.105 at 42lp/mm. It can be seen from Table 5 that the maximum RMS value of the spot is 860µm, and the minimum value is 802µm. The results of tolerance analysis show that CFIL has machinability.
Table 4. Tolerance results of CFIL in IR
Table 5. Tolerance results of CFIL in laser band
Parameters such as curvature, thickness, and refractive index of the system are affected by the temperature of the application environment. In order to ensure the stability of the imaging quality, thermal analysis of the system is required. Different from traditional refractive or catadioptric optical systems, the CFIL consists of only a single optical element, so the system exhibit defocus at different temperatures. The distance required to refocus the detector is shown in Table 6, and the detector compensation curve is shown in Fig. 10. Detector compensation is linear in trend. From Fig. 11 and Fig. 12, the MTF of CFIL is greater than 0.1 and the spot diagram is less than 860µm in the temperature range of -20°C to 50°C.
Table 6. Detector compensation distance
3.3 Analysis and suppression of stray light
In this paper, the point source transmittance (PST) is used to evaluate the stray light suppression capability of optical systems, which is defined by the equation:
where θ is the off-axis angle of the stray light source, ${E_d}(\theta )$ is the irradiance received by the detector, and ${E_I}(\theta )$ is the irradiance at the entrance of the optical system. According to the structure in Section 3.1, the PST curves of each band are plotted. The off-axis angle of stray light is from 5° to 90°, and the number of rays traced at each angle is two billion. The logarithmic PST curves of infrared and laser are shown in Fig. 13(a) and Fig. 13(b), respectively. The stray light of the CFIL without suppression structure is serious. The point source transmittance of the infrared system is 10−2 to 10−3, and the point source transmittance of the laser system is 10−3 to 10−4.In order to reduce the PST of the two bands, the stray light suppression structure design method in Section 2.2 is adopted. The direct light incident optical system and focus on the detector. Due to the high energy of the focused spot, it seriously affects the imaging quality. The light path diagram is shown in Fig. 14. Figure 15(a) and Fig. 15(b) are the stray light illumination diagrams of the infrared band and the laser band, respectively.
According to the analysis of stray light, the stray light characteristic angle θ1 = 14.5°, θ2 = 35.2°. Substituting the angle into Eq. (10) and Eq. (13), the lengths of the outer and inner hood are obtained as L1 = 48.7 mm and L2 = 13.3 mm, respectively.
Figure 16 is the illuminance diagram of the infrared and laser light path spots after stray light optimization. In the illuminance diagrams of the two bands, there is no spot formed by the focusing of direct light, and the entire energy is evenly distributed on the image surface, so the stray light is effectively suppressed. The PST comparisons curve about before and after optimization are shown in Fig. 17 in infrared and laser band. The PST curve after stray light optimization is smooth and the overall PST curve drops significantly. In Table 7, the PST data for the key angles of the infrared light path and the laser light path are given.
Fig. 16. Illumination diagram of the spot after stray light optimization (a) infrared light path (b) laser light path
Fig. 17. The PST comparison curve before and after stray light optimization (a) infrared system (b) laser system
Table 7. PST data for critical angles of IR and laser optical paths
For the infrared system, the initial PST value of stray light at an angle of 9° is 0.051916, and the optimized PST value is 1.18E-04; the initial PST value of stray light at an angle of 14.5° is 0.012552, and the optimized PST value is 1.66E-05; the initial PST value of stray light at an angle of 30° is 0.007687, and the optimized PST value is 1.91E-06. The PST value of the off-axis angle less than 14.5° decreased by 2 orders of magnitude, and the PST value of the off-axis angle greater than 14.5° decreased by 2 to 4 orders of magnitude. For the laser system, the initial PST value of stray light at an angle of 8° is 5.504E-05, and the optimized PST value is 1.21505E-06; the initial PST value of stray light at an angle of 14.5° is 0.000147, and the optimized PST value is 1.89008E-06; the initial PST value of stray light at an angle of 20° is 0.000204, and the optimized PST value is 1.88742E-06. The PST value of the off-axis angle less than 14.5° decreased by 1 or 2 orders of magnitude, and the PST value of the off-axis angle greater than 14.5° decreased by 3 to 5 orders of magnitude. Stray light is effectively suppressed at all angles.
4. Conclusion
In summary, a monolithic infrared/laser dual-band CFIL is presented in this paper. The CFIL is applied to the dual-band system, and the structure of the CFIL is reasonably used to design the light-splitting structure, which realizes the miniaturization of the dual-band system. In order to improve the ability to suppress stray light, a double-layer hood structure for the CFIL is designed. According to the design method in this paper, an example of the monolithic infrared/laser dual-band CFIL is designed. In this system, the focal lengths of the infrared band and the laser band are 56 mm and 40 mm respectively, the corresponding field of view are 10.32° and 6.12°, and the total length is 16.5 mm. The design results show that the minimum MTF for all fields of view is greater than 0.125 at 42lp/mm. The maximum value of the spot radius in the laser band is 860µm, the minimum value is 802µm, and spot consistency is greater than 90%. After tolerance analysis, the MTF of CFIL is greater than 0.1, and the spot diagram is less than 880um. The working temperature of the system is -20∼50°C, and the compensation distance of the detector at different temperatures is a linear trend. After stray light optimization, the PST value of the off-axis angle less than 15° in the infrared band is reduced by 2 orders of magnitude, and the PST value of the off-axis angle greater than 15° is reduced by 2 to 4 orders of magnitude. The PST value of the off-axis angle less than 15° in the laser band is reduced by 1 or 2 orders of magnitude, and the PST value of the off-axis angle greater than 15° is reduced by 3 to 5 orders of magnitude. Compared with the traditional co-axial multiple reflectance system, the monolithic infrared/laser dual-band CFIL has a compact optical structure, which provides a new idea for the integration and miniaturization of dual-band systems.
Funding
National Natural Science Foundation of China (62105041).
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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