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Abstract
A novel imaging system design is proposed, in which the FOV and maximum resolution are improved simultaneously while the detector remains fixed. These improvements are realized using freeform optical surfaces and field-dependent characteristic parameters. The resulting imaging system design has optical properties that vary continuously with the field angle. In the central FOV, the system is equivalent to a long-focal-length camera, while in the marginal FOV, it is equivalent to a short-focal-length camera; however, the system has a constant F-number across the FOV. A 2× variation in the field-dependent characteristic parameters across the FOV is achieved.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The field-of-view (FOV) and the focal length are important specifications for imaging systems. The FOV reflects the range of objects that can be observed and the focal length reflects the resolution of the imaging system. If the full FOV of an imaging system is 2ω, where the FOV angle is ω, the relationship between the image height H and the focal length f is given by H = ftanω. When H is fixed, if the focal length is increased, the resolution will also increase, and the range of objects that can be observed will decrease. Imaging systems are commonly expected to be designed with larger FOVs and longer focal lengths, but the equation H = ftanω indicates that the focal length f and FOV angle ω cannot be increased simultaneously when the image height H remains unchanged. It thus appears that this contradiction cannot be resolved within a single imaging system. Finding a way to design an imaging system that has a large FOV and a long focal length simultaneously, which would provide a larger observation range and higher resolution, is therefore one of the most challenging subjects in optical design.
It is relatively difficult to produce an imaging system with a large FOV and a long focal length. On the one hand, the image size of the system may be very large and a sufficiently large detector must then be found. On the other hand, the system volume may be very large, which results in increased difficulty in system fabrication. To realize an imaging system with a larger FOV and high resolution, one possible solution is to integrate multiple cameras into a single system. One example of such a system is the multi-scale camera, which has an objective lens surrounded by an array of secondary microcameras and can realize megapixel- and gigapixel-scale imaging using a small entrance pupil [1,2]. Similarly, a biologically-based artificial compound eye lens has been able to achieve an extremely large FOV on a small detector by a process of stitching sub-apertures [3,4]. With multiple lenses integrated into a single system, both the resolution and the FOV of the system were improved by expanding the scale of the lens array, where each lens in the system still satisfied the relationship H = ftanω.
Conventionally, in the equation H = ftanω, the focal length f is a constant for a given non-zooming imaging system. The optical properties of the non-zooming system are considered to be fixed and are described using only one set of first-order parameters, e.g., the focal length, the entrance pupil diameter and the F-number. However, imaging systems can have different optical properties for objects set at different field angles and these properties are defined as the field-dependent optical properties of the optical system [5]. These field-dependent characteristics reflect the differences between the optical properties at different field angles in the system. Sometimes, these differences in the system can be large and the system should then be described using field-dependent parameters. In other words, the optical power of the system varies with the field angle and this feature cannot be described using the conventional first-order parameters.
In previous work, a field-dependent parameter called the field focal length (FFL) was proposed to describe the focal length of each field in an imaging system [5], and the FFL can be used to calculate the resolution values at the different field angles. In an imaging system, if the FFL at a specific field angle is larger, then the system resolution at this field angle is higher and the corresponding partial image height will also be larger. Additionally, if the FFL at a specific field angle is smaller, then the system resolution at this field angle is also lower and the corresponding partial image height will be smaller. However, in conventional imaging systems, there are small differences between the FFLs at the different field angles, and thus the system resolutions at the different fields are close.
Using the field-dependent properties described above, the imaging system FFL can be designed to ensure that both the FOV and the resolution can be improved simultaneously while the detector remains fixed. First, we consider a conventional imaging system that has a large FOV and a specific focal length. Then, we increase the partial image height that corresponds to the central part of the FOV and reduce the partial image height that corresponds to the marginal part of the FOV, while the full image height is unchanged. Consequently, the FFL at the central field angle is increased, the maximum resolution is thus also increased and the FFL of the marginal field angle is reduced, but the large full FOV of the system is maintained throughout.
During the design of imaging optical systems, both the focal length and the entrance pupil size must be considered, and this is also true for systems with designed field-dependent optical properties. As stated above, the focal length for each field can be described using the FFL. To describe the entrance pupil size for each field, a new field-dependent parameter called the field entrance pupil (FENP) is proposed in this paper. In addition, based on the FFL and the FENP, another new field-dependent parameter called the field F-number (FFN) is defined. As with the first-order parameters in imaging systems, these field-dependent parameters, i.e., the FFL, FENP and FFN, can be used to describe the optical properties of each field in an imaging optical system.
In this work, the FFL, FENP and FFN are used to characterize and direct the design of a stripe-field three-mirror freeform imaging system that has carefully designed field-dependent optical properties across its FOV. The FFL of this system is longer at its central field than at its marginal field. The system’s performance is thus equivalent to a long-focal-length camera in its central field and to a short-focal-length camera in its marginal field.
Design of an imaging system that offers both pre-designed field-dependent optical properties and good imaging quality at the same time is a new challenge. Freeform optical surfaces provide powerful abilities to correct aberrations in an optical system by providing the system with more degrees of freedom. Benefiting from the advancement in processing and design method [6–8], freeform surfaces are becoming feasible in practical application. Use of freeform surfaces allows better system performances and specifications to be achieved in both imaging and illumination systems [9–11], and also allows optical systems with novel functions and features to be realized [12]. The high number of degrees-of-freedom of freeform surfaces is conducive to the design of an imaging system with specially-designed field-dependent properties. In this work, a direct design method is proposed that can be used to calculate the shapes of the freeform surfaces in the system according to the FENP sizes that are given at the different field angles. An initial system with the designed field-dependent characteristics can be obtained using the proposed method and this then provides a good starting point for further optimization.
2. Field-dependent characteristic parameters of the imaging optical system
2.1 Review of the field focal length
First, the field focal length (FFL) concept must be reviewed. The FFL is the focal length of a specific field within an imaging system and has been defined previously in [5]. In coaxial systems, only the properties within a tangential plane need to be considered. In a non-rotationally symmetrical system with a stripe FOV, only the properties within the plane in which the FOV lies must be considered. However, in a non-rotationally symmetrical system with a rectangular FOV, the optical properties must be characterized at every field position. In this paper, bold letters are used to represent vectors. In an imaging system, we consider the specific field ω and its adjacent field ω’. The field ω has two components, denoted by ωx and ωy, which are the angle components in the x and y directions, respectively. The angle between these two fields is Δω and the distance between the two corresponding image points is Δh. The FFL of the field ω is then defined as:
Specifically, when Δωy=0 and Δωx=0, the following holds:
2.2 Principle for simultaneous improvement of the FOV and resolution
For a perfect lens, which is designated Typical System 1, the curve of the variation of the FFL with the FOV is shown in Fig. 1(a). The variation of the FFL and thus of the angular resolution does not show major changes across the FOV. The values of the resolution at the central field and the marginal field are similar. From Eq. (3), the area between the FFL curve and the horizontal axis within the range between −ω0 and ω0 is equal to the full size of the detector, i.e., the black shaded area shown in Fig. 1(a) is equal to H0.
Fig. 1. Curves of FFL variation with the FOV in (a) Typical System 1, (b) Typical System 1 and Novel System 1, (c) Typical System 1, Typical System 2 and Novel System 1, and (d) Typical System 1 and Novel System 2.
An imaging system can be designed to have a specific FFL distribution across the field; this system is designated Novel System 1 and the FFL curve of this system is shown in Fig. 1(b). The FFL in the central field of Novel System 1 is longer than that of Typical System 1. Therefore, the maximum resolution of Novel System 1 is increased when compared with that of Typical System 1. However, the detector size remains unchanged. The area between the FFL curve of Novel System 1 and the horizontal axis within the range between −ω0 and ω0 is equal to H0, and thus the red slash-shaded area and the blue grid-shaded area are equal.
For comparison, we consider another perfect lens, designated Typical System 2, which is designed to have the same maximum resolution as Novel System 1. The full FOV must be reduced if the detector is unchanged. The FFL curve for Typical System 2 is drawn in Fig. 1(c). Comparison of the FFL curves of Novel System 1 and Typical System 2 shows that Novel System 1 can enlarge the full FOV, while the FFL remains long in the central field and high resolution is thus maintained in the central field.
Through appropriate design of the shape of the FFL curve, systems with higher performance can also be achieved. For example, as shown in Fig. 1(d), the FFL in the central field of Novel System 2 is much longer than that in its marginal field, while the area between the FFL curve of Novel System 2 and the horizontal axis within the range from −ω0 to ω0 is still equal to H0. Therefore, the maximum resolution of the system is improved further when compared with that of Novel System 1 and its FOV is much larger than that of a conventional system with the same maximum focal length. In summary, by designing the shape of the FFL curve appropriately and increasing the ratios of the FFL values at the central and marginal fields, the system’s overall performance can be improved. A large object range is covered, while high-resolution images can be achieved by aiming the central field at a specific objective point.
2.3 Field entrance pupil and field F-number
When designing an imaging system, in addition to the focal length, the system aperture must also be considered. In imaging systems, the entrance pupil diameter characterizes the total light flux that enters the system. Division of the focal length by the entrance pupil diameter allows the F-number of the system to be obtained; the F-number characterizes the image irradiance and the limitations of the resolution capability. A three-mirror imaging system that operates in the visual band, which is shown in Fig. 2(a), is considered as an example [13]. The system has a stripe FOV of 70° that varies between −5° and −75° along the y direction, and it has a circular aperture stop (AS) located on the secondary mirror. This example system has a focal length of 75 mm, an entrance pupil diameter of 13 mm, and an F-number of 5.8.
Fig. 2. (a) Example system: three-mirror imaging system with a stripe field. (b) Entrances for light rays from distant fields are separated.
By definition, the entrance pupil of an imaging system is the image of the AS produced by the surfaces that precede it in the system. The entrance pupil is the entrance through which the light rays from each field enter the system. The size and the location of the entrance pupil are calculated using first-order optics, and are among the first-order parameters of optical systems. As shown in Fig. 2(b), by extending the incident light rays from each field, it is evident that entrances for the light rays from two distant fields are separated. Therefore, in imaging optical systems, the locations and sizes of the entrance pupils of the different fields are varied in a physical sense. The field-dependent parameter that describes this phenomenon is called the field entrance pupil (FENP).
In the system shown in Fig. 2(a), the light rays from the different fields use different areas on the primary mirror to form images. The area on the mirror surface that the light rays from a specific field actually use to form images is defined as the working area of that specific field. For a specific field, the image formed using the AS through the working area corresponding to the field is defined as the FENP of this particular field. As shown in Fig. 3, point C is the center of the AS, and U and L are the upper and lower points of the AS, respectively. Points C, U, and L indicate the location and size of the AS. The working area corresponding to the field ω is shown in Fig. 3. By performing real ray tracing, the image of point C acquired through the working area can be obtained as C’, which describes the location of the FENP. The left and right points of the AS and their corresponding images can be obtained via real ray tracing in a similar manner. Points that are located on the edge of the AS, e.g., points U and L, are imaged through the working area and the corresponding image points, i.e., points U’ and L’, describe the shape and size of the FENP, respectively.
In this work, the FENP location and size are calculated via real ray tracing. For the case of a specific field ω and its adjacent field ω’, the angle between these two fields is small and the intersection point of the chief rays of these two fields is at point C’, which is the image of point C. The image points of U and L, which are denoted by U’ and L’, respectively, can be obtained in a similar manner. By following the procedures above, the FENP location and size for each field in the example system are calculated and are drawn as shown in Fig. 4. Note that the left and right edge points of the FENP at every field point are also obtained and drawn in Fig. 4, but these points are overlaid on the joint line of U'C’ and C'L’.
The FENPs calculated using the procedures described above do not necessarily lie perpendicular to the chief ray of the corresponding field. In other words, the line of U'C’ and C'L’ are not necessarily normal to the chief ray, and the edge points obtained for the FENP may not be located on a plane. However, when the FENP in the system is considered, we are more concerned about the actual size of the light beam that enters the optical system than the position and shape of the FENP. Therefore, by projecting the FENP onto a plane that is located at point C and lies perpendicular to the chief ray, the effective FENP can then be obtained. The shape of the effective FENP reflects the shape of the light beam of the specific field, and the size of the effective FENP can be used to describe the energy carried by the light beam and has a practical physical meaning. For the field ω, the shape and size of the effective FENP are described by the function R(ω, φ), where φ is the angle of the aperture in the polar coordinates. If the effective FENP is circular under the field ω, then R(ω, φ) is independent of φ.
The diameter of the effective FENP is denoted by FENPD and is defined as:
2.4 Validity of the field-dependent parameters
In the example system, the FFL, FENPD and FFN values in the y and x directions are calculated at eight field points. The results are shown in Table 1.
Table 1. Values of the field-dependent parameters of the example system
The example system has a focal length of 75 mm, an entrance pupil diameter of 13 mm, and an F-number of 5.8. The optical properties of this example system vary greatly along the y direction (i.e., the direction in which the stripe field lies). The FFLY varies between 48.47 mm and 114.94 mm, while the FENPDY varies between 5.34 mm and 12.96 mm. In contrast, the optical properties along the x direction show little variation. The FFLX is approximately 15 mm and the FENPDX is approximately 16 mm. In the example system, the FENPDY and FENPDX show a major difference and the effective FENP is elliptical. However, the average values of the FFNY and the FFNX are 8.92 and 9.46, respectively, which are reasonably close. In summary, the example system is equivalent to a short-focal-length camera at the end of the field at −75° and a long-focal-length camera at the end of the field at −5°. Later in Section 3, we present a system that has varied field-dependent parameters across the field, while their values in the x and y directions are close at every field position.
Next, the field-dependent parameters are used to calculate optical specifications to verify the validity of the system. The radius of the Airy disk can reflect the system’s ability to distinguish the details of objects, and can also characterize the system resolution. In coaxial systems, the Airy disk diameter is calculated using the formula d=2×1.22×λ×F/#, where λ is the working wavelength and F/# is the F-number. When the field-dependent parameter FFN is used, the scales of the Airy disk in the y and x directions of the field ω are given by:
In coaxial systems, the F-number can be used to calculate the system’s depth of focus. In a perfect optical system, according to the Rayleigh criterion, if the wavefront aberration caused by defocusing is less than 1/4λ, then the system can still be considered to be a perfect imaging system. The amount of defocusing that occurs before and after the Gaussian image point that produces the 1/4λ wavefront error is defined as the depth of focus (DOF). In perfect optical systems, the DOF is calculated using DOF=±2×λ×(F/#)2. Therefore, the DOF of each field in the system is given by:
Table 2. DOF values obtained from the FFN and by real ray tracing
Table 2 shows that the DOF calculated using the FFN is close to the DOF that was obtained by performing real ray tracing. Using the field at −5° as an example, when defocusing amounts of +0.0924 mm and −0.0924 mm are set in the system, the wavefront errors caused by these defocusing amounts are 0.23λ and 0.24λ, respectively. However, if the F-number of 5.8 is used to perform the calculations, the DOF obtained is ±0.0391 mm, which differs considerably from the results obtained using the FFN and by performing real ray tracing.
In conclusion, the field-dependent parameters FFL, FENP, and FFN can be used to characterize the optical properties of the system at the different field positions very well. When compared with the conventional parameters, including the focal length, the entrance pupil diameter and the F-number, the description of the optical system provided by the field-dependent parameters is more accurate.
3. Design of imaging optical system with specific field-dependent optical properties
From the analysis performed in Section 2.2, it is known that when the detector size is fixed, the system’s FOV and resolution can then be increased simultaneously by increasing the ratio of the FFL values at the central field and the marginal field. In this work, a three-mirror freeform imaging system is designed that has a stripe field of 40° that lies along the x direction. The system’s FFL in the central field is twice the value at the marginal field. The AS is located at the secondary mirror. The system specifications are listed in Table 3.
Table 3. Specifications of the designed system
3.1 Design method
A direct design method is proposed to perform the initial design of the imaging system with the given field-dependent optical properties. Using the initial design as a starting point, a system that satisfies the given specifications with sufficiently high imaging quality can be obtained by performing further optimizations.
When designing a system with given FFL and FENPD values, the system must satisfy the following requirements. First, the image height on the image plane for each field angle must be calculated via integration of the given FFL with respect to the field angle to allow the corresponding target image point coordinates to be determined. The light rays from each field should finally reach the image plane at these image points. Second, the shapes and sizes of the light ray bundles for each field that enter the system should be consistent with the shape and size of the given FENPD. In addition, the light rays that are incident from the same aperture position for each field should intersect at the same corresponding positions on the AS plane. For example, the upper and lower rays of each field should intersect at the upper and lower edges of the AS, and the left and right rays should intersect at the left and right edges of the AS, and so on.
The method proposed in this paper is a point-by-point design method based on feature light rays (FLRs) and feature data points (FDPs). This type of method has been proven to be both fast and effective in the design of various types of optical system [15,16]. The FLRs of a specific field are a series of rays at the different apertures that belong to this field. The FDPs on a specific optical surface refers to a series of intersection points of the FLRs for a specific point with the optical surface, and the FDPs contain the information about the coordinates and the normal directions. The basic procedures of the point-by-point design method are described as follows. Using the given object-image relationship, and based on Fermat’s principle and the laws of refraction and reflection, we calculate the propagation paths of the FLRs through the system and the FDPs on each optical surface, and we then obtain the shape for each optical surface via fitting processes. This process is then repeated to calculate the surface shape of each optical surface one by one in a specified order, and an initial system that can be used to perform further optimizations is finally obtained.
The method proposed to design systems with specific FFL and FENP values is given as follows. The following descriptions of the optical system and the associated parameters are given in the global coordinate system o-xyz.
- (1) According to the specifications of the FFL and the FENP given in Table 3, the functions FFLX(ω), FENPDX (ω) and FENPDY(ω) are given, where ω=ωx because ωy=0.
- (2) Without consideration of obscuration, the functions are solved for a three-mirror coaxial spherical system with a focal length equal to FFLX(0). The system’s AS is set on the secondary mirror and its diameter DAS is determined based on the entrance pupil diameters at the central field, i.e., FENPDX(0) and FENPDY(0). Then, the positions and tilt angles of each component in the system are adjusted to eliminate any obscuration. An unobscured system is finally obtained that contains three spherical mirrors, designated M1, M2 and M3, and an AS with a diameter DAS at the secondary mirror.
- (3) A series of field angles ωk (k=1, …, K) is used to provide the feature FOV angles for the subsequent calculations. In this case, because the system is symmetrical in the x direction, only 0≤ωk≤20°, ω1=0 and ωK=20° are required.
- (4) A radial grid GMN(dx, dy) is defined in plane xy, where M and N are integers and dx and dy are the scales of the grid in the x and y directions, respectively. The coordinates of the grid points in GMN are denoted by Gmn(dx, dy) = (dx/2)ρmcosθnx+(dy/2)ρmsinθny, where ρm=m/M, m=0, 1, …, M, θn=n×360°/N, and n=0, 1, …, N−1. Specifically, when dx=dy, GMN is then a circular radial grid.
- (5) Let k=1.
- (6) Consider the set of k fields ω1, ω2, …, ωk, which is denoted by {ωk}. Based on the position of the AS and the shape at the position of M1, the starting points of the chief rays of fields {ωk} are determined on plane xy and these points are denoted by o({ωk}). Because the scales of the light beams of the fields {ωk} in the x and y directions are known and are denoted by FENPDX({ωk}) and FENPDY({ωk}), respectively, radial grids can then be defined on the xy plane and are given by GMN({ωk})=GMN(FENPDX({ωk})×cos{ωk}, FENPDY({ωk})). By shifting the centers of these grids to o({ωk}), a series of new grids is obtained and this series is given as GMN({ωk})+o({ωk}). Using the new grid points as the starting points and by taking the directions of the fields {ωk} as the propagation directions, the FLRs can be defined for all fields and are denoted by FLR({ωk}).
- (7) A grid GMN(AS)=GMN(DAS, DAS) is defined on the AS plane. Then, the FLR({ωk}) that leave the grid points GMN({ωk})+o({ωk}) should intersect with the AS plane at the corresponding points in the grid GMN(AS). Using the mapping relationship given above, the coordinates and the normal directions of the FDPs on M1 are calculated and the freeform shape of M1 is then obtained by fitting.
- (8) A new grid GM'N'({ωk})=GM'N’ (FENPDX({ωk})×cos{ωk}, FENPDY({ωk})) is then defined on plane xy, where M'≥M and N'≥N. Therefore, the grid density of GM'N'({ωk}) is greater than that of GMN({ωk}). The FLRs that start from GM'N'({ωk})+o({ωk}) are defined and are denoted by FLR'({ωk}).
- (9) Using Eq. (3), the image heights of field {ωk} are calculated by integrating the FFL with respect to the field angle over the range from 0 to {ωk}. The target image point coordinates can then be obtained and are denoted by IMG({ωk}).
- (10) According to the object-image relationship in the system, through deflection by M1, M2, and M3, the FLR'({ωk}) should eventually intersect with the image plane at IMG({ωk}). Using the mapping relationship given above, the coordinates and the normal directions of the FDPs on M3 can be calculated and the freeform shape of M3 can then be obtained by fitting.
- (11) Using the object-image relationship above, the coordinates and normal directions of the FDPs on M2 are calculated and the freeform shape of M2 is then obtained by fitting.
- (12) Because the shape and the position of M2 have been changed, the placement of the AS will then need to be reset.
- (13) Let k = k+1, and then repeat steps (6) to (12) until k = K.
Fig. 6. Flow chart of the proposed design method for imaging system with the given field-dependent optical properties.
3.2 Design results
The FFLX of the system is 40 mm in the central field and 20 mm in the marginal field. Let the function for FFLX be
The FENPDX and FENPDY of the system are 20 mm in the central field and 20 mm in the marginal field, while the FFNX has a constant value of 2 across the FOV. Therefore, let the function of FENPDX,Y be:
Because the system is symmetrical in the x direction, only the fields in half of the full FOV need to be considered. Six fields denoted by ωk (k=1, …, 6) are selected as the feature fields for the subsequent calculations and are separated by intervals of 4°. When the FDPs and the shape of M1 are calculated, the grid used is GMN,{ωk}, where M=3 and N=16. Figure 8(a) shows the FLRs of field ω1 that are incident on M1; these FLRs were obtained based on GMN,{ωk}. When the FDPs and shapes of M2 and M3 are calculated, the grid used was GM'N’,{ωk}, where M'=6 and N'=16. Figure 8(b) shows the FLRs of field ω1 that are incident on M1, where the FLRs were obtained based on GM'N’,{ωk}. The FLRs for all six fields that enter the system are shown in Fig. 8(c). The diameter of the light beam in the central field is twice that in the marginal field.
Fig. 8. (a) FLR(ω1) used to calculate the shape of M1. (b) FLR'(ω1) used to calculate the shapes of M2 and M3. (c) FLR'({ωk}, k=1, …, 6) used to calculate the shapes of M2 and M3. The starting points of all light rays are located on a plane that lies perpendicular to the chief ray of the corresponding field.
Using Eq. (11) and Eq. (3), the image heights can be obtained for each field, with results as shown in Table 4.
Table 4. Image heights for each field obtained via integration of the FFL with respect to the field angle
The system that is eventually obtained using the proposed method is shown in Fig. 9(a). The AS is located at M2, and DAS=14.67 mm. This system contains three freeform mirrors with shapes that are described using XY polynomials with terms ranging up to the 4th order. The associated modulation transfer function (MTF) curve is shown in Fig. 9(b).
The FFL, FENPD and FFN of the system are listed in Table 5 and the variations of the curves of the FFL and FENPD with the FOV are shown in Fig. 10. The FFL and the FENPD of each field are close to the given specifications, and the system obtained can thus be used as a good starting point for further optimization to improve the system imaging quality.
Table 5. FFL, FENPD and FFN values of the designed system
The constraints used in the optimization process are as follows. (1) The upper, lower, left and right light rays are constrained to intersect with the AS plane at their corresponding edge points. (2) The image height of each field is controlled because FFLX is determined by the image height. (3) The FENPDX and FENPDY of each field are controlled. (4) A small field of 0.1° is added to ensure that the FFLY is controlled. After optimization, the final system design obtained is as shown in Fig. 11(a) and its MTF curve is shown in Fig. 11(b).
The FFL, FENPD and FFN values for each field are listed in Table 6 and the variations in the curves of the FFL and FENPD with the field angle are shown in Fig. 12.
Table 6. FFL, FENPD and FFN values of the final system design
4. Conclusion
The final system design is equivalent to a camera that contains multiple lenses aimed in the directions of different field angles, as illustrated in Fig. 13. In this camera, the lenses have various optical specifications across the FOV and also have independent detectors. The lens located at the central field has a focal length of f=40 mm and an entrance pupil diameter of D=20 mm, while each lens located at the marginal field has a focal length of f/2 = 20 mm and an entrance pupil diameter of D/2 = 10 mm. In this work, the final system design has the FFLX,Y varying from approximately 20 mm to 40 mm and the FENPDX,Y varying from approximately 10 mm to 20 mm. The system’s FFNX and FFNY across the FOV have a constant value of approximately 2. The field-dependent parameters and thus the optical properties change continuously with variations in the field angle, and a continuous image is formed on one integral detector. The novel design proposed in this work can realize the function of a splicing camera containing multiple lenses in a single imaging system.
Fig. 13. The final system design is equivalent to a splicing camera composed of multiple lenses. The field-dependent parameters change continuously in the proposed design. The function of the multiple-lens camera is realized in a single system using the FFL, the FENP and the FFN to characterize the optical properties of each field.
In this paper, an imaging system design is proposed based on use of the FFL, a field-dependent characteristic parameter, which can improve the system’s FOV and maximum focal length simultaneously, and can thus also improve the maximum resolution when the detector size and the pixel size are fixed. The proposed imaging system will have a wide application in the field of such as remote sensing and traffic monitoring, where large observing range and high resolution are required simultaneously. A design method is proposed to design such systems using specific field-dependent parameters. Under the direction of field-dependent characteristic parameters that include the FFL, the FENP and the FFN, and by using the high number of degrees of freedom of optical freeform surfaces, a three-mirror freeform system is obtained in which the FFL and the FENPD at the central field are twice the corresponding values at the marginal field, while the FFN remains constant across the FOV. The system has a full FOV of 40°, an FFL of 40 mm, and an FENPD of 20 mm at the central field, and an FFL of 20 mm and an FENPD of 10 mm at the marginal field. In this work, it is verified that imaging systems with large variations in their field-dependent parameters can be realized and an effective system design method is proposed. The ratio of the FFL and the FENPD at both the central field and the marginal field is 2, but the system’s FOV and maximum focal length can be improved further by increasing this ratio. Based on the proposed design method, this type of system having rectangular field-of-view, smaller volume and more compact structure are possible to be achieved. By appropriate design of the shapes of the curves of these field-dependent parameters with respect to the field angle, additional designs with novel and interesting functions could also be realized.
Funding
National Natural Science Foundation of China (61775116).
Acknowledgment
We thank Dr. Jannick P. Rolland and Dr. Aaron Bauer, from Institute of Optics, University of Rochester, for stimulating discussion about this work.
Disclosures
The authors declare no conflicts of interest.
Supplemental document
See Supplement 1 for supporting content.
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