Off-axis Reflective Imaging Systems Research Articles

Designing reflective imaging systems with multiple-surfaces-integrated elements using a Gaussian function freeform surface.

We propose a design scheme and method of a freeform off-axis reflective imaging system with multiple mirrors integrated into one element. The use of a multiple-surfaces-integrated element, described by the Gaussian basis functions freeform surface with local and nonsymmetric properties, significantly decreases the system complexity, as well as reduces the assembly and fabrication difficulty, and achieves high imaging performance. The design theory and process including the initial system design, surface conversion, and system optimization are demonstrated in detail. Three design examples are demonstrated to validate the effect and feasibility of the proposed method, and good imaging performance is obtained.

Design of off-axis reflective imaging systems based on freeform holographic elements.

Holographic optical element (HOE) can be used in many areas in optics due to its characteristics of thin structure, flexible wavefront reconstruction/control ability and angular/wavelength selectivity. In this paper, we propose a design method of off-axis reflective imaging systems based on freeform HOEs, which are fabricated by freeform wavefronts. The freeform HOEs offer many degrees of design freedom and can correct the aberrations in nonsymmetric imaging systems. The initial imaging system with freeform HOEs is generated using a point-by-point design approach, and is used for the preliminary design of the imaging system and the freeform recording system of each HOE. Then a joint optimization is conducted for all the systems, simultaneously considering the imaging performance, the diffraction efficiency, the system constraints and fabrication to get the final design results. To validate the feasibility and effectiveness of the proposed method, an off-axis reflective head-up display system with good performance based on freeform HOEs is designed and fabricated. Detailed procedures of the design and development process of the prototype are demonstrated.

Off-axis reflective imaging system design with a conicoid-based freeform surface.

In this paper, we propose an off-axis reflective system design method based on a non-rotational symmetric conicoid-based freeform (CBF) surface description. The base description avoids complicated calculation of decenter and tilt when using the conventional conic expression, thus simplify the system modeling and optimization process, and it can reduce the number of coefficients that needed to represent mild freeform surfaces. A design method that includes the automatic initial system searching, preliminary optimization with rotationally symmetric surface deviation and fine-tuning with non-symmetric surface deviation is proposed. Two three-mirror systems have been designed to demonstrate the feasibility and conveniences of the proposed method.

Automatic design method of starting points of freeform off-axis reflective imaging systems of small volume.

For off-axis reflective systems, there is no effective method that can obtain a small-volume starting point automatically. Reducing system volume using the optimization method is usually a difficult and cumbersome process, which usually takes the designer a long time. This paper proposes a method of designing small-volume starting points of freeform off-axis reflective imaging systems, which does not require human involvement after inputting a planar system, specifications and constraints. In the design example presented in this paper, it took only about ten minutes to obtain a small-volume starting point. The starting point obtained by this method makes the optimization process easier, takes less time of designers and more likely to succeed. In the design example, it is also demonstrated that the method has the ability of establishing small-volume starting points with different specifications, which can be used to quickly estimate the minimum volumes that systems with different specifications can achieve and provide guidance for determination of specifications and optimization.

Freeform optical surface design in an off-axis reflective imaging system by a double seed curve extension algorithm.

A double seed curve extension (DSCE) method is proposed to design a freeform surface directly in an off-axis reflective imaging system. Compared with the basic seed curve extension (SCE) method, the DSCE can effectively reduce the error of freeform surface construction and improve the imaging quality of the off-axis reflective imaging system. In addition, the method can be employed to design an off-axis reflective imaging system consisting of multiple freeform surfaces with several virtual image points set in advance. In order to verify the DSCE method, three examples are given. One is the off-axis freeform one-mirror system, one is a compact off-axis three-mirror imaging system with two freeform surfaces, and the other is an off-axis reflective system with three freeform surfaces. The modulation transfer function (MTF) of the one-mirror system is greater than 0.9 at 20 lp/mm, which is close to the diffraction limit. The average of the sagittal and tangential MTFs of the second system designed by the SCE and DSCE methods are 0.26 and 0.74 at spatial frequency of 20 lp/mm, respectively. And the MTF of the last system designed by the DSCE method is greater than 0.9 at 20 lp/mm, which is better than that of the SCE method.

Optical design of the freeform reflective imaging system with wide rectangular FOV and low F-number

In recent years, freeform optical surfaces have been used increasingly in a variety of off-axis reflective imaging systems with high performance levels. However, it is a difficult and challenging task to design an off-axis reflective imaging system that has a low F-number and a wide rectangular field-of-view (FOV) simultaneously. In this paper, the field extension construction (FEC) design method is proposed to design a freeform imaging system with both a low F-number and a wide rectangular FOV. When using an existing normal system with a small rectangular FOV as the input, an initial configuration that simultaneously has both a low F-number and a wide rectangular FOV can be obtained after several system construction attempts. A freeform reflective infrared camera is then successfully designed after optimization and has a focal length of 9.3 mm, an F-number of 1.39, and a wide rectangular FOV of 40° × 30°. The image quality is close to the diffraction-limited level in the far-infrared band and the maximum relative distortion is 5.5%. In addition, the system prototype is presented after fabrication and its good practical imaging performance is demonstrated.

Manufacturing-constrained optical design methodology for cylindrical freeform reflective imaging system.

Off-axis reflective imaging systems are widely used, but manufacturing issues are seldom considered in their design. This paper proposes a direct design method for cylindrical freeform imaging systems considering manufacturing constraints to facilitate ultraprecise raster milling. The initial freeform shapes of a well-restricted system configuration are constructed using feature data points and calculated based on the constant optical path length condition. An iterative process with coefficient adjustment of the surface expression is employed to optimize the freeform mirrors for both image quality and the degree of deviation from a reference surface. The method's feasibility is validated by designing an off-axis three-mirror imaging system that operates at F/2.0 with a 100 mm entrance pupil diameter and a 4° × 4° field of view. The freeform surfaces are guaranteed to be distributed along a cylinder 150 mm in radius for ultraprecise raster milling.

Off-axis two-mirror laser communication antenna designed using differential equations

In satellite laser communication technology, which is built between planets and between a planet and the Earth, the optical antenna is the key point. Thus, research on optical system design is important. The off-axis reflective system has no obscuration and hence possesses a high efficiency for energy transfer. This study proposes a novel method for designing a free-form off-axis reflective imaging system. This study also introduces differential equations that depend on Fermat’s principle and sine condition. Finally, a free-form off-axis two-mirror optical system was designed by using the differential equation method. This system includes one intermediate image plane, in which the field of view (FOV) is–5° to–4° in the y-axis and–1° to 0° in the x-axis. The modulation transfer function was greater than 0.7 at 50 lp/mm, and the efficiency of energy transmission was high. The free-form off-axis two-mirror optical system involves a wide range of application prospects in the optical antenna used in the satellite laser communication systems. Moreover, the design method that used differential equations was proven simple and effective.

Point-by-point design method for mixed-surface-type off-axis reflective imaging systems with spherical, aspheric, and freeform surfaces.

In this paper, mixed-surface-type optical system is defined as the optical system comprised of various types of surfaces, including spherical, aspheric, and freeform surfaces. A general point-by-point design method for mixed-surface-type systems is proposed. In detail, methods for spherical system design and optical power assignment are proposed during the point-by-point design process. Additionally, three surface evolutions are proposed: from spherical to aspheric surfaces and freeform surfaces, and from aspheric surfaces to freeform surfaces. A mixed-surface-type off-axis three-mirror system is designed as an example and as a starting point for further optimization. The sphere receives most of the system optical power while the freeform surface has little power, which can reduce system fabrication difficulty.

Linear astigmatism of confocal off-axis reflective imaging systems with N-conic mirrors and its elimination.

Linear astigmatism of plane-symmetric confocal off-axis reflective imaging systems with an arbitrary number of conic mirrors is derived. Linear astigmatism, a consequence of tilted astigmatic image planes, is the dominant aberration of this type of imaging system. In this work, the tilt angles of astigmatic image planes are obtained in closed form. An equation to eliminate the linear astigmatism is also derived. The presented theory is verified by examples.

Assembly of a freeform off-axis optical system employing three φ-polynomial Zernike mirrors.

We report on the assembly of an off-axis reflective imaging system employing freeform, φ-polynomial optical surfaces. The sensitivity of the system to manufacturing errors is studied for both a passive and active alignment approach. The as-built system maintains diffraction-limited performance in the long-wave infrared.

Design method of freeform off-axis reflective imaging systems with a direct construction process.

In this paper, a novel method is proposed to design the freeform off-axis reflective imaging systems. A special algorithm is demonstrated to calculate the data points on the unknown freeform surface using the rays from multiple fields and different pupil coordinates. These points are used to construct the multiple three-dimensional freeform surfaces in an imaging system which works for a certain object size and a certain width of light beam. An unobscured design with freeform surfaces can be obtained directly with this method, and it can be taken as a good starting point for further optimization. The benefit of this design method is demonstrated by designing a freeform off-axis three-mirror imaging system with high performance and system specifications. The final system operates at F/1.49 with a 64mm entrance pupil diameter and an 8° × 9° field-of-view (FOV). The performance of the system is diffraction limited at LWIR (long-wavelength-infrared).

Linear astigmatism of confocal off-axis reflective imaging systems and its elimination

Linear astigmatism of a confocal off-axis reflective imaging system when the object plane is tilted and located at a finite distance from the imaging system is derived. We show that linear astigmatism can be eliminated by proper configuration of the parent mirror axes in confocal off-axis two-mirror systems. The tilt angle of the image plane is also derived. The developed theory is verified by ray-tracing analysis of an example system.