Freeform Imaging Systems Research Articles

Description and tolerance analysis of freeform surface figure error using specific-probability-distributed Gaussian radial basis functions.

Freeform surfaces have important applications in optical design. However, the complex surface figure error of freeform imaging systems affects the performance of as-built systems. In this paper, a method for the representation and tolerance analysis of the freeform surface figure error using a sum of specific-probability-distributed Gaussian radial basis functions is presented. This method is easy-used and practical. In addition, the actual manufacturing difficulty of different areas of the freeform surface is considered. Tolerance analysis of a nonsymmetric freeform off-axis three-mirror system was performed, including considering only the surface figure error, as well as an overall tolerance analysis considering both figure error and assembly error. The results demonstrated the effectiveness and feasibility of the proposed 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.

Phase space aberrations in freeform and gradient index imaging systems

Phase space provides the natural formalism with which to formulate optical imaging problems as a system with constraints. We consider the general formulation of optical imaging problems and look at two examples. The first example is a completely asymmetric freeform prism that has titled surfaces. The second example is a gradient index medium that is exactly solvable. This gives an alternative formalism to standard Seidel aberrations and nodal aberration theory, which can be used in the design process.

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.

Multiple surface expansion method for design of freeform imaging systems.

The relative aperture size and the field-of-view (FOV) are two significant parameters for optical imaging systems. However, it is difficult to improve relative aperture size and FOV simultaneously. In this paper, a freeform design method is proposed that is particularly effective for high performance systems. In this step-by-step method, the FOV is enlarged from a small initial value in equal-length steps until it reaches the full FOV; in each step, part of the area of one system surface is constructed. A freeform off-axis three-mirror imaging system with large relative aperture size and a wide FOV is designed as an example. The system operates at F/2.5 with 150 mm effective focal length and a 60° × 1° FOV. The average root-mean-square wavefront error of the system is 0.089λ (working wavelength λ = 530.5 nm).

Automated design of freeform imaging systems

The automated design of imaging systems involving no or minimal human effort has always been the expectation of scientists, researchers and optical engineers. In addition, it is challenging to choose an appropriate starting point for an optical system design. In this paper, we present a novel design framework based on a point-by-point design process that can automatically obtain high-performance freeform systems. This framework only requires a combination of planes as the input based on the configuration requirements or the prior knowledge of designers. This point-by-point design framework is different from the decades-long tradition of optimizing surface coefficients. Compared with the traditional design method, whereby the selection of the starting point and the optimization process are independent of each other and require extensive amount of human effort, there are no obvious differences between these two processes in our design framework, and the entire design process is mostly automated. This automated design process significantly reduces the amount of human effort required and does not rely on advanced design skills and experience. To demonstrate the feasibility of the proposed design framework, we successfully designed two high-performance systems as examples. This point-by-point design framework opens up new possibilities for automated optical design and can be used to develop automated optical design in the areas of remote sensing, telescopy, microscopy, spectroscopy, virtual reality and augmented reality.

Design of image-side telecentric freeform imaging systems based on a point-by-point construction-iteration process

In this Letter, we present a novel design method of image-side telecentric freeform imaging systems. The freeform surfaces in the system can be generated using a point-by-point design approach starting from an initial system consisting of simple planes. The proposed method considers both the desired object–image relationships and the telecentricity at the image-side during the design process. The system generated by this method can be taken as a good starting point for further optimization. To demonstrate the benefit and feasibility of our method, we design two freeform off-axis three-mirror image-side telecentric imaging systems in the visible band. The systems operate at F/1.9 with a 30 mm entrance pupil diameter and 5° diagonal field-of-view. The modulation-transfer-function curves are above 0.69 at 100 lps/mm.

Starting configuration design method of freeform imaging and afocal systems with a real exit pupil.

Optical system configurations with a real exit pupil have important applications. However, there are few effective design methods of these systems for choice, especially for the systems using freeform surfaces. In this paper, we propose a novel starting configuration design method of freeform optical systems with a real exit pupil before the image plane. This method works for both the cases of imaging systems with optical power and afocal systems. Each single freeform surface in the starting configuration is generated directly using the light rays of multiple fields and different pupil coordinates. With a proposed multi-step design strategy, not only the given system specifications and the desired object-image relationships (or magnification for the afocal system) are achieved, the generation of a real, small-distorted exit pupil with a given size and shape (which means the imaging relationships of the pupils) can be also considered. The system generated by this method can be taken as a good starting configuration for further optimization. The benefits and feasibility of this design method are demonstrated by two design examples. One example is a freeform off-axis three-mirror imaging system. The other example is a freeform off-axis three-mirror afocal telescope. Both of the systems have a modulation transfer function (MTF) that is closed to the diffraction limit.

Construction method through forward and reverse ray tracing for a design of ultra-wide linear field-of-view off-axis freeform imaging systems

In this paper, a construction method through forward and reverse ray tracing for a design of ultra-wide linear field-of-view (FOV) off-axis freeform systems is proposed. The freeform initial system is numerically constructed by a point-by-point calculation. This method begins with a spherical system solved by the paraxial optical theory. In this method, the primary mirror is calculated through the reverse ray tracing; hence, the size and position of the aperture stop is not affected by the changes of mirrors. The fields in the reverse system are selected to cause certain beam overlaps on the primary mirror between adjacent fields. These overlaps offer a more uniform distribution of data points, improving the calculation of this mirror. As an example, an off-axis freeform system with an ultra-wide linear field-of-view of 70° is designed by this method. The effective focal length of the system is 75 mm, and the F-number is 5.8. The diffraction-limited performance of this freeform system in the visible band and the near infrared and near ultraviolet bands validate the construction method presented in this paper.

Direct design of freeform surfaces and freeform imaging systems with a point-by-point three-dimensional construction-iteration method.

In this paper, we proposed a general direct design method for three-dimensional freeform surfaces and freeform imaging systems based on a construction-iteration process. In the preliminary surfaces-construction process, the coordinates as well as the surface normals of the data points on the multiple freeform surfaces can be calculated directly considering the rays of multiple fields and different pupil coordinates. Then, an iterative process is employed to significantly improve the image quality or achieve a better mapping relationship of the light rays. Three iteration types which are normal iteration, negative feedback and successive approximation are given. The proposed construction-iteration method is applied in the design of an easy aligned, low F-number off-axis three-mirror system. The primary and tertiary mirrors can be fabricated on a single substrate and form a single element in the final system. The secondary mirror is simply a plane mirror. With this configuration, the alignment difficulty of a freeform system can be greatly reduced. After the preliminary surfaces-construction stage, the freeform surfaces in the optical system can be generated directly from an initial planar system. Then, with the iterative process, the average RMS spot diameter decreased by 75.4% compared with the system before iterations, and the maximum absolute distortion decreased by 94.2%. After further optimization with optical design software, good image quality which is closed to diffraction-limited is achieved.

Design of freeform imaging systems with linear field-of-view using a construction and iteration process

In this paper, a design method based on a construction and iteration process is proposed for designing freeform imaging systems with linear field-of-view (FOV). The surface contours of the desired freeform surfaces in the tangential plane are firstly designed to control the tangential rays of multiple field angles and different pupil coordinates. Then, the image quality is improved with an iterative process. The design result can be taken as a good starting point for further optimization. A freeform off-axis scanning system is designed as an example of the proposed method. The convergence ability of the construction and iteration process to design a freeform system from initial planes is validated. The MTF of the design result is close to the diffraction limit and the scanning error is less than 1 μm. This result proves that good image quality and scanning linearity were achieved.