Vector Aberration Research Articles

Compact freeform-surface-based Offner imaging spectrometer with both a long-slit and broadband.

Current imaging spectrometers with conventional optical elements face major challenges in achieving a large field of view (FOV), broadband and compact structure simultaneously. In this paper, a compact freeform-surface-based Offner imaging spectrometer with both a long-slit and a broadband (CISLS) is proposed. To keep a long slit and an anastigmatic imaging, the slit off-axis amount of the initial system is within a specific range theoretically. While to achieve a compact structure, the slit off-axis amount should be away from the specific range and as small as possible. Based on the vector aberration theory and the analytical study, Zernike polynomial terms Z5 and Z6 introduce the astigmatism independent of FOV. They are utilized to well balance the astigmatism when the slit off-axis amount is away from the specific range, helping a miniaturization of the system. Other Zernike polynomial terms below the eighth order introduce the astigmatism related to FOV. They contribute to balancing the astigmatism that produced with the increasing of the FOV, thus achieving a wide FOV. The design results show that the proposed CISLS with a high spectral resolution of 2.7 nm achieves a long slit of 30 mm in length but a small size of only 60 mm × 64 mm × 90 mm in volume under a broadband from 400 nm to 1000 nm.

Ultra-compact dual band imaging spectrometer with freeform prisms.

Wide spectrum and miniaturization are the main challenges in the imaging spectrometer design. In this paper, we propose an ultra-compact dual band imaging spectrometer (CDBIS) with cemented freeform prisms, which works at both the visible-near-infrared (VNIR) from 400nm to 1000nm and the shortwave-infrared (SWIR) from 1000nm to 1700nm. The imaging spectrometer is only composed of three cemented prisms, a primary prism and two triangular prisms. And a freeform surface characterized by the Zernike polynomial is introduced in each prism. The CDBIS is dispersed by a diffraction grating, which is designed on the second surface of the primary prism. Based on vector aberration theory (VAT), the relationship among the astigmatism generated by the introduced freeform surfaces, the wavelength, and the field of view is studied. Accordingly, a wideband is realized by introducing the freeform surfaces after the diffraction grating. Furthermore, through optimizing the coefficients of Zernike polynomial terms, residual astigmatism at different wavelengths is well balanced. An imaging spectrometer with a volume of only 100c m 3 is obtained, with a spectral resolution of 1.45nm at VNIR and 2.40nm at SWIR, respectively. It has a huge potential for broadband space exploration.

Design of tilted and decentered anamorphic optical system based on nodal aberration control

This paper proposes a design method for tilted and decentered anamorphic projection optics. In this method, the structure is designed in groups according to the magnification requirements; the anamorphic system section’s primary aberration is analyzed based on vector aberration theory, the tilted and decentered system section’s node behavior is analyzed based on node aberration theory, and spatial ray tracing is used to control the anamorphic optical system’s pupil to be elliptical to realize pupil matching between groups. A mathematical aberration balance and constraint control model is established. The node position is used as an evaluation function such that the node is close to or within the full field, thus controlling the primary aberration for the initial system over the full field. The initial system is constructed with increased optimization potential to satisfy the aberration and structural constraints. The initial structure for the tilted and decentered anamorphic projection optics (βx=1/4,βy=1/8) is constructed with the coma and astigmatism nodes close to or within the full field. The structure is then optimized to achieve a wavefront root-mean-square error for the EUV tilted and decentered anamorphic objective with NA= 0.55 of better than 0.025λ (λ = 13.5 nm).

Design method for an off-axis reflective anamorphic optical system with aberration balance and constraint control.

This paper proposes a design method for an off-axis reflective anamorphic optical system (ORAOS). This method first applies vector aberration theory to establish a mathematical model to balance the aberration of an ORAOS. It then builds the error function of structural parameters and constraints through spatial ray tracing and grouping design. Next, it introduces automatic adjustment of weight factors for dynamic balance of aberrations and constraints. A particle swarm simulated annealing algorithm is used to iteratively calculate the initial structure of the ORAOS. Finally, we use an extreme ultraviolet (EUV) lithographic projection objective with off-axis six-reflective anamorphic mirrors (${\beta _x} = 1/4,{\beta _y} = 1/8$) as an example to verify the effectiveness of this method. We obtain an EUV lithographic anamorphic objective with a numerical aperture of 0.55 and a root mean square wavefront error better than $1/30\lambda$ (${\hat{\text I}}\gg\, = 13.5\;{\rm nm}$).

Analysis method of the Offner hyperspectral imaging spectrometer based on vector aberration theory.

Compact hyperspectral imaging spectrometers with a wide field of view (FoV) have significant application value. However, the aberration field of such imaging spectrometers is sensitive, and varies for different wavelengths when reducing the spectrometer volume. It is difficult to explain the variation in the aberration field using traditional aberration theory. In this study, we extend the vector aberration theory (VAT) to the Offner imaging spectrometer. We deduce the expression of the aberration field decenter vector of the Offner spectrometer based on the real ray-trace method. Furthermore, we derive the expression of the third-order vector aberration of the system. Subsequently, we explain some common phenomena in the Offner imaging spectrometer. This new analysis method can provide useful guidance for designing a compact wide FoV Offner imaging spectrometer. With this new insight, we designed a compact wide FoV Offner imaging spectrometer with a freeform tertiary mirror. Compared to conventional spectrometers with the same specifications, the total length of the spectrometer decreased by 37%, and the volume by 75%. After the tolerance analysis, the freeform optics satisfied the existing machining technology. The analysis method presented in this paper furthers the designer's understanding of the aberration field of the Offner imaging spectrometer. The method is significant in the design of a compact wide FoV Offner imaging spectrometer with freeform optics.

Initial configuration design of off-axis reflective optical system based on vector aberration theory

The traditional method of designing the initial configuration of off-axis reflective optical system is to first obtain the initial configuration of coaxial reflective optical system, and then achieve the unobscured design with an offset aperture stop or a biased input field, or both. Because the aberration distribution of coaxial reflective optical system is not applicable to the off-axis reflective optical system, the obtained unobscured off-axis reflective optical system has large aberration, and the unobscured design process is complicated. In this paper we present a method of designing an initial configuration of off-axis reflective optical system based on vector aberration theory. With this design method, a good unobscured initial configuration of off-axis reflective optical system can be directly obtained by using an offset aperture stop or a biased input field, or both. Based on the vector aberration theory and gaussian brackets, the third-order aberration coefficient is derived for off-axis reflective optical system. Initial configuration performance is important for optical design, especially for the complicated optical system design. The selection of initial configuration highly affects the final system imaging performance, fabrication difficulty and alignment difficulty. An error function is established to evaluate the performance of off-axis reflective optical system, and it consists of aberration coefficients and other constraints. The genetic algorithm is a highly parallel, random and adaptive global optimization algorithm. To obtain a good initial configuration for the off-axis reflective optical system, the genetic algorithm is used to search for the initial configuration with minimum residual aberration. This method can obtain a good initial configuration of off-axis reflective optical system for further optimization. The benefit of this design method is demonstrated by designing an off-axis three-mirror optical system. For the focal plane array, a long-wave infrared off-axis three-mirror optical system is designed. A good initial configuration is obtained with the proposed method, which achieves the unobscured design by using an offset aperture stop and a biased input field. To improve the performance of initial configuration, the obtained initial configuration is optimized with the optical design software. The designed optical system has good imaging quality. As the mirrors are free from the tilts and decenters, the designed optical system is aligned easily.

基于矢量像差的自由曲面光学系统像差特性研究

基于矢量像差的自由曲面光学系统像差特性研究

High performance Czerny–Turner imaging spectrometer with aberrations corrected by tilted lenses

The design of the high performance imaging spectrometer using low-cost plane grating is researched in this paper. In order to correct the aberrations well, under the guidance of the vector aberration theory, the modification of Czerny–Turner system with inserted tilt lenses is proposed. The novel design of a short-wave infrared imaging spectrometer working at between wavelengths of 1–2.5μm is shown as an example, whose numerical aperture achieves 0.15 in image space. The aberrations are corrected well and the Modulation Transfer Function (MTF) performance is the same as the convex gratings systems. The smiles and keystones of the spectral image are acceptable. Advantages of the proposed design with a plane grating are obviously that the diffraction efficiency is high while the cost is very low.

含偏心、倾斜元件的共形光学系统设计

We investigate the aberration properties of the conformal optical system with decentered and tilted elements by vector aberration theory. By decentering and tilting the window and corrector of the system, two elements are effectively used together in a particular manner by aberration compensation to achieve off-axis imaging. A conceptual design is performed with a half-field of 2?, the F# of 4, and the wavelength ranging of 3700~4800 nm. The imaging quality can reach the optical diffraction limit and satisfy corresponding requirements.

Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the comatic aberrations

Building on an earlier work on the nodal aberration theory of the 3rd-order aberrations [J. Opt. Soc. Am. A22, 1389 (2005)] and the first paper in this series on the nodal aberration theory of higher-order aberrations [J. Opt. Soc. Am. A26, 1090 (2009)], this paper continues the derivation and presentation of the intrinsic, characteristic, often multinodal geometry for each type/family of the 3rd- and 5th-order optical aberrations as categorized by parallel developments for rotationally symmetric optics. The first paper in this series on the higher-order terms developed the nodal properties of the spherical aberration family, including W(060), W(240M), and W(242), and for completeness 7th-order spherical aberration W(080). This second paper in the series develops and presents the intrinsic, characteristic, often multinodal properties of the family of comatic aberrations through 5th order, specifically W(151), W(331M), and W(333) [field-linear, 5th-order aperture coma; field-cubed, 3rd-order aperture coma; and field-cubed, elliptical coma (a 3rd-order in aperture 5th-order vector aberration)]. This paper will present the first derivations of trinodal aberrations by the author.

Design of unobscured reflective zoom system with three mirrors

A method for the design of an unobscured reflective zoom system with three mirrors is described. This method applies the vector aberration theory, which helps designers analyze third-order aberrations for optical systems with decentered and tilted surfaces. As the vector aberration theory presents the variation of third-order aberrations in asymmetric systems through analytic expressions, real ray tracing is unnec-essary. Hence, the design with vector aberration theory is faster, and the analytic expressions are more comprehensive and intuitive. To demonstrate the practicability of the method, a design example is given, which shows that the presented method can guide designers achieve a good unobscured reflective zoom system with three mirrors.

基于矢量波像差理论的两镜系统装调技术研究

基于矢量波像差理论的两镜系统装调技术研究

Systematic errors analysis for a large dynamic range aberrometer based on aberration theory

In Ref. 1, it was demonstrated that the significant systematic errors of a type of large dynamic range aberrometer are strongly related to the power error (defocus) in the input wavefront. In this paper, a generalized theoretical analysis based on vector aberration theory is presented, and local shift errors of the SH spot pattern as a function of the lenslet position and the local wavefront tilt over the corresponding lenslet are derived. Three special cases, a spherical wavefront, a crossed cylindrical wavefront, and a cylindrical wavefront, are analyzed and the possibly affected Zernike terms in the wavefront reconstruction are investigated. The simulation and experimental results are illustrated to verify the theoretical predictions.