Catadioptric Research Articles

Method of calculation of paraxial design parameters of hybrid catadioptric zoom system with focus tunable elements

Method of calculation of paraxial design parameters of hybrid catadioptric zoom system with focus tunable elements

Design and application of omnidirectional mirror for catadioptric optical system dedicated to high-speed video registration of lightning

Omnidirectional optical mirrors are widely used in many scientific, industrial and military applications but there is still a lot to do to improve their projection characteristics. The paper presents design method for a novel class of omnidirectional mirrors characterized by their settable reflection angle and 3D/2D image projection. Such approach can effectively improve the mirrored image distribution on matrix of optical sensor. A complex mirror curvature was manufactured with application of computerized numerical control milling machines and Physical Vapor Deposition technique. Three prototypes with 15°, 30° and 45° vertical top view angles were tested. Mirrors were applied to get a set of wide range cloud-to-ground lightning video registrations. Analysis of the high-speed video confirmed design assumptions, and using lightning location system data, enabled dimensioning and measurement of the lightning channel geometry in 3D. Proposed method can be easily implemented in other applications involving omnidirectional observation and photogrammetry.

Exact solution of telescopic aplanatic lens and catadioptric optical systems

Exact solution of telescopic aplanatic lens and catadioptric optical systems

An experimental evaluation of Siamese Neural Networks for robot localization using omnidirectional imaging in indoor environments

The objective of this paper is to address the localization problem using omnidirectional images captured by a catadioptric vision system mounted on the robot. For this purpose, we explore the potential of Siamese Neural Networks for modeling indoor environments using panoramic images as the unique source of information. Siamese Neural Networks are characterized by their ability to generate a similarity function between two input data, in this case, between two panoramic images. In this study, Siamese Neural Networks composed of two Convolutional Neural Networks (CNNs) are used. The output of each CNN is a descriptor which is used to characterize each image. The dissimilarity of the images is computed by measuring the distance between these descriptors. This fact makes Siamese Neural Networks particularly suitable to perform image retrieval tasks. First, we evaluate an initial task strongly related to localization that consists in detecting whether two images have been captured in the same or in different rooms. Next, we assess Siamese Neural Networks in the context of a global localization problem. The results outperform previous techniques for solving the localization task using the COLD-Freiburg dataset, in a variety of lighting conditions, specially when using images captured in cloudy and night conditions.

Real-time ghost image characterization for panoramic annular lenses

As a common but troublesome branch of stray light, ghost images in catadioptric optical systems greatly limit the performances of such optics, including panoramic annular lenses (PAL). A versatile and robust real-time characterization algorithm for ghost images in PAL systems is proposed, with a new ray behavior quantifying index. It characterizes any kind of ghost image in the catadioptric unit with a high reliability, regardless of the actual existence of the ghost images. With newly extracted common feature and properly designed numerical methods specified to PAL systems locating representative rays, the evaluation runs almost instantly, allowing itself to be implemented in optical design process to perform real-time analyses on and to suppress ghost images. Multiple examples show the ability of the method on analyzing ghost image behaviors and achieving ghost-image-suppressed PAL designs. Along with further discussions, the potential of extending the method and its possible wider prospects can be reflected.

Ghost Fringe Suppression by Modifying the f-Number of the Diverger Lens for the Interferometric Measurement of Catadioptric Telescopes

A high-precision catadioptric telescope such as a space-borne telescope is usually tested with interferometer to check the optical quality in assembly. The coarse and fine alignment of the telescope are mainly based on the information from the coordinate measuring machine and the fringe pattern of the interferometer, respectively. In addition, further fine-tuning can be achieved according to the variation in wavefront error and Zernike data. The issue is that the vast majority of the catadioptric telescopes contain plural lens surfaces which could produce unwanted ghost fringes, disturbing the wavefront measurement. Technically, off-axis installation to shift away ghost fringes from central interferogram could be acceptable in some cases. Nevertheless, in this paper, the source of ghost fringe in interferometric measurement for catadioptric telescopes is investigated with light path simulation, and a solution of reducing the f-number of the diverger lens is proposed to eliminate the ghost fringe disturbance. Both simulation and experimental results verify the effectiveness of the proposed concept.

Ghost image analysis for pancake virtual reality systems

Pancake optics (also known as polarization-based catadioptric system) has been widely used as the imaging lens for virtual reality (VR) and mixed reality (MR) headsets because of its compact formfactor and excellent image quality. However, such a folded pancake optics not only dramatically lowers the optical efficiency to 25% because of the utilization of a half mirror, but also suffers from ghost images due to the stray light from multiple surface reflections and imperfect polarization control inside the optical system. In this paper, the origins including the light paths of the ghost images are explored by experiment and then analyzed by simulation. The effect of different incident angles on the intensity of each ghost is also investigated.

Design methodology for catadioptric zoom panoramic optical systems based on image plane bending matched correction.

Zoom panoramic optical systems incorporate a panoramic peripheral vision zoom imaging function, enabling swift wide-area coarse and localized precise detection. These systems find applicability in examining pipes and other internal structures. This study centers on the catadioptric zoom panoramic optical system and its associated optical design method. A mathematical model of the front mirror was formulated based on the imaging relationship. Subsequently, the bending of the image plane of the front mirror was computed and simplified through curve fitting. The object surface bending of the zoom subsystem was established correspondingly, leveraging the solution for the mirror bending curve matched correction, culminating in deriving the initial structure of the zoom. Integrating the front mirror and zoom subsystems facilitated the comprehensive design realization of the catadioptric zoom panoramic optical system. A catadioptric zoom panoramic optical system was designed to validate the proposed design method. This study introduces a novel, to the best of our knowledge, conceptual approach to crafting catadioptric zoom panoramic optical systems.

An alternative, versatile, high‐tolerance design of a modified Richter–Slevogt camera, using standard glasses

AbstractPrime‐focus catadioptric astrographs have been used for a long time in various astronomical applications. The prime advantage offered by them is the capability to produce remarkably wide fields of view, and hence generate a huge amount of data in relatively less observation time. An emerging application of such wide‐field astrographs is in the form of telescope arrays. While this has been implemented mostly, using commercial refractive lenses, low‐cost catadioptric objectives can be used as an alternative for wide‐field or high‐contrast array applications. Commercial catadioptric systems are generally available as modifications of Schmidt and Maksutov systems, that too, mostly in the Cassegrain configuration. Here, we present a low‐cost alternative prime focus camera design of Richter–Slevogt configuration, which is in turn an extension of the Houghton correctors. The Richter–Slevogt design has the potential for a very high performance due to several degrees of freedom. The presented one is a 150 mm aperture, system, providing 3.5° (circular) diffraction‐limited FOV (strehl ), using only standard glasses, N‐BK7 and F2. We present the performance analysis, tolerance sensitivity, and statistical (Monte‐Carlo) analysis for this design. Potential applications of the system, other than as an array are also briefly discussed.

Lightweight and High-Stiffness Metal Optical Systems Based on Additive Manufacturing.

To build a long-wave infrared catadioptric optical system for deep space low-temperature target detection with a lightweight and wide field of view, this work conducted a study that encompasses a local cooling optical system, topology optimization-based metal mirror design, and additive manufacturing. First, a compact catadioptric optical system with local cooling was designed. This system features a 55 mm aperture, a 110 mm focal length, and a 4-degree by 4-degree field of view. Secondly, we applied the principles of topology optimization to design the primary mirror assembly, the secondary mirror assembly, and the connecting baffle. The third and fourth modes achieved a resonance frequency of 1213.7 Hz. Then, we manufactured the mirror assemblies using additive manufacturing and single-point diamond turning, followed by the centering assembly method to complete the optical assembly. Lastly, we conducted performance testing on the system, with the test results revealing that the modulation transfer function (MTF) curves of the optical system reached the diffraction limit across the entire field of view. Remarkably, the system's weight was reduced to a mere 96.04 g. The use of additive manufacturing proves to be an effective means of enhancing optical system performance.

Polarization aberration analysis of catadioptric anamorphic optical systems and its effect on the point spread function

Polarization aberration analysis of catadioptric anamorphic optical systems and its effect on the point spread function

Alignment method of intermediate image plane imperfect imaging near-infrared catadioptric system

Alignment method of intermediate image plane imperfect imaging near-infrared catadioptric system

Design of an image-based BRDF measurement method using a catadioptric multispectral capture and a real-time Lambert calibration.

By utilizing a catadioptric system and a calibration Lambertian sample, a compact measurement method of bidirectional reflectance distribution function (BRDF) has been proposed for rapid and accurate measurement. With the help of an ellipsoidal dome mirror, a hyperboloid mirror, and a high-resolution camera, spatial reflectance distributions from reflected directions with a large field of view (FOV) can be obtained. The built-in Lambertian standard allows for real-time calibration to account for fluctuations in the illumination spectrum, effectively reducing the measurement drift and achieving a high accuracy. Moreover, a multispectral camera captures images at 8 spectral bands for accurate spectral color reconstruction from different directions. To verify the method, a prototype capable of fast, high-resolution measurements with a large FOV has been developed for characterizing the scattering properties of objects. It achieves a measured angular range up to 160°. Multispectral BRDF data for each sample can be obtained within 5 minutes with an angular resolution of less than 0.6°. Eight ceramic samples with different colors were selected for the verification of measurement accuracy, and their mean relative bias of BRDF measurement was found to be as low as 2.5%.

Neutral density filter-based catadioptric optical design for thin virtual reality head-mounted device

Virtual reality (VR) has been a popular trending technology affecting the lifestyles of humans. Especially for near-eye displays, VR head-mounted devices (HMDs) are designed accordingly and widely used in different fields. Nowadays, small structure size is a challenge and an urgent need for the VR HMD, while catadioptric optics is an effective and promising approach to solving this problem. Thus, this paper develops three kinds of catadioptric optical systems for thin VR HMDs by adjusting the configuration positions of the light refraction module created by the aspheric lens and the light partial reflection module formed by the neutral density (ND) filter. The comparison results of the three designs in terms of structure size and imaging quality show that multiple reflections during the light divergence process can effectively reduce the thickness of the optical structure. Reasonable transmission during the reflection process is also favorable for size reduction. Based on the designed catadioptric optical module, a varifocal VR HMD is developed to mitigate the vergence-accommodation conflict, thereby improving the image quality and the sensory experience of users.

Equations to design an aplanatic catadioptric freeform optical system.

The present paper introduces a set of equations to design an aplanatic catadioptric freeform optical system. These equations form a partial differential equation system, in which a numerical solution defines the first and last surfaces of the catadioptric freeform optical system, composed of an arbitrary number of reflective/refractive surfaces with arbitrary shapes and orientations. The solution of the equation can serve as an initial setup of a more complex design that can be optimized. An illustrative example is presented to show the methodology introduced in this paper.

A 3D Estimation Method Using an Omnidirectional Camera and a Spherical Mirror

As the demand for 3D information continues to grow in various fields, technologies are rapidly being used to acquire such information. Laser-based estimation and multi-view images are popular methods for sensing 3D information, while deep learning techniques are also being developed. However, the former method requires precise sensing equipment or large observation systems, while the latter relies on substantial prior information in the form of extensive learning datasets. Given these limitations, our research aims to develop a method that is independent of learning and makes it possible to capture a wide range of 3D information using a compact device. This paper introduces a novel approach for estimating the 3D information of an observed scene utilizing a monocular image based on a catadioptric imaging system employing an omnidirectional camera and a spherical mirror. By employing a curved mirror, it is possible to capture a large area in a single observation. At the same time, using an omnidirectional camera enables the creation of a simplified imaging system. The proposed method focuses on a spherical or spherical cap-shaped mirror in the scene. It estimates the mirror’s position from the captured images, allowing for the estimation of the scene with great flexibility. Simulation evaluations are conducted to validate the characteristics and effectiveness of our proposed method.

Power set of stigmatic freeform catadioptric systems.

A method to design catadioptric systems from scratch based on optimizing an element of the power set of stigmatic catadioptric systems is presented. This set contains all possible stigmatic catadioptric systems. The deduction of the set is also presented in this paper, and its derivation is totally analytical. Additionally, an illustrative example of optimization of an element of the mentioned set is presented. The results are as expected.

Optical system design of double-sided telecentric microscope with high numerical aperture and long working distance.

The working distance of the high numerical aperture visible video microscope is extremely short, which greatly limits its application scenarios. To solve this problem, this paper proposes an unobstructed design method of double-sided telecentric microscope with high numerical aperture and long working distance. First, aiming at the obstruction problem of the image-side telecentric catadioptric microscope objective, the structure of the catadioptric optical system is improved. Then, the aspheric design method based on the best aberration compensation is analyzed theoretically to better correct the primary aberration of the high-numerical aperture microscope objective. Finally, a double-sided telecentric microscope optical system with a numerical aperture (NA) of 0.8 and a working distance of 10.0 mm was designed, which is composed of a spherical reflector, a beam splitter plate, a collimating lens group, and an image-side telecentric eyepiece optical system. The design results show that the imaging resolution of this high numerical aperture video microscope is as high as 0.42 µm, and the microscope has a magnification of about 220× for the image with 1080P (1920 × 1080 pixels) resolution. This double-sided telecentric microscope has the advantages of a large field of view, compact structure, good stray light suppression ability, and manufacturability, and has high practical value in the field of high-precision measurement and detection.

High-Speed Rail Tunnel Panoramic Inspection Image Recognition Technology Based on Improved YOLOv5.

In order to meet the fast and accurate automatic detection requirements of equipment maintenance in railway tunnels in the era of high-speed railways, as well as adapting to the high dynamic, low-illumination imaging environment formed by strong light at the tunnel exit, we propose an automatic inspection solution based on panoramic imaging and object recognition with deep learning. We installed a hyperboloid catadioptric panoramic imaging system on an inspection vehicle to obtain a large field of view as well as to shield the high dynamic phenomena at the tunnel exit, and proposed a YOLOv5-CCFE object detection model based on railway equipment recognition. The experimental results show that the mAP@0.5 value of the YOLOv5-CCFE model reaches 98.6%, and mAP@0.5:0.95 reaches 68.9%. The FPS value is 158, which can meet the automatic inspection requirements of railway tunnel equipment along the line and has high practical application value.

Achromatic and Athermal Design of Aerial Catadioptric Optical Systems by Efficient Optimization of Materials.

The remote sensing imaging requirements of aerial cameras require their optical system to have wide temperature adaptability. Based on the optical passive athermal technology, the expression of thermal power offset of a single lens in the catadioptric optical system is first derived, and then a mathematical model for efficient optimization of materials is established; finally, the mechanical material combination (mirror and housing material) is optimized according to the comprehensive weight of offset with temperature change and the position change of the equivalent single lens, and achieve optimization of the lens material on an athermal map. In order to verify the effectiveness of the method, an example of a catadioptric aerial optical system with a focal length of 350 mm is designed. The results show that in the temperature range of -40 °C to 60 °C, the diffraction-limited MTF of the designed optical system is 0.59 (at 68 lp/mm), the MTF of each field of view is greater than 0.39, and the thermal defocus is less than 0.004 mm, which is within one time of the focal depth, indicating that the imaging quality of the optical system basically does not change with temperature, meeting the stringent application requirements of the aerial camera.