Freeform surface descriptions. Part I: Mathematical representations

2017 ◽  
Vol 6 (5) ◽  
Author(s):  
Anika Broemel ◽  
Uwe Lippmann ◽  
Herbert Gross
Keyword(s):  
Optical Systems ◽  
Freeform Surface ◽  
Surface Representation ◽  
Freeform Surfaces ◽  
Mathematical Representations ◽  
The Right

AbstractOptical systems can benefit strongly from freeform surfaces; however, the choice of the right surface representation is not trivial and many aspects must be considered. In this work, we discuss the general approach classical globally defined representations, as well as the basic mathematics and properties of the most commonly used descriptions and present a new description developed by us for describing freeform surfaces.

Freeform surface descriptions. Part II: Application benchmark

2017 ◽  
Vol 6 (5) ◽  
Author(s):  
Anika Broemel ◽  
Chang Liu ◽  
Yi Zhong ◽  
Yueqian Zhang ◽  
Herbert Gross
Keyword(s):  
Design Optimization ◽  
Influencing Factors ◽  
Design Process ◽  
Boundary Function ◽  
Optical Systems ◽  
Freeform Surface ◽  
Surface Description ◽  
Surface Representations ◽  
The Right

AbstractOptical systems can benefit strongly from freeform surfaces; however, the choice of the right representation is not trivial, and many aspects must be considered. Many possibilities to formulate the surface equations in detail are available, but the experience with these newer representations is rather limited. Therefore, in this work, the focus is to investigate the performance of several classical descriptions as well as one extended freeform surface description in their performance in concrete design optimization tasks. There are different influencing factors characterizing the surface representations, the basic shape, the boundary function, the symmetry, a projection factor, as well as the deformation term describing higher order contributions. We discuss some possibilities and the consequences of describing and using these options with success. These surface representations were chosen to evaluate their impact on all these aspects in the design process. As criteria to distinguish the various options, the convergence over the polynomial orders, as well as the quality of the final solutions, is considered. As a result, recommendations for the right choice of freeform surface representations for practical issues in the optimization of optical systems can be given under restrictions of the benchmark assumptions.

Study on Profile-Adaptive Tool System for Small Robots in Large Freeform Surface Polishing

2010 ◽  
Vol 37-38 ◽  
pp. 1327-1331
Author(s):  
Qi Tong Liu ◽  
Jian Ming Zhan ◽  
Jian Hua Mao
Keyword(s):  
Freeform Surface ◽  
Polishing Process ◽  
Processing Efficiency ◽  
Kinematic Equation ◽  
Freeform Surfaces ◽  
Surface Polishing ◽  
Adaptive Tool

An adaptive tool system of polishing robots for large freeform surface which is installed discoid tool is proposed. To improve processing efficiency, the mechanical of adaptive tool system adjust to curvature changing of large freeform surface is designed. Adaptability of the processing is analyzed and simulated, and kinematic equation of tool system is established. The polishing process of large freeform surfaces with tool system is analyzed.

Inspection Technology for F-Theta Lens: Practices and Discussions

2007 ◽  
Vol 364-366 ◽  
pp. 1191-1196 ◽  
Author(s):  
Hua Li ◽  
Suet To ◽  
Ling Bao Kong ◽  
Chi Fai Cheung ◽  
Wing Bun Lee
Keyword(s):  
Measurement Methods ◽  
Freeform Surface ◽  
Measurement Technology ◽  
Measuring Instruments ◽  
Freeform Surfaces ◽  
Existing Problems ◽  
Laser Scanners ◽  
Pros And Cons ◽  
Lens Surface

This paper presents the inspection technology for a freeform surface component which is named F-theta lens. F-theta lens is widely used in laser scanners, printers, etc. Freeform characterization is one of the main approaches to verify the manufacturing precision of freeform surface. At present, there is still a lack of techniques for the characterization of freeform surfaces. This study aimed to explore some approaches to inspect freeform surfaces. Two types of measurement methods, namely contact and non-contact measurement methods, are employed to measure the F-theta lens surface. The pros and cons, the existing problems, different applications and areas for improvement of the two methods are discussed. A series of advanced measuring instruments are used in the measurement process. A brief description of measurement mechanisms of these instruments is also presented. As a whole, this paper contributes to the development of the precision measurement technology for optical freeform surfaces.

scholarly journals The Manufacturing of a Multi-surface Monolithic Telescope with Freeform Surfaces

2019 ◽  
Vol 215 ◽  
pp. 06004
Author(s):  
Todd Blalock ◽  
Brian Myer ◽  
Brittany Cox ◽  
Jessica Nelson
Keyword(s):  
Mechanical Stability ◽  
Optical Systems ◽  
Optical Performance ◽  
Freeform Surfaces ◽  
Optical Surfaces ◽  
Spherical Surfaces

Monolithic multi-surface telescopes combined with freeform optical surfaces provide improvements in optical performance in a smaller footprint as compared to systems with spherical surfaces, while providing superior mechanical stability to traditional telescope assemblies. Three different monolithic telescope concepts, in different configurations and optical performance were produced as proof of concepts. The results of the telescopes are presented as well as the unique manufacturing and testing challenges to produce these monolithic optical systems.

Features of Teaching Mathematics to Younger Schoolchildren with Speech Defects in the Framework of Inclusive Education

2017 ◽  
Vol 5 (5) ◽  
pp. 26-31
Author(s):  
О. Павлова ◽  
O. Pavlova ◽  
А. Демидова ◽  
A. Demidova
Keyword(s):  
Primary School ◽  
Inclusive Education ◽  
Children With Disabilities ◽  
Teaching Mathematics ◽  
Mathematical Representations ◽  
The Right ◽  
Special Children ◽  
Speech Defects

The article presents an author’s view on the problem of the formation of mathematical representations in children with speech defects that are taught in the primary school in the system of inclusive education. Modern realities are such that children with disabilities have the right to study in ordinary classes on a par with other younger schoolchildren, so the author considers specific changes in the process of organizing the education of special children, in particular – with speech defects, which the teacher must take into account when working in conditions of inclusion.

5-Axis Freeform Surface Milling Using Piecewise Ruled Surface Approximation

1997 ◽  
Vol 119 (3) ◽  
pp. 383-387 ◽  
Author(s):  
G. Elber ◽  
R. Fish
Keyword(s):  
Surface Finish ◽  
End Milling ◽  
Ruled Surface ◽  
Freeform Surface ◽  
Freeform Surfaces ◽  
Surface Approximation ◽  
Side Milling ◽  
Scallop Height ◽  
Ball End Milling ◽  
Milling Operation

This paper presents a 5-axis side milling scheme for freeform surfaces based on automatic piecewise ruled surface approximation. With this scheme, resulting surface finish is accurate and pleasing, and has a smaller scallop height compared to ball-end milling. The ruled surface approximation can be made arbitrarily precise resulting in an overall fast milling operation that satisfies tight tolerances, and smoother surface finish. The class of surfaces that can take advantage of this type of 5-axis milling operation includes both convex and saddle-like (hyperbolic) shapes.

Design and fabrication of imaging optical systems with freeform surfaces

2012 ◽  
Author(s):  
Xin Zhang ◽  
Ligong Zheng ◽  
Xin He ◽  
Lingjie Wang ◽  
Feng Zhang ◽  
...  
Keyword(s):  
Optical Systems ◽  
Freeform Surfaces

scholarly journals Modeling and Analysis of System Error for Highly Curved Freeform Surface Measurement by Noncontact Dual-Axis Rotary Scanning

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 554
Author(s):  
Li Miao ◽  
Linlin Zhu ◽  
Changshuai Fang ◽  
Ning Yan ◽  
Xudong Yang ◽  
...  
Keyword(s):  
High Precision ◽  
Measurement Accuracy ◽  
Rotation Axis ◽  
Optical Probe ◽  
Measuring System ◽  
Freeform Surface ◽  
Normal Vector ◽  
Profile Measurement ◽  
Freeform Surfaces ◽  
System Error

Profile measurement is a key technical enabler in the manufacturing of highly curved freeform surfaces due to their complex geometrical shape. A current optical probe was used to measure nearly rotary freeform surfaces with the help of one rotation axis, because the probe needs to measure along the normal vector of the surface under the limitation of the numerical aperture (NA). This kind of measuring system generally has a high cost due to the high-precision, multi-axis platform. In this paper, we propose a low-cost, dual-axis rotation scanning method for a highly curved freeform surface with an arbitrary shape. The optical probe can scan the surface profile while always keeping consistent with the normal vector of the measuring points with the help of the double rotation axis. This method can adapt to the changes in curvature in any direction for a highly curved freeform surface. In addition, the proposed method provides a system error calibration technique for the rotation axis errors. This technique can be used to avoid the dependence of the measuring system on the high-precision platform. The three key system errors that affect the measurement accuracy such as installation error of the B-axis, A-axis, and XZ perpendicularity error are first analyzed through establishing an error model. Then, the real error values are obtained by the optimal calculation in the calibration process. Finally, the feasibility of the measurement method is verified by measuring one cone mirror and an F-theta mirror and comparing the results to those obtained using commercial equipment. The maximum measurable angle of the system is ±90°, the maximum measurable diameter is 100 mm, and the measurement accuracy of the system reaches the micron level in this paper.

scholarly journals Coordination in theory extension: how Reichenbach can help us understand endogenization in evolutionary biology

Synthese ◽  
2021 ◽  
Author(s):  
Michele Luchetti
Keyword(s):  
Natural Selection ◽  
Evolutionary Biology ◽  
Niche Construction ◽  
Mathematical Representations ◽  
Selection Theory ◽  
Semantic Extension ◽  
Three Stages ◽  
Functional Extension ◽  
The Right ◽  
Natural Selection Theory

AbstractReichenbach’s early solution to the scientific problem of how abstract mathematical representations can successfully express real phenomena is rooted in his view of coordination. In this paper, I claim that a Reichenbach-inspired, ‘layered’ view of coordination provides us with an effective tool to systematically analyse some epistemic and conceptual intricacies resulting from a widespread theorising strategy in evolutionary biology, recently discussed by Okasha (2018) as ‘endogenization’. First, I argue that endogenization is a form of extension of natural selection theory that comprises three stages: quasi-axiomatisation, functional extension, and semantic extension. Then, I argue that the functional extension of one core principle of natural selection theory, namely, the principle of heritability, requires the semantic extension of the concept of inheritance. This is because the semantic extension of ‘inheritance’ is necessary to establish a novel form of coordination between the principle of heritability and the extended domain of phenomena that it is supposed to represent. Finally, I suggest that—despite the current lack of consensus on the right semantic extension of ‘inheritance’—we can fruitfully understand the reconceptualization of ‘inheritance’ provided by niche construction theorists as the result of a novel form of coordination.

scholarly journals Optical System for Led Luminaire

2019 ◽  
pp. 62-67
Author(s):  
A. Kolesnyk
Keyword(s):  
Light Source ◽  
Light Emitting Diodes ◽  
New Technology ◽  
Light Distribution ◽  
Optical Systems ◽  
Light Sources ◽  
Optical Elements ◽  
Light Emitting ◽  
The Right ◽  
Led Luminaire

Lighting devices are an important element of a large number of technical systems, including road, living, industrial lighting, lighting systems of vehicles. It is known that the light instrument must fulfill two basic lighting tasks: to redistribute the light source of light source in the right way and to limit its dazzling effect. The introduction of light-emitting diodes (LEDs) for lighting necessitated a completely new quality in the construction of luminaires. The different production technology required new methods and designing tools. It also challenged designers with new problems to solve. LEDs are light sources emitting in one hemisphere, which requires a special approach to designing an LED lighting unit. However, for the illumination of premises with high spans or streets, roads such a light distribution is not suitable. For luminaires with solid-state light sources, other materials and new technology must be used; moreover, light distribution needs to be formed using different methods. This paper presents the design process of a LED luminaire from concept to implementation, exemplified by road lighting, and describes the methods and procedures used by the designer. Also, technological problems influencing the quality of the above lighting are addressed. Optical systems for LEDs are considered. The peculiarities of the use of secondary optical elements in the form of lenses for purpose of obtaining different diagrams of the spatial distribution of light intensity of light-emitting diodes are analyzed. Features and problems of calculation of secondary optical systems are considered. Massive collimators do not have to be elements that focus a narrow beam of light. They are able to form a beam in accordance with any accepted distribution that is appropriate for a given application. They are also able to form a beam in a specific way that is required for outdoor lighting luminaires. The stages of a project for designing a road luminaire require the application of the knowledge and experience gained in various research projects. The design methods described in this paper have been developed designing activity and are also to be used successfully in lighting production.  

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