Axially Symmetric Lens with Extended Depth of Focus
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Solution Overview
Problem
Conventional optical systems using thin lens approximation are inadequate for industrial applications like laser material processing, lithography, and light projection due to limited depth of focus, necessitating an optical system with an extended depth of focus.
Innovation Solution
An axially symmetric physical lens is constructed using a method that involves deducing an equation from depth-of-focus characteristics and Snell's law, with partial differentiation to obtain a differential equation, solved numerically to yield a surface curve, enabling coherent superposition of lens layers for extended depth of focus.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If thin lens approximation is used, then the optical system is simple, but the depth of focus is limited
Solution Approach 1:
The lens surface is divided into multiple axially symmetric layers, each contributing to the extended depth of focus. The segmentation of the focal curve into linear segments allows each lens layer to focus light onto specific segments, creating a composite optical system that achieves extended DOF while maintaining manufacturing feasibility through modular construction.
Solution Approach 2:
The invention transitions from a conventional single-surface lens to a multi-layer axially symmetric structure. By adding the dimensional complexity of multiple layers with different focal characteristics, the system extends the depth of focus beyond what a simple thin lens can achieve, resolving the contradiction between simplicity and DOF performance.
2Manufacturing precision
If multiple lens layers are constructed, then the depth of focus is extended, but the manufacturing complexity increases
Solution Approach 1:
The complex lens construction is segmented into manageable axially symmetric layers, each with defined focal characteristics. This segmentation allows the complex manufacturing task to be broken down into standardized repetitive processes, making the extended DOF lens more manufacturable despite the multiple layers required.
Solution Approach 2:
The invention systematically varies parameters such as layer thickness, refractive indices, and focal distances across the multiple lens layers. By controlling these parameters according to the deduced equations and differential relationships, the patent achieves extended depth of focus while providing a systematic manufacturing approach that reduces complexity through parameter standardization.
3Manufacturing precision
If numerical analysis is used to solve differential equations, then accurate lens surface curve is obtained, but the computational complexity increases
Solution Approach 1:
The patent replaces manual or trial-and-error lens design methods with a systematic mathematical approach based on Snell's law and differential equations. By substituting computational mathematics for empirical design, the invention achieves accurate surface curve determination while providing a reproducible design methodology that reduces overall system complexity through formalization.
Solution Approach 2:
The numerical analysis approach allows flexible adjustment of optical parameters (refractive indices, focal distances, layer thicknesses) to achieve desired depth of focus characteristics. This parameter-based design methodology provides accurate surface curves while maintaining computational efficiency through systematic variation of key parameters rather than complex iterative optimization.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The resulting optical system provides a clear image across a range of distances with improved symmetry, simplified point spread function, and continuous lens surface, enhancing image clarity and focus in industrial applications.
Implementation Method 1
an equation is deduced by substituting a depth-of-focus characteristic and a relation between vectors at a point of the lens surface into Snell's law
Data Source
AI summary
A method of constructing a physical lens based on depth of focus characteristics and an axially symmetric lens with an extended depth of focus constructed by the method are provided. An expression is deduced by substituting a depth of focus characteristic and a relation between vectors of arbitrary points on a lens surface into Snell's law, and partial differentiation is performed on the expression to yield a differential equation satisfied with arbitrary points on the lens surface. The differential equation is solved by, for example, numerical analysis to obtain a curve of an axially symmetric physical lens surface.