Convex Protrusion Geometry in TIR Displays for Dark-Pupil Reduction
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Solution Overview
Problem
Conventional TIR-based displays suffer from a 'dark pupil' problem due to non-reflective regions where light rays are absorbed, reducing brightness and overall reflectance.
Innovation Solution
Modifying the shape of convex protrusions in TIR-based displays to optimize height, width, and aspect ratio, using polar coordinate systems and specific equations to enhance reflectance, diffusion, and viewing angle performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Illumination intensity
If conventional hemispherically-shaped convex protrusions are used in TIR-based displays, then the structure is simple to manufacture, but non-reflective dark pupil regions form that reduce brightness and reflectance
Solution Approach 1:
The patent modifies the convex protrusion shape from a conventional hemisphere to a super-ellipse form with the equation |x/a|^n + |y/b|^n = 1, where n > 2. This curvature modification eliminates the dark pupil region by ensuring all incident light rays strike the protrusion surface at angles greater than the critical angle for total internal reflection, thereby maximizing brightness without complicating the manufacturing process
Solution Approach 2:
The patent changes the geometric parameters of the convex protrusion by introducing the super-ellipse equation with specific constraints (n > 2, a > b). This parameter change transforms the light reflection characteristics to eliminate non-reflective regions while maintaining manufacturing feasibility through controlled aspect ratios and dimensional relationships
2Area of stationary object
If the convex protrusions are closely packed to maximize surface coverage, then the reflectance should improve, but the dark pupil problem persists and reduces overall brightness
Solution Approach 1:
By using super-ellipse shaped protrusions with n > 2 instead of hemispheres, the patent ensures that even when closely packed, each protrusion reflects light effectively without creating dark pupil regions. The modified curvature allows maximum surface coverage while maintaining high reflectance across the entire array
3Ease of manufacture
If hemispherically-shaped protrusions are used, then manufacturing is easier, but the reflectance and diffusion performance is suboptimal
Solution Approach 1:
The patent modifies the protrusion shape parameters to a super-ellipse with n > 2, which can still be manufactured using conventional techniques such as injection molding or embossing. The parameter change optimizes reflectance performance while remaining compatible with existing manufacturing processes, achieving high reflectance without sacrificing ease of manufacture
Solution Approach 2:
The super-ellipse curvature with n > 2 provides optimized light reflection properties that improve reflectance and diffusion performance compared to hemispheres, while the overall form remains suitable for conventional manufacturing methods
4Illumination intensity
If conventional protrusion shapes are used, then the device complexity is low, but the viewing angle performance and reflectance consistency vary significantly
Solution Approach 1:
By changing the geometric parameters to a super-ellipse with n > 2 and specific aspect ratio constraints (a > b), the patent achieves consistent reflectance across various viewing angles. The parameter optimization ensures uniform optical performance without requiring complex multi-element structures
Solution Approach 2:
The super-ellipse curvature provides superior viewing angle performance compared to hemispheres, maintaining consistent reflectance across different observation angles while keeping the protrusion geometry as a single, simple mathematical form that does not increase device complexity
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
Enhances brightness and visual appearance by minimizing non-reflective regions, improving overall reflectance and maintaining consistent reflectance across various viewing angles.
Implementation Method 1
Light rays incident upon the interface at angles greater than θc may undergo TIR at the interface. The convex structures may be hemispherically-shaped but other shapes may be used.
Implementation Method 2
Conventional TIR-based reflective image displays further include electrophoretically mobile, light absorbing particles. The electrophoretically mobile particles move in response to a bias between two opposing electrodes.
Implementation Method 3
When particles are moved by a voltage bias source to the surface of the front sheet they may enter the so-call evanescent wave region where TIR may be frustrated. The depth of the evanescent wave region can be typically about 0.25 μm
Data Source
AI summary
Total internal reflection (TIR) based image displays comprise at least one high refractive index (>˜1.5) convex protrusion interfaced with a low refractive index (<˜1.5) medium. Total internal reflection of light is frustrated at this interface by movement of electrophoretically mobile particles into and out of the evanescent wave region. The size, shape and arrangement of the convex protrusions, typically in the shape of lenses, affects TIR at the interface and ultimately the brightness of the display. The brightness is a critical aspect of reflective displays. The degree of brightness determines what applications the displays may be used for and their ultimate acceptance by consumers. For example, high brightness displays allow for the use of color filter arrays for applications requiring color. The shape of the convex protrusions may be described by a polar coordinate system.