Fresnel Lens Sheet Deflection Control Formula
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Solution Overview
Problem
Fresnel lens sheets in rear-projection-type displays often suffer from image distortion due to deflection, especially when made thinner, and face challenges in mold releasing during production, with existing solutions failing to adequately address these issues.
Innovation Solution
A Fresnel lens sheet with unit total reflection Fresnel lenses, characterized by a specific relationship between its size, thickness, and modulus of elasticity (H×H/(10×E×T×T)≦3L/2000), and optionally incorporating a backing sheet or lenticular lenses to minimize deflection and improve mold releasing efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Volume of moving object
If the Fresnel lens sheet is made thinner, then the display becomes thinner and more compact, but the Fresnel lens sheet undergoes deflection causing image distortion
Solution Approach 1:
The patent applies parameter changes by establishing a specific mathematical relationship between the sheet thickness T and the deflection amount, given by T≥√(10×E×W×L²/H³). This formula allows optimization of the thickness parameter to achieve the desired balance between display compactness and image quality, ensuring the Fresnel lens sheet is thin enough for compact displays while thick enough to prevent excessive deflection and image distortion
Solution Approach 2:
The patent implements beforehand cushioning by designing the Fresnel lens sheet with sufficient thickness according to the established formula before actual use. This preventive approach ensures that the sheet has adequate rigidity to resist deflection under its own weight and operational conditions, thereby preventing image distortion before it occurs rather than correcting it after the fact
2Volume of moving object
If the Fresnel lens sheet is made thinner, then the display profile is improved, but mold releasing during production becomes difficult
Solution Approach 1:
The patent applies parameter changes by establishing a lower bound for sheet thickness T through the formula T≥√(10×E×W×L²/H³). This parameter optimization ensures the sheet is thin enough for compact displays while maintaining sufficient thickness for easy mold releasing during production, resolving the contradiction between display profile and manufacturing ease
3Volume of moving object
If the Fresnel lens sheet is made thinner, then the display is more compact, but the position of the Fresnel lens shifts causing image position variation
Solution Approach 1:
The patent applies parameter changes by using the thickness formula T≥√(10×E×W×L²/H³) to control the rigidity of the Fresnel lens sheet. By optimizing the thickness parameter, the sheet maintains sufficient stiffness to prevent position shifts of the Fresnel lens under gravitational and operational loads, thereby ensuring image position accuracy while still achieving compact display thickness
4Volume of moving object
If the Fresnel lens sheet is made thinner, then the display profile is improved, but the straight-line image appears curved causing distortion
Solution Approach 1:
The patent applies parameter changes by establishing the thickness formula T≥√(10×E×W×L²/H³) to control the deflection characteristics of the Fresnel lens sheet. By optimizing this parameter, the sheet maintains adequate rigidity to prevent excessive deflection that would cause straight-line images to appear curved, thereby preserving image geometry accuracy while achieving improved display profile
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 solution effectively reduces image distortion and enhances production efficiency by maintaining the Fresnel lens sheet's flatness and ease of mold release, allowing for thinner, higher-quality rear-projection displays.
Implementation Method 1
a Fresnel lens element for refracting the imaging light from the light source that has been spread and projected on the Fresnel lens element, to make the light parallel or almost parallel and emitting this light toward the viewer side
Implementation Method 2
unit total reflection Fresnel lenses arranged on the light-entering side, each unit total reflection Fresnel lens having a light-entering surface and a total reflection surface that totally reflects a part of or all of the imaging light
Data Source
AI summary
The present invention provides a Fresnel lens sheet that scarcely makes the projected image distorted, and others. The Fresnel lens sheet has a plurality of unit total reflection Fresnel lenses arranged on the light-entering side, each unit lens having a light-entering surface and a total reflection surface that totally reflects a part of or all of the imaging light that has passed through the light-entering surface to deflect the light in the desired direction. This Fresnel lens sheet is formed so that it fulfills the relationship H1×H1/(10×E1×T1×T1)≦3L/2000, where H1 represents the length (cm) in the vertical direction of the Fresnel lens sheet; L1, the length (cm) in the horizontal direction of the Fresnel lens sheet; T1, the thickness (cm) of the Fresnel lens sheet; and E1, the modulus of elasticity (kgf/cm2) of the Fresnel lens sheet. Further, by using, to make up the Fresnel lens sheet, a Fresnel-lens-molded sheet having unit total reflection Fresnel lenses and a backing sheet laminated to the light-emerging surface of the Fresnel-lens-molded sheet, improvement in the efficiency of mold releasing operation that is conducted in the production of the Fresnel lens sheet is achieved.