Gradient-Index Rod Lens Array for Large Depth-of-Field Imaging
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Solution Overview
Problem
Existing gradient-index rod lenses have large aperture angles, which are not advantageous for achieving a large depth of field, leading to issues in capturing clear images of objects with varying thicknesses and non-uniform surfaces.
Innovation Solution
A rod lens array comprising gradient-index rod lenses with a refractive-index distribution of n(r)=n0·{1−(A/2)·r2} and an aperture angle of 3 to 6°, along with a base glass composition of specific mol% ranges, is used to achieve a depth of field of 1.5 to 3.0 mm and a modulation transfer function of 30% or more at a spatial frequency of 6 lp/mm.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Illumination intensity
If gradient-index rod lenses with large aperture angles are used, then light collection capability is improved, but depth of field deteriorates
Solution Approach 1:
The patent applies parameter changes by precisely controlling the aperture angle parameter to fall within 2° to 8° and the refractive index difference parameter (Δn) to fall within 0.002 to 0.008. This optimization resolves the contradiction by finding the optimal parameter range that simultaneously achieves sufficient light collection capability and adequate depth of field, rather than using excessively large aperture angles that would compromise depth of field.
2Reliability
If gradient-index rod lenses with small aperture angles are used, then depth of field is improved, but light collection capability deteriorates
Solution Approach 1:
The patent resolves this contradiction through parameter optimization by establishing that the aperture angle should be in the range of 2° to 8° and the refractive index difference should be in the range of 0.002 to 0.008. This balanced parameter selection ensures both sufficient light collection capability and adequate depth of field, avoiding the pitfall of using excessively small aperture angles that would compromise light collection.
3Ease of manufacture
If conventional gradient-index rod lenses are used, then manufacturing simplicity is maintained, but imaging quality for non-uniform objects deteriorates
Solution Approach 1:
The patent applies parameter changes by specifying precise ranges for the refractive index difference (0.002 to 0.008) and aperture angle (2° to 8°), which enables conventional manufacturing processes to produce lenses with improved imaging quality for non-uniform objects. This resolves the contradiction by adjusting parameters within manufacturable ranges while achieving superior optical performance.
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 provides a rod lens array with a large depth of field, enabling clear imaging of objects with non-uniform thickness and enhancing the accuracy of appearance inspection.
Implementation Method 1
A gradient-index rod lens is a rod-like (bar-like) lens that has a refractive-index distribution in which the refractive index continuously decreases from the center toward the outer periphery
Data Source
AI summary
A rod lens array 10a includes a plurality of gradient-index rod lenses 1b arrayed to have optical axes parallel to each other, and forms an erecting equal-magnification image. The gradient-index rod lenses 1b each have a refractive-index distribution in a radial direction thereof. The refractive-index distribution n(r) is approximated by n(r)=n0·{1−(A/2)·r2}, where a refractive index at a center of the gradient-index rod lens 1b is represented by n0, a refractive-index distribution constant of the gradient-index rod lens 1b is represented by √A, and a distance from the center of the gradient-index rod lens 1b is represented by r. The gradient-index rod lens 1b has an aperture angle θ of 3 to 6°, the aperture angle θ represented by θ=sin−1(n0·√A·r0), where a radius of the gradient-index rod lens is represented by r0. The rod lens array 10a has an imaging distance of 45 to 75 mm and a depth of field of 1.5 to 3.0 mm with value of modulation transfer function (MTF) of 30% or more at a spatial frequency of 6 lp/mm.