Microlens array and optical system including the same

• US 10,443,811 B2
• Filed: 11/23/2016
• Issued: 10/15/2019
• Est. Priority Date: 05/27/2014
• Status: Active Grant

• Current Assignee: Nalux Co., Ltd (Nalux Holdings Corp.)
• Original Assignee: Nalux Co., Ltd (Nalux Holdings Corp.)
• Inventors: Seki, Daisuke, Fujimura, Kayoko, Okano, Masato, Nishio, Yukinobu, Kuwagaito, Tomohito
• Primary Examiner(s): Alexander, William R
• Assistant Examiner(s): O'Neill, Gary W
• Application Number:
  US15/359,716
• Publication Number:
  US 20170074481A1
• Time in Patent Office: Days
• Field of Search: None
• CPC Class Codes: F21V 5/004 using microlenses
• CPC Class Codes: F21Y 2115/30 Semiconductor lasers
• CPC Class Codes: G02B 19/0014 at least one surface having optical power
• CPC Class Codes: G02B 27/425 in illumination systems mask illumination systems in photolithographic systems G03F7/70158
• CPC Class Codes: G02B 3/0043 Inhomogeneous or irregular arrays, e.g. varying shape, size, height

Abstract

A microlens array includes N microlenses arranged in a predetermined direction on an x-y plane. A projection onto the x-y plane of the vertex of each microlens is arranged in the vicinity of a lattice point of a reference lattice on the x-y plane, the lattice spacing of the reference lattice in the predetermined direction being D/M (millimeters) where M is a positive integer. A distance between two sides of a lens facing each other is approximately equal to D, and a distance between the projection onto the x-y plane of the vertex of the lens and the projection onto the x-y plane of a side of the lens is D/2+εi. Letting n represent the refractive index of the material of each microlens and letting f (millimeters) represent the focal length of each microlens, the following relationships are satisfied.

$\frac{0.0042}{D}<\frac{D}{2f}=\frac{D\left(n-1\right)}{2R}$ $0.0048\sqrt{f}\left\{1+{\left(D/2f\right)}^2\right\}<\sigma <0.014\sqrt{f}\left\{1+{\left(D/2f\right)}^2\right\}$ ${\sigma }^2=\sum _{i=1}^N\frac{{\left({\varepsilon }_i-\stackrel{\_}{\varepsilon }\right)}^2}{N}$ $\stackrel{\_}{\varepsilon }=\sum _{i=1}^N\frac{{\varepsilon }_i}{N}=0$

Claims

1. A microlens array including N microlenses arranged in at least one direction on an x-y plane, wherein a projection onto the x-y plane of the lens vertex of each microlens is arranged on or near a lattice point of a reference lattice on the x-y plane, the lattice spacing of the reference lattice in the at least one direction being D (millimeters), and when a boundary between two microlenses adjacent in the at least one direction is referred to as a side of a lens, a projection onto the x-y plane of the side is located approximately at the middle of projections onto the x-y plane of the vertexes of the two microlenses and therefore a distance between two sides facing each other and spaced in the at least one direction is approximately equal to D, and

wherein a distance between a projection onto the x-y plane of a lens vertex i and a projection onto the x-y plane of a side between the lens vertex i and a lens vertex i+1 is

D/2+ε

_i

where ε

_i represents a dispersion of the distance from D/2 and for the N microlenses,

2. A microlens array according to claim 1, wherein in the x-y plane, a boundary between the lens vertex i and the lens vertex i+1, which are adjacent to each other in the at least one direction, is the perpendicular bisector of the line connecting the lens vertex i and the lens vertex i+1, or an amount of displacement of the boundary from the perpendicular bisector is negligible.

3. A microlens array according to claim 1, wherein the reference lattice is rectangular or hexagonal.

4. A microlens array according to claim 1, wherein a projection onto the x-y plane of the vertex of each microlens is displaced by η

_i in the at least one direction from the corresponding lattice point so as to generate ε

i, η

_i representing a dispersion of a position of the vertex of each micro lens with respect to the corresponding lattice point.

5. A microlens array according to claim 4, wherein the at least one direction includes x and y directions, the reference lattice on the x-y plane is rectangular, the lattice spacing D in the x direction being represented by Dx and the lattice spacing D in the y direction being represented by Dy, and a projection onto the x-y plane of the vertex of each microlens is displaced by (η

_xi, η

_yi) from the corresponding lattice point where η

_xi represents η

_i in the x direction and η

_yi represents η

_i in the y direction.

6. A microlens array according to claim 1, wherein the at least one direction includes x and y directions, the reference lattice on the x-y plane is rectangular in the x and y directions, and in the vicinity of the center of each of the microlenses, the curvature radius in the x direction is Rx (millimeters) and the curvature radius in the y direction is Ry (millimeters).

7. A microlens array according to claim 1, wherein the relationship

8. A microlens array according to claim 1, wherein the relationship

0.0064√

{square root over (f)}{1+(D/2f)²}<

σ

<

0.014√

{square root over (f)}{1+(D/2f)²}

is further satisfied.

9. A microlens array according to claim 1, wherein the vertex positions of plural microlenses are displaced with respect to one another in the direction that is perpendicular to the x-y plane so as to weaken a dark spot.

10. A microlens array according to claim 1, wherein when the maximum value of the absolute value of ε

_i is represented by |ε

_i|_max and a standard deviation of ε

_i is represented by σ

, the relationship

|ε

_i|_max<

3 σ

is satisfied.

11. An optical system including a light source emitting lights of the wavelength of λ

(micrometers), and a microlens array configured to diverge the lights from the light source,

wherein the microlens array includes N microlenses arranged in a at least one direction on an x-y plane, a projection onto the x-y plane of the lens vertex of each microlens is arranged on or near a lattice point of a reference lattice on the x-y plane, the lattice spacing of the reference lattice in the at least one direction being D (millimeters), and when a boundary between microlenses is referred to as a side of a lens, a projection onto the x-y plane of the side is located approximately at the middle of projections onto the x-y plane of the vertexes of the two microlenses and therefore a distance between two sides facing each other and spaced in the at least on direction is approximately equal to D, and

wherein a distance between a projection onto the x-y plane of a lens vertex i and a projection onto the x-y plane of a side between the lens vertex i and a lens vertex i+1 is

D/2+ε

_i

where ε

_i represents a dispersion of the distance from D/2 and for the N microlenses,

12. An optical system according to claim 11, wherein in the x-y plane, a boundary between the lens vertex i and the lens vertex i+1, which are adjacent to each other in the at least one direction, is the perpendicular bisector of the line connecting the lens vertex i and the lens vertex i+1, or an amount of displacement of the boundary from the perpendicular bisector is negligible.

13. An optical system according to claim 11, wherein in the microlenses of the microlens array, the relationship

14. An optical system according to claim 11, wherein in the microlenses of the microlens array, the relationship

0.0083√

{square root over (λ

f)}{1+(D/2f)²}<

σ

<

0.019√

{square root over (λ

f)}{1+(D/2f)²}

is further satisfied.

15. An optical system according to claim 11, wherein the vertex positions of plural microlenses are displaced with respect to one another in the direction that is perpendicular to the x-y plane so as to weaken a dark spot.