Microlens array and optical system including the same

摘要

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.; $$ \frac{0.0042}{D}\frac{D}{2\&\#x2062;\&\#x2062;f}=\frac{D\&\#x2061;\left(n-1\right)}{2\&\#x2062;\&\#x2062;R}$$ $$ 0.0048\&\#x2062;\sqrt{f}\&\#x2062;\left\{1+{\left(D/2\&\#x2062;\&\#x2062;f\right)}^2\right\}\sigma 0.014\&\#x2062;\sqrt{f}\&\#x2062;\left\{1+{\left(D/2\&\#x2062;\&\#x2062;f\right)}^2\right\}$$ $$ {\sigma }^2=\underset{i=1}{\overset{N}{\&\#x2211;}}\&\#x2062;\frac{{\left({\varepsilon }_i-\stackrel{\_}{\varepsilon }\right)}^2}{N}$$ $$ \stackrel{\_}{\varepsilon }=\underset{i=1}{\overset{N}{\&\#x2211;}}\&\#x2062;\frac{{\varepsilon }_i}{N}=0$$