JPH01250902A - Micro-fresnel lens - Google Patents

Abstract

PURPOSE:To facilitate the manufacture and to decrease the chromatic aberration by specifying the height of an uneven pattern in each Fresnel zone. CONSTITUTION:Height of an uneven pattern of each zone is set to a value for giving a phase shift of 2npi (n is a positive integer of >=2). Accordingly, a period of each zone becomes two times, comparing with a conventional Fresnel lens having a value for giving a phase shift whose height is 2pi. That is, even in case of the same numerical aperture NA, the period of each zone becomes (n) times by setting the height of the lens to (n) times. In such a way, the manufacture accuracy is improved, the lens efficiency is raised, and also, the period of the Fresnel zone is lengthened, by which a light beam is curved by a refraction rather than a diffraction effect, and a chromatic aberration caused by a use wavelength variation is decreased.

Description

[Detailed Description of the Invention] Summary of the Invention The lens height of the micro Fresnel lens is determined by the phase difference or 2.
By fabricating the lens so that nπ (a positive integer greater than or equal to n.2), the period becomes n times larger, making fabrication easier. Improving fabrication accuracy increases lens efficiency. Color aberration due to changes in the wavelength used is reduced. You can get an effect like this.

Background of the invention This invention relates to micro Fresnel lenses.

A flat micro Fresnel lens uses the diffraction phenomenon of light to condense light, and has a concentric periodic structure (
The period becomes smaller towards the outside). That is,
A Fresnel lens has a plurality of concentric Fresnel zones, each having a height of asperity that provides a 2π phase shift at each point within each zone. These uneven patterns are very fine and are often produced by electron beam lithography.

Conventional micro Fresnel lenses have the following problems.

When the numerical aperture of the Fresnel lens to be produced increases, the number of zones with a circumference Jυj on the order of several μm increases, and the lens becomes difficult to manufacture. For example, if NA=0.5,
The period less than 5 lt m occupies more than 90% of the area of the Fresnel lens.

Due to manufacturing errors of periodic structures on the order of several μm, Fresnel
Lens efficiency decreases.

Since this lens uses light diffraction, chromatic aberration occurs as the wavelength used changes.

SUMMARY OF THE INVENTION An object of the present invention is to provide a micro Fresnel lens that is relatively easy to manufacture and has little chromatic aberration.

In the micro Fresnel lens according to the present invention, the height of the concavo-convex pattern in each Fresnel zone is 2nπ(n
is a positive integer of 2 or more).

Needless to say, even with such a structure, a lens effect (for example, light condensing, collimating effect, etc.) is performed. The height of the uneven pattern (thickness of the lens) in each zone is 2
By taking a value that provides a phase shift of nπ, the period (width) of each zone is n times greater than that of a conventional Fresnel lens whose height can vary by a transport shift of 2π.

As described above, according to the present invention, even if the NA is the same, by increasing the height of the lens by n times, the period of each zone is increased by n times, making manufacturing easier compared to the conventional method.

This also improves manufacturing accuracy and increases lens efficiency.

Furthermore, by increasing the period of the Fresnel zone, light is bent by refraction rather than by diffraction effects, and chromatic aberration due to changes in the wavelength used is reduced.

By reducing the wavelength dependence of the Fresnel lens, it is possible to provide a sufficient lens function even for light sources with wavelength dispersion such as LEDs.

This invention applies not only to Fresnel lenses with a circular pattern of Fresnel zones, but also to Fresnel lenses with an oval pattern.
Needless to say, the invention is also applicable to two-point Fresnel lenses with zones and other types of Fresnel lenses.

DESCRIPTION OF THE EMBODIMENTS FIG. 1 shows an optical path used to study the phase shift of light in a Fresnel lens.

Generally, if the amplitude when light propagates through the optical path length is A, then this amplitude A is A = (1/, e) Aosin [(j!/λ)
2π].

A here. is the initial amplitude and λ is the wavelength.

In FIG. 1, the amplitude A OQ at point Q of the first light wave passing through point 0 and reaching point Q is given by the following equation.

AOQ= (1/f)Ao sin [(f/λ)
2π] where f is the focal length of the Fresnel lens.

Similarly, the amplitude A PQ at point Q of the second light wave passing through point P and reaching point Q is given by the following equation.

APQ - (1/(δ, g+f)] Aosin (((δ, 6+f)/λ)] 2π) When the first light wave with amplitude A and the second light wave Q with amplitude A PQ are superimposed at point Q, , the condition for the maximum amplitude of the superimposed and synthesized light waves is the first
and the second light wave have the same phase at point Q. For this purpose, we need to inject the second light wave at point P into φ(r)=−(δ(/λ)2π+2mπ (4)(m
is a positive integer).

As a result, the sine term in equation (3) representing the second light wave becomes as follows.

5inf((δ, g+f)/λ) 2π−(δ(/λ)
2π+2mπ) −sinf(f/λ)2π+2myr)=sin((f
/λ)2πl (5) Therefore,
The composite wave of the first light wave and the second light wave at point Q is given by the following equation and has the maximum amplitude.

AoQ+APQ=(2/f) AosLn[(f/λ)2π] Therefore, by giving the second light wave a phase shift of φ(r) at point P, a lens action that focuses light on point Q can be realized.

A Fresnel lens has a concavo-convex pattern that provides a phase shift expressed by equation (4).

Since δ in equation (4) is a function of the distance r in the radial direction, if equation (4) is expressed as a function of r, it becomes approximately as follows.

φ(r)−πr2/λf(7) λ This is generally referred to as the phase shift function of a lens having a focal length f at a wavelength hole.

This phase shift function φ(r) is shown in FIG.

In a conventional Fresnel lens, the phase shift that can be achieved is in the range of 0 to 2π, so this function φ(r) is divided into every 2π, and the function φ(r) in each divided zone is A Fresnel lens with a concavo-convex pattern corresponding to the shape indicated by diagonal lines in the right half of FIG. 2, determined by the values, was manufactured.

However, even if the phase shift function φ(r) is divided by 2nπ (n is a positive integer greater than or equal to 2), the result will be exactly the same.
Equation 5) is established, and the lens has a strong effect. This invention divides the phase shift function φ(r) by 2nπ, and provides a Fresnel lens having a concavo-convex pattern corresponding to the shape determined by the value of the function φ(rl) in each divided zone. The shaded shape in the left half of the figure is the function φ(r) divided by 4π.

As is clear from comparing the uneven patterns of the right half (conventional example) and the left half (invention) of FIG. 2, in the Fresnel lens according to the invention, the period (width) A of each zone is different from that of the conventional period It is larger than 4 π Δ2□.

Such a Fresnel lens can be manufactured using electron beam lithography. Furthermore, a mold is created using the Fresnel lens manufactured by this method as a prototype, and a large number of Fresnel lenses of the same shape can be mass-produced by a molding method using this mold.

[Brief explanation of the drawing]

FIG. 1 is a diagram for examining the phase shift of light in a Fresnel lens, and FIG. 2 is a diagram showing a transport shift function and its division pattern. that's all

Claims (1)

[Claims] In the case where a plurality of concentric Fresnel zones are formed and a concavo-convex pattern giving a predetermined phase shift is formed in each zone, the height of the concavo-convex pattern in each zone is 2nπ (n is a positive integer of 2 or more). ) is set to a value that gives a phase shift of
lens.