JPS59105605A - Fresnel zone plate - Google Patents

Abstract

PURPOSE:To condense light sharply and to eliminate coma by forming the 1st Fresnel zone on the side of transparent and parallel glass plates, etc. where parallel light is made incident and the 2nd Fresnel zone on the exit side, and specifying the radii rk Rk of respective annular bands by the equations. CONSTITUTION:The 1st Fresnel zone 2a is prepared on the side of a sheet of glass plate 1 where parallel light 5 is made incident and the 2nd Fresnel zone 2b is prepared on the exit side. the radii rk, Rk of the annular bands of the respective Fresnel zones are determined so that sine wave conditions are satisfied and that the spot diameter of a refractive limit is attained in the material having >=1 refractive index. More specifically, the equations are solved as the simultaneous equations relating to rk, Rk and (h) with (k) as a parameter to determine the radii rk and Rk, then even if the incident parallel light 5 incline relatively with an optical axis 4, the coma of the exit light is eliminated and sharp spot is obtd. at a condensing point 13.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention focuses parallel light on a point in a transparent substance having a refractive index of 1 or more compared to air, and has no comatic aberration.
This relates to the Nelzone plate. .

In the conventional heel Fresnel zone plate, the radius rk of the annular zone has a value given by equation (1), and the Fresnel zone is formed only on one side of a parallel flat glass plate. No. (
In formula 1), λ is the wavelength, f is the focal length, and: l, 2
,3. ...is... The action of this Fresnel zone plate is shown in FIG. In Figure 1, (1) is a glass plate, (2) is a Fresnel zone, (3) is a Fresnel zone plate, (41 is an optical axis, (5) is an incident parallel beam, (6) is an output beam, (7) is a Fresnel zone plate, (41 is an optical axis, (5) is an incident parallel beam, (6) is an output beam, ) is the condensing point. When incident light parallel to the optical axis (4) enters the 7-Resnel zone plate (3) configured in this way, the incident parallel light (5) reaches the Fresnel zone (2).
) is diffracted at the radius rk of the condensing point (7) and is converted into an outgoing beam ()i131 (61), and the other incident rays are similarly converted into an outgoing beam (6) which is directed toward the condensing point (7). Ru.

In this case, condensed light having a diffraction-limited spot size can be obtained at the condensing point (7) without producing any aberration.

Next, when collimating parallel light from air into a transparent substance with a refractive index n2〉1 using a Fresnel zone plate having an annular zone given by equation (11), the air and the transparent substance Spherical aberration occurs because refraction occurs at the boundary between the two and the focal point, and the spot diameter at the focal point becomes larger than the value due to the diffraction limit, making it impossible to focus the light sharply. This situation is shown in Figure 2. In Figure 2, (3)
(81 is a transparent material with a refractive index n2>1).

(9) is the boundary between the transparent substance and air. The outgoing light (6) diffracted by the Fresnel zone plate (3) becomes a light beam heading towards the focal point α0, but since it is refracted at the boundary (9), the direction is changed according to the law of refraction on this surface, and the optical axis (4) intersects with the focal point aO at a different position.

Other light rays are similarly refracted at the boundary (9) and focused at the focal point (7).
) intersects the optical axis near. The position at which the light intersects with this optical axis differs for each light beam, so it does not intersect at one point, and the image at the condensing point (7) is blurred, and its spot diameter becomes larger than the value determined by the diffraction limit.

Furthermore, when parallel light (II) tilted with respect to the optical axis (4) is incident on the Fresnel zone plate (3) shown in Fig. 1, comatic aberration occurs and the spot at the condensing point is The diameter becomes larger than the value due to the diffraction limit.

It becomes impossible to focus light sharply. FIG. 3 shows this state. In Figure 3 (11),
(11a), (111)) is the incident parallel light with an inclination to the optical axis (4), 0.2 t (12a)
, (12b) is the incident parallel light aυ, (11a) , (
11b), and 03 is a condensing point for the incident parallel light αB. The outgoing light α2 diffracted by the Fresnel zone (2) is refracted at the boundary (9) and becomes a light beam heading towards the condensing point α□□□. Parallel light θD and incident parallel light (
11a) and (Nb) are different.

The output light a2 diffracted by the Fresnel zone (2), the output light (12a), and the output light (121)) do not intersect at one point but at different positions even after being refracted at the boundary surface (9). The same applies to other light rays. This difference appears as so-called coma aberration, the image at the focal point Q is blurred, and the spot diameter becomes larger than the value due to the diffraction limit. FIG. 4 shows a spot diagram at the focal point Q3 in FIG. There is a drawback that if the incident parallel light is tilted with respect to the optical axis, coma aberration occurs and it is not possible to focus the light sharply.

In order to eliminate the following drawbacks, this invention creates a first Fresnel zone on the parallel light incident side of a single glass plate and a second 7 Fresnel zone on the exit side to satisfy the sine condition. , and determine the annular radius of each Fresnel zone so as to have a diffraction-limited spot diameter in a substance with a refractive index of 1 or more,
It is designed to avoid coma aberration, and the drawings will be explained in detail below.

FIG. 5 is a schematic diagram for determining the annular radius of the Fresnel zone plate of the present invention. The incident parallel light (5) is focused without aberration at a distance t from the surface (9) into a transparent material (8) with a refractive index n2>1 located at a distance 1 from the Fresnel zone plate and without coma aberration. The annular radii of the two Fresnel zones are determined so as to satisfy the condition that this does not occur, that is, the sine condition. In Figure 5, (2a
) is the first Fresnel zone where parallel light enters? (21
)) is the second Fresnel zone, and (L9 is the diffracted light by the first Fresnel zone (2a)).

In Fig. 5, in order to condense the incident light to one point on the condensing point F, it is necessary to move from the point A on the first Fresnel zone to the second 7
Point B on the Rennel zone and the transparent material (810 surface (9
) The difference between the optical distance from point C to point F above and the optical distance from point A to point R from point P and point Q is 1/
It is necessary that the wavelength be an integral multiple of two wavelengths. That is, this condition can be written as the following formula (2), where nl is the refractive index of the glass plate (1).

Next, in order to prevent coma aberration from occurring, the height of the incident light and the height of the emitted light at the main surface may be made equal. That is, in FIG. 5, a point G where a straight line F1, which is an extension of the light ray from point F along the direction FC of the refracted light, intersects the straight line A1, and a point K are located at a radius of 112 with the point F as the center.
The radius of the annular zone of the first Fresnel zone rk (= A o)
The annular radius of the second Fresnel zone is Rk(”' B H
)! If the thickness J of the glass plate (1) is d, and the height of incidence of the emitted light (6) at the surface (9) is h, the above conditions can be written as follows.

n, f [〒(Rh = rh)' +, /12 + (R
kh) 2+n26 acrylic, 2- (n1d+1+n2
t) = to' (k=1.

2,...)−−−−−−−−−−−−−−−−−−−
−−−−−(31f(Rk ”) = rk” +(R
hh)'------(41hv' (n2f)2-
17 to 2 =: trk-------------, (5), that is, the equations (3), (4), and (5) are expressed as k
This can be solved as simultaneous equations regarding Rk and h with parameters Rk and h.

In this way, if the annular radii rk and Rk of the first Fresnel zone and the second Fresnel zone are determined, even if the incident parallel light is tilted with respect to the optical axis (4), comatic aberration of the output light can be removed. Therefore, a sharp spot can be obtained at the focal point (13+). Figure 6 shows this situation.

FIG. 7 shows an embodiment of the present invention, in which a transparent glass plate (1
) or on a plastic plate, No. (4).

Between 0 and rl of the annular radius rk determined by equation (5) and r
Transparent between 2 and r2 ++ (k=1, 2, -).

A first Fresnel zone is created on the incident side by making the space between -1 and r2k (k:1 t 2 , "') opaque for r2.

Between 0 and R1 of the annular radius Rk and between R2 and +l
Transparent between (k: 1, 2...), -1 and R in R2
2k (k=1.2...) and the second
A Fresnel zone is created on the output side.

FIG. 8 shows another embodiment of the present invention, in which a transparent glass plate (
11 or on a plastic plate, the thickness of the refractive group n(~1) is λ/(n- 1)
Create the first 7 Renel zones on the incident side by attaching the above transparent material (Iz), and add the radius Rk of the two annular zones between 0 and R1 and between R2 and R2++ (k=1, 2,...
・) between the transparent material α2 and the thickness λ/(n-1)
This is a phase-type Fresnel zone plate in which a second 7-Resnel zone is created on the output side by attaching the plate as described above.

FIG. 9 shows another embodiment of the present invention, on a transparent glass plate (1) or a plastic plate.

+2 from 0 to r2 and r2 to r2 of radius rk of ring zone
Between the annular zones of (k=1, 2...), a transparent material Q2+ with a refractive index of n that becomes thicker continuously is attached to create a first Fresnel zone on the incident side, and the two annular zones are +2 (k=1.2
．． This is a phase-type Fresnel zone plate that creates a blaze by attaching a transparent material that becomes thinner continuously between the annular zones to form a second Fresnel zone.

If the Fresnel zone plate according to the present invention shown in FIGS. 7, 8, and 9 is used, the incident parallel light will be Since coma aberration does not occur even if the lens is relatively tilted, sharp light condensation with a diffraction-limited spot diameter can be obtained.

Note that above 2 describes the case where one glass plate is used to create Fresnel zones on both sides, but the first Fresnel zone is created on one glass plate and the second 7 Fresnel zones are created on the other glass plate. The structure may be such that the two glass plates are optically glued together.

As described above, in the Fresnel zone plate according to the present invention, the first seven glass plates are arranged on the side of one glass plate on which parallel light enters.
Create a second Fresnel zone on the exit side, and calculate the annular radius of each 7 Renel zone "k t R
A diffraction-limited spot is obtained in a transparent material with a refractive index of 1 or more by determining k to be the solution of equations (3), (4), and (5), which are simultaneous equations. , the sine condition is satisfied to avoid coma aberration, and even if the incident parallel light is tilted with respect to the optical axis (4) of the Fresnel zone plate (3), the diffraction-limited spot diameter is This has the effect of providing sharp light condensing characteristics.

[Brief explanation of the drawing]

Figure 1 is a schematic diagram of a conventional Fresnel zone plate used to focus incident parallel light parallel to the optical axis. Figure 2 is a conventional Fresnel zone plate used to focus light onto a transparent material of n) 1. Schematic diagram of the case. Figure 3 is a schematic diagram of the case where a conventional Fresnel zone plate is used to focus incident parallel light that is tilted with respect to the optical axis.
Figure 4 is a spot diagram at the focal point for Figure 3, Figure 5 is a schematic diagram for determining the annular radius of the Fresnel zone plate according to the present invention, and Figure 6 is a diagram using the Fresnel zone plate according to the present invention. 7 is a diagram showing an embodiment of the Fresnel zone plate according to the present invention, and FIG. 8 is a diagram showing the Fresnel zone plate according to this explanation. FIG. 9 is a diagram showing another embodiment of the Fresnel zone plate according to the present invention. In the figure, (ill! glass plate, (21, (2a),
(2b) is Fresnel # so y, (31 is Fresnel zone plate, (4) is optical axis, (5) is incident parallel light,
(6) is the emitted light, (8) is a transparent material with a refractive index of 1 or more,
(9) is the surface, (II is the focal point, Qll. (11a), (11b) is the incident parallel light, (121
, (12a) and (12b) are the emitted light, (31 is the condensing point, I is the focal point, and (2) is the diffracted light. aQ is a transparent material. Note that the same or equivalent parts in the two figures are denoted by the same reference numerals. It is shown with the following. Agent Makoto Kuzuno - Elephant 11 included S Nose L ÷, C7) 1 Humiliation Rimata Holi Soto stem Z Kushi - - A certain mu (1) + = * 6 Color P ■ IY Boiled (+3) i te 1 ゛ last 3 points ho 9 tne 7 ρ ne ? 1 color 11

Claims (4)

[Claims] (1) In a Fresnel zone plate that focuses parallel light onto one point in a transparent material with a refractive index of 1 or more. forming a first Fresnel zone on the side of a parallel transparent glass plate or transparent plastic plate on which the parallel light is incident;
A second Fresnel zone is formed on the exit side of the glass plate or plastic plate, and the annular radius rk of the first Fresnel zone and the annular radius Rk of the second Fresnel zone are defined as "k+Rk and h are variables. Simultaneous equations (%) (where: 1, 2..., d is the thickness of the glass plate or plastic plate, rJ is its refractive index, 1 is the refractive index n2 from the output side of the Fresnel zone plate The distance to the surface of the transparent object, t is the distance from the surface of the transparent material to the focal point, f is the focal length of the Fresnel zone plate,
λ is the wavelength). (2) On a transparent glass plate or plastic plate L,
Transparent between 0 and rl of the annular radius rk of the first border zone and 4-+ (k = 1, 2, =), -1 and r2k (k = = 1,
2, "i Make this space opaque, and make the area between 0 and R1 of the annular radius Rk of the second 7-Renel zone and between R2 and R2 +1 (k = i, 2...) transparent, R2 ni-1
The Fresnel zone plate according to claim 11, characterized in that the space between and R2k (k=1.2...) is made opaque. (3) On a transparent glass plate or glass plate,
The refractive index is n (~1) only between r2 of the annular radius rk of the first Fresnel zone and r2k (k'' t 2 r ''i), and its thickness is λ/(n-0 or more). Attach a transparent material such that -H(k=
1.2. ), a transparent material having a refractive index of n and a thickness of λ/(n-1) or more is attached only between the Fresnel zone and the Fresnel zone according to claim (1). plate· (4) On a transparent glass plate or plastic plate,
+2 from 0 to r2 and r2k to r2 of the annular radius rk of the first Fresnel zone (k = 1.2, , ,
), the thickness becomes thick (with refractive index n(N
1), and the annular radius Rk of the second Fresnel zone is continuous from 0 to R2 and from R2k to R2++ (k=1, 2, . . . ). A 7-Resnel zone plate according to claim 11, characterized in that a transparent material having a refractive index n (~1) is formed to have a thinner thickness so that the Fresnel zone is blazed.