JPH01142604A - Phase type zone plate - Google Patents

Abstract

PURPOSE:To obtain the efficiency of utilizing light as sufficiently high as the efficiency of a blazed Fresnel zone plate in practicability by constituting a phase type zone plate in such a manner that the optical path difference between the 1st rays passing respective zones and the 2nd rays passing the optical axis is 2nd integer times a fraction of the 1st integer of the wavelength to be used and that the 1st integer is >=3. CONSTITUTION:The diffracted light rays from the plural zones 13A1-13A4, 13B1-13B4, 13C1 of the prescribed optical path differences are condensed onto the optical axis LO so as to be intensified by each other. The zone plate is so constituted that the optical path difference between the 1st rays passing the respective zones and the 2nd rays passing the optical axis consists of the 2nd integer m times a fraction of the 1st integer M of the wavelength to be used and that the 1st integer M is >=3. The 1st rays passing the respective zones 13A1-13A4, 13B1-13B4, 13C1 are, therefore, condensed at such a phase at which said rays are intensified by the 2nd rays passing the optical axis at the image point on the optical axis LO with each other. The much higher efficiency of utilizing light than the efficiency of the conventional phase type zone plate is thereby obtd.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a phase zone plate, and is suitable for use in, for example, objective lenses and condensing lenses of X-ray microscopes.

[Summary of the invention]

The present invention provides a phase type zone plate that focuses diffracted light at a predetermined position by advancing the phase of diffracted light obtained from a plurality of zones by a predetermined amount. By selecting M) λ, the light utilization efficiency can be improved.

[Conventional technology]

Conventionally, in order to form an image in an X-ray microscope, an X-ray source with sufficiently high intensity and an X-ray source with sufficiently high sensitivity have been used.
Since a line detector cannot be obtained, it is necessary to use objective lenses and condensing lenses with high light condensing efficiency.

In particular, when observing a living body using an X-ray microscope, it is not possible to irradiate the living body to be observed with high-intensity X-rays, so an objective lens with even higher light collection efficiency is required. .

As a condensing means that can be practically applied to such a purpose, a zone plate utilizing a diffraction phenomenon has been proposed, as shown in FIG.

The zone plate ZPI (FIG. 9(A)), which is a Fresnel zone plate (FZP), forms an annular zone 2 made of a concentric light-shielding member around the optical axis LO on a transparent substrate 1, and a zone between the annular zones 2. The light transmitted through the light-transmitting portion 3 is focused on a focal point on the optical axis LO.

Here, the radius of the annular zone 2 is the radius r, as shown in FIG. 10 when an infinite object point type lens is constructed.

The optical path difference between the light beam consisting of the diffracted light emitted from the m-th annular zone 2 and the reference light beam passing through the center is selected to be an integral multiple of the wavelength used, so that these two light waves form an image point. This results in mutual reinforcement at the focal point F, and thus the light diffracted at the zone plate ZP1 is focused at the focal point F.

However, in this zone plate ZPI, since the annular zone 2 is constituted by a light shielding member, the light utilization efficiency of the incident light is low, and there is a problem that, for example, only about 10% of the incident light can be focused.

As a configuration to solve this problem, zone plate ZP2 (
Figure 9(B)) has been proposed. In this case, Fig. 9 (A
), instead of the ring zone 2 made of a light-shielding member, a ring zone 2A made of a transparent material is used, and the height of the ring zone 2A in the direction along the optical axis LO is changed from a transparent material. The value is selected such that the phase of the emitted light emitted from the annular zone 2A is shifted by ±λ/2 with respect to the light emitted from the light section 3 (wavelength used).

In this way, the light rays emitted from the transparent part 3 can be focused at F.
At the same time, the light rays emitted from the annular zone 2A can be focused on the focal point F (Fig. 10) so as to strengthen each other, and the light rays focused on the focal point F can be utilized. The efficiency can be improved approximately four times as compared to the Fresnel zone plate (FIG. 9(A)).

Furthermore, as a method to solve the problem of low light utilization efficiency of the zone plate ZP1 shown in FIG. 9(A), the method shown in FIG. 9(C)
Blazed Fresnel zone plate as shown in (B
A zone plate ZP3 consisting of ZP) has been proposed.

In this case, on the exit side surface of the transparent substrate 1, compared to the case of FIG. A light-transmitting inclined surface 4 is formed, the height of which is linearly inclined by λ in the radial direction.

According to the zone plate ZP3 having such a configuration, the light rays emitted from each position in the radial direction of the light-transmitting inclined surface 40 can be continuously focused on the focal point F, and the light utilization efficiency can be calculated as shown in FIG. )
This can be improved by about 10 times compared to the case of .

[Problem that the invention seeks to solve]

As mentioned above, if we consider zone plates ZPI to ZP3 from the point of view of light utilization efficiency, Fresnel zone plates (
A zone plate ZP2 made of a phase type Fresnel zone plate (PZP) is more advantageous than a zone plate ZP1 made of a blazed Fresnel zone plate (BZP) than a zone plate ZP1 made of a blazed Fresnel zone plate (BZP). It turns out that this is even more advantageous.

However, the zone plate ZP3 (Fig. 9 (C)), which is a blazed Fresnel zone plate, has a light-transmitting slope that continuously changes the phase of the diffracted light diffracted from each position in the radial direction. It is necessary to form the surface 4, and it is actually difficult to process the light-transmitting inclined surface 4 having such a configuration with high precision.

The present invention has been made in consideration of the above points, and proposes a phase-type zone plate that has a sufficiently high light utilization efficiency comparable to that of a blazed Fresnel zone plate in practice, and is thus easy to manufacture. This is what I am trying to do.

[Means for solving problems]

In order to solve this problem, in the present invention, as shown in FIG.
3A4.13B1 to 13B4. In a zone plate configured to focus the diffracted lights from 13C1 on the optical axis L○ so as to mutually strengthen each other, each zone 13A1 to 1
The optical path difference between the first ray passing through 3A4.13B1 to 13B4.13C1 and the second ray passing through optical axis LO is the wavelength used λ
, and the first integer M is 3 or more.

[Effect]

Each zone 13A1~13A4.13B1~13B4.1
The first light ray passing through 3C1 is focused at an image point on the optical axis LO with a phase such that the second light ray passing through the optical axis and the second light ray mutually strengthen each other.

In this way, by setting the optical path difference between the first and second light beams to be a second integer m times 1/1 of the first integer M of the wavelength λ used, it is different from the conventional phase type zone plate. In comparison, it is possible to significantly improve the efficiency of light use.

〔Example〕

An embodiment of the present invention will be described in detail below with reference to the drawings.

[1] First Embodiment In FIG. 1, 11 indicates a phase type zone plate as a whole, and the optical axis LO is placed on a transparent substrate 12 in the radial direction.
Ring zones 13A1 to 13A4.13 concentrically centered on
B1 to 13B4.13C1 are formed as zones that cause a diffraction phenomenon.

Here, the innermost first ring zone 13A1.13B1.
13C1 protrudes from the incident surface 12A of the transparent substrate 12 by a length t in the direction along the optical axis LO, and a second annular zone 13A2.13B is adjacent to the outside with the light exit surface as a reference.
2, the wavefront of the light beam emitted from the exit surface is the first annular zone 1
It is formed at a position where the phase advances by λ/4 compared to the wavefront of the light beam emitted from 3A1.13B1.13C1.

Further, in the third annular zone 13A3.13B3 adjacent to the outside, the phase of the wavefront of the light ray emitted from its exit surface is 2λ/4 with respect to the wavefront of the light ray emitted from the first annular zone 13A1.13B1.13C1. It is formed at a position where the phase advances.

Further, in the fourth annular zone 13A4.13B4 adjacent to the outside, the phase of the wavefront of the light beam emitted from the exit surface is the first
It is formed at a position that advances by 3λ/4 with respect to the wavefront of the light beam emitted from the annular zone 13A1.13B1.13C1.

In this way, the first, second, third, and fourth annular zones (13A
1.13A2.13A3.13A4), (13B1.1
3B2.13B3.13B4), (13CI) are the first, second, and third ring groups GRI, GR2, and G in order from the inside.
R3, and in each of the annular groups GRI, GR2, and GR3, the wavefront of the incident light is divided into four annular zones, and the phase is sequentially advanced at a phase pitch of λ/4 as it goes outward. As shown in FIG. 2, the radial position of each annular zone is selected so that the light is focused on a focal point F (FIG. 2) that forms an image point on the optical axis LO.

That is, the mth position in the radial direction from the position 0 of the optical axis LO (m=
1.2...9) When the distance to the outer position of the annular zone is r, (mwl, 2...9), the light from the object point at infinity is focused at F. When condensing light into the m-th annular zone, the radius r, (mml, 2...9
). Here, f is the focal length and λ is the used wavelength of light.

In this way, the annular zones (13A1 to 13A4) and (13B1 to 1
The diffracted lights emitted from 3B4) and (13C1) strengthen each other at the focal point F, so that the light incident on the transparent substrate 12 is eventually condensed at the focal point F. The amount of phase advance increases as it goes outward in the radial direction, for each ring zone group GRI, GR2.
, GR3 advances by one period for each region R1.

According to the phase type zone plate 11 having the configuration shown in FIG. 1, the conventional phase type Fresnel zone plate ZP2 (FIG. 9 (B
)), the annular zone is finely divided in the direction of the radius r, and the phase difference pitch between the phase of the wavefront of the reference beam and the phase of the wavefront of the light beam emitted from each zone is finely divided. By doing so (with a pitch of λ/4), the energy of the light condensed at the focal point F becomes much larger than in the conventional case.

In this case, in the case of the conventional blazed Fresnel zone plate type zone plate ZP3 (Fig. 9 (C)), since it is sufficient to form a plane perpendicular to the direction along the optical axis LO as each ring zone. It is possible to avoid manufacturing difficulties such as

[2] Light usage efficiency The light usage efficiency of the phase type zone plate 11 having the configuration shown in FIG.
ZP) (Fig. 9 (B)), it is much improved compared to the case of blazed Fresnel zone plate (Fig. 9 (C)).
) can be approximated.

In other words, generally in this type of zone plate, 1
It can be considered that the energy of the first-order diffracted light is focused on the focal point F because the energy of the second-order diffracted light is significantly larger than the energy of other diffracted lights. However, in general, when light is perpendicularly incident on a grating whose phase advances with a period T, the diffraction efficiency l of the first-order diffracted light can be expressed as follows (2). Here, A (x) is the absolute value of the amplitude transmittance, φ(x) is the amount of phase change, and X is the distance in the direction of the period T of the grating (in the direction of the radius r in FIG. 1).

Equation (2) is a general equation for a lattice, and for example, the Fresnel zone brake shown in FIG. 9(A)) (
Applying the conditions of zone plate ZP1 consisting of Then A(x)=1...
・In contrast to (4), □≦x;5T ・Old...In the range of (5), A(x)=O...(6).

In addition, at this time, the amount of phase change φ(x) is considered to be φ(x) −0 (7) as shown in FIG. 3(B), so in the end, as shown in FIG. 9(A) The diffraction efficiency η of the first-order diffracted light of the conventional Fresnel zone plate type zone plate ZP1 as shown in 2. is ηF2. =□
It can be obtained as (8) π2.

Next, the diffraction efficiency ηPZF of the first-order diffracted light in the case of the zone plate ZP2 made of the conventional phase type Fresnel zone plate (PZP) shown in FIG. 9(B) is expressed as... (9) . Here, d is the height of the ring zone 2A, and Δn
is the difference in refractive index between the part with and without the member forming the annular zone. And α indicates the range where the phase change occurs, φ(x)=0 (0≦X≦αT) ・・・・・・(1o)
φ(x)−2πΔn/λ (αT≦X≦T) ・・・・・・(11)
, and the maximum value is reached when (13).

The amplitude transmittance A(x) and the amount of phase change φ(X) exhibit changes as shown in FIGS. 4(A) and 4(B), respectively.

Furthermore, the diffraction efficiency ηIZP of the first-order diffracted light in the case of the zone plate zP3 made of a blazed Fresnel zone plate (BZP) in FIG. 9(C) is 77 mzr-! from equation (2). 1ine”π(And-λ)・・・・・・
・It can be expressed as (15) (sinc is a sink function), so when λ, η of the first-order diffracted light, 2te is the maximum value ηZr”1 ・・・・・・(
17).

The analysis of the above-mentioned equations (1) to (17) is disclosed in the literature "Optics" Vol. 16, No. 2 (February 1987).

On the other hand, the phase type zone plate 1 having the configuration shown in FIG.
1 is amplitude transmittance A (x) is 0≦X≦T
......For the range of (18), as shown in Figure 5 (A), A(x) = 1
......(19), and by further changing the phase lead amount at a phase pitch of λ/4, as shown in Fig. 5 (
As shown in B), O≦X≦□ ・・・・・・ (
20) in the range φ(x) -0...(21), and in the range φ(X)-□...(23)
Then, in the further range φ(X)=π ・・・・・・(25
), and in the further range φ(X)=□π ・・・・・・(27)
becomes.

Therefore, the diffraction efficiency η of the first-order diffracted light in the phase type zone plate 11 shown in FIG. 1 can be determined by the following equation.

Comparing the diffraction efficiency η,1 of this equation (28) with the case of the zone plate ZP1 of FIG. 9(A) expressed by the equation (8), in the case of the phase type zone plate ZP1 of FIG. It can be seen that the light usage efficiency has increased eight times.

Also, as expressed by the above equation (14), as shown in FIG. 9(B)
(conventional zone play) ZP2 diffraction efficiency η, 2. It can be seen that the phase type zone plate 11 of FIG. 1 has twice the light utilization efficiency.

Furthermore, as expressed by equation (17), the diffraction efficiency η, 2. Compared to,
It can be seen that the phase type zone plate 11 shown in FIG. 1 has a light utilization rate of approximately the same level.

As described above, according to the configuration shown in FIG. 1, it is possible to obtain the phase type zone plate 11 in which the light utilization efficiency is further improved. In this way, since each ring zone of the zone plate 11 has a surface composed of a plane orthogonal to the optical axis LO, it is actually easy to process each ring zone, and thus, regarding FIG. 9(C) It can be manufactured much more easily than the difficulty in manufacturing the blazed Fresnel zone play 1- (BZP) described above.

[3] Second Embodiment In the embodiment shown in FIG. 1, the case where the phase difference pitch was selected to be λ/4 was described, but the phase difference pitch δ can be expressed by the general formula as described below. . That is, M≧3 (29
), the amplitude transmittance A (x) is A ( x)=1
...(31), and the amount of phase change φ1 (x) in the m-1m range for the m-th annular zone is therefore, by substituting this relationship into the above equation (2). Therefore, the diffraction efficiency η of the first-order diffracted light under general conditions. If we find 9, we get ηGEM.

Here, as shown in FIG. 6, the optical path of the light beam emitted from the radius r of the m-th annular zone 13Am, (m=L 2...M) until it converges on the focal point F, and Optical path difference ΔLG of the optical path from the reference ray passing through the axis LO to the focal point F! N satisfies the following relationship.

By the way, if the amount of phase change φ, (X) in equation (33) is expressed using the wavelength λ used, the amount of phase change δ, (X) occurring in the m-th annular zone 13Am is...・(
36) becomes. (36) In the second term of the equation in parentheses, [
] is a Gagara symbol, and generally represents "the largest integer that does not exceed X for a real number X" by the symbol [X].

So, for example, in the 15th ring zone where M=3 and m=[
4,667] -4...(37) Eventually, the phase change amount δ@-15(X) of equation (36)
is = 0.667λ (38
)become.

In equation (35), in practice the numerical aperture N A (nume
When rt(al aperture) is small, the optical path difference ΔLG- can be approximated as r, t r =□λ (39)M. Therefore, the radius Rm of the m-th annular zone can be calculated from equation (39) [4] Third Example In the embodiments of equations (29) 2 to (40), when the incident light is a parallel ray (that is, the object point at infinity ), but the present invention, as shown in FIG.
It can be applied to incident light that has .

That is, as shown in FIG. 7, the phase type zone plate 1
1 has a focal point F, which is an image point on the exit side, and a focal point F, which is an object point on the incident side.
5) Instead of the formula, use the following formula - (aO+a+) =□λ... (41)
The relationship holds true. Here, do represents the focal length from the focal point F6 serving as the object point to the phase type zone plate 11, and d represents the focal length from the phase type zone plate 11 to the focal point F serving as the image point.

In the case of this embodiment as well, the mth ring zone 13Am (Fig. 6)
The phase of the light beam emitted from the optical axis LO advances by the phase expressed by the above equation (36) with respect to the phase of the light beam passing through the optical axis LO.

Also, in equation (41), if the numerical aperture NA is small,
In the same way as described above for equations (39) and (40), the annular zone 13 Am is added to the distance r and (m-1, 2...M) expressed by the following equation % equation % (42) I know what I need to do is form it.

Note that in equations (41) and (42), the focal length d0
If we approach infinity (Fig. 7), we can obtain, as its limit, a relational expression that is equal to equations (39) and (40). Thus, the phase type zone plate 11 of an object point at infinity can be expressed by equations (41) and (42).

[5] Other Examples (1) (29) In the second embodiment described above for equations (29) to (40) and the third embodiment described above for equations (41) and (42), generally within the period T The case where the number of annular zones is M and the phase difference pitch δ is δ - λ/M (formula (30)) was described above, but in reality, as shown in Fig. 8, M =
By selecting No. 3, it is possible to form a phase type zone plate 31 that is practically useful.

In this case, the diffraction efficiency η,I of the first-order diffracted light can be obtained as follows by substituting M=3 into equation (34). Therefore, the diffraction efficiency η in the conventional phase-type Fresnel zone plate (Fig. 9 (B))
It is possible to realize a phase type zone plate with significantly higher light utilization efficiency than PDF (formula (14)).

In this case, the radius of the m-th ring is the above (35)
The selection may be made so as to satisfy the relationship by substituting M-3 in the equation.

At this time, for example, the phase advance amount δ, (X) in the m=3rd annular zone 32A3 becomes 2λ/3 as shown in equation (34).

The above-mentioned formulas (29)2 to (40), and (41)2 to (4)
The general formula represented by formula 2) can be applied not only to the case of M-3 but also to a wide range of cases where M is 3 or more.

For example, as in the phase type zone plate 11 having an object point at infinity described above as the first embodiment, the phase difference pitch δ is λ/
4, M=4 in equations (29)2 to (42)
By substituting , the phase type zone plate 11 described above with reference to FIG. 1 can be expressed.

That is, in the phase type zone plate 11 of FIG. 1, the diffraction efficiency η is obtained by substituting M-4 into equation (34), and the optical path difference ΔL11 at that time is obtained by substituting M-4 into equation (35). The amount of phase advance of the ray exiting the m-th annular zone from the reference ray δ, (
X) can be obtained by substituting M=4 into equation (36).

(2) In equation (31), it is assumed that the transmittance of the transparent substrate 12 is 1, but in reality, absorption occurs in the transparent substrate 12, so the amplitude transmittance is It is often smaller than l.

If such conditions hold, there is a risk that the light utilization efficiency will decrease slightly, but according to the present invention, it is possible to effectively avoid the possibility that the imaging accuracy will deteriorate due to such a cause.

(3) In the above embodiment, a case was described in which the annular zones as zones were formed concentrically to condense light so as to form a point image. However, the shape is not limited to the above, and it is also possible to apply a contour shape that forms a linear image by arranging them in a straight line, for example.

〔Effect of the invention〕

As described above, according to the present invention, the light utilization efficiency can be further improved compared to the conventional phase-type Fresnel zone plate, and thus, the possibility that the manufacturing process becomes complicated and difficult can be effectively avoided. A zone plate can be realized.

[Brief explanation of the drawing]

FIG. 1 is a vertical cross-sectional view showing a phase zone plate according to the present invention, FIG. 2 is a route diagram for explaining its light collecting operation, and FIGS. 3 to 5 are curve diagrams for explaining light utilization efficiency. , FIG. 6 is a vertical cross-sectional view showing another embodiment of the phase type zone plate according to the present invention, FIG. 7 is a route diagram for explaining the condensing operation in still another embodiment of the present invention, and FIG. FIG. 9 is a vertical cross-sectional view showing a phase type zone plate according to still another embodiment of the present invention, FIG. 9 is a vertical cross-sectional view showing a conventional zone plate, and FIG. 10 is a route diagram for explaining its light focusing operation. 11.21.31... Zone plate, 12.
...Transparent substrate, (13A1 to 13A4.13B1
~13B4.13C1), (32A1~32A3.32
B1~32B3.32C1~32C3)... Ring zone.

Claims (2)

[Claims] (1) In a zone plate configured to focus diffracted lights from a plurality of zones having a predetermined optical path difference on the optical axis so as to mutually strengthen each other, the first light beam passing through each zone and the optical axis are A phase type zone plate characterized in that an optical path difference with a second light beam passing therethrough is a second integer multiple of a first integer fraction of the used wavelength, and the first integer is 3 or more. (2) It has the plurality of zones concentrically formed around the optical axis, and has an object point and an image point on the optical axis, and the focal distance to the object point is d_0, and the image The focal length to the point is d_1, the wavelength used is λ,
When the radius from the inside of the plurality of zones to the outer edge of the m-th zone representing the second integer is r_m, and when a natural number M is selected as the first integer, the optical path difference is expressed by the following formula: There are chemical formulas, tables, etc. ▼・・・・・・(CL
1) The following relationship holds true, and the relationship M≧3...(CL2) holds true, and the wavefront of the first light beam passing through the m-th zone is the same as the wavefront of the second light beam passing through the optical axis. δ_m=((m-1)/M-[(m-1)/M])λ・
・・・・・・Advances by phase δ_m expressed by (CL3) (
[] is a Gauss symbol) The phase type zone plate according to claim 1, which is formed as follows.