JP2759635B2 - Method and apparatus for generating undiffracted light beam - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an undiffracted light beam generating method and apparatus for generating an undiffracted light beam.

[0002]

2. Description of the Related Art A coherent light beam such as a laser beam has excellent straightness, and a narrow beam having a small beam width is used in many fields such as positioning. However, when light is transmitted with a certain aperture diameter, the beam expands due to diffraction. The divergence angle due to diffraction is proportional to λ / D, where λ is the wavelength of light and D is the aperture, so that a divergence angle due to diffraction increases as the beam diameter decreases.

[0003]

The spread of the beam width is proportional to the product of the spread angle and the propagation distance L (therefore, λ / D ·
(Proportional to L), a narrow beam becomes a thick beam when it propagates over a long distance. For example, a beam having a wavelength of 0.5 μm and a diameter of 1 mm spreads to about 50 cm at 1 km, and the accuracy of positioning and the like is improved. There was a problem of lowering.

[0004]

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and radiates a spherical wave having a concave light wavefront from an aperture of an optical system. Another object of the present invention is to provide a method for generating a non-diffracted light beam that distorts the light wavefront such that the curvature becomes smaller as the spherical wave moves toward the periphery of the light wavefront.

According to the present invention, there is provided an optical system which emits a spherical wave having a concave light wave front from an aperture surface, and the curvature becomes smaller near the front of the aperture surface of the optical system as the spherical wave moves toward the periphery of the light wave surface. It is an object of the present invention to provide a non-diffracted light beam generator comprising a correction optical system for distorting a light wavefront.

According to the present invention, there is provided a non-diffracted light beam generating a spherical wave having a concave light wave front and distorting the light wave front such that the curvature becomes smaller toward the periphery of the light wave front from an aperture surface of the optical system. It provides a method.

According to the present invention, there is provided an undiffracted light beam having an optical system having a concave light wavefront and radiating a spherical wave whose lightwave front is distorted so that the curvature becomes smaller toward the periphery of the light wavefront from an aperture surface. A generator is provided.

According to the present invention, in an optical system in which a spherical wave having a convex light wavefront is incident, the curvature becomes smaller or smaller as the spherical wave approaches the periphery of the light wavefront at the aperture of the optical system. The present invention provides a method for generating a non-diffracted light beam that distorts the light wavefront near or in the front of the optical system so as to be equivalent to the following.

According to the present invention, in an optical system in which a spherical wave having a convex light wave front is incident, the curvature decreases as the spherical wave approaches the periphery of the light wave front near the front surface of the aperture of the optical system. An object of the present invention is to provide a non-diffracted light beam generator provided with a correction optical system for distorting the light wavefront near the front surface of the optical system or in the optical system so as to be equivalent to reducing the size.

[0010]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The outline of the present invention will be described below. The present invention provides a method for distorting an optical wavefront near an aperture surface of an optical system such as a telescope, or distorting an optical wavefront at another place so as to be equivalent to distorting near an aperture surface, thereby obtaining an original light beam. To generate a non-diffracted beam at the center of. Here, the non-diffracted beam refers to a beam whose beam width does not change during propagation and looks as if it propagates without diffracting, or a beam close thereto.

Here, an optical system which is optically equivalent to a telescope will be described as an example of the optical system. First, the light beam radiated from the aperture surface is converted into a spherical wave having a concave light wavefront (a convex wave on the opposite side to the incident wave). Radiation of a spherical wave having a concave light wavefront, that is, a spherical wave of a convergent type (or incidence of a spherical wave in a divergent type) is based on the distance between an objective lens and an eyepiece of an optical system optically equivalent to a telescope (refractive type). Or the distance between the primary mirror and the secondary mirror (in the case of the reflection type) can be changed, and the distance may be made larger than the standard position of incidence and emission of a plane wave.

Then, a negative distortion is applied to the spherical wave. In other words, the optical wavefront is distorted so that the curvature becomes smaller toward the periphery (as the radius increases) (see FIG. 1). It is possible to generate an undiffracted beam with this distorted spherical wave.

Next, the principle of the present invention will be described in detail. When the light wavefront of the spherical wave is distorted as described above, the light beam
It becomes as shown in. At this time, an undiffracted beam is generated at the center due to the interference phenomenon of the light that crosses each other. Here, the shape of the light wavefront (distorted spherical surface) at the aperture is defined as h (ρ). However, assuming axial symmetry, the radius of the opening is a, and ρ is defined as a radius of a unit (ρ = 0 at the center, ρ = 1 at the end of the radius a). Further, assuming that the amplitude at an arbitrary point P separated from the aperture is u (P) and the light intensity is I (P), I (P) is represented by the following Equation 1.

[0014]

(Equation 1)

On the other hand, u (P) can be expressed using Fresnel integral, and is expressed by the following equation 2 when considering the axial symmetry of the optical system. (However, z≫ρ, r)

[0016]

(Equation 2)

Here, z and r (r = (x ² + y ² ) ^1/2 )
Are the coordinates of the point P, and indicate the distance from the opening surface and the distance from the z-axis, respectively. K is a wave number, and k = 2
π / λ. J ₀ is a 0th-order Bessel function. Further, ζ is the z-direction coordinate of a point on the light wavefront at the aperture,
It is represented by Equation 3 shown below.

[0018]

(Equation 3)

F (aρ) is the amplitude at the aperture,
Typical examples include a uniform distribution (light amplitude is constant without changing with radius) and a Gaussian distribution. Sub-beams generated in the center of the main beam (non-diffracted beam) is an intensity distribution in the form of a J ₀ ^2. (More precisely, as shown in Equation 2, the integral of the J ₀ ²⁾

In order to accurately obtain the beam profile (light intensity along the radius), the calculation of the Fresnel integral is executed according to Equation 2. On the other hand, it is also possible to determine the width of approximately undiffracted beam based on J _0. That is, a good approximation is obtained near the optical axis, and when the intensity distribution at the observation point is I (r), it is expressed by the following Expressions 4 and 5. Note that c 'is a constant.

[0021]

(Equation 4)

[0022]

(Equation 5)

Where θ is a ray (point Q on the light wavefront at the aperture)
, Which is the normal to the light wavefront at) with the z-axis. At this time, since θ is very small, sin θ ≒ θ. Further, if the moving radius of the point Q from the optical axis is ρ _a (ρ _a = aρ), the following Expression 6 is established.

[0024]

(Equation 6)

Here, the value of the zero-order Bessel function J ₀ is 1 /
2, that is, half value when the variable is 1.125.
That is, since J ₀ (1.125) ² = 0.5, the full width at half maximum (FWHM: Full Width Half)
If the Maximum) is 2r _b (r _b radius) to, .alpha.r _b =
Since the value is 1.125, the following Expression 7 holds.

[0026]

(Equation 7)

Further, the following Expression 8 is derived from Expressions 5 and 7.

[0028]

(Equation 8)

For example, wavelength 0.5 μm, diameter 10 cm
Ρ _a = 4 at the aperture of the laser beam (radius 5 cm)
When a light wavefront of 1 cm crosses the z-axis at 1 km,
θ = 4 × 10−5. Therefore, the half value width of the sub beam (undiffracted beam) at a distance of 1 km is FWHM = 0.44.
7 cm.

For reference, an example of an accurate calculation of the Fresnel integral is shown in FIGS. For a distorted spherical light wavefront as shown in FIG. 3, a beam pattern as shown in FIG. 4 is obtained. This is an example when the wavelength is 0.5 μm and the aperture diameter is 10 cm.
km).

A general thin laser beam is largely spread by diffraction, whereas the spread of the sub-beam at the center is very small. Further, if the light wavefront is made to be close to a conical shape, a purely undiffracted (light beam width does not change with distance and is constant) sub-beam can be obtained approximately.

The undiffracted beam to be propagated over a longer distance is obtained by using an optical system optically equivalent to a telescope having a larger aperture, forming a spherical surface having a smaller curvature, and applying an appropriate small negative distortion. realizable. (Ex. Caliber 10c
100m to 10km for m, 1km to 100k for 1m in diameter
m is possible)

Next, specific embodiments of the present invention are shown in FIGS. 5 (a) to 5 (c). FIG. 5A shows a first embodiment of the present invention. In FIG. 5A, a correction plate 6 is disposed in front of an opening surface 5 of an optical system 10 optically equivalent to a telescope, and a non-diffracted beam 4 is provided. 'Is a conceptual diagram showing a method of generating'.

FIG. 5 (b) shows an optical system optically equivalent to a telescope composed of an objective lens system 7 and an eyepiece lens system 8. As the eyepiece lens system 8, a concave lens system having a moderately small spherical aberration is used. FIG. 6 is a conceptual diagram showing a method of generating a non-diffracted beam 4 ′ using the method shown in FIG.

FIG. 5C shows a method in which light emitted from an optical system 10 which is optically equivalent to a telescope is reflected by a deformable mirror 9 to distort the light wavefront and generate an undiffracted beam 4 '. FIG.

In each of the above embodiments, the method of generating the undiffracted beam 4 'using each of the above optical systems as a transmitting device has been described. In FIGS. 5 (a) to 5 (c), By using each optical system as a receiving device and receiving the incident beam 4 '(in this case, the direction of the light beam is reversed in each figure), the imaging position in the optical system optically equivalent to the telescope is kept constant. can do.

As described above, the present invention has been described based on the embodiments. However, the present invention is not limited to the above-described embodiments, and can be implemented in any manner unless the configuration described in the claims is changed. it can.

[0038]

As described above, in the method and apparatus for generating a non-diffracted light beam according to the present invention, a thin beam can be produced over a long distance by generating a non-diffracted beam with a laser beam. And can be used for highly accurate positioning over a long distance. Also, if a telescope having a non-diffracting beam is used for receiving light, it is possible to view an object at an arbitrary distance with almost the same resolution (take an image) without changing the focal point position. Play.

[Brief description of the drawings]

FIG. 1 is a conceptual diagram illustrating a cross-sectional shape of a light wavefront having a distorted spherical surface according to the present invention.

FIG. 2 is a conceptual diagram illustrating a trajectory of a light ray on a light wavefront of a distorted spherical surface according to the present invention.

FIG. 3 is a graph showing a cross-sectional shape of a light wavefront having a distorted spherical surface according to the present invention.

FIG. 4 is a three-dimensional graph showing a beam pattern according to the present invention.

FIGS. 5A, 5B, and 5C are conceptual diagrams showing each embodiment of the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Distorted spherical surface 2 spherical surface 3 optical axis 4 light beam 4 'undiffracted beam 5 aperture 6 correction plate 7 objective lens system 8 eyepiece lens system 9 deformable mirror 10 optical system

Claims (6)

(57) [Claims] 1. A spherical wave having a concave light wavefront is radiated from an aperture surface of an optical system, and the curvature decreases as the spherical wave approaches the periphery of the light wavefront near the front surface of the aperture surface of the optical system. A non-diffracted light beam generating method characterized by distorting the light wavefront as described above. 2. An optical system for radiating a spherical wave having a concave light wavefront from an aperture surface, and near the front surface of the aperture surface of the optical system, the curvature decreases as the spherical wave approaches the periphery of the light wavefront. A non-diffracting light beam generator comprising: a correction optical system for distorting a light wavefront. 3. A non-diffracting light wave which has a concave light wavefront and radiates a spherical wave whose lightwave front is distorted so that the curvature becomes smaller toward the periphery of the light wavefront from an aperture surface of an optical system. Light beam generation method. 4. An optical system comprising: a concave optical wavefront; and an optical system that emits a spherical wave whose optical wavefront is distorted so that the curvature becomes smaller toward the periphery of the optical wavefront from an aperture surface. Diffracted light beam generator. 5. In an optical system in which a spherical wave having a convex light wavefront is incident, the curvature becomes smaller or smaller as the spherical wave approaches the light wavefront at the aperture of the optical system. A method for generating a non-diffracted light beam, wherein the optical wavefront is distorted in the vicinity of the front surface of the optical system or in the optical system. 6. In an optical system in which a spherical wave having a convex light wavefront is incident, the curvature decreases or decreases as the spherical wave approaches the light wavefront near the front surface of the aperture surface of the optical system. A non-diffracting light beam generating apparatus provided with a correction optical system for distorting the light wavefront near or in front of the optical system so as to be equivalent to the above.