JPH043106A - Endoscope - Google Patents

Abstract

PURPOSE:To obtain images having high quality by specifying the length of an image guide fiber bundle to <=1m and the average value of the spacing between adjacent cores to <=9mum. CONSTITUTION:An insertion part 12 is constituted of an inside pipe 19 which contains an objective lens 23 of an observation optical system and a part of the image guide fiber bundle 24, a disposing means inserting pipe 20 into which a disposing means is inserted, an outside pipe 21 contg. the two pipes 19, 20, and the image guide fiber bundle 22 filling the spacings between the pipes 19, 20 and the outside pipe 21. The image guide fiber bundle 24 is formed to <=1m length and <=9mum average value of the spacing between the adjacent cores. The number of picture elements is increased and bright images are obtd. The images which are high in contrast, are free from coloration and have the high quality are obtd. in this way.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to endoscopes, particularly endoscopes that are relatively short and have an extremely small diameter.

[Conventional technology]

A fiberscope, which is one of the conventional endoscopes of this kind, is provided in the rigid tip end of the fiberscope body 1 and has a built-in brightness diaphragm 2a, as shown in FIG. 11, for example. an objective lens 2 for forming an image;
It is equipped with an observation optical system 5 consisting of an image guide fiber bundle 3 that transmits an image by an objective lens 2 to the rear end of the fiberscope main body 1, and an eyepiece 4 for observing the transmitted image. Scope body 1
A light source lamp 7 in a light source device 6 provided outside, a condensing lens 8 that condenses the light from the light source lamp 7, and a condensing lens 8 that transmits the light collected by the condensing lens 8 to the tip of the fiberscope body 1. It was equipped with an illumination optical system 11 consisting of a light guide fiber bundle 9 and an illumination lens 10 that is provided within the rigid tip end portion of the fiberscope body 1 and irradiates the transmitted light toward the object O.

The reason why the image guide fiber bundle 3 is twisted once in the middle is to invert an inverted image formed on the entrance end surface by the objective lens 2 to form an erect image at the exit end surface.

Furthermore, even if the insertion section of a fiberscope is bent, there is no vignetting of the field of view unlike a rigid scope that uses a relay lens, so there is little deterioration in image quality even if the insertion section is lengthened; It is determined by the number of cores, that is, the number of pixels, and is inferior to a rigid mirror using a relay lens. In addition, the image guide fiber bundle 3 is a very flexible one that is constructed by bundling a large number of fibers with a cladding with a lower refractive index wrapped around the core, and a cladding with a lower refractive index between the many cores. There are less flexible conduits that are filled and hardened with a material that acts as a low cladding, and light leakage (crosstalk) due to evanescent waves occurs in all conduits, but is particularly noticeable in the case of conduits.

[Problem to be solved by the invention]

By the way, in recent years, the scope of application of endoscopes has expanded, and extremely thin endoscopes with a length of about 50σ and an outer diameter of a few thresholds or less at the insertion part, which are used for the ureter, uterus, nostrils, biliary tract, etc., have been developed. It's starting to happen. When considering the image transmission system of such an endoscope, the core spacing of the image guide fiber bundle 3 used in conventional fiberscopes is generally 10μ.
m or more, so in the case of a very thin fiberscope, a sufficient number of pixels cannot be secured and the image quality deteriorates.

In addition, when the core spacing is shortened to increase the number of pixels, the cladding thickness becomes thinner, and from a core spacing of about 9 μm, light leakage due to evanescent waves increases crosstalk in the case of conduits and reduces image contrast. In addition, in the case of a flexible material, the total amount of transmitted light decreases, resulting in a dark image, and there is a problem in that the deterioration is particularly significant when the diameter is about 7 μm or less. Furthermore, since light leakage due to evanescent waves depends on the wavelength, it is known to have a negative effect on image quality in terms of coloring, and in both cases it has been extremely difficult to obtain good images. Furthermore, in order to prevent light leakage due to evanescent waves, the rad thickness (
However, if the core spacing is shortened to ensure a sufficient rad thickness, the core diameter will become smaller and the area occupied by the core in the image guide fiber bundle 3 will decrease. Therefore, there was a problem that the amount of light transmitted by the image guide fiber bundle 3 decreased and the image became dark.

In view of the above-mentioned problems, the present invention provides an endoscope with a relatively short overall length and an extremely narrow outer diameter of the insertion section, which has a large number of pixels, a bright image, high contrast, and no coloration, and which provides high image quality. The purpose is to provide an endoscope that can obtain images.

[Means and effects for solving the problems] One endoscope according to the present invention includes an objective lens and an image guide fiber bundle that transmits an object image formed by the objective lens. The image guide fiber bundle is characterized in that the length is 1m or less and the average value of the spacing between adjacent cores is 9μm or less.

In addition to the above configuration, the objective lens is equipped with an aperture diaphragm, and the image-side numerical aperture of the objective lens is NAoB4, and the numerical aperture of the image guide fiber bundle is NA lc. When doing so, it is characterized by satisfying the following conditions.

N A + N AoBJ ” When −α, α
≧0.01 This will be explained below.

There are major restrictions on the image transmission system of an endoscope whose insertion portion has an extremely small outer diameter, and it is generally necessary to keep the outer diameter to about 1 mm or less. Even if a conventional image guide fiber bundle with a fiber spacing of 10 μm or more is used in the image transmission system of such an endoscope, a good image cannot be obtained for the reasons mentioned above.

Here, we will quantitatively discuss the leakage of light due to evanescent waves caused by the thinning of the cladding of the fibers in the image guide fiber bundle. The intensity of an evanescent wave with a certain wavelength λ at a position a distance t from the interface between the core and the cladding to the cladding side i (
When t) is determined from the intensity of refracted light derived from Maxwell's equation, it can be expressed by the following equation.

(1□1(OllXp(-(r(+/λl) [[-nl
−nl n + ]・・・(1) However, l (0) is the intensity of refracted light when 1=0, nl
nl is the refractive index of the core cladding, no is the refractive index of the medium on the incident side of the image guide fiber bundle (1 if it is air), and θ. represents the incident angle of the light ray from the incident medium to the core of the image guide fiber bundle. When the thickness of the cladding is T, the intensity i (
It is considered that some of the light in T) leaks into or is absorbed by the outer medium, so as is clear from equation (1), the thickness of the cladding (the distance between adjacent cores in the case of a conduit) T is This is one factor that determines the amount of light leakage.

Equation (1) here specifies the loss of light due to one total reflection by the cladding, but in an actual image guide fiber bundle, the light is repeatedly reflected through the image guide fiber bundle. Propagates within each core. Therefore, even if there is a large amount of light leakage per total reflection determined by equation (1), it is possible to obtain a relatively good image if the number of total reflections of light in the image guide fiber bundle is small. For example, if the length of the image guide fiber bundle is relatively short, such as 1 m or less, the influence of light leakage will be small even if the core spacing of the image guide fiber bundle is set to 9 μm or less. In this case, by reducing the core spacing from the conventional approximately 10 μm to, for example, 7 μm or less, it is possible to obtain a good image with approximately twice the number of cores, that is, the number of pixels.

Also, if the leakage of light per total reflection can be reduced,
Even better images can be obtained, but for this purpose, i
The total amount of evanescent waves can be reduced by reducing (t). For this purpose, (nl ” ng ri
(no Stnθ.) The value of 2 should be made as large as possible, and for an image guide fiber bundle of lm or less, its NA (n, −n2”) is set as NAIG”, and nosioθ. is the image side N on the optical axis of the objective lens
A(NAOBJ) If the following equation is satisfied, light leakage due to evanescent waves is within a practically acceptable range and does not pose a problem.

When NAI NAOBJ '=α, α≧0.0
1...(2) Furthermore, the formula (
In order to reduce the value of nosinθ in 1) over the off-axis images, in addition to equation (2), the maximum value 1θIo1 of the inclination angle with respect to the principal ray and the optical axis at each image height satisfies the following equation. This is desirable in order to obtain a good image up to the periphery.

θ...≦10°...(3) Furthermore,
The relationship between the average core diameter (φ,) and the average core spacing (D) of the image guide fiber bundle preferably satisfies the following equation in order to obtain bright images with extremely little crosstalk and coloring.

0, 4≦φ, /D≦0.9 (4
) If the values of φ and /D become smaller than the lower limit of conditional expression (4) above, the area occupied by the core in the cross section of the image guide fiber bundle becomes small, making it impossible to obtain an image of sufficient brightness. Furthermore, when the value of φl//'D increases beyond the upper limit, the thickness of the cladding becomes thinner, and the leakage of light due to the evanescent wave described above increases.

Furthermore, in order to reduce the leakage of light due to evanescent waves, it is conceivable to reduce the number of total reflections as described above. The number of total reflections η(θ0) when a light beam incident at a certain incident angle (θ.) propagates eastward through an image guide fiber of a certain length (L) can be expressed by the following equation.

η(θ, ) = (L/φ1) X (nl I:l
lθ1)/a lower] π■π■...(5) As is clear from this equation (5), the number of total reflections η(θ.

) depends on the length (L) and core diameter (φ1) of the image guide fiber bundle. Therefore, in order to reduce the number of total reflections, reduce light leakage due to evanescent waves, and ensure high image quality, it is practically desirable to satisfy the following equation.

lXl0-'≦φ, /L (6) Note that the objective lens may be a non-homogeneous medium lens. or,
As the image guide fiber bundle, use a conduit or one consisting of a conduit on the light incidence side and a flexible part on the light exit side.It is recommended that at least the light incidence side be a conduit. This is preferable for reducing the diameter of the part. At this time, when these image guide fiber bundles are used in a rigid scope with a length of about 50 ann,
It is also excellent in practical use because it does not cause vignetting of the field of view when the insertion section is curved, which occurs with rigid endoscopes that use relay lenses in the image transmission system. In addition, in a rigid endoscope having a figure-7 or crank-shaped eyepiece, in order to simplify the structure of the refracting part, the image guide fiber bundle in this part is flexible or bendable. It is desirable to use an image guiding fiber bundle that includes both a conduit and a flexible section. The image guide fiber bundle may be made of glass, quartz, or plastic.

〔Example〕

Hereinafter, the present invention will be described in detail based on the illustrated embodiments.

Fig. 1 is an overall view of the first embodiment of the endoscope according to the present invention, Fig. 2 is a sectional view taken along the line ■-■ in Fig. 1, and Fig. 3 is a diagram showing the observation optical system of the first embodiment. It is.

This embodiment is a rigid endoscope consisting of an insertion part 12 and a main body part 13, as shown in FIG. The eyepiece tube 15 is provided with an eyepiece tube 15 that has a cylindrical shape, and a treatment instrument insertion opening 16 provided at the rear.The eyepiece tube 15 is also provided with a diopter correction ring I7 and an eyepiece 18.

In addition, as shown in FIG. 2, the insertion section 12 includes an inner tube 19 that houses an objective lens of an observation optical system to be described later and a part of an image guide fiber bundle, and a treatment instrument insertion tube into which a treatment instrument (not shown) is inserted. A tube 20 and an outer tube 21 containing both tubes 19 and 20.
and a light guide fiber bundle 22 (part of the illumination system) that fills the gap between both tubes 19 and 20 and the outer tube 21.

The observation optical system is composed of an objective lens 23, an image guide fiber bundle 24, and an eyepiece optical system 25, as shown in FIG. The objective lens 23 includes a wedge-shaped prism 27 whose object side surface is perpendicular to the optical axis and whose image side surface is oblique to the optical axis, and an aperture stop 26 is provided on the image side surface.
Two positive lenses 29 fixed by a lens frame 28.
It consists of 30. Note that the aperture stop 26 may be formed on the image side surface of the wedge prism 27 by vapor deposition,
It may also be formed by pasting a thin plate. The image guide fiber bundle 24 is a very flexible bundle of fibers made of multicomponent glass consisting of a core, a cladding, and an acid-eluting glass layer, and has an 18-degree angle in the middle.

By twisting, the inverted image formed on the entrance end surface by the objective lens 23 becomes an erect image on the exit end surface, and both ends are bundled with bases 31 and 32, and the middle part is placed inside the protective tube 33. It is contained. The objective lens 23 and the distal end of the image guide fiber bundle 24 are housed in the inner tube 19.

The eyepiece optical system 25 includes a field stop 34 attached to the exit end face of the image guide fiber bundle 22, a dustproof cover glass 35, an eyepiece lens 36, and an eyepiece cover glass 37.

A numerical example of this example is shown below.

! Objective lens N A OBJ O, 1 Image guide fiber bundle Flexible fiber bundle (with acid-dissolved layer) Material
Multi-component glass length 1000mm Outer diameter 1.1++on NA, 0.6 Average core spacing 7μm Average core diameter 4.3μm Average cladding thickness 1μm (i) α=0.35 (ii) l θl,,,=1. 78°(ii)
φ1/D=0.614 (iv) φ,/L=41X10! Main objective lens N A oalo, 2 Image guide fiber bundle Flexible fiber bundle (with acid-dissolved layer) Material
Multicomponent glass Length 300- Outer diameter 0.8am NA+c O,6 Average core spacing 5μm Average core diameter 3μm Average cladding thickness 0.7μm (i) α=0. ．． 32 (ii) l θ 1,, = 1.24° (ii
i) φ, /D=0.6 (iv) φ, /L=lOX10 [What objective lens N A OBJ O,2 Image guide fiber bundle Flexible fiber bundle (with acid-soluble layer) Material
Multi-component glass length 500 am Outer diameter 1.1+nm NA IG 0.6 Average core spacing 6°3μm Average core diameter 3.9μm Average cladding thickness 0.9μm (i) α=0.32 (ii) lθ1. ,, -1.78°(ii)
φ, /D = 0.619 (iv) φ, /L = 7.8X10 This example is configured as described above, the length force of the image guide fiber bundle is less than lm, and the average core spacing is also 9 μm. In addition to the following, the above conditional expression (2), (31, (4),
<6), the number of pixels is large (and the image is bright, and the contrast power is high and there is no coloration).
High quality images can be obtained.

In addition, in the case of this embodiment, since the optical axis on the object side is refracted by about 8 degrees with respect to the longitudinal axis (optical axis) of the image guide fiber bundle 24 by the wedge prism 27 included in the objective lens 23, the actual When the treatment instrument is inserted into the treatment instrument insertion tube 20 for treatment, the treatment instrument can be observed at the center of the visual field, which is very preferable.

FIG. 4 is a diagram showing the observation optical system of a rigid endoscope according to the second embodiment, and FIG. 5 is an enlarged sectional view of the main parts of the endoscope insertion section and main body of the second embodiment.

This uses a conduit 38 between the objective lens 23 and the eyepiece optical system 25 in the part corresponding to the insertion part, and uses a flexible fiber bundle 24 in the part behind it that is bent toward the eyepiece optical system 25. , both are base 31
It is made by connecting. Note that since the conduit 38 is relatively hard, there is no need to cover it with a protective tube, and on the contrary, there is no need to provide a cap at the tip where the objective lens 23 is located.
This is advantageous in reducing the diameter of the insertion portion. Further, the fiber bundle 24 is twisted by 180° in the middle as in the first embodiment.

It should be noted that the image guide fiber bundle may be entirely composed of a conduit if it is sufficiently thin and can sufficiently withstand bending at least in the bendable portion.

A numerical example of this example is shown below.

! Objective lens NAOBJ O,I 5 Image guide fiber bundle conduit + flexible fiber bundle (with acid-dissolved layer) Material Multi-component glass Length 500+n+a Outer diameter 1.1 tmn NA+c O,56 Average core spacing 6μm Average core Diameter: 3.8 μm Average cladding thickness: 0.9 μm (i) α=0°291 (ii) θ ,,, =5. 1 36
(iii) φ, /D=0.633(1v)
φ, /L=7.6XlO FIG. 6 is a diagram showing the observation optical system of the third embodiment.

This consists of using a radial inhomogeneous medium lens whose refractive index changes depending on the distance from the optical axis as the objective lens 23, and a conduit 38 in which the entire image guide fiber bundle is twisted by 180 degrees in the middle. And brightness aperture 2
6 is arranged in the eyepiece optical system 25.

Note that NAOBI in this embodiment is not the image-side NA of the objective lens 23 but the NA defined by the aperture diaphragm 26 of the eyepiece optical system 25;
The image side N of the objective lens 23 in the sense of defining
As with A, it is desirable to satisfy the conditional expressions (21, (3)) described above.

A numerical example of this example is shown below.

Viewing 1 Image objective lens Radial heterogeneous medium lens Eyepiece lens NA OBJ O, 125 Image guide fiber bundle conduit (no acid-dissolved layer) Material Multi-component glass Length 500 mm Outer diameter 1.1 NAIG O, 6 Average core spacing 6μm Average core diameter 3.8μm Average cladding thickness 0.9μm (i) α=0.344 (ii) l θ 1ffi,,=0.8゜(i
ii) φ, /D=0.633(iv) φ
, /L = 7.6 Therefore, the insertion portion can be made even thinner.

FIG. 7 is a diagram showing the observation optical system of the fourth embodiment.

This means that the entire image guide fiber bundle is connected to the conduit 38.
Since the conduit 38 is normally not twisted and the image of its end surface becomes an inverted image, a relay lens 3 is installed between the end surface of the shooting hole and the eyepiece optical system 25 in order to turn the inverted image into an erect image.
9 is arranged. A field diaphragm 34 is placed at the position where this relay lens 38 forms an image. The objective lens 23 consists of a cover glass 4o, a positive lens 29 cemented with an aperture diaphragm 26 in between, and a positive lens 30 behind the positive lens 29, and does not include a wedge prism. Note that the relay lens 39 may be a multiple-time relay instead of a one-time relay as long as the obtained image is an erect image. Further, the relay lens may be placed on the objective lens 23 side, or may be placed on both the eyepiece optical system 25 side and the objective lens 23 side.

A numerical example of this example is shown below.

Objective lens N AOEI O, 15 Image guide fiber bundle conduit (no acid-dissolved layer) Material Multi-component glass Length 700 mm Outer diameter 1 mm NA, 0.56 Average core spacing 6 μm Average core diameter 4.2 μm ( i) α=0.291 (ii) θ l ffi,, =2.3
5゜(ij) φ, /D=0.7 (iv) φ, /L=6 Since adjacent fibers share a cladding with each other, even if the distance between the cores is small compared to a flexible fiber bundle, the area occupied by the cores can be made thicker (as a result, a brighter image can be obtained. Since a relay lens is used, it is also possible to correct aberrations.

FIG. 8 is a diagram showing the observation optical system of the fifth embodiment.

This means that the entire image guide fiber bundle is connected to the conduit 38.
In addition, during the manufacturing process of the conduit 38, the middle part is twisted by 180 degrees.

A numerical example of this example is shown below.

11 Supervision 1 Objective lens N A OBJ O, 1 Image guide fiber bundle conduit (no acid-dissolved layer) Material Quartz Length 500 mm Outer diameter 0.5 mm NA 0.35 Average core spacing Average core diameter 4 μm 3.2 μm (i ) (ii) (iii) (1v)! 8M [Ki Objective Lens AOBJ Image Guy Conduit Material Length Outer Diameter A lc Average Core Spacing Average Core Diameter α = 0.113 θ 1□, = 1.78” φ, /D = 0.8 φ, /L = 6 .4X10 0.1 Fiber bundle (no acid-dissolved layer) Quartz 700 菰0, 8鵬0.35 6μm 4.2μm (i) α=0.113 (ii) l θ l□, = 1.78° (city )
φ, /D=0.7 (iv) φ, /L=6X10 FIG. 9 is a diagram showing the observation optical system of the sixth embodiment.

This means that the entire image guide fiber bundle is
It consists of a twisted conduit 38, and between the exit end of the conduit 38 and the eyepiece optical system 25, a reflecting prism 41. Relay lens 39, reflective prism 41.
A crank-shaped optical path consisting of a relay lens 39 is arranged so that the eyepiece section faces straight back. Although the aperture stop 26 is arranged inside the relay lens 39, it goes without saying that it may be arranged inside the objective lens 23 or the eyepiece optical system 25.

A numerical example of this example is shown below.

il supervisory relay lens N A OBJ O,2 Image guide fiber bundle conduit (no acid-dissolved layer) Material Plastic Length 200mm Outer diameter 1. lmm NA O,52 Average core spacing 7μm Average core diameter 5.2μm (i) α=0.23 (ii) l θ 1□,,=9.15゜(ii
i) φ, /D=0.743(iv) φ,
/L=3.5XI (1 FIG. 10 is an overall view mainly showing the observation optical system of the seventh embodiment.

This is because, in the eyepiece optical system of the first embodiment, an imaging lens 42 is arranged in place of the eyepiece, and then an optical low-pass filter 43 made of a crystal plate and a solid-state image sensor 44 are arranged.
A TV left camera 5 with a built-in camera is attached.

In this case, the conduit 38 is not twisted 180 degrees, nor is there a relay lens to reflect the image back and forth. This is because observation is carried out on a TV monitor.
This is because the solid-state image sensor 44 of the left camera 5 may be placed with respect to the conduit 38 so that the image on the TV monitor is not reversed.

Furthermore, interference fringes called moire occur on the TV monitor due to interference between the regular arrangement of fibers on the exit end face of the conduit 38 and the regular arrangement of pixels of the solid-state image sensor 44, but this moire is harmful to observation. Therefore, in order to reduce this to a level that poses no problem in practice, an optical low-pass filter 43 is disposed in front of the solid-state image sensor 44 in this embodiment. In addition, the optical low-pass filter 43
Similar effects can be obtained by using a phase plate, aberration of the imaging lens 42, or defocus of the imaging lens 42 instead.

A numerical example of this example is shown below.

! Objective lens NAoB, 0.25 Image guide fiber bundle conduit (no acid-dissolved layer) Material Quartz Length 1000mm Outer diameter 0.8 mm NA+c 0-35 Average core spacing 4μm Average core diameter 2.8μm (i ) α = 0.0 6 (ii) l θ 1□,, = 1.78° (ii
) φ, /D=0゜7 (iv) φ+ / L = 2.8 X l
O However, in each numerical example above, α=NAi −N
AOBJ”.

〔Effect of the invention〕

As described above, the endoscope according to the present invention has a relatively short overall length and an extremely narrow outer diameter of the insertion section, has a large number of pixels, has a bright image, has high contrast, is not colored, and has a high quality. It has a practically important advantage of being able to obtain high-quality images.

[Brief explanation of drawings]

Fig. 1 is an overall view of the first embodiment of the endoscope according to the present invention, Fig. 2 is a sectional view taken along the line ■-■ in Fig. 1, and Fig. 3 is a diagram showing the observation optical system of the first embodiment. , FIG. 4 is a diagram showing the observation optical system of the second embodiment, FIG. 5 is an enlarged cross-sectional view of main parts of the endoscope insertion section and main body of the second embodiment, and FIGS. 6 to 9 are respectively FIG. 10 is an overall view mainly showing the observation optical system of the seventh embodiment, and FIG. 11 is an overall view of the conventional example. 12...Insertion section, 13...Main body section, 14...
・Light guide base, 15...Eyepiece tube, 16...
...Treatment instrument insertion port, 17...Diopter correction ring, 18
...Eyepiece, 19...Inner tube, 20...
Treatment instrument insertion tube, 21...outer tube, 22...light guide fiber bundle, 23...objective lens, 24...
... Image guide fiber bundle, 25 ... Eyepiece optical system, 26 ... Brightness diaphragm, 27 ... Wedge prism, 28 ... Lens frame, 29.30 ... Positive Lens, 31.32...Base, 33...Protection tube, 34...Field diaphragm, 35...Dust-proof cover glass, 36...Eyepiece, 37...Eyepiece Cover glass, 38...Conduit, 39...Relay lens, 4o...Cover glass, 41...
Reflection prism, 42...imaging lens, 43...
Optical low-pass filter 44...solid-state image sensor, 45...TV camera. Figure 11 Procedural amendment (formality) Item "3. Detailed explanation of the invention J" in the specification to be amended. August 8, 1990 7, Contents of amendment Specification of the Commissioner of the Japan Patent Office, page 1, 1 In line 8, “3゜Claims” was corrected to “3. Detailed Description of the Invention.” The case is listed in Japanese Patent Application No. 104936/1996. Above 2゜Name of invention

Claims (2)

[Claims] (1) In an endoscope equipped with an objective lens and an image guide fiber bundle that transmits an object image formed by the objective lens, the image guide fiber bundle has a length of 1 m or less and a distance between adjacent cores. An endoscope characterized in that the average value of the intervals between them is 9 μm or less. (2) The objective lens is equipped with an aperture diaphragm, and when the image-side numerical aperture of the objective lens is NA_O_B_J and the numerical aperture of the image guide fiber bundle is NA_I_G, the following conditions are satisfied. Claim (1)
The endoscope described in. When NA_I_G^2-NA_O_B_J^2=α, α≧0.01