JPH06194571A - Objective lens of endoscope - Google Patents

Abstract

PURPOSE:To eliminate chromatic aberrations, to decrease the number of lens elements and to reduce a cost by arranging a diffraction type optical element having a positive effect nearer the image side than a full-aperture diaphragm in a lens system. CONSTITUTION:The focal length of the diffraction type optical element of the objective lens of the endoscope applied to an extremely fine fiber scope to be mainly used for a blood vessel, etc., is about 10 times the focal length of ordinary lenses and, therefore, the overall length of the telecentric optical system in which the lens near the image plane is the diffraction type optical element increases too much. This objective lens is, thereupon, constituted, successively from the object side, the diffraction type optical element (provided on the image side surface of a parallel plane plate) having the diaphragm and the positive effect and the positive lens consisting of ordinary glass. The conditions of equation 1<fD/D<3 are satisfied when the focal length of the diffraction type optical element is defined as fD and the distance from the diaphragm to the optical element as D. The maintenance of the telecentric characteristic is difficult when the lower limit of the above-mentioned conditions is exceeded. The eclipse by the total reflection of the positive lens is of a problem when the upper limit is exceeded.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention is used for inserting into a human body cavity for diagnosis and treatment, or for inserting into a pipe and inspecting the state of corrosion of its inner wall. The present invention relates to an objective lens of an endoscope.

[0002]

2. Description of the Related Art Many conventional objective lenses for endoscopes have a retrofocus type lens structure as shown in FIG. This is because the end face of the image guide fiber bundle, which is a bundle of glass fibers, is placed on the image plane, or a solid-state image sensor such as a CCD is placed. Therefore, if the incident angle on the image plane is large, light will leak through the glass fibers. Or
This is because the solid-state imaging device of the mosaic filter type causes color shading, so that the objective lens needs to satisfy a telecentric condition, and an objective lens having a wide angle of view is desired from the viewpoint of operability of the endoscope. As such a retrofocus endoscope objective lens, for example,
A lens system described in JP-A-2-74912 is known.

In such a conventional endoscope objective lens, a cemented lens is used to correct chromatic aberration, and the number of constituent lenses increases.

In recent years, a diffractive optical element utilizing the diffraction phenomenon, that is, a diffractive optical element [Di
ffractive Optics Elements
(DOE)] is known. This diffractive optical element
It has the following actions.

A normal optical glass refracts according to Snell's law represented by the following equation in FIG.

Nsin θ = n′sin θ ′ (1) where n is the refractive index of the incident side medium, n ′ is the refractive index of the exit side medium, θ is the incident angle of the light beam, and θ ′ is the outgoing angle of the light beam. .

On the other hand, in the diffraction phenomenon, light is refracted according to the law of diffraction represented by the following equation, as shown in FIG.

Nsin θ−n′sin θ ′ = mλ / d (2) where m is the order of diffracted light, λ is the wavelength, and d is the lattice spacing.

An optical element that refracts a light beam according to the above equation (2) is a diffractive optical element. In this equation (2), d is changed according to the ray height, the outgoing angle θ ′ of the primary light is changed according to the ray height, and the light is condensed at one point. An optical element (diffractive lens) can be made. However, as it is, it is generally called a Fresnel zone plate, and because it is shielded in a lattice shape and light of an order other than the first order is generated, a large amount of light is wasted. The cross-sectional shape called a kinoform as shown in (A) is serrated. As a result, the incident light is blazed and the first-order diffraction efficiency becomes 100%. actually,
It is difficult to process into a complete sawtooth shape, and as shown in FIG.
Even so, the diffraction efficiency is almost 90% or more.

Next, the effect of using the above-mentioned diffractive optical element will be described.

In the case of a thin lens, the relationship shown in the following equation (3) is established.

1 / f = (n−1) (1 / r ₁ −1 / r ₂ ) (3) where f is the focal length, r ₁ and r ₂ are the radii of curvature of the entrance and exit surfaces, and n Is the refractive index of the lens.

Differentiating both sides of the above equation (3) with respect to the wavelength λ yields the following equation (4).

Df / dλ = −f (dn / dλ) / (n−1) Δf = −f {Δn / (n−1)} (4) In the case of a diffractive optical element, λf = C (constant). Because there is
f = C / λ. Differentiating both sides of this f = C / λ by λ yields equation (5) as follows.

Df / dλ = −C / λ ² = −f / λ Δf = −f (Δλ / λ) (5) Since Δn / (n−1) = ν, equations (4) and (5) Therefore, ν = λ / Δλ. Therefore, v _d of the diffractive optical element is as follows.

Ν _d = λ _d / (λ _F −λ _C ) = − 3.453 (6) As described above, the diffractive optical element has a very large negative dispersion characteristic. Normal glass has a dispersion property of about 20-100.
Therefore, by combining an ordinary lens and a diffractive optical element, a great effect can be exerted in removing chromatic aberration. The simplest design method of such a diffractive optical element is to use an automatic design program having a function of designing HOE, that is, Holographic Optics Elements, among the commonly used automatic design programs. Is. Ultra-high index lens (U
By assuming a lens called intra-High Index Lens) as a diffractive optical element, it can be designed even by using a normal lens automatic design program. In this regard, SPIE Vol. 126, 4
6-53 (1977). In the ultra-high index lens in which the refractive index n is n >> 1, the relationship expressed by the following equation (7) is established.

(N-1) dz / dh = nsin θ−n′sin θ ′ (7) where n ′ is the refractive index of the medium on the exit side, θ, θ ′ are the incident and exit angles of the light beam, and n is The refractive index of the substrate of the diffractive optical element, z is the wall thickness of the ultra-high index lens.

The following expression (8) is obtained from the expressions (2) and (7).

(N-1) dz / dh = mλ / d (8) If an aspherical surface is defined as an ultra-high index lens, it is expressed as follows. z = Cy ² / [1+ (1-C ² Py ² ) ^1/2 ] + By ² + Ey ⁴ + Fy ⁶ + Gy ⁸ + ... (9) However, as shown in FIG. 28, z is the optical axis (image Direction is positive), y is the coordinate axis in the meridional direction among the coordinate axes orthogonal to the z axis with the origin at the intersection of the surface and the z axis, C is the curvature of the reference surface, P is the conical constant P = 1-e ² (e Is a value given by eccentricity), B, E, F, G, ... are secondary and 4 respectively.
It is an aspherical coefficient of the next order, the sixth order, the eighth order, .... Fig. 28
In, O is an object and I is an image.

From the expressions (8) and (9), the pitch d of the diffractive optical element at a certain ray height is expressed by the following expression (10). d = m [lambda / Hence [(n-1) {Ch / (1-C 2 Ph 2) 1/2 + 2Bh + 4Eh 3 + 6Fh 5 + 8Gh 7 + ····}] (10), Ultra - using high index lens By designing, the surface shape of the diffractive lens equivalent to the lens data can be obtained.

[0021]

In the lens system having the structure shown in FIG. 24 described above, it is necessary to use a cemented lens composed of at least two lenses in order to remove chromatic aberration. There was a problem that it increased and the cost increased.

It is an object of the present invention to provide an endoscope objective lens in which chromatic aberration is eliminated and the number of lenses is reduced to reduce the cost by using a diffractive optical element instead of the cemented lens.

[0023]

The endoscope objective lens of the present invention includes at least an aperture stop in the lens system,
It is characterized in that a diffractive optical element having a positive action is arranged on the image side of this diaphragm.

Further, in the endoscope objective lens of the present invention, by disposing a lens component having a positive refractive power further on the image side than the diaphragm, a better lens system can be obtained.

Further, in the endoscope objective lens of the present invention,
It is also preferable to arrange a lens distribution having a negative refractive power on the object side of the stop.

In a normal endoscope objective lens, in order to secure a certain degree of telecentricity (preferably the light exit angle is within 0 ° ± 10 °), a diaphragm is arranged near the front focal point of the positive lens. It is necessary to be done at least. However, in the case of such a lens configuration, lateral chromatic aberration occurs in the −y direction and axial chromatic aberration occurs in the −z direction on the image plane.

The diffractive optical element is equivalent to an ultra-high index lens having a negative Abbe number, and if a diffractive optical element having a positive action is arranged closer to the image side than the diaphragm, it will have chromatic aberration of magnification and axial power. Upper chromatic aberration can be corrected well.

Further, in a normal endoscope objective lens, a negative lens is arranged on the object side of the diaphragm in order to widen the angle of view. When the negative lens is arranged closer to the object side of the stop, the chromatic aberration of magnification is largely generated in the −y direction on the image plane, and the axial chromatic aberration is slightly canceled by the action of the negative lens and the action of the positive lens. It fits, but occurs in the -z direction. The chromatic aberration of these magnifications and the axial chromatic aberration can be satisfactorily corrected by the diffractive optical element having a positive action arranged on the image side of the diaphragm.

When aberration correction is performed by the ultra-high index lens, the achromatic condition of the contact thin lens of the following formula (11) will be considered. Σ 1 / (f _i ν _i ) = 0 (11) Since the Abbe number of ordinary glass and the Abbe number of ultra-high index lenses are different by one order, the focal length of ultra-high index lenses is , It is necessary to make the order different by one digit compared with the focal length of other glass lenses. Therefore, in order to correct chromatic aberration using an ultra-high index lens, the focal length of the entire system is f, and the ultra-high index is
If the focal length of the index lens is f _D , it is desirable to satisfy the following condition (12). 3f <f _D <100f (12) When the lower limit of the condition (12) is exceeded, it becomes difficult to correct the axial chromatic aberration, and when the upper limit of the condition (12) is exceeded, the correction capability of a normal glass lens can only be obtained. Therefore, it is meaningless to use a diffractive optical element.

[0030]

EXAMPLE Examples of the endoscope objective lens of the present invention will be described below. Examples 1 to 6 described below have the following data with the configuration shown in FIGS. Example 1 f = 1, F / 2.3, 2ω = 51.0 °, IH = 0.3952 r ₁ = ∞ (aperture) d ₁ = 1.2587 n ₁ = 1.883 ν ₁ = 40.78 r ₂ = 3334.5350 (aspherical surface) d ₂ = 0 (DOE) n ₂ = 1001.42 ν ₂ = -3.45 r ₃ = ∞ d ₃ = 0.3688 r ₄ = 1.1245 d ₄ = 1.7455 n ₃ = 1.883 ν ₃ = 40.78 r ₅ = ∞ d ₅ = 0.0376 n ₄ = 1.56384 ν ₄ = 60.69 r ₆ = ∞ aspherical surface coefficient P = 1, B = 0, E = -0.78889 × 10 ^-4 , F = 0.99820 ×
10 ^-4 G = -0.45346 × 10 ^-3 f _D = 3.333, h _M = 0.225, h _C = 0.296, f _D / D =
2.648 E ₁ = 1.3, E ₂ = 1.7, E ₂ / E ₁ = 1.31, f _D / f
= 3.333 1-D ₂ (f ₁ -D ₁ ) / f ₁ D ₁ = 0.818 h _C / h _M · F _NO · IH = 0.782

Example 2 f = 1, F / 6.2, 2ω = 102.68 °, IH = 0.815 r ₁ = ∞ d ₁ = 0.4782 n ₁ = 1.883 ν ₁ = 40.78 r ₂ = 0.7562 d ₂ = 0.5002 r ₃ = ∞ _{d 3 = 0.6173 n 2 = 1.52287} ν 2 = 57.89 r 4 = ∞ d 4 = 0.3086 r 5 = ∞ d 5 = 0.9568 n 3 = 1.52 ν 3 = 74.0 r 6 = ∞ ( stop) d ₆ = 0.29 r ₇ = _{1.6192 d 7 = 0.8403 n 4 =} 1.883 ν 4 = 40.78 r 8 = ∞ d 8 = 0 (DOE) n 5 = 1001.42 ν 5 = -3.45 r 9 = -40.9515 ( _{aspherical) d 9 = 2.3704 r 10 =} ∞ d ₁₀ = 1.5432 n ₆ = 1.51633 ν ₆ = 64.15 r ₁₁ = ∞ aspherical coefficient P = 1, B = 0.12168 × 10 ^-1 , E = 0.17450 × 10 ^-4 F = 0.13663 × 10 ^-2 G = -0.41386 × 10 ^-2 f _D = 12.020, h _M = 0.286, h _C = 0.17, | f ₁ | / D
= 0.401 h _C / h _M · F _NO · IH = 0.127, f _D / f ₂ = 7.31

Example 3 f = 1, F / 2.8, 2ω = 91.5 °, IH = 0.759 r ₁ = ∞ d ₁ = 0.3408 n ₁ = 1.45875 ν ₁ = 67.80 r ₂ = 0.5414 d ₂ = 0.8676 r ₃ = ∞ _{(stop) d 3 = 0.0077 r 4 =} 6.9149 d 4 = 0.8154 n 2 = 1.45875 ν 2 = 67.80 r 5 = -0.9261 d 5 = 0 r 6 = 2.4647 d 6 = 0.5061 n 3 = 1.45875 ν 3 = 67.80 r 7 = -1985.943 _{(aspherical) d 7 = 0 (DOE)} n 4 = 1001.42 ν 4 = -3.45 r 8 = ∞ d 8 = 1.4819 r 9 = 2.6822 d 9 = 0.8807 n 5 = 1.45875 ν 5 = 67.80 r 10 = ∞ Aspherical coefficient P = 1, B = 0.29699 × 10 ^-3 , E = -0.52072 × 10 ^-4 F = 0.43806 × 10 ^-4 G = -0.44209 × 10 ^-4 H = -0.33752 × 10 ^-4 I =- 0.23462 × 10 ⁻⁵ f _D = 11.052, h _M = 0.35, h _C = 0.338, | f ₁ | / D
= 1.36 f _D / f ₂ = 8.696, h _C / h _M · F _NO · IH = 0.46

Example 4 f = 1, F / 4.47, 2ω = 93.4 °, IH = 0.740 r ₁ = ∞ d ₁ = 0.3324 n ₁ = 1.45875 ν ₁ = 67.80 r ₂ = 0.5905 d ₂ = 0.9516 r ₃ = ∞ (Aperture) d ₃ = 0.7953 n ₂ = 1.45875 ν ₂ = 67.80 r ₄ = 1.112 d ₄ = 0 r ₅ = 2.5939 d ₅ = 0.4936 n ₃ = 1.45875 ν ₃ = 67.80 r ₆ = -2474.5145 (aspherical surface) d _{6 = 0 (DOE) n 4} = 1001.42 ν 4 = -3.45 r 7 = ∞ d 7 = 1.3592 r 8 = 1.6118 d 8 = 1.6794 n 5 = 1.45875 ν 5 = 67.80 r 9 = ∞ aspherical coefficients P = 1, B = 0.25386 × 10 ^-3 , E = -0.54928 × 10 ^-4 F = 0.80482 × 10 ^-4 G = -0.3876 × 10 ^-4 H = -0.42264 × 10 ^-4 I = -0.30885 × 10 ^-5 f _D = 9.649, h _M = 0.229, h _C = 0.342, | f ₁ | /
D = 1.35 f _D / f ₂ = 6.5, h _C / h _M · F _NO · IH = 0.45

Example 5 f = 1, F / 2.44, 2ω = 110.0 °, IH = 0.829 r ₁ = ∞ d ₁ = 0.372 n ₁ = 1.45875 ν ₁ = 67.80 r ₂ = 0.6033 d ₂ = 0.9735 r ₃ = ∞ _{(stop) d 3 = 0.0076 r 4 =} -8.9636 d 4 = 0.8902 n 2 = 1.45875 ν 2 = 67.80 r 5 = -1.0299 d 5 = 0 r 6 = 2.4339 d 6 = 0.4481 n 3 = 1.45875 ν 3 = 67.80 r ₇ = 1700.1112 _{(aspherical) d 7 = 0 (DOE)} n 4 = 1001.42 ν 4 = -3.45 r 8 = ∞ d 8 = 1.2456 r 9 = 1.7524 d 9 = 1.9166 n 5 = 1.45875 ν 5 = 67.80 r 10 = ∞ Aspherical coefficient P = 1, B = -0.27291 × 10 ^-3 , E = -0.40356 × 10 ^-4 F = 0.38175 × 10 ^-4 G = -0.15833 × 10 ^-4 H = -0.63409 × 10 ^-5 I = 0.40434 × 10 ^-11 f _D = 23.59, h _M = 0.437, h _C = 0.407, | f ₁ | /
_{D = 1.351 f D / f 2} = 15.1, h C / h M · F NO · IH = 0.46

Example 6 f = 1, F / 2.45, 2ω = 102.6 °, IH = 0.785 r ₁ = ∞ d ₁ = 0.3526 n ₁ = 1.45875 ν ₁ = 67.80 r ₂ = 0.6062 d ₂ = 0.8780 r ₃ = ∞ (Aperture) d ₃ = 0.006 r ₄ = -10.2198 d ₄ = 0.8436 n ₂ = 1.45875 ν ₂ = 67.80 r ₅ = -0.9714 d ₅ = 0.3949 r ₆ = 2.3065 d ₆ = 0.4174 n ₃ = 1.45875 ν ₃ = 67.80 r ₇ = 1087.3734 _{(aspherical) d 7 = 0 (DOE)} n 4 = 1001.42 ν 4 = -3.45 r 8 = ∞ d 8 = 1.0845 r 9 = 1.6606 d 9 = 1.7852 n 5 = 1.45875 ν 5 = 67.80 r 10 = ∞ Aspherical coefficient P = 1, B = -0.43907 × 10 ^-3 , E = -0.35378 × 10 ^-4 F = 0.28031 × 10 ^-4 G = -0.12212 × 10 ^-4 f _D = 24.083, h _M = 0.395, h _C = 0.519, | f ₁ | /
D = 1.321 f _D / f ₂ = 15.35, h _C / h _M · F _NO · IH = 0.684 where r ₁ , r ₂ , ... Are the radii of curvature of each lens surface, d
₁ , d ₂ , ... Are surface spacings, n ₁ , n ₂ , ... Are refractive indices,
ν ₁ , ν ₂ , ... Are Abbe numbers, F _No is F number bar, I
H is the image height, and h _M and h _C are the axial marginal ray and the off-axis chief ray height, respectively.

Example 1 is an endoscope objective lens having a configuration shown in FIG. 1 and applied to an ultrafine fiber scope mainly used for blood vessels and the like. Here, the focal length of the diffractive optical element is about 10 times that of an ordinary lens, so that the total length of the telecentric optical system in which the lens near the image plane is the diffractive optical element becomes too large. This Example 1 is
In order from the object side, a stop, a diffractive optical element having a positive action (provided on the image-side surface of a plane-parallel plate), and a positive lens made of normal glass are used. When the focal length of the diffractive optical element is f _D and the distance from the diaphragm to the optical element is D, the following conditions are satisfied.

1 <f _D / D <3 (13) If the lower limit of this condition is exceeded, it becomes difficult to maintain telecentricity. If the upper limit is exceeded, the problem of vignetting due to the total reflection of the positive lens becomes a problem. Ultra-high
Since the index lens has a very high refractive index, it has a small Petzval sum, and its field curvature is better corrected than that of a conventional blood vessel endoscope objective lens as shown in FIG.

The condition for the rays above the principal ray to be unobscured by the lens outer diameter is obtained by paraxial calculation in FIG. In the first lens L ₁ , the following relation holds based on Newton's formula.

(Z′−f ₁ ) (f ₁ −D ₁ ) = − f ₁ ² (14) Further, the ray height of the light ray incident on the second lens L ₂ is h ₂ , the first
If the height of the light ray incident on the lens L ₁ is h ₁ , the following relationship holds.

[0040] _{h 2 / h 1 = 1-} D 2 (f 1 -D 1) / (f 1 · D 1) (15) Thus, the outer diameter E ₁ of the first lens L ₁ second lens L
Letting E _{2 be} the outer diameter of ₂ , the conditions under which the rays above the chief ray cannot be deflected by the outer diameter are as follows.

E ₂ / E ₁ ≧ 1−D ₂ (f ₁ −D ₁ ) / (f ₁ · D ₁ ) (16) Further, as shown in FIG. Needless to say, the chamfered portion having the function of a diaphragm also has the same effect as that of this embodiment.

The second embodiment has an arrangement as shown in FIG. 2 and is an objective lens mainly used for a video endoscope. In this embodiment, a diffractive optical element is provided on the image side surface of the positive lens which is closer to the image side than the diaphragm. Although the objective lens of Example 2 has a slightly deteriorated telecentricity, it can be used without causing color shading if a plane-sequential solid-state image sensor is used. Further, in FIG. 2, the second plane-parallel plate F ₂ is a YAG cut filter in which YAG cut coating is applied to the white plate glass, and the third plane-parallel plate F ₃ is an infrared cut filter for removing infrared light. is there. Generally, in an endoscope, a YAG cut filter is arranged in the image pickup optical path, but light reflected by a metal surface other than the light receiving portion of a solid-state image pickup device such as a CCD is reflected again by the YAG cut filter and causes a ghost.

In the present invention, the intensity of the ghost light is reduced by disposing the infrared cut filter between the CCD and the YAG cut filter.

In the second embodiment, aberrations other than chromatic aberration are removed by combining a negative lens and a positive lens with a diaphragm interposed therebetween.
First, as for the spherical aberration, the positive aberration generated on the image side surface of the first negative lens is canceled by the negative aberration generated on the object side surface of the fourth positive lens. The coma aberration cancels out the coma aberration of the positive lower dependent light beam generated on the image side surface of the first positive lens by the negative aberration generated by the ultra high index lens. The ultra-high index lens has a very high refractive index and the Petzval sum is almost zero.

The axial chromatic aberration is slightly overcorrected as a whole because the negative lens and the positive lens cancel each other to some extent, but the chromatic aberration of magnification is corrected very well. Further, the fourth positive lens is a convex plano lens having a convex surface on the object side. However, in the case of such a configuration, it is advantageous in correcting coma aberration, and according to the expression (10), the diffractive optical element is used. When the element is processed on a flat surface, light close to parallel light can be made incident on the diffractive surface, so that the diffraction efficiency is not deteriorated, which is desirable.

The diffractive optical element may be arranged in the vicinity of ordinary glass. For example, as shown in FIG. 15 (A), the diffractive optical element (DOE) may be directly processed on the plane portion of the convex plano lens L. Good. Further, as shown in FIG. 15B, a diffractive optical element (DO
E) may be attached to the plane of the convex plano lens or may be mechanically applied thereto. Further, as shown in FIG. 15C, a diffractive optical element (DOE) pressed with a material such as plastic or glass may be arranged via a spacer S also serving as a flare stop.

In Embodiments 2 to 6, the distance D between the diaphragm and the first negative lens is conditioned in order to widen the angle.

0.2 <| f ₁ | / D <3.2 (17) where f ₁ is the focal length of the first negative lens. Also, the focal length of all systems is standardized to 1.

If the wide angle is achieved while the distance D between the stop and the first negative lens is narrowed, the power of the fourth positive lens becomes strong, the coma aberration of the upper dependent ray is strongly generated in the negative side, and the diffractive optical element is produced. Correction becomes difficult. In order to prevent such a phenomenon, it is desirable to satisfy the above condition (17). If the lower limit of this condition is exceeded, it will not be possible to satisfactorily correct aberrations as described above, and if the upper limit is exceeded, the first negative lens will cause eclipse. Further, with such a structure, the YA as in the second embodiment is obtained.
It is preferable because the G cut filter and the infrared cut filter can be arranged without difficulty.

Embodiments 3 to 6 are each composed of a negative first lens group on the object side of the stop and a positive second lens group on the image side of the stop, and a third positive lens which is the second lens of the second lens group. A diffractive optical element is provided on the image side of the lens. These examples are radiation objective endoscope objective lenses used in nuclear power plants and the like. An endoscope objective lens using a normal glass material uses only quartz, which is a glass material that does not discolor due to radiation, because the glass material is discolored by radiation and becomes unobservable. Since the optical system is composed of only a single glass material in this way, large chromatic aberration occurs,
This chromatic aberration is removed using a diffractive optical element. Ultra-high index to eliminate chromatic aberration
When using a lens, its placement position must be an appropriate position. In the case of an optical system composed of a negative lens, a diaphragm, and a positive lens from the object side, if a diffractive optical element is arranged between the first negative lens and the diaphragm, the axial chromatic aberration and the chromatic aberration of magnification can be corrected. The directions are completely opposite, so it is difficult to correct these chromatic aberrations to almost zero at the same time. In order to make these chromatic aberrations almost zero at the same time, it is desirable to dispose the diffractive optical element between the diaphragm and the second positive lens. Also in this case, it is necessary to weight the axial chromatic aberration and the chromatic aberration of magnification. That the glass material and structure of the lens other than the diffractive optical element, since the generation amount of chromatic aberration of magnification and axial chromatic aberration is changed, ultra - high index lens of off-axis principal ray height h _C and the marginal ray height h _M in the plane of the It is desirable to dispose this diffractive optical element at a position where the value satisfies an appropriate condition, and in the case of Examples 1 to 6, it is preferable to satisfy the following condition, whereby the axial chromatic aberration and the magnification are reduced. Chromatic aberration can be made almost zero at the same time.

0.1 <h _C / (h _M × F _NO × IH) <2.52 (18) where F _NO is the F number and IH is the image height.

If the lower limit of the above conditions is exceeded, it will be difficult to correct lateral chromatic aberration. If the upper limit is exceeded, it will be difficult to correct axial chromatic aberration.

The third and fourth embodiments are examples in which weight is attached to the correction of lateral chromatic aberration rather than the correction of axial chromatic aberration. Further, the fifth and sixth embodiments are examples in which weight is given to correction of axial chromatic aberration rather than correction of chromatic aberration of magnification.

Further, among other aberrations, spherical aberration occurs positively as in the fourth and fifth embodiments when the power of the image side surface of the second positive lens is weakened, and the spherical aberration of the second positive lens When the power of the image side surface is increased, it is negatively generated as in the third and sixth embodiments.

Further, the amount of coma generated on each surface is suppressed to a small level, and the coma aberrations are satisfactorily corrected by canceling each other as a whole. In particular, Example 3 and Example 4
The coma is well corrected. Further, the power of the second positive lens influences the generation of astigmatism, and if the power of the convex surface on the object side of this lens is increased and the power of the convex surface on the image side is weakened as in the third embodiment, the power is reduced. Generation of point aberration can be suppressed.

In each of Embodiments 2 to 3, the first lens group having a negative action is arranged on the object side with the diaphragm interposed therebetween, and the second lens group having a positive action is arranged on the image side. There is.
In the lens having such a configuration, the chromatic aberration Δf is obtained as follows.

In FIG. 13, the following equation (19) is obtained from the relationship between the ray heights.

L = (f ₁ −D) × f / f ₁ (19) Further, the following equation (20) is obtained from Newton's formula.

(D−f ₁ −f ₂ ) (1−f ₂ ) = − f ₂ ² (20) From the equations (19) and (20), l is deleted to obtain the following equation (21).

F = −f ₁ · f ₂ / (D−f ₁ −f ₂ ) (21) The following equation is obtained by differentiating both sides of the equation (21) by n. Δf = Δf ₁ · Δf ₂ {D (ν ₁ + ν ₂ ) − (f ₁ ν ₁ + f ₂ ν ₂ )} / (D−f ₁ −f ₂ ) ² (22) Δf is the axial chromatic aberration and magnification. If Δf = 0 in terms included in both chromatic aberrations, both axial chromatic aberration and lateral chromatic aberration can be removed. Here, since the diffractive optical element is attached to the second lens group having a positive action, the focal length and Abbe number of the glass other than the diffractive optical element in the second lens group having a positive action are calculated by the formula ( to distinguish between f ₂ and [nu ₂ in 20) through (22), F ₂ and V
_{If the value is 2} , the following equation (23) is established.

1 / f ₂ = 1 / F ₂ + 1 / f _D (23) When both sides of this equation (23) are differentiated by n, the following equation (2)
It becomes like 4).

Δf ₂ = −f ₂ ² {(1 / (F ₂ · N ₂ ) + 1 / (f _D · ν _D )} (24) Since f _D is larger than F ₂ by one digit, 1 If / f ₂ ≈1.1 / F ₂ (25), then Δ (f = 0) is obtained by the following equation (22): D (ν ₁ + ν ₂ ) − (f ₁ ν ₁ + f ₂ ν ₂ ) = 0 Since it is sufficient that (26), formula (6), formula (23) to formula (2)
From 5), the focal length f _{D of the} diffractive optical element where Δf = 0
Can be calculated by the following equation (21).

1 / f _D ≈−3.45 [(f ₂ −D) / {(D−f ₁ ) ν ₁ f ₂ } −1 / (N ₂ · f ₂ )] (27) Therefore, the above equation (27) If the lens is designed so as to satisfy), chromatic aberration can be eliminated. In the objective lens of the endoscope, f ₁ , f ₂ , ν ₁ , N ₂ and D are almost fixed values, so if the ratio of f _D and f ₂ satisfies the following condition, chromatic aberration Δf is good. Can be corrected to.

0 <f _D / f ₂ <50 (28) Here, the focal length of the entire system is standardized to 1.

If the lower limit of this condition (28) is exceeded, the chromatic aberration cannot be removed because the lens system is a retrofocus type. If the upper limit of the condition (28) is exceeded, the power of the diffractive optical element tends to be weakened, but the number of lenses forming the second lens group increases and the number is the same as that of the conventional example shown in FIG. 24, which is not preferable.

That is, f that satisfies the following condition
_{If 1} , f ₂ , ν ₁ , N ₂ , D, then chromatic aberration Δ
f can be corrected well.

0 <1 / [− 3.45 [(f ₂ −D) / {(D−f ₁ ) ν
₁ f ₂ } −1 / (N ₂ f ₂ )] f ₂ ] <50 However, the focal length of the entire system is standardized to 1.

The focal length of the diffractive optical element used in the present invention means not only the diffractive focal length but also the focal length of the ultra-high index lens. In formulas (6) to (6),
The objective lens of the present invention is an objective lens provided with the converted diffractive optical element by converting the ultra-high index lens into a diffractive optical element.

Next, the diffraction efficiency of the diffractive optical element will be considered. FIG. 16 is a diagram showing the spectral transmittance characteristics of the infrared cut filter used in the second embodiment, and FIG. 17 is a diagram showing the spectral sensitivity characteristics of the solid-state imaging device used in the same second embodiment. FIG. 18 is obtained by multiplying the characteristics of FIGS. 16 and 17 and normalized, and shows the total sensitivity characteristics of the infrared cut filter and the solid-state imaging device.

Generally, in a diffractive optical element, even a kinoform that can make the first-order diffracted light 100% has different diffraction efficiency depending on the wavelength, and unnecessary-order light other than the zero-order light is generated, which causes flare. . The ratio of the unnecessary order light can be obtained as the diffraction efficiency shown by the following equation (29). η _m = sin c ² [π {m−m ₀ (λ ₀ / Δn (λ ₀ )) · (Δn (λ) / λ)}] (29) where λ ₀ is the wavelength at which the diffraction efficiency is 1. λ is the wavelength for which the diffraction efficiency is to be obtained, n ′ (λ) is the refractive index of the medium of the emitted light at a certain wavelength, usually 1, n (λ) is the refractive index of the medium of the incident light at a certain wavelength, Usually, the refractive index of the medium for processing the diffractive optical element, m ₀ is the order for making the diffraction efficiency 1 and m is the order for which the diffraction efficiency is desired.

For example, using the glass material of Example 2, 1 of d line
When the next light is blazed by kinoform (the diffraction efficiency at a certain order and a certain wavelength is 100% as described above), the equation (29) becomes as follows. η _m = sin c ² [π {m−m ₀ (587.56 / 1-1.883) (1-n (λ) / λ)}] (30) This is calculated as follows.

-1 0 1 2 3 n (λ) g-line (435.83nm) 1.57% 4.64% 59% 24.1% 3.46% 1.91049 F-line (486.13nm) 0.89% 2.92% 83.8% 7.44% 1.41% 1.89822 e Line (546.07nm) 0.15% 0.56% 97.8% 0.79% 0.18% 1.88814 d line (587.56nm) 0% 0% 100% 0% 0% 1.88300 C line (656.27nm) 0.33% 1.5% 96% 0.96% 0 .27% 1.87656 A line (768.19nm) 1.62% 8.75% 81.5% 3.19% 0.98% 1.86947 The graph of the above calculation result is shown in FIG. In the formula (30), when attention is paid only to m = 1 and all the light other than the primary light becomes flare, the ratio ε of incident light to flare can be expressed as follows.

Ε = 1−η ₁ (31) FIG. 21 is a conceptual diagram showing the relationship between the wavelength and the above ratio ε.
It becomes like (A). Wavelength range λ ₁ <λ <λ ₂ (λ ₁ <
The flare F in λ ₂ ) is represented by the area of the hatched portion in FIG. 21 (A) and is as follows. In the figure, λ ₀ is the blazed wavelength. For example, if the sectional shape approximates to the kinoform as shown in FIG. 27B instead of the kinoform as shown in FIG. 27A, the ideal kinoform has a diffraction efficiency at the blaze wavelength λ ₀ . While η ₁ = 1 is obtained, the diffraction efficiency η ₁ ′ is η ₁ ′ ≈0.95 to 0.99, and therefore the flare ratio ε is ε = 1-η as shown in FIG.
₁ ', but a certain wavelength range λ ₁ <λ <λ ₂ (λ ₁ <λ ₂ )
The flare F in is similarly expressed by the equation (32). Here, if the curve ε is moved in the wavelength direction as shown in FIG. 21C, the area of the shaded portion can be reduced. This suggests that the blazed wavelength λ ₀ that minimizes the amount of flare in the used wavelength range is present other than the d-line. If this is expressed by an equation, the following equation (33) is established, where λ ₀ is a blazed wavelength that minimizes the flare F in a certain wavelength range λ ₁ <λ <λ ₂ (λ ₁ <λ ₂ ). . In the discussion in equation (31), the order used is the first order,
Since the flare is reduced as much as possible in the blazing order, it is desirable that m ₀ = m, and m ₁ = 1 and m ₀ =
It is 1. Further, in the equation (33), Min means that the value of F becomes the minimum. In the above formula (32), λ
₁ = 400 nm, λ ₂ = 700 nm, m = 1, n (d)
When calculated concretely with = 1.88300, the result is as shown in FIG. As a result, F is the blazed wavelength lambda ₀ to be minimum is lambda ₀ = 560 nm near, lambda ₀ the approximate 500nm <λ ₀ <flare light F can be suppressed to near minimum if in the range of 610 nm. That is, FIG. 19 is an integration of the values of the equation (32). If this value is small, flare is small. This indicates that flare becomes minimum or close to the minimum when the diffractive optical element is made so that the blazed wavelength λ ₀ is between 500 nm and 610 nm.

Next, when the transmittance characteristic of the infrared cut filter is the characteristic shown in FIG. 16 and the spectral sensitivity characteristic of the solid-state image sensor is the characteristic shown in FIG. 17, the infrared cut filter and the solid-state image sensor are Figure 1 shows the total sensitivity characteristics of
As shown in 8. In the case of this characteristic, the spectral sensitivity characteristic peaks near the d line, and the sensitivity characteristic slightly deteriorates near the F line and C line. Therefore, the blue signal and the red signal are actually increased during the video signal processing. 22 and amplified.
As shown in (A), the sensitivity between the F line and the C line is flat. Therefore, the flare light by the diffractive optical element is also amplified, and the flare light by the diffractive optical element does not depend on the characteristics of the image sensor or the infrared cut filter, and the blaze such that the expression (33) is satisfied as shown in FIG. Must be set to the wavelength λ ₀ . In that case, it is applied when using a natural color such as a still video camera. However, in the endoscope, the illumination light is transmitted by the optical fiber bundle of the light guide cable, and the short wavelength light is absorbed by the core material as a characteristic of the optical fiber, so the light of the wavelength near the F line is attenuated. Becomes Therefore, the image obtained by the endoscope is C from the F line because the light of the wavelength near the F line is attenuated.
In order to flatten the sensitivity up to the line, it is necessary to increase the amplification factor of the wavelength near the F line. When the amplification factor is increased in this way, the S / N ratio is deteriorated and noise is increased, so that the amplification factor cannot actually be increased so much. Therefore, the image obtained by the endoscope is in the wavelength region between the F line and the C line, and the sensitivity in the vicinity of the F line is slightly lowered (FIG. 24B).
The sensitivity characteristics are as shown in. When the weighted sensitivity characteristic is W (λ), the ratio ε ′ of the incident light ray to the flare light in the equation (26) is given by the following equation (3).
4). ε '= W (λ) ( 1-η 1) (34) Matashiki (35) is rewritten as follows. When this is expressed in a conceptual diagram similar to FIG. 21, ε ′ becomes smaller on the short wavelength λ ₁ side as shown in FIG. 23A due to the influence of the weight of W (λ). Therefore, in the above discussion, as shown in FIG. 19, λ _{0 is} approximately λ ₀ = 560 mm.
However, if the weight is taken into consideration, setting λ ₀ on the longer wavelength side than λ ₀ = 560 mm gives a flare light ratio, as can be seen from FIG. 23B. Becomes smaller as a whole. That is, the value of F'is small. As described above, the flare caused by the unnecessary order light can be made inconspicuous by appropriately setting it according to the characteristics of the imaging body, the light source device, and the signal processing device that use the wavelength for blazing. For example, when the data of Example 2 is converted into a diffractive optical element, λ ₀
When blazing is performed at = 560 nm, the pitch d (h) with respect to the height of the diffractive ray is as follows.

From this, the following values are obtained. h 0.1 0.2 0.3 0.4 0.5 d (h) 71.5 41.9 55.3 1300 16.1 The above-mentioned conditions are conditions in consideration of manufacturing, and are for providing an endoscope objective lens at low cost. Further, although only the solid-state image pickup device is considered here as the image pickup means, an image guide fiber bundle or a silver salt film may be used. Further, the wavelength to be used can be applied not only to the visible range but also to the infrared wavelength range and the ultraviolet wavelength range.

[0077]

The endoscope objective lens of the present invention uses an optical element having a diffractive action to eliminate chromatic aberration,
The number of lenses can be reduced without using two cemented lenses unlike the conventional one.

[Brief description of drawings]

FIG. 1 is a sectional view of a first embodiment.

FIG. 2 is a sectional view of a second embodiment.

FIG. 3 is a sectional view of a third embodiment.

FIG. 4 is a sectional view of a fourth embodiment.

FIG. 5 is a sectional view of the fifth embodiment.

FIG. 6 is a sectional view of Example 6.

7 is an aberration curve diagram of Example 1. FIG.

8 is an aberration curve diagram of Example 2. FIG.

FIG. 9 is an aberration curve diagram of Example 3

FIG. 10 is an aberration curve diagram of Example 4.

11 is an aberration curve diagram of Example 5. FIG.

FIG. 12 is an aberration curve diagram for Example 6.

FIG. 13 is a diagram showing the relationship between the lens spacing and the like of a lens system having negative and positive refracting powers with the diaphragm interposed and the ray height.

FIG. 14 is a diagram showing the relationship between the height of a light beam and the lens spacing of an optical system in which a diaphragm is located closest to the object side.

FIG. 15 is a diagram showing a configuration of a diffractive optical element.

16 is a spectral transmittance characteristic of an infrared cut filter used in Example 2. FIG.

17 is a spectral sensitivity characteristic of the solid-state imaging device used in Example 2. FIG.

FIG. 18 is a composite characteristic of the infrared cut filter and the solid-state imaging device.

FIG. 19 is a diagram showing a flare value with respect to a wavelength by a diffractive optical element.

FIG. 20 is a diagram showing the diffraction rate with respect to wavelength in a diffractive optical element.

FIG. 21 is a conceptual diagram of a flare ratio with respect to wavelength by a diffractive optical element.

FIG. 22 is a diagram showing sensitivity characteristics of an image of an endoscope.

FIG. 23 is a conceptual diagram of a flare rate when weighted.

FIG. 24 is a sectional view of a conventional endoscope objective lens.

FIG. 25 is a sectional view of another conventional endoscope objective lens.

FIG. 26 is a diagram showing refraction and diffraction of light.

FIG. 27 is a diagram showing an example of a sectional shape of a diffraction grating.

FIG. 28 is a diagram showing coordinate axes in an optical system.

[Procedure amendment]

[Submission date] November 1, 1993

[Procedure Amendment 1]

[Document name to be amended] Statement

[Correction target item name] 0017

[Correction method] Change

[Correction content]

( N _v −1) dz / dh = nsin θ−n ′ sin θ ′ (7) where n ′ is the refractive index of the medium on the emission side, θ and θ ′ are the incident angle and the emission angle of the light beam, and n Is the refractive index of the substrate of the diffractive optical element, and n _v is the refractive index of the ultra-high index lens.
Folding rate, z is ultra-high index lens and light
It is the coordinate in the optical axis direction of the intersection with the ray of line height h.

[Procedure Amendment 2]

[Document name to be amended] Statement

[Correction target item name] 0019

[Correction method] Change

[Correction content]

( N _v −1) dz / dh = mλ / d (8) If an aspherical surface is defined as an ultra-high index lens, it is expressed as follows. ^{z = Cy 2 / [1+ (} 1-C 2 Py 2) 1/2] + By 2 + Ey 4 + Fy 6 + Gy 8 + ···· (9) However, z as shown in FIG. 28 the optical axis (image Direction is positive), y is the coordinate axis in the meridional direction of the coordinate axes orthogonal to the z axis with the origin at the intersection of the surface and the z axis, C is the curvature of the reference surface, P is the conic constant, and P = 1-e ² (e Is a value given by eccentricity), B, E, F, G, ... are secondary and 4 respectively.
It is an aspherical coefficient of the next order, the sixth order, the eighth order, .... Fig. 28
In, O is an object and I is an image.

[Procedure 3]

[Document name to be amended] Statement

[Correction target item name] 0020

[Correction method] Change

[Correction content]

From the expressions (8) and (9), the pitch d of the diffractive optical element at a certain ray height is expressed by the following expression (10). d = m [lambda / Hence _{^{[(n v -1) {Ch}} / (1-C 2 Ph 2) 1/2 + 2Bh + 4Eh 3 + 6Fh 5 + 8Gh 7 + ····}] (10), Ultra - with a high-index lens If the design is performed by using such a design, the surface shape of the diffractive lens equivalent to the lens data can be obtained.

[Procedure amendment 4]

[Document name to be amended] Statement

[Name of item to be corrected] 0030

[Correction method] Change

[Correction content]

[0030]

EXAMPLE Examples of the endoscope objective lens of the present invention will be described below. Examples 1 to 6 described below have the following data with the configuration shown in FIGS. In each example,
The index of refraction of the line labeled (DOE) corresponds to n _v . Example 1 Aspherical coefficient

[Procedure Amendment 5]

[Document name to be amended] Statement

[Correction target item name] 0073

[Correction method] Change

[Correction content]

Ε = 1−η ₁ (31) The relationship between the wavelength and the ratio ε is conceptually shown in FIG.
It becomes like (A). Wavelength range λ ₁ <λ <λ ₂ (λ ₁ <
The flare F in λ ₂ ) is represented by the area of the hatched portion in FIG. 21 (A) and is as follows. In the figure, λ ₀ is the blazed wavelength. For example, if the cross-sectional shape approximates to the kinoform as shown in FIG. 27B instead of the kinoform as shown in FIG. 27A, the ideal kinoform has a diffraction efficiency at the blaze wavelength λ ₀ . While η ₁ = 1 is obtained, the diffraction efficiency η ₁ ′ is η ₁ ′ ≈0.95 to 0.99, so the flare rate ε is ε ′ = 1 as shown in FIG.
−η ₁ ′ (where ε ′> ε), but a certain wavelength range λ
The flare F in ₁ <λ <λ ₂ (λ ₁ <λ ₂ ) is similarly expressed by the equation (32). Normally blaze
Although the wavelength is the d-line, the area of the shaded portion can be reduced by moving the curve ε in the wavelength direction as shown in FIG. This suggests that the blazed wavelength λ ₀ that minimizes the amount of flare in the used wavelength region exists other than the d-line. If this is expressed by an equation, the following equation (33) is established, where λ ₀ is the blazed wavelength that minimizes the flare F in a certain wavelength range λ ₁ <λ <λ ₂ (λ ₁ <λ ₂ ). . In the discussion in equation (31), the order used is the first order,
Since the flare is reduced as much as possible in the blazing order, it is desirable that m ₀ = m, and m ₁ = 1 and m ₀ =
It is 1. Further, in the equation (33), Min means that the value of F becomes the minimum. In the above formula (32), λ
₁ = 400 nm, λ ₂ = 700 nm, m = 1, n (d)
When calculated concretely with = 1.88300, the result is as shown in FIG. As a result, F is the blazed wavelength lambda ₀ to be minimum is lambda ₀ = 560 nm near, lambda ₀ the approximate 500nm <λ ₀ <flare light F can be suppressed to near minimum if in the range of 610 nm. That is, FIG. 19 is an integration of the values of the equation (32), and if this value is small, flare is small. This indicates that flare becomes minimum or close to the minimum when the diffractive optical element is made so that the blazed wavelength λ ₀ is between 500 nm and 610 nm.

[Procedure correction 6]

[Document name to be amended] Statement

[Correction target item name] 0075

[Correction method] Change

[Correction content]

Next, when the transmittance characteristic of the infrared cut filter is the characteristic shown in FIG. 16 and the spectral sensitivity characteristic of the solid-state image sensor is the characteristic shown in FIG. 17, the infrared cut filter and the solid-state image sensor are Figure 1 shows the total sensitivity characteristics of
As shown in 8. In the case of this characteristic, the spectral sensitivity characteristic peaks near the d line, and the sensitivity characteristic slightly deteriorates near the F line and C line. Therefore, the blue signal and the red signal are actually increased during the video signal processing. 22 and amplified.
As shown in (A), the sensitivity between the F line and the C line is flat. Therefore, the flare light by the diffractive optical element is also amplified, and the flare light by the diffractive optical element does not depend on the characteristics of the image sensor or the infrared cut filter, and the blaze such that the expression (33) is satisfied as shown in FIG. It must be set to the wavelength λ ₀ . In that case, it is applied when using a natural color such as a still video camera. However, in the endoscope, the illumination light is transmitted by the optical fiber bundle of the light guide cable, and the short wavelength light is absorbed by the core material as a characteristic of the optical fiber, so the light of the wavelength near the F line is attenuated. Becomes Therefore, the image obtained by the endoscope is C from the F line because the light of the wavelength near the F line is attenuated.
In order to flatten the sensitivity up to the line, it is necessary to increase the amplification factor of the wavelength near the F line. When the amplification factor is increased in this way, the S / N ratio is deteriorated and noise is increased, so that the amplification factor cannot actually be increased so much. Therefore, the image obtained by the endoscope is in the wavelength region between the F line and the C line, and the sensitivity in the vicinity of the F line is slightly lowered (FIG. 24B).
The sensitivity characteristics are as shown in. When the weighted sensitivity characteristic is W (λ), the ratio ε ′ of the incident light ray to the flare light in the equation (26) is given by the following equation (3).
4). ε '= W (λ) (1-η ₁ ) (34) Further, the equation (35) can be rewritten as follows. When this is expressed in a conceptual diagram similar to FIG. 21, ε ′ is smaller on the short wavelength λ ₁ side due to the influence of the weight of W (λ) as shown in FIG. Therefore, in the above discussion, as shown in FIG. 19, λ _{0 is} approximately λ ₀ = 560 m.
A good result was obtained when m was reached, but considering weights, setting λ ₀ on the longer wavelength side than λ ₀ = 560 mm produces flare light, as can be seen from FIG. 23B. The ratio becomes small as a whole. That is, the value of F'is small. As described above, the flare caused by the unnecessary order light can be made inconspicuous by appropriately setting it according to the characteristics of the imaging body, the light source device, and the signal processing device that use the wavelength for blazing. For example,
When the data of Example 2 is converted into a diffractive optical element, λ
_When blazing is performed at ₀ = 560 nm, the pitch d (h) with respect to the height of the diffractive light beam is as follows.

[Procedure Amendment 7]

[Document name to be amended] Statement

[Correction target item name] 0076

[Correction method] Change

[Correction content]

From this, the following values are obtained. The above-mentioned conditions are conditions in consideration of manufacturing, and are for providing an endoscope objective lens at low cost. Further, although only the solid-state image pickup device is considered here as the image pickup means, an image guide fiber bundle or a silver salt film may be used. Further, the wavelength to be used can be applied not only to the visible range but also to the infrared wavelength range and the ultraviolet wavelength range.

Claims (4)

[Claims] 1. An endoscope objective lens comprising an aperture stop and a diffractive optical element having a positive action and arranged on the image side of the aperture stop. 2. The endoscope objective lens according to claim 1, wherein a lens component having a positive refractive power is arranged on the image side of the aperture stop. 3. The endoscope objective lens according to claim 1, wherein a lens component having a negative refractive power is arranged on the object side of the aperture stop. 4. A predetermined wavelength range λ ₁ <λ <λ ₂ (λ ₁ <λ
_The diffractive optical element used in ₂ ), characterized in that it is blazed in the vicinity of the wavelength λ ₀ such that the value of F defined by the following formula is minimized. element. Where λ ₀ is the wavelength at which the diffraction efficiency is 1, λ is the wavelength for which the diffraction efficiency is desired, n ′ (λ) is the refractive index of the exit side medium of the diffractive optical element with respect to the wavelength λ, and n (λ) is the wavelength λ. Is the refractive index of the incident-side medium of the diffractive optical element, m ₀ is the order at which the diffraction efficiency is 1, and m is the order at which the diffraction efficiency is desired.