JP2006171430A - Optical element and optical system having the same - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To obtain an optical element which can easily be provided with a fine unevenness structure, having an antireflective function on an optical surface over the entire optical surface and has proper antireflection characteristics. <P>SOLUTION: The optical element has the fine unevenness structure on the optical surface and the fine unevenness structure is made of a material containing a metal compound, the fine unevenness structure has numeral ranges of the mean surface roughness R<SB>a</SB>and surface area ratio S<SB>ratio</SB>set properly. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to an optical element having a function of suppressing the amount of reflected light from an interface and an optical system having the same. For example, an imaging device such as a camera or a video camera, an observation device for a telescope or an anti-glass, a liquid crystal projector, and an electronic device It is suitable for an optical system of various optical devices such as an optical scanning device of a photographic device.

  Conventionally, wet methods such as a vacuum deposition method, a sputtering method, and a dip method have been widely used as a method of forming an antireflection film for reducing light reflection on the optical surface of an optical element such as a lens.

  In recent years, many antireflection structures have been proposed in which a fine periodic structure of a wavelength or less is formed on the optical surface without using an optical thin film (Patent Documents 1 and 2).

Patent document 1 is disclosing the window material of the display apparatus which reduces a reflectance by providing a specific fine periodic structure in the surface of a transparent base material. The shape of the fine periodic structure is such that the period P _MAX at the most convex portion is equal to or less than the minimum wavelength λ _MIN in vacuum in the visible light wavelength band, and the occupation ratio of the cross-sectional area of the transparent substrate portion in the horizontal section is the fine periodic structure The number gradually increases from the most convex part to the most concave part, and is set to 1 in the most concave part.

  The fine concavo-convex shape is manufactured by forming a resist layer on a glass substrate, then exposing and etching the pattern by an electron beam drawing method or a laser interference method, and corroding the glass substrate.

Patent Document 2 discloses a low-temperature formation method in which a solution containing an aluminum compound is applied to a substrate to form a film, and a fine uneven structure is formed on the surface by being immersed in warm water without being particularly heat-treated. In addition, an excellent anti-water-repellent state with a contact angle of 150 ° or more and an antireflection film exhibiting high transparency with a transmittance of 90% or more in the visible range are realized.
JP 2003-4916 A Japanese Patent Laid-Open No. 2001-17907

  In the formation of an antireflection film by vacuum deposition or sputtering, the apparatus is large, and in addition to the film formation time, a lot of time is required for evacuation and the production tact (process) becomes long. It was.

  In addition, a method for forming an antireflection film by a wet method such as a dip method cannot provide high antireflection performance with a single layer, and it is necessary to repeat a coating process and a drying process in order to make a multilayer, eventually, Like the vacuum deposition method, the manufacturing process tends to be long.

  The method of providing fine irregularities on the transparent substrate of Patent Document 1 is a fine processing apparatus (electron beam drawing apparatus, laser interference exposure apparatus, semiconductor exposure apparatus, etching apparatus, etc.) capable of forming a periodic structure with a wavelength equal to or less than the wavelength in the visible range. Need. In general, these devices are extremely large and have a very complicated structure.

  Although it is suitable for forming a fine uneven structure on a flat surface, it is very difficult to form it on a complicated shape such as a curved surface.

  An object of the present invention is to provide an optical element having an excellent antireflection characteristic and an optical system having the same, which can easily provide a fine concavo-convex structure having an antireflection function on the optical surface over the entire optical surface. To do.

The optical element of the present invention is an optical element having a fine concavo-convex structure, and the fine concavo-convex structure is made of a material containing a metal compound, and the fine concavo-convex structure has an average surface roughness of R _a , When the surface area ratio S _ratio is satisfied, the following conditional expressions (1) and (2) are satisfied.

  According to the present invention, a fine concavo-convex structure having an antireflection function can be easily provided on the entire optical surface, and an optical element having good antireflection characteristics can be obtained.

  Embodiments of the optical element and the manufacturing method thereof according to the present invention will be described below with reference to the drawings.

  The optical element of the present invention is an optical surface such as a flat surface or a curved surface (including a spherical surface, an aspherical surface, a rotationally asymmetric surface) or a curved surface group in which a plurality of curved surfaces are arrayed (a cylindrical surface, a toric surface, or a surface in which those surfaces are arrayed). It has a configuration in which a fine concavo-convex structure body having an antireflection function composed of a plurality of fine concavo-convex portions made of a metal compound such as an aluminum compound is formed thereon.

  Here, the fine concavo-convex structure body can suppress the amount of light reflected at the interface by forming fine concavo-convex portions on the surface of the optical surface with a pitch equal to or less than the design wavelength (for example, wavelength 550 nm).

  Examples of the optical element include a lens, an fθ lens, a prism, a parallel plate, and a fly eye integrator.

  The optical optical element of the present invention is used in various optical systems such as an imaging optical system, an observation optical system, a photographing optical system, and a scanning optical system.

  The optical element of the present invention can be used in a visible light region (wavelength 400 nm to 700 nm) or an infrared region (wavelength 700 nm or more).

In Example 1 and the following examples, the average surface roughness R _a and the surface area ratio S _ratio on the optical surface on which the fine concavo-convex structure is provided are

Is satisfied.

  Reflection of light on the optical surface is reduced by using an optical element provided on the optical surface with a fine concavo-convex structure satisfying these conditions (1) and (2), and flare light is also used when used in an optical system. An optical system with good optical performance in which the generation of harmful light such as ghost light is suppressed. More preferably, the formulas (1) and (2) are set as follows.

Here, the average surface roughness Ra and the surface area ratio S _ratio have X, Y and Z as orthogonal coordinates,
H (X, Y): Fine area of an arbitrarily sampled area in the plane when the optical surface is the XY plane
A function X ₁ representing a value in the Z direction (height of the unevenness) of the uneven shape of the fine uneven portion: X-direction sampling start coordinate X _M : X-direction sampling end coordinate Y ₁ : Y-direction sampling start coordinate Y _N : Sampling end coordinates in the Y direction H _ave : Average value of H (X, Y) S ₀ : Area when an arbitrarily sampled area is a plane = | (X _M −X ₁ ) (Y _N −Y ₁ ) |
λ _min : shortest wavelength in the wavelength range of use of the optical element S: when the actual surface area of the concavo-convex structure surface in an arbitrarily sampled area

Is defined by

When it is difficult to find the true values of the average surface roughness R _a and the surface area ratio S _ratio as defined above in the actual shape of the fine concavo-convex portion, for example, using an AFM (atomic force microscope) The height is measured at a certain interval, and the conditional expression (1) ′ (2) ′ substituting with the average surface roughness R _a ′ and the surface area ratio S ′ _ratio defined as follows is used from the obtained measurement values. May be.

That is,
H (m, n): The optical surface is an XY plane, and the measured value (height) is mth in the X direction and nth in the Y direction when measured at an arbitrary interval.
M: Number of measurements in the X direction N: Number of measurements in the Y direction MN: Number of all sampled data H _ave : Average value of all measured H (m, n)

here,

P _{m, n} : The coordinates of the mth measurement point in the X direction and the nth measurement point in the Y direction, that is, when the measurement interval in the X direction is d _X and the measurement interval in the Y direction is d _Y ,

age,

And when

It is.

  In addition, when actually measuring a finer shape than visible light with an AFM (Atomic Force Microscope) or the like, the area to be measured at a time is about several square mm, which is extremely small compared to the effective area of the optical element. It is common. Therefore, in the above definition, even when the shape of the fine uneven portion is formed in a curved surface such as a lens, the change in the value of H (m, n) due to the curvature of the base surface is almost negligible. If it is not negligible, it is redefined with the corrected value after subtracting the change due to the shape of the base surface.

If lateral extent of the concave-convex nanostructure is smaller than the wavelength of light, the effective refractive index n _e at a certain height, the n _1, the high refractive index of the material forming the fine uneven structure From the Lorentz-Lorenz formula where the space occupancy is f ₁

Can be obtained as follows.

Therefore, when the space occupation ratio of the fine concavo-convex structure gradually changes from the air (incident medium) toward the substrate (exit medium), the effective refractive index _ne also changes gradually.

  Even if the refractive index changes gradually, the reflected light corresponding to the minute change amount is generated at each height according to Fresnel's formula. Further, although the reflected light generated at each height interferes, if the height of the fine concavo-convex structure is a certain level or more, they cancel each other out due to the interference, and the reflected light is reduced. Therefore, it is preferable that the fine uneven structure has a large height.

In addition, it is necessary that the antireflection structure of the optical element does not cause diffraction / scattering of incident light. In order not to generate the diffracted and scattered light in a fine concavo-convex structure, the distance p of the mountain adjacent to each other, when the angle of incidence of the ray was theta _inc,

It is necessary to satisfy the following formula.

  As a result of intensive studies, the inventor found the relational expressions (1) and (2) above as conditions for a fine concavo-convex structure having low light reflectance and no diffracted / scattered light.

  That is, if the relational expression (1) is satisfied, the fine concavo-convex structure has a height sufficient to reduce the reflection of light on the optical surface. The distance between adjacent peaks of the concavo-convex structure is sufficiently small so that no diffracted / scattered light is generated.

  Next, each example of the optical element of the present invention, an optical system having the optical element, and a method for manufacturing the optical element will be described.

  FIG. 1 is a front view of an optical element according to Example 1 of the present invention. In FIG. 1, the optical element 1 is a concave lens having concave shapes on both sides, and has a configuration in which a fine uneven structure 3 for preventing reflection is provided on both sides of a substrate 2.

FIG. 2 is a cross-sectional view of the optical element 1 of Example 1 cut along the AA ′ cross-section in FIG. Here, the substrate 2 is formed of two non-parallel optical surfaces (both concave surfaces) 2a and 2b. The optical surface has an average surface roughness _Ra of 20 nm or more and a surface area ratio S _ratio of 1. An antireflection film composed of the fine concavo-convex structure 3 mainly composed of 42 or more aluminum oxide is formed. This reduces the reflection of light on the optical surfaces 2a and 2b.

  Here, since the use wavelength region of the optical element 1 of Example 1 is a visible region, the shortest wavelength in the use wavelength region is set to 400 nm.

  In the first embodiment, a concave lens is shown as the optical element. However, the optical element of the present embodiment is not limited to this, and the lens shape may be either a convex surface or a meniscus shape.

  FIG. 3 is a front view of an optical element according to Example 2 of the present invention. In the figure, the optical element 1 is a prism and has a structure in which an antireflection structure 3 is provided on the optical surface of a base 2.

FIG. 4 is a cross-sectional view of the optical element 1 of Example 2 cut along the AA ′ cross-section in FIG. 3. Here, the substrate 2 is formed of three non-parallel optical surfaces 2a, 2b, and 2c. Each optical surface has an average surface roughness _Ra of 20 nm or more and a surface area ratio S _ratio of 1.42. The antireflection structure 3 having a fine concavo-convex structure mainly composed of the above aluminum oxide is formed. Thereby, the reflection of light on the optical surface is reduced.

  Here, since the use wavelength region of the optical element of Example 2 is a visible region, the shortest wavelength in the use wavelength region is set to 400 nm.

  In the second embodiment, the angle formed by each optical surface of the prism is 90 ° and 45 °. However, the second embodiment is not limited to this, and the prism in which the optical surface is configured at any angle. It doesn't matter.

  FIG. 5 is a front view of an optical element according to Example 3 of the present invention. In the drawing, an optical element 1 is a fly eye integrator, and has a structure in which an antireflection structure 3 is provided on an optical surface of a substrate 2.

FIG. 6 is a cross-sectional view of the optical element 1 of Example 3 cut along the line AA ′ in FIG. 5. Here, the substrate 2 is formed of two non-parallel optical surfaces (one is an optical surface 2a composed of a plurality of curved surfaces and the other is a flat surface 2b), and each optical surface has an average surface roughness R _a. The antireflection structure 3 having a fine concavo-convex structure mainly composed of an aluminum oxide having a surface area ratio S _ratio of 1.42 or more is formed.

  Thereby, the reflection of light on the optical surface is reduced. Here, since the use wavelength region of the optical element of Example 3 is a visible region, the shortest wavelength in the use wavelength region is set to 400 nm.

  In the third embodiment, the case where one of the two non-parallel surfaces of the fly-eye integrator is an optical surface 2a composed of a plurality of curved surfaces and the other is a flat surface, but the third embodiment is not limited to this. One may be an optical surface composed of a plurality of curved surfaces, and the other may be a similar curved surface.

  FIG. 7 is a front view of an optical element according to Example 4 of the present invention. In the figure, the optical element 1 is an fθ lens and has a structure in which an antireflection structure 3 is provided on a substrate 2.

FIG. 8 is a cross-sectional view of the optical element 1 of Example 4 cut along the AA ′ cross-section in FIG. 7. Here, the substrate 2 is formed of two non-parallel optical surfaces 2a and 2b, and each optical surface has an average surface roughness _Ra of 21 nm or more and a surface area ratio S _ratio of 1.45 or more. An antireflection structure 3 having a fine concavo-convex structure mainly composed of aluminum oxide is formed. Thereby, reflection of light on the optical surface is reduced. Here, the use wavelength of the optical element 1 of Example 4 is 405 nm.

  FIG. 9 is a schematic view of a main part in which an optical element is used in an observation optical system as Example 5 of the present invention.

  FIG. 9 shows a cross section of one of the pair of optical systems of the binoculars.

In FIG. 9, 4 is an objective lens for forming an observation image, 5 is a prism (expanded and shown) as an image inverting means for inverting the image, 6 is an eyepiece, 7 is an imaging plane of the observation image, 8 Is the pupil plane (evaluation plane). In FIG. 9, reference numeral 3 denotes an antireflection structure according to the present invention, which comprises a fine concavo-convex structure mainly composed of an aluminum oxide having an average surface roughness _Ra of 20 nm or more and a surface area ratio S _ratio of 1.42 or more. It is provided on each optical surface to reduce light reflection. Here, since the use wavelength region of the optical system of Example 5 is a visible region, the shortest wavelength in the use wavelength region is set to 400 nm. In Example 5, the optical surface 9 closest to the object side of the objective lens 4 and the optical surface 10 closest to the evaluation surface of the eyepiece lens 6 are not provided with the antireflection structure 3 having a fine concavo-convex structure. This is not provided because the performance deteriorates due to contact or the like during use of the antireflection structure 3, but is not limited thereto, and the antireflection structure 3 may be provided on the optical surfaces 9 and 10. .

  FIG. 10 is a main part schematic diagram in which an optical element is used in an imaging optical system as Example 6 of the present invention. FIG. 10 shows a cross section of a photographic lens such as a camera.

In FIG. 10, reference numeral 7 denotes an image plane, on which a film or a solid-state imaging device (photoelectric conversion device) such as a CCD or CMOS is arranged. Reference numeral 11 denotes an aperture. In FIG. 10, reference numeral 3 denotes an antireflection structure according to the present invention, which comprises a fine concavo-convex structure mainly composed of an aluminum oxide having an average surface roughness _Ra of 20 nm or more and a surface area ratio S _ratio of 1.42 or more. It is provided on each optical surface to reduce light reflection. Here, since the use wavelength region of the optical system of Example 6 is the visible region, the shortest wavelength in the use wavelength region is set to 400 nm.

  In Example 6, the optical surface 9 closest to the object side of the objective lens is not provided with the antireflection structure 3 having a fine concavo-convex structure. This is not provided because the performance deteriorates due to contact of the antireflection structure 3 during use or the like, but is not limited thereto, and the antireflection structure 3 may be provided on the optical surface 9.

  FIG. 11 is a main part schematic diagram in which an optical element is used in a projection optical system (projector) as a seventh embodiment of the present invention.

  FIG. 11 shows a cross section of the projector optical system.

In FIG. 11, 12 is a light source, 13a and 13b are fly eye integrators, 14 is a polarization conversion element, 15 is a condenser lens, 16 is a mirror, 17 is a field lens, and 18a, 18b, 18c and 18d are prisms for color separation / synthesis. , 19a, 19b, 19c are light modulation elements, and 20 is a projection lens. In FIG. 11, reference numeral 3 denotes an antireflection structure according to the present invention, which comprises a fine concavo-convex structure mainly composed of an aluminum oxide having an average surface roughness _Ra of 20 nm or more and a surface area ratio S _ratio of 1.42 or more. It is provided on each optical surface to reduce light reflection. Here, since the use wavelength region of the optical system of Example 7 is the visible region, the shortest wavelength in the use wavelength region is set to 400 nm.

  In addition, since the antireflection structure 3 of Example 7 is mainly composed of aluminum oxide, it has high heat resistance, and even when used at the position of the optical surface 13a that is exposed to high heat close to the light source 12, the performance deteriorates. There is no worry.

  FIG. 12 is a schematic diagram of a main part in which an optical element is used in a scanning optical system (laser beam printer) as an eighth embodiment of the present invention.

  FIG. 12 shows a cross section of the scanning optical system.

In FIG. 12, 12 is a light source, 21 is a collimator lens, 11 is an aperture stop, 22 is a cylindrical lens, 23 is an optical deflector, 24a and 24b are optical elements constituting an fθ lens, and 7 is an image plane. In FIG. 12, reference numeral 3 denotes an antireflection structure according to the present invention, which comprises a fine concavo-convex structure mainly composed of an aluminum oxide having an average surface roughness _Ra of 21 nm or more and a surface area ratio S _ratio of 1.45 or more. It is provided on each optical surface to reduce the reflection of light and realize high-quality image formation. Here, the operating wavelength of the optical system of Example 8 is 405 nm.

  FIG. 13 is a schematic view of a method for manufacturing an optical element (prism) including the antireflection structure 3 as Embodiment 9 of the present invention.

  In FIG. 13, reference numeral 2 denotes a substrate, for example, a prism.

  The substrate 2 was sequentially washed with a neutral detergent, pure water rinse, and alcohol, dried, and then fixed with a support member 25 as shown in FIG.

Aluminum-secondday-butoxide (Al (O-sec-Bu) ₃ ) was added to 2-propanol (IPA), and after stirring, ethyl acetoacetate (EAcAc) was added and stirred at room temperature for about 3 hours. Further, 0.01 M dilute hydrochloric acid (HClaq.) Was added, and the molar ratio of the solution was changed to Al (O-sec-Bu) ₃ : IPA: EAcAc: HClaq. = 1: 20: 1: 1
The ratio of This was stirred for about 1 hour at room temperature to prepare a coating solution 26.

  Next, the substrate 2 fixed to the support member 25 was immersed in the coating solution 26 and pulled up at a speed of 1 mm / sec to form a transparent film on the optical surface of the substrate 2 (film formation process).

  Subsequently, after drying at about 60 ° C. for 30 minutes, as shown in FIG. 13 (B), it is immersed in warm water 27 at about 60 ° C. for a predetermined time and dried again at about 60 ° C. to prevent reflection on the surface of the substrate 2. The structure 3 was formed (a fine uneven part forming step).

When the surface shape of this antireflection structure 3 was measured with an AFM apparatus (SPA-500 + SPI3800N manufactured by Seiko Instruments Inc.) using a cantilever having a sharp tip shape (SI-DF20S manufactured by the same company), the formula (1) The average surface roughness R _a ′ defined as ′ was 22.8 nm, and the surface area ratio S _ratio ′ defined as formula (2) ′ was 1.996. Further, when the visible light transmittance of the prism was measured, there was no generation of unnecessary light such as diffraction and scattering, and an extremely excellent transmittance of 99.3% or more in the entire visible region as shown in FIG. Met.

  In this method, since the processing temperature during the manufacturing process is as low as about 60 ° C., problems such as deformation and alteration may occur even when a resin or the like is used as the substrate or the base 2 of the optical element 1. Absent.

  In the ninth embodiment, the case where the substrate of the optical element 1 is a prism has been described. However, the present invention is not limited to this, and various other substrates such as a convex lens, a concave lens, a meniscus lens, a fly eye integrator, and an fθ lens can be used. In the same manner, an excellent antireflection structure can be formed.

  Further, in Example 9, after the coating was formed and dried, it was immersed in warm water for a predetermined time. However, the present invention is not limited to this, and it may be exposed to water vapor for a predetermined time.

  FIG. 15: is principal part schematic of the manufacturing method of the optical element (fly eye integrator) which comprises the reflection preventing structure 3 as Example 10 of this invention. In FIG. 15, reference numeral 2 denotes a substrate, for example, a fly eye lens.

  The substrate 2 was sequentially washed with a neutral detergent, pure water rinse, and alcohol, dried, and then fixed with a support member 25 as shown in FIG.

After stirring was added aluminum nitrate 9 hydrate _{(Al (NO 3) 3 ·} 9H 2 O) in 2-propanol (IPA), was stirred at room temperature for about 3 hours and further adding ethyl acetoacetate (EAcAc). Here, the molar ratio of the solution is
_{Al (NO 3) 3 · 9H} 2 O: IPA: EAcAc = 1: 20: 1
The ratio of This was stirred for about 1 hour at room temperature to prepare a coating solution 26.

  Next, the substrate 2 fixed to the support member 25 was immersed in the coating liquid 26 and pulled up at a speed of 1 mm / sec to form a transparent film on the optical surface of the substrate 2.

  Subsequently, after drying at about 60 ° C. for 30 minutes, as shown in FIG. 15B, it is exposed to water vapor 28 for a predetermined time and dried again at about 60 ° C. to form the antireflection structure 3 on the surface of the substrate 2. did.

When the surface shape of this antireflection structure 3 was measured with an AFM apparatus (SPA-500 + SPI3800N manufactured by Seiko Instruments Inc.) using a cantilever having a sharp tip shape (SI-DF20S manufactured by the same company), the formula (1) The average surface roughness R _a ′ defined as ′ was 23.6 nm, and the surface area ratio S _ratio ′ defined as formula (2) ′ was 1.776. Further, when the transmittance of visible light of the fly eye integrator was measured, there was no generation of unnecessary light such as diffraction and scattering, and it was extremely excellent at 98.5% or more in the entire visible region as shown in FIG. Transmittance.

  Further, in this method, since the processing temperature during the manufacturing process is low, problems such as deformation and deterioration do not occur even when a resin or the like is used as the substrate or the base 2 of the optical element 1.

  In the tenth embodiment, the case where the substrate of the optical element 1 is a fly-eye integrator has been described. However, the present invention is not limited to this, and there are various substrates such as a convex lens, a concave lens, a meniscus lens, a prism, and an fθ lens. In the same manner, an excellent antireflection structure can be formed.

  Further, in Example 10, after the coating was formed and dried, it was exposed to water vapor for a predetermined time. However, the present invention is not limited to this, and it may be immersed in warm water for a predetermined time.

  As described above, according to Examples 1 to 8, reflection of light on the surface of the optical element is reduced, and generation of harmful light such as flare light and ghost light is suppressed even when used in an optical system. An optical system with excellent optical performance can be realized.

  In addition, according to the optical element manufacturing methods of Examples 9 and 10, an electron beam lithography apparatus, a laser interference exposure apparatus, a semiconductor exposure apparatus, and an etching apparatus can be used by a simple method that does not require a large and expensive apparatus such as a dip method. It is possible to easily form a high-performance antireflection structure on an optical element having an optical surface that is difficult to form even using, for example.

: Front view of Embodiment 1 of the present invention : Cross-sectional view of Example 1 of the present invention : Front view of Embodiment 2 of the present invention : Cross-sectional view of Example 2 of the present invention : Front view of Embodiment 3 of the present invention : Cross section of Example 3 of the present invention : Front view of Embodiment 4 of the present invention : Cross section of Example 4 of the present invention : Cross section of Example 5 of the present invention : Cross section of Example 6 of the present invention : Cross section of Example 7 of the present invention : Cross section of Example 8 of the present invention : Process diagram of Example 9 of the present invention : The figure which shows the transmittance | permeability of the reflection preventing structure of Example 9 of this invention : Process diagram of Example 10 of the present invention : The figure which shows the transmittance | permeability of the reflection preventing structure of Example 10 of this invention

Explanation of symbols

DESCRIPTION OF SYMBOLS 1: Optical element 2: Board | substrate, base | substrate 3: Antireflection structure 4: Objective lens 5: Prism 6: Eyepiece lens 7: Imaging surface 8: Pupil surface 9: Optical surface of the most object side 10: Most evaluation surface (pupil) Optical surface on the surface or imaging surface) side 11: Aperture 12: Light source 13: Fly eye integrator 14: Polarization conversion element 15: Condenser lens 16: Mirror 17: Field lens 18: Prism 19: Light modulation element 20: Projection lens 21 : Collimator lens 22: Cylindrical lens 23: Optical deflector 24: fθ lens 25: Support member 26: Coating liquid 27 Hot water 28 Water vapor 29 Lid

Claims (5)

An optical element having a fine concavo-convex structure on an optical surface, wherein the fine concavo-convex structure is made of a material containing a metal compound, and the fine concavo-convex structure has an average surface roughness Ra and _a surface area ratio. S _ratio , X, Y, Z are taken as Cartesian coordinates,
When
However,
H (X, Y): The area of an arbitrarily sampled area in the plane when the optical plane is the XY plane
Function X ₁ : X direction sampling start coordinate X _M : X direction sampling end coordinate Y ₁ : Y direction sampling start coordinate Y _N : Y direction sampling end coordinate H _ave : Average value of H (X, Y) S ₀ : Area when an arbitrarily sampled area is a plane = | (X _M −X ₁ ) (Y _N −Y ₁ ) |
λ _min : shortest wavelength in the used wavelength region S: actual surface area of the surface of the fine concavo-convex structure in an arbitrarily sampled region
An optical element characterized by satisfying:   The optical element according to claim 1, wherein the optical surface is a flat surface, a curved surface, or a curved surface array in which a plurality of curved surfaces are arranged.   A film forming step of forming a film by applying a metal-containing solution on the optical surface, and a fine uneven portion forming step of forming a fine uneven structure by warm water treatment or steam treatment of the film. A method for manufacturing a fine concavo-convex structure.   The method for producing a fine concavo-convex structure according to claim 3, wherein the temperature of the hot water treatment is 40 ° C or higher and 100 ° C or lower.   An optical system comprising the optical element according to claim 1.