JP4598177B2 - Design method of antireflection film - Google Patents

Description

The present invention relates to a method of designing the anti-reflection film, suitable in particular an optical pickup apparatus, a semiconductor device, an optical element having a large numerical aperture for use in an endoscope or the like (NA), and the ball-shaped optical element used in an optical communication The present invention relates to a method for designing an antireflection film.

  The surface of the objective lens of the optical pickup device or the semiconductor device is coated with an antireflection film to efficiently transmit incident light. For example, in a single-layer antireflection film, the optical path difference between the reflected light on the surface of the antireflection film and the reflected light at the boundary between the antireflection film and the lens is an odd multiple of half the wavelength, and these lights are It is designed to have a thickness that cancels out due to interference. In general, it is often designed to have a film thickness that maximizes the anti-reflection effect near the center of the lens (light incident angle is 0 °). The minimum value is shown in a region where light is perpendicular to the antireflection film.

  The objective lens is arranged so that the light to be collected is incident perpendicularly to the center of the surface (light incident angle is 0 °). However, since the lens surface of the objective lens is a curved surface, the condition for normal incidence is set. Only a very limited range around the optical axis is almost satisfied. At the lens periphery, the incident angle of the light beam is large, so that it deviates greatly from the design conditions of the antireflection film, and the reflectance of the incident light is high.

  The antireflection film is formed by vacuum deposition, sputtering, CVD, or the like. When an antireflection film is formed by these methods, the optical film thickness at the lens periphery tends to be smaller than that at the lens center. For this reason, the optical film thickness of the antireflection film is small at the lens peripheral portion and deviates from the design film thickness, and since the light incident angle is large as described above, the antireflection effect cannot be sufficiently obtained and the amount of reflected light is Very many. Therefore, although such an optical element has a large amount of transmitted light at the center, there is a problem that the amount of transmitted light is not sufficient for the entire element.

  Japanese Patent Laid-Open No. 2001-52366 (see Patent Document 1) includes a light source that emits laser light having a predetermined wavelength, and an objective lens that converges the laser light from the light source onto a recording surface of an optical disc, and the surface of the objective lens Discloses an optical system of an optical head in which an antireflection film is applied, and a design reference wavelength of the antireflection film (a wavelength indicating a minimum reflectance at the time of vertical incidence) is set longer than the wavelength of the laser light. ing. Further, it is described that the design reference wavelength of the antireflection film is preferably 50 to 60 nm longer than the wavelength of the laser beam.

  In the case of a single-layer antireflection film, to increase the design reference wavelength, the physical film thickness of the antireflection film is increased. It will be larger than the wavelength. For this reason, the reflectance at the center of the lens is not an optimized value, but the reflectance at the periphery of the lens is relatively small. Since the area around the lens occupies a large proportion of the surface area of the lens, the total amount of light transmitted through the objective lens of this optical system is often small compared to the case where the wavelength of the laser beam is the design reference wavelength. However, the total amount of transmitted light depends on the curvature of the lens and the wavelength of light to be irradiated, and there is a problem that an optical element having a sufficient amount of transmitted light cannot be obtained depending on the shape of the lens.

JP 2001-52366 JP

Accordingly, an object of the present invention has an antireflection film, it is to provide a method of designing the anti-reflection film of the transmitted light quantity with many optical elements in the entire device.

  As a result of diligent research in view of the above object, the present inventors have obtained an optical element having an antireflection film on the lens surface, the antireflection film being divided into a plurality of regions within the effective diameter, and (i) for each region. Designed to minimize the total amount of reflected light obtained, or (ii) those designed to maximize the total amount of light transmitted through the film for each region. The inventors have found that the antireflection film can be designed so as to have, and have arrived at the present invention.

That is, the first antireflection film designing method of the present invention, when the antireflection film is a single layer, an antireflection film was formed in a predetermined film forming conditions to the lens surface, the effective diameter of the lens substrate The optical film of the antireflection film is divided at each inclination angle range Δθ, and the optical film thickness D (θ) at the substrate inclination angle θ of the antireflection film is measured at each substrate inclination angle range Δθ. Thickness D (θ) is expressed by the following formula (1)
D (θ) = D ₀ ・ (cosθ) ^x ... (1)
(Where θ represents the substrate tilt angle, D ₀ represents the optical film thickness of the antireflection film at the center of the lens, and X represents a constant not less than 0 and not more than 1). The film thickness ratio of θ) to the optical film thickness D ₀ is determined, the incident light amount ratio P (Δθ _m ) of the lens is determined for each substrate tilt angle range Δθ, and the reflectance R (Δθ _m ) of the antireflection film is calculated. By expressing using the optical film thickness D ₀ , the optical film thickness D ₀ is changed while keeping the film thickness ratio constant, and the product of the incident light amount ratio P (Δθ _m ) and the reflectance R (Δθ _m ). The optical film thickness of the antireflection film that minimizes the sum of the values is obtained .
Further, when the antireflection film has a plurality of layers, an antireflection film is formed on the lens surface under predetermined film formation conditions, the effective diameter of the lens is divided for each substrate tilt angle range Δθ, and the antireflection film optical thickness D in the substrate tilt angle of each layer theta a (theta) measured every substrate inclination angle range [Delta] [theta], the substrate inclination angle of each layer optical thickness D in the theta (theta) the following formula (1)
D (θ) = D ₀ ・ (cosθ) ^x ... (1)
(Where θ represents the substrate tilt angle, D ₀ represents the optical film thickness of the antireflection film at the center of the lens, and X represents a constant of 0 or more and 1 or less). The film thickness ratio of D (θ) to the optical film thickness D ₀ is determined, and the incident light amount ratio P (Δθ _m ) of the lens is determined for each substrate tilt angle range Δθ, and the reflectance R (Δθ _m ) of the antireflection film is determined. ) by the expressed using the optical thickness D ₀ of each layer, said thickness ratio by changing the optical thickness D ₀ of each layer in the uniform the incident light intensity ratio P ([Delta] [theta] _m) and the reflectance R It is characterized in that the optical film thickness of each layer that minimizes the sum of products of (Δθ _m ) is obtained.

The amount of reflected light in each region, the incident light amount ratio P ([Delta] [theta] _m) in each area, is the product _{P (Δθ m) × R (} Δθ m) between the reflectance of light R ([Delta] [theta] _m) in each region, each It is preferable that the reflectance in the region is obtained by approximating it as being constant.

In the second antireflection film design method of the present invention, when the antireflection film is a single layer, an antireflection film is formed on the lens surface under predetermined film formation conditions, and the effective angle of the lens is within the substrate tilt angle. The optical film thickness D (θ) at the substrate inclination angle θ of the antireflection film is measured for each substrate inclination angle range Δθ, and the optical film thickness D of the antireflection film at the substrate inclination angle θ is divided for each range Δθ. (θ) is expressed by the following formula (1)
D (θ) = D ₀ ・ (cosθ) ^x ... (1)
(Where θ represents the substrate tilt angle, D ₀ represents the optical film thickness of the antireflection film at the center of the lens, and X represents a constant not less than 0 and not more than 1). The film thickness ratio of θ) to the optical film thickness D ₀ is determined, the incident light quantity ratio P (Δθ _m ) of the lens is determined for each substrate tilt angle range Δθ, and the film transmittance T (Δθ _m ) of the antireflection film By using the optical film thickness D ₀ , the optical film thickness D ₀ is changed while keeping the film thickness ratio constant, and the incident light amount ratio P (Δθ _m ) and the film transmittance T (Δθ _m ). The optical film thickness of the antireflection film that maximizes the sum of the products is obtained .
Further, when the antireflection film has a plurality of layers, an antireflection film is formed on the lens surface under predetermined film formation conditions, the effective diameter of the lens is divided for each substrate tilt angle range Δθ, and the antireflection film The optical film thickness D (θ) at each substrate tilt angle θ is measured for each substrate tilt angle range Δθ, and the optical film thickness D (θ) of each layer at the substrate tilt angle θ is expressed by the following formula (1)
D (θ) = D ₀ ・ (cosθ) ^x ... (1)
(Where θ represents the substrate tilt angle, D ₀ represents the optical film thickness of the antireflection film at the center of the lens, and X represents a constant of 0 or more and 1 or less). The film thickness ratio of D (θ) to the optical film thickness D ₀ is obtained, the incident light quantity ratio P (Δθ _m ) of the lens is obtained for each substrate tilt angle range Δθ, and the film transmittance T (Δθ of the antireflection film is obtained. by represented using optical thickness D ₀ of each layer _m), the membrane permeability the thickness ratio and the set constant layers of optical thickness D ₀ changes are allowed the incident light amount ratio P ([Delta] [theta] _m) It is characterized in that the optical film thickness of each layer is obtained so that the total sum of products of the rates T (Δθ _m ) is maximized.

The amount of light transmitted through the membrane in each region is the product P (Δθ _m ) × T (Δθ _m ) of the incident light amount ratio P (Δθ _m ) in each region and the film transmittance T (Δθ _m ) of light in each region. The membrane transmittance in each region is preferably obtained by approximating it as constant.

The substrate tilt angle θ within the effective diameter of the lens is preferably 0 to 70 ° .

The antireflection film design method of the present invention divides the effective diameter of the lens into a substrate tilt angle range Δθ, and optically measures the optical film thickness D (θ) at the lens center at the substrate tilt angle θ of each layer of the antireflection film. The film thickness ratio with respect to the film thickness D ₀ is obtained, and the incident light quantity ratio of the lens and the reflectance and / or film transmittance of the antireflection film are obtained for each substrate inclination angle range Δθ, and the substrate inclination angle range Δθ is obtained from the product. The amount of reflected light and / or the amount of light transmitted through the film is obtained. For this reason, it is possible to efficiently calculate the reflected light amount and / or the film transmitted light amount for each substrate tilt angle range Δθ.

[1] Design method of antireflection film Of the antireflection film formed on the lens surface, a portion corresponding to the effective diameter E of the lens is divided into minute areas a, and the amount of reflected light and / or film transmission is divided for each area a. Find the amount of light. The amount of reflected light can be represented by the product of the reflectance r of the light beam and the incident light amount ratio p, and the amount of light transmitted through the film can be represented by the product of the film transmittance t of the light beam and the incident light amount ratio p. The incident light amount ratio p indicates the proportion of light incident on each region a out of light incident on the effective diameter E of the optical element.

  In the region a, it is preferable to set the region a so that the reflectance and film thickness of the antireflection film 2 or the film transmittance and film thickness can be approximated to be constant. For example, when the region a is sufficiently small, it can be approximated that the reflectance r and the film transmittance t and the film thickness of the antireflection film 2 are constant in the region a. When the lens is rotationally symmetric about the optical axis, the reflectance r and film transmittance t of the antireflection film are constant on a circle centered on the optical axis of the lens. For this reason, by setting the region a to be divided by a concentric circle centered on the optical axis of the lens and calculating the reflectance r and / or the film transmittance t, the reflected light amount and / or the film transmitted light amount can be obtained efficiently. Can do. Hereinafter, a method of dividing the antireflection film by the concentric circles and designing the antireflection film will be described.

  FIG. 1 shows an example of the optical element of the present invention. The optical element shown in FIG. 1 includes a lens 1 having a convex first surface 11 on the surface 1a side, and an antireflection film 2 formed on the first surface 11. The back surface 1b side of the optical element is a concave second surface 12. The antireflection film 2 in the drawing is drawn thicker than the actual thickness. For simplicity, the antireflection film 2 has a single-layer structure, and the design of the antireflection film 2 for preventing this reflection will be described assuming that parallel light of wavelength λ is incident from the surface 1a of the optical element.

(1) First method
(a) Board tilt angle range Δθ
FIG. 4 shows an example of a method for designing the antireflection film 2. First, the antireflection film corresponding to the effective diameter E of the lens 1 is divided. Specifically, a plurality of substrate tilt angle ranges Δθ are set on the first surface 11. In the present specification, the substrate tilt angle range Δθ indicates a region on the first surface divided by the substrate tilt angle θ. As shown in FIG. 2, the substrate inclination angle θ represents an angle formed by a surface Fo that is in contact with the center 110 of the first surface 11 and a surface F that is in contact with the point t on the first surface 11.

In the case of a lens having a maximum substrate tilt angle θ of 70 ° in a portion within the effective diameter E, as shown in FIG. 1, when the substrate tilt angle range Δθ is 10 °, the first surface 11 is divided into seven. The smaller the substrate tilt angle range Δθ is, the more accurately the thickness of the antireflection film 2 can be designed. However, practically it is about 1 ° to 10 °, and the number of substrate tilt angle ranges Δθ is about 2 to 100. is there. For convenience, it will be described below as the substrate inclination angle range [Delta] [theta] [Delta] [theta] ₁ in this order from the center 110 _{side, Δθ 2 ·· Δθ m ·· Δθ} 7 (m is an integer of up to 1-7.).

(b) Light incident angle The light incident angle at a point on the optical element is determined geometrically according to the shape of the optical element and the nature of the incident light (whether it is parallel light, diffused light, or convergent light). Can do. When the incident light is parallel light, the light incident angle of the optical element is equal to the substrate tilt angle θ of the antireflection film 2.

Since the thickness of the antireflection film 2 is not uniform, the substrate inclination angle θ of the lens 1 at the point t and the substrate inclination angle at the point t ′ on the antireflection film 2 on the point t are strictly speaking. Is different. However, since the thickness of the antireflection film 2 is very small, the difference is also very small compared to the substrate tilt angle θ. Therefore, the reflectance or the film transmittance may be obtained assuming that the substrate inclination angle θ of the antireflection film 2 is the same as the substrate inclination angle θ of the lens 1. Preferred to use an average or median of the substrate inclination angle theta at each point of the substrate inclination angle range [Delta] [theta] _m as the substrate inclination angle theta _m of the substrate inclination angle range [Delta] [theta] _m.

(c) Optical film thickness D (θ)
The optical film thickness D (θ) of the antireflection film 2 is obtained for each substrate tilt angle range Δθ. The optical film thickness depends on the substrate tilt angle θ, and the optical film thickness D (θ) of the antireflection film 2 in the substrate tilt angle range Δθ is expressed by the following equation (1).
D (θ) = D ₀・ (cosθ) ^x ... (1)
(Where θ represents the substrate tilt angle, D ₀ represents the optical film thickness of the antireflection film 2 at the center of the lens, X represents a constant of 0 or more and 1 or less, and 0 ° <θ <90 °. ). The optical film thickness D (θ) decreases as θ increases. X is a constant depending on the film formation conditions (film formation method, film formation material, film formation apparatus, etc.) of the antireflection film 2.

FIG. 5 shows an example of the relationship between the substrate tilt angle θ and the film thickness ratio D (θ) / D ₀ of the antireflection film 2. This antireflection film 2 is formed by forming an antireflection film 2 made of magnesium fluoride on the first surface 11 by a vacuum deposition method (decompression degree 1 × 10 ⁻⁶ Torr, vacuum deposition 4 minutes). This graph is approximated to (cosθ _m ) ^0.7 .

The optical film thickness D ₀ of the antireflection film 2 at the center of the lens is expressed by the following formula (2)
D ₀ = n ・ d ₀ ... (2)
(Where n represents the refractive index of the antireflection film 2 at the wavelength λ, and d ₀ represents the physical film thickness of the antireflection film at the center of the lens). From the above equation (2) and the following equation (1), the physical film thickness d _m of the antireflection film 2 formed in the substrate tilt angle range Δθ _m of the lens 1 can be obtained.

(d) Optical characteristic value The optical characteristic value of each substrate tilt angle range Δθ _m is
(i) wavelength of incident light,
(ii) the refractive index of the incident medium (usually air),
(iii) The refractive index of the exit medium (substrate such as a lens)
(iv) Ray incidence angle,
(v) number of membrane layers,
(vi) Refractive index of each layer and
(vii) It can be calculated from the film thickness of each layer. The reason why the optical characteristic value is obtained from (i) to (vii) is that the optical characteristic value of the antireflection film 2 depends on the reflectance and the transmittance, and the absorptance can be ignored.

In general, the optical property value depends on the reflectance, transmittance, and absorptance, and the following formula (3):
Reflectivity + transmittance + absorptance = 1 (100%) (3)
Is known to hold. Therefore, in order to accurately calculate the optical characteristic value, it is necessary to consider the absorptance in addition to the reflectance and transmittance. However, since it is common to use a material that does not absorb light or a material that has very little light as the material of the antireflection film of the optical element, it is very small to take absorption into consideration when calculating the optical characteristic value. If the absorptivity of the antireflection film material can be ignored, the following formula (4):
Reflectivity + transmittance = 1 (100%) (4)
Holds. When the absorption rate by the antireflection film is so large as to significantly affect the optical property value, it is necessary to obtain the optical property value in consideration of the absorption rate.

As shown in the above equation (4), there is a correlation between the reflectance R (Δθ _m ) and the membrane transmittance T (Δθ _m ), and the larger the reflectance R (Δθ _m ), the more the membrane transmittance T (Δθ _m ). Is small. For this reason, when designing the antireflection film 2, attention may be paid to the reflectance R (Δθ _m ) or the film transmittance T (Δθ _m ). Specifically, the total amount of reflected light (the total amount of reflected light within the effective diameter E) is obtained from the reflectance R (Δθ _m ) of each substrate tilt angle range Δθ, and the film thickness of the antireflection film 2 is set so that this is minimized. It is also possible to determine the total sum of the amount of transmitted light from the membrane transmittance T (Δθ _m ) in each substrate tilt angle range Δθ (the total amount of transmitted light in the effective diameter E), and to maximize this. good. Hereinafter, a case where the film thickness of the antireflection film 2 is determined using the reflectance R (Δθ _m ) will be described as an example.

The wavelength of the light h ₁ incident on the antireflection film 2 of the optical element shown in FIG. 1 is λ, and the incident medium is air. Further, the antireflection film 2 is composed of a single layer, and as described above, the thickness of each substrate tilt angle range Δθ is obtained by the equation (1). Since the incident light h ₁ is parallel light, the light incident angle is equal to the substrate tilt angle θ. When designing the antireflection film 2 of the specific lens 1 in this way, since (i) to (v) are determined among the above parameters, (vi) the refractive index of the antireflection film 2 and (vii) film If the thickness is determined, the reflectance R (Δθ _m ) is uniquely determined for each light incident angle. Incidentally not described in detail since specific calculation methods of the reflectance R ([Delta] [theta] _m) are very complex.

(e) Incident light quantity ratio P (Δθ _m )
Incident light intensity ratio P ([Delta] [theta] _m) shows a ratio of (the amount of light incident on each substrate inclining angle range [Delta] [theta]) / (total amount of incident light that enters the interior of the lens 1 effective diameter E). Since the incident light h ₁ to the lens 1 is parallel light, the incident light intensity ratio P ([Delta] [theta] _m) is equivalent to the ratio of the projected area of each substrate inclining angle range [Delta] [theta] to the cross-sectional area of the lens 1 in the effective diameter E. The projected area of the substrate tilt angle range Δθ can be calculated geometrically from the shape of the lens 1 and the light incident angle.

As shown in FIG. 1B, the projected area of each substrate tilt angle range Δθ increases as the distance from the optical axis of the lens increases. Therefore, the incident light amount ratio P (Δθ _m ) increases as the distance from the optical axis of the lens increases. That is, there is a relationship of P (Δθ ₁ ) <P (Δθ ₂ ) <... <P (Δθ _M ).

(f) Incident light quantity ratio / reflectance P (Δθ _m ) × R (Δθ _m )
The product of the incident light quantity ratio and the reflectance R (Δθ _m ) and the incident light quantity ratio / reflectance P (Δθ _m ) × R (Δθ _m ) are calculated. Comparing the area of each substrate tilt angle range Δθ _m , Δθ ₁ is the smallest as shown in FIG. Thus the light is incident substantially perpendicularly in [Delta] [theta] _1, although the reflectivity R ([Delta] [theta] ₁₎ is small, the amount of light transmitted through the substrate inclination angle range [Delta] [theta] ₁ is not always large compared to the other [Delta] [theta] _m. Thus, the transmitted light amount of each Δθ _m depends on the reflectance R (Δθ _m ) determined by the light incident angle and the like and the incident light amount ratio P (Δθ _m ).

The incident light amount ratio / reflectance P (Δθ _m ) × R (Δθ _m ) is obtained by multiplying the reflectance R (Δθ _m ) by the area ratio of the portion showing the reflectance R (Δθ _m ) on the antireflection film 2. Therefore, it can be said that the ratio of the region showing a constant reflectance to the lens 1 is a value that takes into account the reflectance. By using the incident light quantity ratio / reflectance P (Δθ _m ) × R (Δθ _m ) for the design of the antireflection film 2, not only the reflectance of light incident on each substrate tilt angle range Δθ but also the reflectance can be determined. The area ratio of the portion to be shown can be reflected.

（ただし、θは基板傾斜角度を示し、Mは基板傾斜角度範囲の数を示し、P(Δθ_m)は入射光量比を示し、R(Δθ_m)は反射率を示す。）により表される。 (g) Sum of incident light ratio and reflectance P (Δθ _m ) × R (Δθ _m ) Sm (R)
Sum of incident light ratio and reflectance Sm (R) is given by the following formula (5)

(Where θ represents the substrate tilt angle, M represents the number of substrate tilt angle ranges, P (Δθ _m ) represents the incident light quantity ratio, and R (Δθ _m ) represents the reflectance). .

As described above, P (Δθ _m ) is obtained geometrically from the shape of the lens 1 and the like. R (Δθ _m ) is uniquely determined by determining the refractive index n and the film thickness of the antireflection film 2. Although the film thickness of the antireflection film 2 is not uniform, the film thickness distribution is determined by the film forming method, the film forming apparatus, etc. of the antireflection film 2. Therefore, when the physical film thickness d _{0 at the} center 110 is determined, the shape of the antireflection film 2 is also determined, and the film thickness in each substrate tilt angle range Δθ is also uniquely determined. Therefore, the sum Sm (R) is the refractive index n of the antireflection film 2, which is a function of the physical thickness d _0.

In order to produce an optical element that effectively transmits incident light, it is preferable to minimize the sum Sm (R). When designing anti-reflection film 2 formed on this end lens 1, to determine the refractive index n and physical thickness d ₀ to minimize the sum Sm (R). For this purpose, a sum Sm (R) was calculated for various refractive index n and physical thickness d _0, the sum Sm (R) may be determined the refractive index n and physical thickness d ₀ as the minimum value . Since the refractive index n is determined by the material of the anti-reflection film 2, by selecting the material the refractive index n is constant, it is practical to determine the total sum Sm (R) only physical film thickness d ₀ as a variable.

When the antireflection film 2 is composed of a plurality of layers, the sum Sm (R) is calculated for each layer with respect to various refractive indexes n and physical film thicknesses d ₀ , and the sum of the sums Sm (R) of each layer is minimized. Thus, the refractive index n and the physical film thickness d ₀ may be determined.

(2) Second Method A method using the film transmittance T (Δθ _m ) of the antireflection film 2 as an optical characteristic value will be described below. In this method, the total sum Sm (T) of the incident light ratio / film transmittance P (Δθ _m ) × T (Δθ _m ) is obtained, and the refractive index n and the physical film thickness d ₀ are determined so as to maximize them. Except for the above, since this is the same as the case of using the reflectance R (Δθ _m ), only the differences will be described below.

When designing the antireflection film 2 of a specific lens 1, the film transmittance T (Δθ _m ) is also determined from (i) to (v) among the parameters of the optical characteristic values described above. (Vi) If the refractive index and (vii) film thickness of the antireflection film 2 are determined, the film transmittance T (Δθ _m ) is uniquely determined for each light incident angle. The specific calculation method of the membrane permeability T (Δθ _m ) is very complicated and will not be described in detail.

The incident light quantity ratio, to calculate the film transmittance T incident light quantity ratio-film transmittance is the product of _{(Δθ m) P (Δθ m} ) × T (Δθ m). The amount of light transmitted through the antireflection film 2 formed in the substrate tilt angle range Δθ _m depends on the film transmittance T (Δθ _m ) determined by the light incident angle and the like and the incident light amount ratio P (Δθ _m ). The incident light ratio / membrane transmittance P (Δθ _m ) × T (Δθ _m ) is the ratio of the area of the portion showing the membrane transmittance T (Δθ _m ) on the antireflection film 2 to the membrane transmittance T (Δθ _m ). Therefore, it can be said that the ratio of the area of the lens 1 occupied by the lens 1 to the film transmittance is added to the film transmittance. By using the incident light quantity ratio / film transmittance P (Δθ _m ) × T (Δθ _m ) for the design of the antireflection film 2, not only the film transmittance of light incident on each substrate tilt angle range Δθ but also the film The area ratio of the portion showing the transmittance T (Δθ _m ) can also be reflected.

（ただし、θは基板傾斜角度を示し、Mは基板傾斜角度範囲の数を示し、P(Δθ_m)は入射光量比を示し、T(Δθ_m)は膜透過率を示す。）により表される。総和Sm(T)も反射防止膜２の屈折率nと、反射防止膜２の物理膜厚d₀との関数である。 Sum of incident light ratio and membrane transmittance Sm (T) is expressed by the following formula (6)

(Where, θ represents the substrate tilt angle, M represents the number of substrate tilt angle ranges, P (Δθ _m ) represents the incident light amount ratio, and T (Δθ _m ) represents the film transmittance). The The sum Sm (T) is also a function of the refractive index n of the antireflection film 2 and the physical film thickness d ₀ of the antireflection film 2.

In order to produce an optical element that effectively transmits incident light, it is preferable to maximize the total sum Sm (T). When designing anti-reflection film 2 formed on this end lens 1, the total sum Sm (T) is to determine the refractive index n and physical thickness d ₀ to maximize. Various refractive index n and physical thickness d ₀ is substituted into Equation (6) computes the total sum Sm (T) is respectively, are determined the refractive index n and physical thickness d ₀ sum Sm (T) is maximized It ’s fine.

(2) Production of Antireflection Film The production method of the antireflection film 2 is not particularly limited, and can be produced by a general method. Examples include physical vapor deposition methods such as vapor deposition, sputtering, ion plating, chemical vapor deposition such as thermal CVD, plasma CVD, and photo CVD, dipping using sol-gel coating liquid, spin method, spray method, etc. .

For example, when the lens 1 for forming an anti-reflection film 2 of the single-layer, by setting the deposition time, or the like as appropriate, a physical film thickness d ₀ may be set to a desired size. For example, when the antireflection film 2 is formed such that the physical film thickness d ₀ of the antireflection film 2 made of magnesium fluoride is about 120 nm, the deposition time is about 4 to 5 minutes.

The case where the antireflection film 2 having a plurality of layers is formed on the lens 1 is the same as the case of the single layer film. Select an antireflection film material for each layer to determine the refractive index n of each layer First, the sum Sm (R) is to minimize (or sum Sm (T) is the maximum) from the optical thickness D _0, the lens The physical film thickness d ₀ at the center 110 is determined. The vapor deposition time and the like are set so that the physical film thickness d ₀ is obtained, and the respective layers may be sequentially formed by the same operation as in the case of the single layer film.

[2] Optical Element The optical element of the present invention has a lens 1 and an antireflection film 2. In the example shown in FIG. 1, the antireflection film 2 is formed only on the first surface 11, but the antireflection film 2 is formed on the first surface 11 and the second surface 12 of the lens 1. It is preferable. The film thickness of the antireflection film 2 is designed so that the amount of transmitted light within the effective diameter E of the lens 1 is maximized. Therefore, a relatively large amount of transmitted light can be obtained even at the periphery of the lens 1 having a large curvature. The antireflection film 2 having such a film thickness can be produced by the method for producing an optical element of the present invention.

  The refractive index of the lens 1 is preferably 1.55-1.85. When the refractive index is less than 1.55, an effective antireflection effect cannot be obtained. As a material having a refractive index of 1.55 to 1.85, Lak14 glass can be mentioned.

  The antireflection film 2 may be a single layer or a plurality of layers. In the case of a single layer, it preferably has a refractive index of 1.35 to 1.5. When the refractive index exceeds 1.5, effective antireflection properties are not exhibited. Examples of the substance having a refractive index of 1.35 to 1.5 include magnesium fluoride and calcium fluoride. In the case of a single layer, the optical film thickness of the antireflection film 2 at the center of the lens 1 is preferably 0.3λ to 0.5λ.

  In the case of a plurality of layers, it is preferable to alternately include at least one high refractive index layer having a refractive index of 1.95 to 2.25 and at least one low refractive index layer having a refractive index of 1.35 to 1.5. When layers having different refractive indexes are laminated, the phase and amplitude of light change at the bonding interface, and reflected light is strengthened or weakened by interference of light from each interface. An antireflection film having excellent antireflection characteristics can be formed by alternately laminating layers having different refractive indexes so that light is weakened by utilizing this property. Examples of the material for the high refractive index layer include zirconium oxide and titanium oxide. Examples of the material for the low refractive index layer include magnesium fluoride, calcium fluoride, and silicon dioxide.

  The present invention will be described in more detail with reference to the following examples, but the present invention is not limited thereto.

Example 1
(1) Design of antireflection film thickness
When the antireflection film 2 made of magnesium fluoride (refractive index n = 1.38) is formed on the first surface 11 of the objective lens 1 made of LAK14 glass (double-sided aspheric lens, refractive index n = 1.72), R ( Δθ _m ) was calculated for each substrate tilt angle range Δθ. The calculated amount of incident light ratio P of the anti-reflection film 2 ([Delta] [theta] _m) for each substrate inclining angle range [Delta] [theta]. The substrate tilt angle θ within the effective diameter E of this lens was 0 to 70 °. The substrate tilt angle range Δθ was 10 °, and the median value of each substrate tilt angle range Δθ was θ. Table 1 shows the incident light amount ratio P (Δθ _m ) in each substrate tilt angle range Δθ.

The total sum Sm (R) of the products P (Δθ _m ) × R (Δθ _m ) was calculated, and the optical film thickness D ₀ at the center of the lens surface was determined to be 0.45λ (nm).

(2) Formation of antireflection film Antireflection film made of magnesium fluoride on the surface 1a of the objective lens 1 by performing vacuum deposition in a vacuum chamber using magnesium fluoride as an evaporation source and decompressed to about ^10-5 Torr. 2 was formed. The vacuum deposition time was about 4 minutes.

(3) Measurement of light transmittance of optical element surface 1a
The optical element obtained in (2) was irradiated with monochromatic light having a wavelength of 405 nm, and the light transmittance of the optical element surface 1a was measured. The results are shown in Table 4. Also shows a graph of the reflectance of the antireflection film 2 obtained in the light incident angle of 10 per ° R (Δθ _m) in FIG.

Example 2
Example 1 except for an antireflection film having an eight-layer structure in which a thin film made of zirconium oxide (refractive index n = 2.04) and a thin film made of magnesium fluoride (refractive index n = 1.38) are alternately formed on the lens surface In the same manner, the optical film thickness D ₀ at the center of each thin film lens was determined. Table 2 shows the optical film thickness of each thin film. Further, an antireflection film was formed on the surface of the objective lens in the same manner as in Example 1 except that the optical film thickness of the antireflection film was changed as shown in Table 2, and the light transmittance of the surface 1a of the obtained optical element was measured. . The results are shown in Table 4. A graph of the reflectance R (Δθ _m ) obtained in the same manner as in Example 1 is shown in FIG.

注 層No.は、レンズ側から順にNo.１、No.２、・・・・No.８とする。

Note Layer No. is No. 1, No. 2,... No. 8 in order from the lens side.

Comparative Example 1
A film made of magnesium fluoride was formed in the same manner as in Example 1 except that the optical film thickness was set so that the reflectance was minimized at the center of the lens. The optical film thickness D ₀ of this magnesium fluoride film was 0.25λ. The light transmittance of the surface 1a of the obtained optical element was measured. The results are shown in Table 4. A graph of the reflectance R (Δθ _m ) obtained in the same manner as in Example 1 is shown in FIG.

Comparative Example 2
The optical film thickness is set so as to have the minimum reflectance at the center of the lens, and a thin film made of zirconium oxide and a thin film made of magnesium fluoride are formed in this order on the lens surface in the same manner as in Example 1. A two-layer film was formed. Table 3 shows the optical film thickness of each thin film. Further, the light transmittance of the surface 1a of the obtained optical element was measured. The results are shown in Table 4. Further, the reflectance R (Δθ _m ) was measured in the same manner as in Example 1. The results are shown in Table 4. A graph of the reflectance R (Δθ _m ) obtained in the same manner as in Example 1 is shown in FIG.

注 層No.は、レンズ側から順にNo.１、No.２とする。

Note Layer No. is No. 1 and No. 2 in order from the lens side.

Comparative Example 3
The light transmittance of the surface 1a of the optical element having no antireflection film was measured. The results are shown in Table 4. A graph of the reflectance R (Δθ _m ) obtained in the same manner as in Example 1 is shown in FIG.

注 −は、反射防止膜が成膜されていないことを示す。

Note-indicates that an antireflection film is not formed.

An example of the optical element of this invention is shown, (a) is a longitudinal cross-sectional view, (b) is a top view. It is a partial expanded sectional view of the optical element shown in FIG. It is another partial expanded sectional view of the optical element shown in FIG. It is a flowchart which shows the design method of an antireflection film. 5 is a graph showing a relationship between a substrate tilt angle θ and a film thickness ratio D (θ) / D ₀ . 6 is a graph showing the relationship between the substrate tilt angle θ and the reflectance R (Δθ _m ).

1. Optical element
11 ... First side
12 ... Second side
1a ... surface
1b ... Back side 2 ... Antireflection film

Claims (7)

In a method for designing a single-layer antireflection film provided on a lens surface of an optical element, an antireflection film is formed on the lens surface under predetermined film formation conditions, and the effective diameter of the lens is within each substrate tilt angle range Δθ. The optical film thickness D (θ) at the substrate inclination angle θ of the antireflection film is measured for each substrate inclination angle range Δθ, and the optical film thickness D (θ) of the antireflection film at the substrate inclination angle θ is determined. The following formula (1)
D (θ) = D ₀ ・ (cosθ) ^x ... (1)
(Where θ represents the substrate tilt angle, D ₀ represents the optical film thickness of the antireflection film at the center of the lens, and X represents a constant not less than 0 and not more than 1). The film thickness ratio of θ) to the optical film thickness D ₀ is determined, the incident light amount ratio P (Δθ _m ) of the lens is determined for each substrate tilt angle range Δθ, and the reflectance R (Δθ _m ) of the antireflection film is calculated. By expressing using the optical film thickness D ₀ , the optical film thickness D ₀ is changed while keeping the film thickness ratio constant, and the product of the incident light amount ratio P (Δθ _m ) and the reflectance R (Δθ _m ). A method of obtaining the optical film thickness of the antireflection film that minimizes the sum of the above. In a method for designing a multi-layer antireflection film provided on a lens surface of an optical element, an antireflection film is formed on the lens surface under predetermined film formation conditions, and the effective diameter of the lens is set for each substrate tilt angle range Δθ. The optical film thickness D (θ) at the substrate inclination angle θ of each layer of the antireflection film is measured for each substrate inclination angle range Δθ, and the optical film thickness D (θ) of each layer at the substrate inclination angle θ is Formula (1)
D (θ) = D ₀ ・ (cosθ) ^x ... (1)
(Where θ represents the substrate tilt angle, D ₀ represents the optical film thickness of the antireflection film at the center of the lens, and X represents a constant of 0 or more and 1 or less). obtains the thickness ratio with respect to the optical thickness D ₀ of the D (θ), the substrate tilt angle range determined incident light intensity ratio P ([Delta] [theta] _m) of the lens for each [Delta] [theta], the reflectivity R ([Delta] [theta] _m of the antireflection film ) by the expressed using the optical thickness D ₀ of each layer, said thickness ratio by changing the optical thickness D ₀ of each layer in the uniform the incident light intensity ratio P ([Delta] [theta] _m) and the reflectance R A method of obtaining an optical film thickness of each layer having a minimum sum of products of (Δθ _m ). 3. The design method according to claim 1 , wherein the reflectance R (Δθ _m ) is obtained assuming that the film thickness of the antireflection film is uniform in the substrate tilt angle range Δθ. In a method for designing a single-layer antireflection film provided on a lens surface of an optical element, an antireflection film is formed on the lens surface under predetermined film formation conditions, and the effective diameter of the lens is within each substrate tilt angle range Δθ. The optical film thickness D (θ) at the substrate inclination angle θ of the antireflection film is measured for each substrate inclination angle range Δθ, and the optical film thickness D (θ) of the antireflection film at the substrate inclination angle θ is determined. The following formula (1)
D (θ) = D ₀ ・ (cosθ) ^x ... (1)
(Where θ represents the substrate tilt angle, D ₀ represents the optical film thickness of the antireflection film at the center of the lens, and X represents a constant not less than 0 and not more than 1). The film thickness ratio of θ) to the optical film thickness D ₀ is determined, the incident light quantity ratio P (Δθ _m ) of the lens is determined for each substrate tilt angle range Δθ, and the film transmittance T (Δθ _m ) of the antireflection film By using the optical film thickness D ₀ , the optical film thickness D ₀ is changed while keeping the film thickness ratio constant, and the incident light amount ratio P (Δθ _m ) and the film transmittance T (Δθ _m ). A method of obtaining an optical film thickness of the antireflection film that maximizes the sum of the products of the above. In a method for designing a multi-layer antireflection film provided on a lens surface of an optical element, an antireflection film is formed on the lens surface under predetermined film formation conditions, and the effective diameter of the lens is set for each substrate tilt angle range Δθ. The optical film thickness D (θ) at the substrate inclination angle θ of each layer of the antireflection film is measured for each substrate inclination angle range Δθ, and the optical film thickness D (θ) of each layer at the substrate inclination angle θ is Formula (1)
D (θ) = D ₀ ・ (cosθ) ^x ... (1)
(Where θ represents the substrate tilt angle, D ₀ represents the optical film thickness of the antireflection film at the center of the lens, and X represents a constant of 0 or more and 1 or less). The film thickness ratio of D (θ) to the optical film thickness D ₀ is obtained, the incident light quantity ratio P (Δθ _m ) of the lens is obtained for each substrate tilt angle range Δθ, and the film transmittance T (Δθ of the antireflection film is obtained. by represented using optical thickness D ₀ of each layer _m), the membrane permeability the thickness ratio and the set constant layers of optical thickness D ₀ changes are allowed the incident light amount ratio P ([Delta] [theta] _m) A method characterized in that the optical film thickness of each layer is obtained so that the total sum of products of rate T (Δθ _m ) is maximized. 6. The design method according to claim 4 , wherein the film transmittance T (Δθ _m ) is obtained assuming that the film thickness of the antireflection film in the substrate tilt angle range Δθ is uniform. In the design method according to any one of claims 1 to 6 wherein the said the board inclination angle θ in the effective diameter of the lens is a 0 to 70 °.

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