Patent Publication Number: US-10782452-B2

Title: Anti-reflection coating and optical member comprising same

Description:
The present application is a divisional of U.S. patent application Ser. No. 14/453,193 filed on Aug. 6, 2014—the disclosure of which is incorporated herein by reference in its entirety—which claims priority from Japanese Patent Application No. 2013-241422 filed on Nov. 22, 2013, and from Japanese Patent Application No. 2013-173437 filed on Aug. 23, 2013. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to an anti-reflection coating having a three- or four-layer structure containing no Al 2 O 3 , and an optical member comprising the anti-reflection coating. 
     BACKGROUND OF THE INVENTION 
     A high-performance, single-focus or zoom lens unit for photograph cameras, broadcasting cameras, etc. generally has about 5-40 lenses in a lens barrel. There are also wide-angle lenses for wide image, which have large incident angles of light beams in peripheral portions. Also, a lens having a small radius of curvature to its effective diameter is sometimes disposed in a light path for optical design. Formed on optical members such as these lenses are multi-layer, anti-reflection coatings comprising a combination of dielectric films having different refractive indices for utilizing interference effects with dielectric film thickness of ½λ or ¼λ to a center wavelength λ. 
     JP 2009-193029 A discloses an anti-reflection coating comprising a first layer of alumina having an optical thickness of 97.0-181.0 nm, a second layer having an optical thickness of 124.0-168.5 nm and a refractive index of 1.33-1.50, which is made of at least one selected from MgF 2 , SiO 2  and Al 2 O 3 , and a third layer of porous silica having an optical thickness of 112.5-169.5 nm formed in this order on a substrate having a refractive index of 1.60-1.93 to light in a wavelength range of 400-700 nm, the first and second layers being formed by a vacuum vapor deposition method, and the third layer being formed by a sol-gel method. JP 2009-193029 A describes that this anti-reflection coating has excellent anti-reflection characteristics, with alumina used in the first layer preventing the weathering of the substrate surface. 
     The anti-reflection coating described in JP 2009-193029 A comprises a porous silica layer having a refractive index of 1.07-1.18 as the third layer, as is clear from Examples. However, it is difficult to stably produce a porous silica layer having extremely high porosity for such a low refractive index. When the porous silica layer has a refractive index of more than 1.18, an optimum anti-reflection coating cannot be obtained by the structure described in JP 2009-193029 A. 
     JP 2009-210733 A discloses an anti-reflection coating comprising a first layer of alumina having an optical thickness of 25.0-250.0 nm, a second layer having an optical thickness of 100.0-145.0 nm and a refractive index of 1.40-1.50, which is made of at least one selected from MgF 2 , SiO 2  and Al 2 O 3 , and a third layer of porous silica having an optical thickness of 100.0-140.0 nm formed in this order on a substrate having a refractive index of 1.53 or more and less than 1.60 to light in a wavelength range of 400-700 nm, the first and second layers being formed by a vacuum vapor deposition method, and the third layer being formed by a sol-gel method. JP 2009-210733 A describes that this anti-reflection coating has excellent anti-reflection characteristics, with alumina used in the first layer preventing the weathering of the substrate surface. However, because this anti-reflection coating fails to exhibit optimum anti-reflection performance when formed on a substrate having a refractive index of 1.60 or more, further improvement is desired. 
     JP 10-319209 A discloses a method for producing an anti-reflection coating on a substrate, which comprises the steps of forming a first anti-reflection layer of a first material by a wet or dry process, and forming a second anti-reflection layer of a second material on the first anti-reflection layer by a wet process. It describes that one or more anti-reflection layers may be additionally formed under the first anti-reflection layer by a wet or dry process, the dry process being selected from vacuum vapor deposition, sputtering and CVD, and the wet process comprises a sol-gel process. It further describes that such method provides an anti-reflection coating having high performance such as low reflectance, and wide wavelength and angle ranges of anti-reflection, particularly in an ultraviolet range, with a small number of layers. 
     JP 10-319209 A discloses an anti-reflection coating having two-layer structure comprising a first layer of SiO 2  (dry process) and a second layer of porous SiO 2  (sol-gel method), and an anti-reflection coating having a three-layer structure comprising a first layer of LaF 3 , NdF 3  or GdF 3  (dry process), a second layer of SiO 2  (wet or dry process), and a third layer of porous SiO 2  (sol-gel method). However, because this anti-reflection coating has insufficient weathering-preventing effects, further improvement is desired. 
     Further, when these anti-reflection coatings are formed on lens substrates having maximum inclination angles of 30° or more, their anti-reflection performance is extremely poor in portions having large inclination angles, failing to obtain sufficient anti-reflection effects. Accordingly, the development of anti-reflection coatings suitable for lens surfaces having such large inclination angles is desired. 
     JP 2012-18286 A discloses an optical member comprising an anti-reflection coating comprising first and second layers formed on a substrate by a dry process, and a third layer of silica aerogel formed by a wet process, to light in a wavelength range of 550 nm, the refractive index of the substrate being higher than that of the first layer and 1.9 or less, the refractive index A of the third layer being in a range of 1.18-1.32, the first to third layers having refractive indices decreasing in this order from the first layer, and the optical thickness Y of the second layer meeting the conditions of −750A+945≤Y≤−750A+1020, and 20≤Y≤120. JP 2012-18286 A further describes that to have high adhesion, and to prevent the weathering of optical glass substrate surfaces, a material forming the first layer is preferably Al 2 O 3 . It has been found, however, that when this optical member is stored under high-temperature, high-humidity conditions for a long period of time, the anti-reflection coating suffers fogging, resulting in deteriorated spectral reflection characteristics. 
     OBJECTS OF THE INVENTION 
     Accordingly, the first object of the present invention is to provide an anti-reflection coating having high anti-reflection performance, with excellent storage stability for a long period of time. 
     The second object of the present invention is to provide an inexpensive optical member comprising an anti-reflection coating, whose anti-reflection performance is not poor even in a peripheral portion of a lens having a small radius of curvature to its effective diameter (having a large surface inclination angle). 
     DISCLOSURE OF THE INVENTION 
     As a result of intensive research in view of the above objects, the inventors have found that (1) in the optical member described in JP 2012-18286 A, the cause of fogging generated when it is stored under high-temperature, high-humidity conditions for a long period of time is a reaction of Al 2 O 3  forming the first layer with materials used for the third layer (silica aerogel coating solution and alkali treatment solution), and that (2) excellent anti-reflection characteristics with no fogging which would occur when stored under high-temperature, high-humidity conditions for a long period of time are obtained without using an Al 2 O 3  layer, when (a) in a three-layer, anti-reflection coating having an uppermost silica aerogel layer, the refractive index of the second layer is set higher than those of the first and third layers, or when (b) in a four-layer, anti-reflection coating having an uppermost silica aerogel layer, the refractive indices of the first to third layers are adjusted. The present invention has been completed based on such findings. 
     Thus, the first anti-reflection coating of the present invention has a three-layer structure comprising first to third layers formed in this order on a substrate,
         the substrate having a refractive index of 1.6-1.9, the first layer having a refractive index of 1.37-1.57, the second layer having a refractive index of 1.75-2.5, and the third layer having a refractive index of 1.18-1.32, to light in a wavelength range of 550 nm;   the third layer being formed by silica aerogel; and   the first and second layers containing no Al 2 O 3 .       

     The first optical member of the present invention comprises the first anti-reflection coating on a lens substrate, whose effective diameter D and radius R of curvature meet the condition of 0.1≤D/R≤2. 
     In the first anti-reflection coating and the first optical member, the first and second layers are preferably formed by a dry process, the third layer is preferably formed by a wet process, and the wet process preferably includes a sol-gel method. 
     In the first optical member, the lens substrate preferably has the maximum inclination angle of 30-65°. 
     In the first optical member, the optical thickness D 1 (θ t ) of the first layer and the optical thickness D 2 (θ t ) of the second layer at an arbitrary inclination angle θ t  of the lens substrate are preferably expressed by the following formulae (1) and (2):
 
 D 1(θ t )= D 1 0 ×(cos θ t ) α   (1), and
 
 D 2(θ t )= D 2 0 ×(cos θ t ) β   (2),
 
wherein D 1   0  and D 2   0  represent the optical thickness of the first and second layers at a center of the lens substrate, and α and β are numbers independently in a range of 0-1.
 
     In the first optical member, the thickness of the third layer is preferably constant regardless of the inclination angle of the lens substrate, or larger in a peripheral portion of the lens substrate than at a center of the lens substrate. 
     The second anti-reflection coating of the present invention has a four-layer structure comprising first to fourth layers formed in this order on a substrate,
         the substrate having a refractive index of 1.6-1.9, the first layer having a refractive index of 1.37-1.57, the second layer having a refractive index of 1.75-2.5, the third layer having a refractive index of 1.37-1.57, and the fourth layer having a refractive index of 1.18-1.32, to light in a wavelength range of 550 nm;   the fourth layer being formed by silica aerogel; and   the first to third layers containing no Al 2 O 3 .       

     The second optical member of the present invention comprises the second anti-reflection coating on a lens substrate, whose effective diameter D and radius R of curvature meet the condition of 0.1≤D/R≤2. 
     The third anti-reflection coating of the present invention has a four-layer structure comprising first to fourth layers formed in this order on a substrate,
         the substrate having a refractive index of 1.6-1.9, the first layer having a refractive index of 1.75-2.5, the second layer having a refractive index of 1.37-1.57, the third layer having a refractive index of 1.75-2.5, and the fourth layer having a refractive index of 1.18-1.32, to light in a wavelength range of 550 nm;   the fourth layer being formed by silica aerogel; and   the first to third layers containing no Al 2 O 3 .       

     The third optical member of the present invention comprises the third anti-reflection coating on a lens substrate, whose effective diameter D and radius R of curvature meet the condition of 0.1≤D/R≤2. 
     In the second and third anti-reflection coatings and the second and third optical members, the first to third layers are preferably formed by a dry process, the fourth layer is preferably formed by a wet process, and the wet process preferably includes a sol-gel method. 
     In the second and third optical members, the lens substrate preferably has the maximum inclination angle of 30-65°. 
     In the second and third optical members, the optical thickness D 1 (θ t ) of the first layer, the optical thickness D 2 (θ t ) of the second layer and the optical thickness D 3 (θ t ) of the third layer at an arbitrary inclination angle θ t  of the lens substrate are preferably expressed by the following formulae (1) to (3):
 
 D 1(θ t )= D 1 0 ×(cos θ t ) α   (1),
 
 D 2(θ t )= D 2 0 ×(cos θ t ) β   (2), and
 
 D 3(θ t )= D 3 0 ×(cos θ t ) γ   (3),
 
wherein D 1   0 , D 2   0  and D 3   0  represent the optical thickness of the first to third layers at a center of the lens substrate, and α, β and γ are numbers independently in a range of 0-1.
 
     In the second and third optical members, the thickness of the fourth layer is preferably constant regardless of the inclination angle of the lens substrate, or larger in a peripheral portion of the lens substrate than at a center of the lens substrate. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic cross-sectional view showing one example of the optical members of the present invention. 
         FIG. 2  is a schematic cross-sectional view showing another example of the optical members of the present invention. 
         FIG. 3  is a schematic cross-sectional view showing the substrate inclination angle of the optical member. 
         FIG. 4( a )  is a schematic cross-sectional view showing the incident angle of light beams at a center point of the optical member. 
         FIG. 4( b )  is a schematic cross-sectional view showing the incident angle of light beams at a point other than the center point of the optical member. 
         FIG. 5  is a schematic cross-sectional view showing the effective diameter and radius of curvature of a lens in the optical member. 
         FIG. 6  is a schematic cross-sectional view showing a further example of the optical members of the present invention. 
         FIG. 7  is a schematic cross-sectional view showing a still further example of the optical members of the present invention. 
         FIG. 8  is a graph showing the relation between spectral reflectance and the incident angle of light beams in the optical member of Example 1. 
         FIG. 9  is a graph showing the relation between average reflectance at each incident angle of light beams and a substrate inclination angle in the optical member of Example 1. 
         FIG. 10  is a graph showing the relation between spectral reflectance and the incident angle of light beams in the optical member of Comparative Example 1. 
         FIG. 11  is a graph showing the relation between average reflectance at each incident angle of light beams and a substrate inclination angle in the optical member of Comparative Example 1. 
         FIG. 12  is a graph showing the relation between spectral reflectance and the incident angle of light beams in the optical member of Comparative Example 2. 
         FIG. 13  is a graph showing the relation between average reflectance at each incident angle of light beams and a substrate inclination angle in the optical member of Comparative Example 2. 
         FIG. 14  is a graph showing the relation between spectral reflectance and the incident angle of light beams in the optical member of Comparative Example 3. 
         FIG. 15  is a graph showing the relation between average reflectance at each incident angle of light beams and a substrate inclination angle in the optical member Comparative Example 3. 
         FIG. 16  is a graph showing the relation between spectral reflectance and the incident angle of light beams in the optical member of Example 2. 
         FIG. 17  is a graph showing the relation between average reflectance at each incident angle of light beams and a substrate inclination angle in the optical member of Example 2. 
         FIG. 18  is a graph showing the relation between spectral reflectance before and after the accelerated environmental testing and a substrate inclination angle in the optical member of Example 1. 
         FIG. 19  is a graph showing the relation between spectral reflectance before and after the accelerated environmental testing and a substrate inclination angle in the optical member of Comparative Example 1. 
         FIG. 20  is a graph showing the relation between spectral reflectance before and after the accelerated environmental testing and a substrate inclination angle in the optical member of Example 2. 
         FIG. 21  is a schematic view showing one example of apparatuses for forming an anti-reflection coating by vacuum vapor deposition. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The present disclosure relates to subject matter contained in Japanese Patent Application No. 2013-173437 filed on Aug. 23, 2013 and Japanese Patent Application No. 2013-241422 filed on Nov. 22, 2013, which are expressly incorporated herein by reference in their entirety. 
     The present invention will be explained in detail below referring to the attached drawings. Explanations of each embodiment will be applicable to other embodiments unless otherwise mentioned. Please note that the refractive index of each layer in the anti-reflection coating is determined to light in a wavelength range of 550 nm, unless otherwise mentioned, and that in the attached drawings, the thickness of each layer is exaggerated to make clear the layer structure of the anti-reflection coating. 
     [1] F IRST ANTI - REFLECTION COATING    
     (1) L AYER STRUCTURE    
       FIG. 1  shows an example of first anti-reflection coatings  3  having a three-layer structure comprising a first layer  3   a , a second layer  3   b  and a third layer  3   c  formed in this order on the substrate  2 . In the first anti-reflection coating  3 , the first layer  3   a  has a refractive index of 1.37-1.57, the second layer  3   b  has a refractive index of 1.75-2.5, and the third layer  3   c  has a refractive index of 1.18-1.32. With such structure that the refractive index of the second layer is larger than those of the first and third layers, excellent anti-reflection performance can be obtained on a substrate  2  having a refractive index of 1.6-1.9, without using Al 2 O 3  (refractive index: 1.76). 
     The first layer is a layer containing no Al 2 O 3 . The refractive index of the first layer is 1.37-1.57, preferably 1.37-1.5, more preferably 1.37-1.48, most preferably 1.37-1.41. Accordingly, the first layer is preferably a MgF 2  layer. The optical thickness of the first layer is preferably 25-100 nm, more preferably 30-80 nm. The refractive index of the second layer is 1.75-2.5, preferably 1.99-2.33, more preferably 1.99-2.33. The optical thickness of the first layer at a substrate inclination angle of 0° is preferably 25-100 nm, more preferably 30-80 nm. The first layer is preferably formed by a dry process. 
     The second layer is a layer containing no Al 2 O 3 . The refractive index of the second layer is 1.75-2.5, preferably 1.99-2.33, more preferably 1.99-2.33, most preferably 1.99-2.3. Accordingly, the second layer is preferably made of TaO 2 +Y 2 O 3 +Pr 6 O 11 . The second layer made of TaO 2 +Y 2 O 3 +Pr 6 O 11  has improved adhesion to the first and third layers. The optical thickness of the second layer at a substrate inclination angle of 0° is preferably 10-50 nm, more preferably 20-45 nm. The second layer is also preferably formed by a dry process. 
     The third layer is a silica aerogel layer preferably formed by a wet process. The wet process preferably includes a sol-gel method. The refractive index of the third layer is 1.18-1.32, preferably 1.18-1.30, more preferably 1.18-1.28. With the third layer having such a low refractive index, excellent anti-reflection effects can be obtained. The optical thickness of the third layer is preferably 90-140 nm, more preferably 100-135 nm. 
     (2) S UBSTRATE    
     The first anti-reflection coating  3  can be formed on a substrate having a refractive index of 1.6-1.9. The use of a substrate having such a refractive index provides an optical member having good anti-reflection performance in a wavelength range of visible light. Materials for the substrate may be optical glass such as BaSF2 (refractive index: 1.6684), SF5 (refractive index: 1.6771), LaF2 (refractive index: 1.7475), LaSF09 (refractive index: 1.8197), LaSF01 (refractive index: 1.7897), LaSF016 (refractive index: 1.7758), LAK7 (refractive index: 1.654), LAK14 (refractive index: 1.6995), etc. The substrate may be in a plate or lens shape. 
     (3) A NTI - REFLECTION CHARACTERISTICS    
     The first anti-reflection coating having a three-layer structure comprising an uppermost layer of silica aerogel, with a higher refractive index in the second layer than in the first and third layers, has excellent anti-reflection characteristics in wide ranges of wavelength and angle without using an Al 2 O 3  layer, free from fogging which would occur in conventional anti-reflection coatings comprising a silica aerogel layer and an Al 2 O 3  layer, when stored under high-temperature, high-humidity conditions for a long period of time. 
     [2] F IRST OPTICAL MEMBER    
       FIG. 2  shows an example of first optical members  11  comprising the first anti-reflection coating  31  formed on a lens substrate  21 . The lens substrate  21  has an effective diameter D and a radius R of curvature, whose ratio D/R is 0.1≤D/R≤2. As shown in  FIG. 5 , the effective diameter D is the maximum diameter of a lens effectively usable as an optical member, and the radius R of curvature is a radius of the curved lens surface when it is approximated to a sphere. The use of a lens substrate having a ratio D/R of 0.1-2 provides more effects of the present invention. Also, the use of a lens substrate having the maximum inclination angle of 30-65°, particularly 30-60°, provides more effects of the present invention. 
     Each of the first and second layers  31   a ,  31   b  preferably has thickness gradually decreasing as it goes from a center portion to a peripheral portion in the lens substrate  21 . The first and second layers  31   a ,  31   b  are the same as the first and second layers  3   a ,  3   b  in the first anti-reflection coating  3  except for the thickness variation. Specifically, the optical thickness D 1 (θ t ) of the first layer  31   a  and the optical thickness D 2 (θ t ) of the second layer  31   b  at an arbitrary inclination angle θ t  of the lens substrate  21  are preferably expressed by the following formulae (1) and (2):
 
 D 1(θ t )= D 1 0 ×(cos θ t ) α   (1), and
 
 D 2(θ t )= D 2 0 ×(cos θ t ) β   (2),
 
wherein D 1   0  and D 2   0  represent the optical thickness of the first and second layers  31   a ,  31   b  at a center of the lens substrate  21 , and α and β are numbers independently in a range of 0-1. α and β are more preferably independently in a range of 0.5-0.95, most preferably independently in a range of 0.6-0.9.
 
     With the first and second layers  31   a ,  31   b  getting thinner toward the peripheral portion, good anti-reflection is obtained regardless of the substrate inclination angle, providing an anti-reflection coating less influenced by the incident angle of light beams. It is particularly effective, when a lens substrate having the maximum inclination angle of 30° or more is used. 
     The optical thickness of the third layer  31   c  is preferably constant regardless of the lens substrate inclination angle, or larger in a peripheral portion of the lens than at a center of the lens. Except for this, the third layer  31   c  is the same as the third layer  3   c  in the first anti-reflection coating  3 . The silica aerogel preferably has pore diameters of 0.005-0.2 μm and porosity of 25-60%. 
     As shown in  FIG. 3 , the substrate inclination angle is an angle θ t  of a normal line at an arbitrary point on the lens surface to a center axis C of the lens, which is 00 at a center of the lens, and larger at a position nearer a periphery of the lens. The incident angle θ i  of light beams at an arbitrary point on the lens surface is an angle of the light beams to a normal line at the above point. The incident angle θ i  is shown at a center of the lens having a substrate inclination angle of 0° in  FIG. 4( a ) , and in a portion having a substrate inclination angle of θ t  in  FIG. 4( b ) . 
     [3] P RODUCTION OF FIRST OPTICAL MEMBER    
     (1) F ORMATION OF FIRST AND SECOND LAYERS    
     The first and second layers in the anti-reflection coating are formed by a dry process. The dry process may be, for example, a physical vapor deposition method such as a vacuum vapor deposition method, a sputtering method, an ion plating method, etc., or a chemical vapor deposition method such as thermal CVD, plasma CVD, photo CVD, etc. These methods may be combined, if necessary. The vacuum vapor deposition method is particularly preferable from the aspect of production cost and precision. 
     The vacuum vapor deposition method may use resistor heating, electron beams, etc. The vacuum vapor deposition method using electron beams will be explained below. As shown in  FIG. 21 , an electron-beam-type vacuum vapor deposition apparatus  130  comprises, in a vacuum chamber  131 , a rotary rack  132  for supporting pluralities of substrates  100  on its inner surface, a vapor deposition source  133  comprising a crucible  136  for a vapor deposition material  137 , an electron beam ejector  138 , a heater  139 , and a pipe  135  connected to a vacuum pump  140 . The substrates  100  are placed on the rotary rack  132  with their surfaces opposing the vapor deposition source  133 . The vapor deposition material  137  is evaporated by heating by the irradiation of electron beams from the electron beam ejector  138 . With the vacuum chamber  131  evacuated by the vacuum pump  140 , anti-reflection coatings are formed by accumulating a vapor of the vapor deposition material  137  on the substrates  100 . To form uniform vapor deposited films, the rotary rack  132  is rotated around a rotary shaft  134  while heating the substrates  100  by the heater  139 . 
     When the lens substrates are vapor-deposited by the vacuum vapor deposition apparatus, the thickness of each layer from a center of the lens substrate to the peripheral portion can be controlled by adjusting the positions of the lens substrates and the vapor deposition source  133 , the intensity of electron beams, the degree of vacuum, etc. 
     In the vacuum vapor deposition method, the initial degree of vacuum is preferably 1.0×10 −6  to 1.0×10 −5  Torr. Outside the above range of the degree of vacuum, vapor deposition takes too much time, resulting in low production efficiency, or insufficient vapor deposition to complete the film formation. The temperature of the substrates  100  during vapor deposition can be properly determined depending on the heat resistance of the substrates and the vapor deposition speed, though it is preferably 60-250° C. 
     (2) F ORMATION METHOD OF THIRD LAYER    
     The third layer in the anti-reflection coating is preferably formed by a dry process, particularly a sol-gel method. The silica aerogel layer formed by a sol-gel method has an extremely lower refractive index than that of a MgF 2  layer (n=1.39), enabling an anti-reflection coating having an extremely low reflectance in wide wavelength and incident angle ranges, which would be difficult conventionally. 
     For example, when a MgF 2  layer is formed as the third layer on the lens substrate by vacuum vapor deposition, the third layer also has thickness gradually decreasing toward a peripheral portion of the lens, like the first and second layers. Accordingly, all of the first to third layers are thinner in a peripheral portion of the lens having a large inclination angle, failing to obtain good anti-reflection performance. 
     Though known sol-gel methods may be used, a preferable sol-gel method for forming the third silica aerogel layer comprises the steps of (i) preparing a first acidic sol having a median diameter of 100 nm or less by mixing an alkaline sol, which is prepared by the hydrolysis and polycondensation of alkoxysilane in the presence of a basic catalyst, with an acidic solution, (ii) preparing a second acidic sol having a median diameter of 10 nm or less by the hydrolysis and polycondensation of alkoxysilane in the presence of an acidic catalyst, (iii) mixing the first and second acidic sols, (iv) applying the resultant mixed sol to a lens substrate provided with the first and second layers, drying the resultant coating, (v) subjecting it to an alkali treatment, (vi) washing it, and (vii) subjecting it to a humid treatment. 
     (i) Preparation of First Acidic Sol 
     (a) Alkoxysilane 
     Alkoxysilane for the first acidic sol is preferably a monomer or oligomer (polycondensate) of tetraalkoxysilane. The use of a four-functional alkoxysilane enables the production of a sol of colloidal silica particles having relatively large particle sizes. Tetraalkoxysilane is preferably represented by Si(OR) 4 , wherein R is an alkyl group having 1-5 carbon atoms (methyl, ethyl, propyl, butyl, etc.), or an acyl group having 1-4 carbon atoms (acetyl, etc.). Specific examples of tetraalkoxysilanes include tetramethoxysilane, tetraethoxysilane, tetrapropoxysilane, tetrabutoxysilane, diethoxydimethoxysilane, etc. Among them, tetramethoxysilane and tetraethoxysilane are preferable. Within a range not hindering the effects of the present invention, a small amount of three-or-less-functional alkoxysilane may be added to tetraalkoxysilane. 
     (b) Hydrolysis and Polycondensation in Presence of Basic Catalyst 
     Hydrolysis and polycondensation proceed by adding an organic solvent, a basic catalyst and water to alkoxysilane. The organic solvent is preferably alcohol such as methanol, ethanol, n-propanol, i-propanol, butanol, etc., more preferably methanol or ethanol. The basic catalyst is preferably ammonia, amine, NaOH or KOH. The preferred amines are alcohol amines or alkyl amines (methylamine, dimethylamine, trimethylamine, n-butylamine, n-propylamine, etc.). 
     A ratio of the organic solvent to the alkoxysilane is preferably set such that the concentration of the alkoxysilane is 0.1-10% by mass as SiO 2  (silica concentration). When the concentration of silica is more than 10% by mass, silica particles have too large particle sizes in the resultant sol. On the other hand, when the concentration of silica is less than 0.1, silica particles have too small particle sizes in the resultant sol. The organic solvent/alkoxysilane molar ratio is preferably in a range of 1 to 10 4 . 
     The basic catalyst/alkoxysilane molar ratio is preferably 1×10 −4  to 1, more preferably 1×10 −4  to 0.8, particularly 3×10 −4  to 0.5. With the basic catalyst/alkoxysilane molar ratio of less than 1×10 −4 , a sufficient hydrolysis reaction of alkoxysilane does not occur. On the other hand, when the molar ratio exceeds 1, a catalytic effect is saturated. 
     The water/alkoxysilane molar ratio is preferably 0.1-30. When the water/alkoxysilane molar ratio is more than 30, a hydrolysis reaction proceeds too fast, making the control of the reaction difficult, making it unlikely to form a uniform silica aerogel layer. On the other hand, when it is less than 0.1, sufficient hydrolysis of alkoxysilane does not occur. 
     An alkoxysilane solution containing a basic catalyst and water is preferably aged by leaving it to stand or slowly stirring at 10-90° C. for about 10-60 hours. By aging, hydrolysis and polycondensation proceed, forming a silica sol. The silica sol includes not only a dispersion of colloidal silica particles, but also a dispersion of colloidal silica particles agglomerated in a cluster. 
     (c) Hydrolysis and Polycondensation in Presence of Acidic Catalyst 
     The resultant alkaline sol is mixed with an acidic catalyst, and if necessary, water and an organic solvent are added, so that hydrolysis and polycondensation further proceed in an acidic state. The acidic catalyst includes hydrochloric acid, nitric acid, sulfuric acid, phosphoric acid, acetic acid, etc. The organic solvent used may be the same as described above. In the first acidic sol, a molar ratio of the acidic catalyst to the basic catalyst is preferably 1.1-10, more preferably 1.5-5, most preferably 2-4. When the molar ratio of the acidic catalyst to the basic catalyst is less than 1.1, sufficient polymerization with the acidic catalyst does not proceed. On the other hand, when it exceeds 10, a catalytic effect is saturated. The organic solvent/alkoxysilane molar ratio and the water/alkoxysilane molar ratio may be the same as described above. The sol containing the acidic catalyst is preferably aged by leaving it to stand or slowly stirring at 10-90° C. for about 15 minutes to 24 hours. By aging, hydrolysis and polycondensation proceed, thereby forming the first acidic sol. 
     Silica particles in the first acidic sol have a median diameter of 100 nm or less, preferably 10-50 nm. The median diameter is measured by a dynamic light scattering method. 
     (ii) Preparation of Second Acidic Sol 
     (a) Alkoxysilane 
     Alkoxysilane for the second acidic sol may be a 2-to-4-functional alkoxysilane represented by Si(OR 1 ) x (R 2 ) 4-x , wherein x is an integer of 2-4. R 1  is preferably an alkyl group having 1-5 carbon atoms (methyl, ethyl, propyl, butyl, etc.), or an acyl group having 1-4 carbon atoms (acetyl, etc.). R 2  is preferably an organic group having 1-10 carbon atoms, for example, a hydrocarbon group such as methyl, ethyl, propyl, butyl, hexyl, cyclohexyl, octyl, decyl, phenyl, vinyl, allyl, etc., and a substituted hydrocarbon group such as γ-chloropropyl, CF 3 CH 2 —, CF 3 CH 2 CH 2 —, C 2 F 5 CH 2 CH 2 —, C 3 F 7 CH 2 CH 2 CH 2 —, CF 3 OCH 2 CH 2 CH 2 —, C 2 F 5 OCH 2 CH 2 CH 2 —, C 3 F 7 OCH 2 CH 2 CH 2 —, (CF 3 ) 2 CHOCH 2 CH 2 CH 2 —, C 4 F 9 CH 2 OCH 2 CH 2 CH 2 —, 3-(perfluorocyclohexyloxy)propyl, H(CF) 4 CH 2 OCH 2 CH 2 CH 2 —, H(CF) 4 CH 2 CH 2 CH 2 —, γ-glycidoxypropyl, γ-mercaptopropyl, 3,4-epoxycyclohexylethyl, γ-methacryloyloxypropyl, etc. 
     Specific examples of two-functional alkoxysilanes include dimethyldialkoxysilanes such as dimethyldimethoxysilane, dimethyldiethoxysilane, etc. Specific examples of three-functional alkoxysilanes include methyltrialkoxysilane such as methyltrimethoxysilane, methyltriethoxysilane, etc., and phenyltrialkoxysilane such as phenyltriethoxysilane, etc. Specific examples of four-functional alkoxysilanes include tetramethoxysilane, tetraethoxysilane, tetrapropoxysilane, tetrabutoxysilane, diethoxydimethoxysilane, etc. Alkoxysilane is preferably three-functional or more, more preferably methyltrialkoxysilane or tetraalkoxysilane. 
     (b) Hydrolysis and Polycondensation in Presence of Acidic Catalyst 
     A monomer or oligomer (polycondensate) of alkoxysilane is mixed with an organic solvent, an acidic catalyst and water, to cause the hydrolysis and polycondensation of alkoxysilane. The organic solvent and acidic catalyst used may be the same as described in the step of preparing the first acidic sol. The acidic catalyst/alkoxysilane molar ratio is preferably 1×10 −4  to 1, more preferably 1×10 −4  to 3×10 −2 , most preferably 3×10 −4  to 1×10 −2 . The organic solvent/alkoxysilane molar ratio and the water/alkoxysilane molar ratio may be the same as described in the step of preparing the first acidic sol. 
     An alkoxysilane solution containing an acidic catalyst and water is preferably aged by leaving it to stand or slowly stirring at 10-90° C. for about 30 minutes to 60 hours. By aging, hydrolysis and polycondensation proceed, thereby forming the second acidic sol. When the aging time exceeds 60 hours, the median diameter of silica particles in the sol have becomes too large. 
     Colloidal silica particles in the second acidic sol have a smaller median diameter than that of colloidal silica particles in the first acidic sol. The median diameter of colloidal silica particles in the second acidic sol is 10 nm or less, preferably 1-5 nm. A median diameter ratio of silica particles in the first acidic sol to those in the second acidic sol is preferably 5-50, more preferably 5-35. With the median diameter ratio of less than 5 or more than 50, the resultant silica aerogel layer has low scratch resistance. 
     (iii) Preparation of Mixed Sol 
     The first acidic sol is preferably mixed with the second acidic sol at 1-30° C. for about 1 minute to 6 hours, while slowly stirring. If necessary, the mixture may be heated at 80° C. or lower. A solid component mass ratio of the first acidic sol to the second acidic sol is preferably 5-90, more preferably 5-80. With the solid component mass ratio of less than 5 or more than 90, the resultant silica aerogel layer has low scratch resistance. 
     (iv) Coating and Drying 
     (a) Coating 
     The mixed sol is coated to the lens substrate provided with the first and second layers. The coating method includes a dip-coating method, a spray-coating method, a spin-coating method, a printing method, etc. When a three-dimensional structure like a lens is coated, a spin-coating method or a dipping method is preferable, and a spin-coating method is particularly preferable. The physical thickness of the resultant gel can be controlled by adjusting the rotation speed of the substrate, the concentration of the mixed sol, etc. in the spin-coating method. The rotation speed of the substrate in the spin-coating method is preferably about 1,000-15,000 rpm. 
     To adjust the concentration and flowability of the mixed sol for higher coatability, the above organic solvent may be added as a dispersant. The concentration of silica in the mixed sol is preferably 0.1-20% by mass. If necessary, the mixed sol may be subjected to an ultrasonic treatment to prevent the agglomeration of colloid particles. The ultrasonic waves preferably have a frequency of 10-30 kHz and a power of 300-900 W, and the treatment time is preferably 5-120 minutes. 
     (b) Drying 
     The drying conditions of the coating are properly selected depending on the heat resistance of the substrate. To accelerate the polycondensation reaction, the coating may be heat-treated at a temperature lower than the boiling point of water for 15 minutes to 24 hours, and then at a temperature of 100-200° C. for 15 minutes to 24 hours. The heat-treated silica aerogel layer exhibits high scratch resistance. 
     (v) Alkali Treatment 
     The silica aerogel layer is treated with an alkali to improve its scratch resistance. The alkali treatment is preferably conducted by applying an alkali solution to the silica aerogel layer, or by placing the silica aerogel layer in an ammonia atmosphere. Solvents for the alkali solution can be properly selected depending on the type of the alkali, preferably water, alcohol, etc. The concentration of the alkali solution is preferably 1×10 −4  to 20 N, more preferably 1×10 −3  to 15 N. 
     The alkalis may be inorganic alkalis such as sodium hydroxide, potassium hydroxide, ammonia, etc.; inorganic alkali salts such as sodium carbonate, sodium hydrogen carbonate, ammonium carbonate, ammonium hydrogen carbonate, etc.; organic alkalis such as monomethylamine, dimethylamine, trimethylamine, monoethylamine, diethylamine, triethylamine, n-propylamine, di-n-propylamine, n-butylamine, di-n-butylamine, n-amylamine, n-hexylamine, laurylamine, ethylenediamine, hexamethylenediamine, anilene, methylanilene, ethylanilene, cyclohexylamine, dicyclohexylamine, pyrrolidine, pyridine, imidazole, guanidine, tetramethylammonium hydroxide, tetraethylammonium hydroxide, tetrabutylammonium hydroxide, monoethanolamine, diethanolamine, triethanolamine, choline, etc.; organic acid-alkali salts such as ammonium formate, ammonium acetate, monomethylamine formate, dimethylamine acetate, anilene acetate, pyridine lactate, guanidinoacetate, etc. 
     10-200 ml of the alkali solution is preferably applied per 1 cm 2  of the silica aerogel layer. The coating of the alkali solution can be conducted by the same method as coating the silica aerogel layer, preferably by a spin-coating method. The substrate is rotated preferably at about 1,000-15,000 rpm in the spin-coating method. The layer coated with the alkali solution is left to stand preferably at 1-40° C., more preferably at 10-30° C. The leaving time is preferably 0.1-10 hours, more preferably 0.2-1 hours. 
     In the case of the ammonia atmosphere, the silica aerogel layer is preferably alkali-treated in an ammonia gas partial pressure of 1×10 −1  to 1×10 5  Pa. The treatment temperature is preferably 1-40° C., more preferably 10-30° C. The treatment time is preferably 1-170 hours, more preferably 5-80 hours. 
     If necessary, the alkali-treated silica aerogel layer is preferably dried at a temperature of 50-200° C. for 15 minutes to 24 hours. 
     (vi) Washing 
     The alkali-treated silica aerogel layer is washed, if necessary. Washing is preferably conducted by a method of immersing the alkali-treated silica aerogel layer in water and/or an alcohol, a method of showering water and/or an alcohol to the alkali-treated silica aerogel layer, or their combination. An ultrasonic treatment may be conducted during immersion. The washing temperature is preferably 1-40° C., and the washing time is preferably 0.2-15 minutes. In washing, 0.01-1,000 ml of water and/or an alcohol is preferably used per 1 cm 2  of the silica aerogel layer. The washed silica aerogel layer is preferably dried at a temperature of 50-200° C. for 15 minutes to 24 hours. The alcohol is preferably methanol, ethanol or isopropyl alcohol. 
     (vii) Humid Treatment 
     The silica aerogel layer after coating, the alkali treatment or washing is subject to a humid treatment under high-humidity conditions. It is presumed that the hydrolysis of unreacted alkoxysilane and the polycondensation reaction of silanol groups occur by the humid treatment, providing the silica aerogel layer with improved mechanical strength, while suppressing the variation of the refractive index of the layer with time. 
     The humid treatment is conducted by placing the substrate having the silica aerogel layer in an environment at a temperature of 35° C. or higher and at relative humidity of 70% or more for 1 hour or more. The humidity of less than 70% RH would not provide sufficient treatment effects. The humidity is preferably 75% RH or more, more preferably 80% RH or more, most preferably 90% RH or more. The treatment temperature is preferably 35-90° C., more preferably 40-80° C., most preferably 50-80° C. The treatment temperature of lower than 35° C. would not provide sufficient effects, and the treatment temperature of higher than 90° C. would saturate the effects. To obtain the above the effects, the treatment time is 1 hour or more, preferably 5-120 hours, more preferably 5-48 hours, though variable depending on the temperature and humidity conditions. With the treatment time of more than 120 hours, the above effects would be saturated. 
     [4] S ECOND AND THIRD ANTI -R EFLECTION COATINGS    
     (1) L AYER STRUCTURE    
       FIG. 6  shows an optical member  4  having a four-layer structure comprising a substrate  5 , and an anti-reflection coating  6  comprising first to fourth layers  6   a ,  6   b ,  6   c ,  6   d  formed in this order on the substrate  5 . The anti-reflection coating  6  has two types of structures described below, on the substrate  5  having a refractive index of 1.6-1.9. 
     (i) Second Anti-Reflection Coating 
     The second anti-reflection coating  6  comprises a first layer  6   a  having a refractive index of 1.37-1.57, a second layer  6   b  having a refractive index of 1.75-2.5, a third layer  6   c  having a refractive index of 1.37-1.57, and a fourth layer  6   d  having a refractive index of 1.18-1.32. With the first to fourth layers having such refractive indices, the second anti-reflection coating  6  formed on a substrate  5  having a refractive index of 1.6-1.9 exhibits excellent anti-reflection without using Al 2 O 3  (refractive index: 1.64). 
     The first to third layers  6   a ,  6   b ,  6   c  are layers containing no Al 2 O 3 , and the fourth layer  6   d  is a silica aerogel layer. The first to third layers  6   a ,  6   b ,  6   c  are preferably formed by a dry process, and the fourth layer  6   d  is preferably formed by a wet process. The wet process preferably includes a sol-gel method. 
     The refractive index of the first layer is 1.37-1.57, preferably 1.38-1.5, more preferably 1.38-1.48. The optical thickness of the first layer is preferably 8-100 nm, more preferably 10-85 nm. The refractive index of the second layer is 1.75-2.5, preferably 1.86-2.33, more preferably 1.99-2.3. The optical thickness of the second layer is preferably 8-60 nm, more preferably 10-50 nm. The refractive index of the third layer is 1.37-1.57, preferably 1.37-1.5, more preferably 1.37-1.48. The optical thickness of the third layer is preferably 8-170 nm, more preferably 10-160 nm. 
     Though materials forming the first and third layers may be the same or different from each other, both of them are preferably made of SiO 2 . The first and third layers made of SiO 2  have improved adhesion. To improve the anti-reflection performance, the second layer is preferably made of TaO 2 +Y 2 O 3 +Pr 6 O 11 . 
     The fourth layer is a silica aerogel layer, preferably formed by a wet process. The refractive index of the fourth layer is 1.18-1.32, preferably 1.2-1.32, more preferably 1.2-1.3. The optical thickness of the fourth layer is preferably 90-180 nm, more preferably 100-170 nm. With the outermost layer having such a low refractive index, excellent anti-reflection effects are obtained. The silica aerogel preferably has pore diameters of 0.005-0.2 μm and porosity of 25-60%. 
     (ii) Third Anti-Reflection Coating 
     The third anti-reflection coating  6  comprises a first layer  6   a  having a refractive index of 1.75-2.5, a second layer  6   b  having a refractive index of 1.37-1.57, a third layer  6   c  having a refractive index of 1.75-2.5, and a fourth layer  6   d  having a refractive index of 1.18-1.32. With the first to fourth layers having such refractive indices, the third anti-reflection coating  6  formed on the substrate  5  having a refractive index of 1.6-1.9 exhibits excellent anti-reflection without using Al 2 O 3  having a refractive index of 1.64. 
     The first to third layers  6   a ,  6   b ,  6   c  are layers not containing Al 2 O 3 , and the fourth layer  6   d  is a silica aerogel layer. The first to third layers  6   a ,  6   b ,  6   c  are preferably formed by a dry process, and the fourth layer  6   d  is preferably formed by a wet process. The wet process preferably includes a sol-gel method. Because the third anti-reflection coating  6  differs from the second anti-reflection coating  6  in the first to third layers  6   a ,  6   b ,  6   c , only the first to third layers  6   a ,  6   b ,  6   c  will be explained below. 
     The refractive index of the first layer is 1.75-2.5, preferably 1.86-2.33, more preferably 1.99-2.3. The optical thickness of the first layer is preferably 8-90 nm, more preferably 10-70 nm. The refractive index of the second layer is 1.37-1.57, preferably 1.37-1.5, more preferably 1.37-1.48. The optical thickness of the second layer is preferably 25-135 nm, more preferably 30-130 nm. The refractive index of the third layer is 1.75-2.5, preferably 1.86-2.33, more preferably 1.99-2.3. The optical thickness of the third layer is preferably 8-80 nm, more preferably 10-70 nm. 
     Though materials forming the first and third layers may be the same or different from each other, both of them are preferably made of TaO 2 +Y 2 O 3 +Pr 6 O 11 . The first and third layers made of TaO 2 +Y 2 O 3 +Pr 6 O 11  has improved adhesion. To have improved anti-reflection performance, the second layer is preferably made of MgF 2 . 
     (2) S UBSTRATE    
     The second and third anti-reflection coatings can be formed on the same substrate as in the first anti-reflection coating. 
     [5] S ECOND AND THIRD OPTICAL MEMBERS    
       FIG. 7  shows an optical member  41  comprising a lens substrate  51  having a refractive index of 1.6-1.9, whose effective diameter D and radius R of curvature meet the condition of 0.1≤D/R≤2, and an anti-reflection coating  61  comprising first to fourth layers  61   a ,  61   b ,  61   c ,  61   d  formed in this order on the lens substrate  51 . The lens substrate  51  may be the same as used in the first optical member, having the maximum inclination angle of 30-65°, particularly 30-60°. The anti-reflection coating  61  includes two types of the above-described second and third anti-reflection coatings. Because the anti-reflection coating  61  is the same as the second and third anti-reflection coatings  6 , and because the lens substrate  51  is the same as the lens substrate  21  in the first optical member, explanation will be made only on other portions. 
     In any of the second and third optical members, each of the first to third layers  61   a ,  61   b ,  61   c  preferably has thickness gradually decreasing as it goes from a center portion to a peripheral portion in the lens substrate  51 , as shown in  FIG. 7 . With the first to third layers  61   a ,  61   b ,  61   c  getting thinner toward the periphery, the anti-reflection coating exhibits good anti-reflection regardless of the inclination angle of a substrate, which is less influenced by the incident angle of light beams. It is particularly effective, when a lens substrate, whose maximum inclination angle is 30° or more, is used. 
     The optical thickness D 1 (θ t ) of the first layer  61   a , the optical thickness D 2 (θ t ) of the second layer  61   b  and the optical thickness D 3 (θ t ) of the third layer  61   c  at an arbitrary inclination angle θ t  of the lens substrate  51  are preferably expressed by the following formulae (1) to (3):
 
 D 1(θ t )= D 1 0 ×(cos θ t ) α   (1),
 
 D 2(θ t )= D 2 0 ×(cos θ t ) β   (2), and
 
 D 3(θ t )= D 3 0 ×(cos θ t ) γ   (3),
 
wherein D 1   0 , D 2   0  and D 3   0  represent the optical thickness of the first to third layers  61   a ,  61   b ,  61   c  at a center of the lens substrate  51 , and α, β and γ are numbers independently in a range of 0-1. α, β and γ are more preferably independently in a range of 0.5-0.95, most preferably independently in a range of 0.6-0.9.
 
     The second and third optical members each having an anti-reflection coating having a four-layer structure comprising an uppermost silica aerogel layer exhibits excellent anti-reflection characteristics in wide ranges of wavelength and incident angle without using an Al 2 O 3  layer, with the refractive indices of the first to third layers adjusted, and is free from fogging which would occur in conventional anti-reflection coatings comprising a silica aerogel layer and an Al 2 O 3  layer, when stored under high-temperature, high-humidity conditions for a long period of time. 
     [6] P RODUCTION METHOD OF SECOND AND THIRD OPTICAL MEMBERS    
     The first to third layers in the second and third anti-reflection coatings can be produced by the same method as the first and second layers in the first anti-reflection coating. The fourth layer in the second and third anti-reflection coatings can be produced by the same method as the third layer in the first anti-reflection coating. 
     Because the above-described first to third optical members have the maximum reflectance of 6% or less in a visible light wavelength range of 400-700 nm, they are suitable for lenses mounted in optical equipments such as TV cameras, video cameras, digital cameras, vehicle cameras, microscopes, telescopes, etc., prisms, diffraction devices, etc. Particularly optical members having anti-reflection coatings on lens substrates having the maximum inclination angle of 300 or more are suitable for ultra-wide-angle lenses, pickup lenses of optical disks, etc., because they have good anti-reflection characteristics even in peripheral portions. 
     To provide waterproofness and durability to the first to third anti-reflection coatings, silica aerogel having organically modified silica end groups may be used for the uppermost layer. Also, a water-repellent, oil-repellent fluororesin coating may be formed on the uppermost layer of silica aerogel. 
     The present invention will be explained in further detail by Examples below without intention of restricting the present invention thereto. 
     EXAMPLE 1 
     A first layer of MgF 2 , a second layer of Ta 2 O 5 +Y 2 O 3 +Pr 6 O 11 , and a third layer of silica aerogel were formed to the optical thickness shown in Table 1 on a flat glass plate of LaSF010 (refractive index: 1.839), to produce each Sample a to g. Because each of the first and second layers formed on a lens substrate having a large maximum inclination angle becomes gradually thinner as it goes from the center toward the periphery (as the inclination angle becomes larger) as shown in  FIG. 2 , the thickness of the first and second layers in each Sample a to g was set equal to the thickness at a lens substrate inclination angle of 0°, 10°, 20°, 30°, 40°, 50° and 60°, respectively, and the thickness of the third layer was set constant, to evaluate anti-reflection performance at each inclination angle of the lens substrate. 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
             
            
               
                 Layer 
                 Material 
                 Refractive Index 
               
               
                   
               
               
                 Substrate 
                 LaSF010 
                 1.839 
               
               
                 First Layer 
                 MgF 2   
                 1.388 
               
               
                 Second Layer 
                 Ta 2 O 5  + Y 2 O 3  +  
                 2.055 
               
               
                   
                 Pr 6 O 11   
                   
               
               
                 Third Layer 
                 Silica Aerogel 
                 1.270 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Optical Thickness [nm] 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
               
               
                 Layer 
                 a 
                 b 
                 c 
                 d 
                 e 
                 f 
                 g 
               
               
                   
               
               
                 Sub- 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                 strate 
                   
                   
                   
                   
                   
                   
                   
               
               
                 First  
                 41 
                 40 
                 39 
                 37 
                 34 
                 30 
                 25 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Second 
                 34 
                 34 
                 33 
                 31 
                 29 
                 25 
                 21 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Third 
                 150 
                 150 
                 150 
                 150 
                 150 
                 150 
                 150 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Angle (1)   
                 0 
                 10 
                 20 
                 30 
                 40 
                 50 
                 60 
               
               
                   
               
               
                 Note: 
               
               
                   (1) A corresponding inclination angle (°) of the lens substrate. 
               
            
           
         
       
     
     The optical thickness D 1 (θ t ) of the first layer and the optical thickness D 2 (θ t ) of the second layer at each inclination angle θ t  of the lens substrate, which are shown in Table 1, were determined by the following formulae (1) and (2):
 
 D 1(θ t )= D 1 0 ×(cos θ t ) α   (1), and
 
 D 2(θ t )= D 2 0 ×(cos θ t ) β   (2),
 
wherein D 1   0  and D 2   0  represent the optical thickness of the first and second layers at a substrate inclination angle of 0°, and both α and β are 0.7.
 
     The production method of each Sample a to g was as follows. 
     (1) F ORMATION OF FIRST AND SECOND LAYERS    
     Using the apparatus shown in  FIG. 21 , a first layer of MgF 2  and a second layer of Ta 2 O 5 +Y 2 O 3 +Pr 6 O 11  were formed to the optical thickness shown in Table 1 on a flat glass plate of LaSF010, by a vacuum vapor deposition method with electron beams. 
     (2) F ORMATION OF THIRD LAYER    
     (i) Preparation of First Acidic Sol 
     17.05 g of tetraethoxysilane was mixed with 69.13 g of methanol, and 3.88 g of an aqueous ammonia solution (3 N) was add to the resultant mixture and stirred at room temperature for 15 hours to prepare an alkaline sol. 40.01 g of this alkaline sol was mixed with 2.50 g of methanol and 1.71 g of hydrochloric acid (12 N), and stirred at room temperature for 30 minutes to prepare a first acidic sol (solid component: 4.94% by mass). 
     (ii) Preparation of Second Acidic Sol 
     30 ml of tetraethoxysilane was mixed with 30 ml of ethanol at room temperature, and then with 2.4 ml of water. Thereafter, 0.1 ml of hydrochloric  acid  (1 N) was added to the resultant mixture, and stirred at 60° C. for 90 minutes to prepare a second acidic sol (solid component: 14.8% by mass). 
     (iii) Preparation of Mixed Sol 
     0.22 g of the second acidic sol was added to a total amount of the first acidic sol, such that a solid component mass ratio of the first acidic sol to the second acidic sol was 67.1, and stirred at room temperature for 5 minutes to prepare a mixed sol. 
     (iv) Coating and Alkali Treatment 
     The mixed sol was applied to the second layer by a spin-coating method, dried at 80° C. for 0.5 hours, and then baked at 180° C. for 0.5 hours. The cooled coating was spin-coated with a 0.1-N aqueous sodium hydroxide solution, and dried at 120° C. for 0.5 hours. 
     Using a lens reflectance meter (USPM-RU available from Olympus Corporation), the spectral reflectance of Sample a (corresponding to a substrate inclination angle of 00) thus obtained was measured at each light beam incident angle of 0°, 10°, 20°, 30°, 40°, 50° and 60°. The results are shown in  FIG. 8 . Average reflectance in a wavelength range of 400-700 nm was calculated from the measured spectral reflectance at each incident angle of light beams. With respect to Samples b to g (corresponding to substrate inclination angles of 100, 20°, 30°, 40°, 50° and 60°, respectively), spectral reflectance was similarly measured at each incident angle of light beams, and average reflectance in a wavelength range of 400-700 nm was calculated at each incident angle of light beams. The relation between the average reflectance at each substrate inclination angle and the incident angle of light beams is shown in  FIG. 9 . 
     COMPARATIVE EXAMPLE 1 
     Anti-reflection coatings (Samples a to g) were produced in the same manner as in Example 1, except for using Al 2 O 3  and SiO 2  as materials for forming the first and second layers, and changing the optical thickness of the first to third layers as shown in Table 2. The anti-reflection coatings of these samples correspond to conventional ones designed to have a refractive index gradually decreasing from the first layer toward the third layer. 
     
       
         
           
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
             
            
               
                 Layer 
                 Material 
                 Refractive Index 
               
               
                   
               
               
                 Substrate 
                 LaSF010 
                 1.839 
               
               
                 First Layer 
                 Al 2 O 3   
                 1.640 
               
               
                 Second Layer 
                 SiO 2   
                 1.469 
               
               
                 Third Layer 
                 Silica Aerogel 
                 1.250 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Optical Thickness [nm] 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
               
               
                 Layer 
                 a 
                 b 
                 c 
                 d 
                 e 
                 f 
                 g 
               
               
                   
               
               
                 Sub- 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                 strate 
                   
                   
                   
                   
                   
                   
                   
               
               
                 First  
                 114 
                 113 
                 109 
                 103 
                 95 
                 84 
                 70 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Second 
                 25 
                 25 
                 24 
                 23 
                 21 
                 18 
                 15 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Third 
                 126 
                 126 
                 126 
                 126 
                 126 
                 126 
                 126 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Angle (1)   
                 0 
                 10 
                 20 
                 30 
                 40 
                 50 
                 60 
               
               
                   
               
               
                 Note: 
               
               
                   (1) A corresponding inclination angle (°) of the lens substrate. 
               
            
           
         
       
     
     The spectral reflectance of Sample a (corresponding to a substrate inclination angle of 0°) thus obtained was measured at each light beam incident angle of 0°, 10°, 20°, 30°, 40°, 50° and 60° in the same manner as in Example 1. The results are shown in  FIG. 10 . As in Example 1, the relation between the average reflectance at each substrate inclination angle and the incident angle of light beams is shown in  FIG. 11 . 
     COMPARATIVE EXAMPLE 2 
     As shown in Table 3, an optical member comprising a seven-layer anti-reflection coating was produced. 
     (1) F ORMATION OF FIRST TO SIXTH LAYERS    
     Using the apparatus shown in  FIG. 21 , first to sixth layers were formed in this order on a flat glass plate of LaSF010 (refractive index: 1.839) by a vacuum vapor deposition method with electron beams, as shown in Table 3. The vapor deposition was conducted at an initial degree of vacuum of 1.2×10 −5  Torr and a substrate temperature of 230° C. 
     (2) F ORMATION OF SEVENTH LAYER    
     The seventh layer of silica aerogel layer was formed in the same manner as in the third layer of Example 1, except for changing the optical thickness as shown in Table 3. 
     
       
         
           
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
             
            
               
                 Layer 
                 Material 
                 Refractive Index 
               
               
                   
               
               
                 Substrate 
                 LaSF010 
                 1.839 
               
               
                 First Layer 
                 Al 2 O 3   
                 1.640 
               
               
                 Second Layer 
                 Ta 2 O 5  + Pr 6 O 11  +  
                 2.055 
               
               
                   
                 Y 2 O 3   
                   
               
               
                 Third Layer 
                 MgF 2   
                 1.388 
               
               
                 Fourth Layer 
                 Ta 2 O 5  + Pr 6 O 11  +  
                 2.055 
               
               
                   
                 Y 2 O 3   
                   
               
               
                 Fifth Layer 
                 MgF 2   
                 1.388 
               
               
                 Sixth Layer 
                 Ta 2 O 5  + Pr 6 O 11  +  
                 2.055 
               
               
                   
                 Y 2 O 3   
                   
               
               
                 Seventh Layer 
                 Silica Aerogel 
                 1.250 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Optical Thickness [nm] 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
               
               
                 Layer 
                 a 
                 b 
                 c 
                 d 
                 e 
                 f 
                 g 
               
               
                   
               
               
                 Sub- 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                 strate 
                   
                   
                   
                   
                   
                   
                   
               
               
                 First  
                 45 
                 45 
                 43 
                 41 
                 38 
                 33 
                 28 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Second 
                 61 
                 60 
                 58 
                 61 
                 51 
                 45 
                 38 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Third 
                 25 
                 25 
                 24 
                 23 
                 21 
                 18 
                 15 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Fourth 
                 262 
                 259 
                 251 
                 237 
                 218 
                 192 
                 161 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Fifth 
                 34 
                 34 
                 33 
                 31 
                 28 
                 25 
                 21 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Sixth 
                 37 
                 37 
                 36 
                 34 
                 31 
                 28 
                 23 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Seventh 
                 135 
                 135 
                 135 
                 135 
                 135 
                 135 
                 135 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Angle (1)   
                 0 
                 10 
                 20 
                 30 
                 40 
                 50 
                 60 
               
               
                   
               
               
                 Note: 
               
               
                   (1) A corresponding inclination angle (°) of the lens substrate. 
               
            
           
         
       
     
     The spectral reflectance of Sample a (corresponding to a substrate inclination angle of 0°) thus obtained was measured at each light beam incident angle of 0°, 10°, 20°, 30°, 40°, 50° and 60° in the same manner as in Example 1. The results are shown in  FIG. 12 . As in Example 1, the relation between the average reflectance at each substrate inclination angle and the incident angle of light beams is shown in  FIG. 13 . 
     As is clear from  FIGS. 12 and 13 , the samples of Comparative Example 2 exhibited much poorer anti-reflection performance than those of Example 1 in portions with large inclination angles (40-60°), despite as many as 7 layers. 
     COMPARATIVE EXAMPLE 3 
     Optical members were produced in the same manner as in Comparative Example 2, except for changing the uppermost layer (seventh layer) of the anti-reflection coating from the silica aerogel layer to a MgF 2  layer formed by a vacuum vapor deposition method. Like other layers, the thickness of the seventh layer decreased gradually in the order of Samples a to g. 
     Using the apparatus shown in  FIG. 21 , first to seventh layers were formed in this order on a flat glass plate of LaSF010 (refractive index: 1.839) by a vacuum vapor deposition method with electron beams, as shown in Table 4. The vapor deposition was conducted at an initial degree of vacuum of 1.2×10 −5  Torr and a substrate temperature of 230° C. 
     
       
         
           
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
             
            
               
                 Layer 
                 Material 
                 Refractive Index 
               
               
                   
               
               
                 Substrate 
                 LaSF010 
                 1.839 
               
               
                 First Layer 
                 Al 2 O 3   
                 1.640 
               
               
                 Second Layer 
                 Ta 2 O 5  + Pr 6 O 11  +  
                 2.055 
               
               
                   
                 Y 2 O 3   
                   
               
               
                 Third Layer 
                 MgF 2   
                 1.388 
               
               
                 Fourth Layer 
                 Ta 2 O 5  + Pr 6 O 11  +  
                 2.055 
               
               
                   
                 Y 2 O 3   
                   
               
               
                 Fifth Layer 
                 MgF 2   
                 1.388 
               
               
                 Sixth Layer 
                 Ta 2 O 5  + Pr 6 O 11  +  
                 2.055 
               
               
                   
                 Y 2 O 3   
                   
               
               
                 Seventh Layer 
                 MgF 2   
                 1.388 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Optical Thickness [nm] 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
               
               
                 Layer 
                 a 
                 b 
                 c 
                 d 
                 e 
                 f 
                 g 
               
               
                   
               
               
                 Sub- 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                 strate 
                   
                   
                   
                   
                   
                   
                   
               
               
                 First  
                 33 
                 33 
                 32 
                 30 
                 28 
                 24 
                 20 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Second 
                 64 
                 64 
                 62 
                 64 
                 54 
                 47 
                 40 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Third 
                 25 
                 25 
                 24 
                 23 
                 21 
                 18 
                 15 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Fourth 
                 283 
                 280 
                 271 
                 256 
                 235 
                 208 
                 174 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Fifth 
                 25 
                 25 
                 24 
                 23 
                 21 
                 18 
                 15 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Sixth 
                 25 
                 25 
                 24 
                 23 
                 21 
                 18 
                 15 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Seventh 
                 116 
                 114 
                 111 
                 105 
                 96 
                 85 
                 71 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Angle (1)   
                 0 
                 10 
                 20 
                 30 
                 40 
                 50 
                 60 
               
               
                   
               
               
                 Note: 
               
               
                   (1) A corresponding inclination angle (°) of the lens substrate. 
               
            
           
         
       
     
     The spectral reflectance of Sample a (corresponding to a substrate inclination angle of 0°) thus obtained was measured at each light beam incident angle of 0°, 10°, 20°, 30°, 40°, 50° and 60° in the same manner as in Example 1. The results are shown in  FIG. 14 . As in Example 1, the relation between the average reflectance at each substrate inclination angle and the incident angle of light beams is shown in  FIG. 15 . 
     As is clear from  FIGS. 14 and 15 , the samples of Comparative Example 3, which had the outermost layers becoming thinner as the substrate inclination angle increased, exhibited extremely poor anti-reflection performance in portions with large substrate inclination angles (30-60°). 
     EXAMPLE 2 
     A first layer of SiO 2  (refractive index: 1.469), a second layer of Ta 2 O 5 +Y 2 O 3 +Pr 6 O 11  (refractive index: 2.055), a third layer of SiO 2  (refractive index: 1.469) and a fourth layer of silica aerogel (refractive index: 1.250) were formed to each optical thickness shown in Table 5 on a flat glass plate of LaSF010 (refractive index: 1.839) by the same method as in Example 1, to produce Samples a to g To evaluate the anti-reflection performance of an anti-reflection coating on a lens substrate having a large maximum inclination angle as shown in  FIG. 7  at each substrate inclination angle, each of Samples a to g comprised first to fourth layers formed on a flat glass plate at thickness corresponding to the thickness of each layer at a lens substrate inclination angle of 0°, 10°, 20°, 30°, 40°, 50° and 60°, the first to third layers becoming gradually thinner from Sample a to Sample g, and the fourth layer having a constant thickness. 
     
       
         
           
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
             
            
               
                 Layer 
                 Material 
                 Refractive Index 
               
               
                   
               
               
                 Substrate 
                 LaSF010 
                 1.839 
               
               
                 First Layer 
                 SiO 2   
                 1.640 
               
               
                 Second Layer 
                 Ta 2 O 5  + Y 2 O 3  +  
                 2.055 
               
               
                   
                 Pr 6 O 11    
                   
               
               
                 Third Layer 
                 SiO 2   
                 1.469 
               
               
                 Fourth Layer 
                 Silica Aerogel 
                 1.250 
               
               
                   
               
            
           
           
               
               
            
               
                   
                 Optical Thickness [nm] 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
                 Sample  
               
               
                 Layer 
                 a 
                 b 
                 c 
                 d 
                 e 
                 f 
                 g 
               
               
                   
               
               
                 Sub- 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                 strate 
                   
                   
                   
                   
                   
                   
                   
               
               
                 First  
                 38 
                 37 
                 36 
                 34 
                 31 
                 28 
                 23 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Second 
                 24 
                 24 
                 23 
                 22 
                 20 
                 18 
                 15 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Third 
                 68 
                 67 
                 65 
                 61 
                 56 
                 50 
                 42 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Fourth 
                 116 
                 116 
                 116 
                 116 
                 116 
                 116 
                 116 
               
               
                 Layer 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Angle (1)   
                 0 
                 10 
                 20 
                 30 
                 40 
                 50 
                 60 
               
               
                   
               
               
                 Note: 
               
               
                   (1) A corresponding inclination angle (°) of the lens substrate. 
               
            
           
         
       
     
     The optical thickness D 1 (θ t ) of the first layer, the optical thickness D 2 (θ t ) of the second layer and the optical thickness D 3 (θ t ) of the third layer at each substrate inclination angle (θ t ), which are shown in Table 5, were determined by the following formulae (1) to (3):
 
 D 1(θ t )= D 1 0 ×(cos θ t ) α   (1),
 
 D 2(θ t )= D 2 0 ×(cos θ t ) β   (2), and
 
 D 3(θ t )= D 3 0 ×(cos θ t ) γ   (3),
 
wherein D 1   0 , D 2   0  and D 3   0  represent the optical thickness of the first to third layers at a substrate inclination angle of 0°, and all of α, β and γ are 0.7.
 
     The spectral reflectance of Sample a (corresponding to a substrate inclination angle of 0°) thus obtained was measured at each light beam incident angle of 0°, 10°, 20°, 30°, 40°, 50° and 60° in the same manner as in Example 1. The results are shown in  FIG. 16 . Average reflectance in a wavelength range of 400-700 nm was calculated from the measured spectral reflectance at each incident angle of light beams. With respect to Samples b to g (corresponding to substrate inclination angles of 10°, 20°, 30°, 40°, 50° and 60°, respectively), spectral reflectance at each incident angle of light beams was similarly measured, and average reflectance in a wavelength range of 400-700 nm was calculated at each incident angle of light beams. The relation between the average reflectance at each substrate inclination angle and the incident angle of light beams is shown in  FIG. 17 . 
     A CCELERATED ENVIRONMENTAL TESTING    
     Each of Samples a, d and f (having substrate inclination angles of 0°, 30° and 50°, respectively) of Example 1, Comparative Example 1 and Example 2 was stored at 60° C. and 90% RH for 48 hours for accelerated environmental testing Their spectral reflection characteristics measured by the same method as described above after the accelerated environmental testing were compared with those before the testing. The results are shown in  FIG. 18  (Example 1),  FIG. 19  (Comparative Example 1) and  FIG. 20  (Example 2). 
     As is clear from  FIGS. 18-20 , the samples of Comparative Example 1 exhibited poor spectral reflection characteristics after the accelerated environmental testing under the high-temperature, high-humidity conditions, while the spectral reflection characteristics of the samples of Examples 1 and 2 were not substantially deteriorated, indicating that their anti-reflection characteristics at high temperatures and humidity were highly durable. 
     EFFECT OF THE INVENTION 
     Because the anti-reflection coating of the present invention has excellent storage stability, particularly exhibiting stable anti-reflection performance even when stored under high-temperature, high-humidity conditions for a long period of time, it is suitable for imaging equipments such as exchange lenses for single-lens reflex cameras, etc. Further, the anti-reflection coating of the present invention can be produced at a high yield, because of excellent production stability. 
     Because the optical member of the present invention exhibits excellent anti-reflection performance in a wide wavelength range even on a lens substrate having a maximum inclination angle of 30° or more, it is particularly suitable for ultrawide-angle lenses, lenses having small radii of curvature to effective diameters, pickup lenses of optical disks, etc.