Optical element, optical system, and optical apparatus

1. An optical element comprising a substrate that is transparent to a d-line, and an antireflection film formed on the substrate,

wherein the antireflection film includes a plurality of thin film layers that include an uppermost layer that is most distant from the substrate and has a refractive index nd of 1.20 to 1.30 to the d-line, a high refractive index layer having a refractive index of 2.00 to 2.40 to the d-line, and at least one of an intermediate refractive index layer having a refractive index of 1.55 to 1.70 to the d-line and a low refractive index layer having a refractive index of 1.40 to 1.52 to the d-line, and

wherein an undercoat layer includes the substrate to the thin film layer adjacent to the uppermost layer, and the following expression is satisfied, where Y(θ, λ) is an optical admittance calculated from a refractive index to the d-line and a film thickness of the undercoat layer, θ is an incident angle in a range of 0° to 60°, and λ is a wavelength in a range of 420 nm and 680 nm:

nd− 0.1 ≦√Y (θ,λ)≦ nd.

2. The optical element according to claim 1 , wherein the antireflection film includes at least nine thin film layers.

3. The optical element according to claim 1 , wherein the uppermost layer is a layer that includes hollow nanoparticles each made of silica as a primary ingredient, and having an average particle diameter of 80 nm or smaller.

4. The optical element according to claim 1 , wherein the high refractive index layer is made of one of titanium, tantalum, zirconium, chrome, niobium, cerium, hafnium, and yttrium singularly or a mixture of one or more of titanium, tantalum, zirconium, chrome, niobium, cerium, hafnium, and yttrium.

5. The optical element according to claim 1 , wherein the intermediate refractive index layer is made of aluminum oxide solely or a mixture of aluminum oxide.

6. The optical element according to claim 1 , wherein the uppermost layer is made of silicon oxide solely or a mixture of silicon oxide.

7. The optical element according to claim 1 , wherein a layer among the plurality of thin film layers closest to the substrate is made of Al 2 O 3 solely or a mixture of Al 2 O 3 .

8. The optical element according to claim 1 , wherein the uppermost layer is formed by a sol-gel method, and the plurality of thin film layers except the uppermost layer is formed by a vacuum evaporation method or a sputtering method.

9. The optical element according to claim 1 , wherein the substrate has a refractive index of 1.50 to 2.00 to the d-line.

10. The optical element according to claim 1 , wherein the uppermost layer has a thickness of 110.00 nm to 135.00 nm.

11. The optical element according to claim 1 , wherein the plurality of thin film layers except the uppermost layer includes, in order from the substrate to the uppermost layer, at least one pair of the intermediate refractive index layer and the high refractive index layer, and the high refractive index layer closest to the uppermost layer contacts the uppermost layer.

12. The optical element according to claim 1 , wherein the plurality of thin film layers except the uppermost layer includes, in order from the substrate to the uppermost layer, at least one pair of the intermediate refractive index layer and the high refractive index layer, and the low refractive index layer that has the refractive index of 1.40 to 1.52 to the d-line is provided between the high refractive index layer closest to the uppermost layer and the uppermost layer.

13. The optical element according to claim 12 , wherein the low refractive index layer is made of silicon oxide solely or a mixture of silicon oxide.

14. The optical element according to claim 12 , wherein there are a plurality of pairs, and one of the plurality of high refractive index layers is thicker than each of upper and lower intermediate refractive index layers.

15. The optical element according to claim 12 , wherein one of the plurality of high refractive index layers is thicker than the uppermost layer.

16. The optical element according to claim 12 , wherein the uppermost layer is thickest among the plurality of thin film layers.

17. An optical system comprising an optical element,

wherein the optical element includes a substrate that is transparent to a d-line, and an antireflection film formed on the substrate,

wherein the antireflection film includes a plurality of thin film layers that include an uppermost layer that is most distant from the substrate and has a refractive index nd of 1.20 to 1.30 to the d-line, a high refractive index layer having a refractive index of 2.00 to 2.40 to the d-line, and at least one of an intermediate refractive index layer having a refractive index of 1.55 to 1.70 to the d-line and a low refractive index layer having a refractive index of 1.40 to 1.52 to the d-line, and

wherein an undercoat layer includes the substrate to the thin film layer adjacent to the uppermost layer, and the following expression is satisfied, where Y(θ, λ) is an optical admittance calculated from a refractive index to the d-line and a film thickness of the undercoat layer, θ is an incident angle in a range of 0° to 60°, and λ is a wavelength in a range of 420 nm and 680 nm:

nd− 0.1 ≦√Y (θ,λ)≦ nd.

18. An optical apparatus comprising an optical element,

wherein the optical element includes a substrate that is transparent to a d-line, and an antireflection film formed on the substrate,

wherein the antireflection film includes a plurality of thin film layers that include an uppermost layer that is most distant from the substrate and has a refractive index nd of 1.20 to 1.30 to the d-line, a high refractive index layer having a refractive index of 2.00 to 2.40 to the d-line, and at least one of an intermediate refractive index layer having a refractive index of 1.55 to 1.70 to the d-line and a low refractive index layer having a refractive index of 1.40 to 1.52 to the d-line, and

wherein an undercoat layer includes the substrate to the thin film layer adjacent to the uppermost layer, and the following expression is satisfied, where Y(θ, λ) is an optical admittance calculated from a refractive index to the d-line and a film thickness of the undercoat layer, θ is an incident angle in a range of 0° to 60°, and λ is a wavelength in a range of 420 nm and 680 nm:

nd− 0.1 ≦√Y (θ,λ)≦ nd.