OPTICAL COMPONENTS INCLUDING LENS HAVING AT LEAST ONE ASPHERICAL REFRACTIVE SURFACE

US 20100157441A1
Filed: 06/22/2006
Published: 06/24/2010
Est. Priority Date: 06/22/2005
Status: Active Grant

First Claim

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1. An optical component comprising:

at least a first aspherical refractive surface, whereinthe first aspherical refractive surface constitute a part of a boundary between a first medium having a refractive index n₁and a second medium having a refractive index n₂,a first curve is defined as a collection of intersections between the x-z plane of a rectangular coordinate system and the first aspherical refractive surface, whereinthe origin of the rectangular coordinate system is located within the second medium, and the z-axis of the rectangular coordinate system passes through the origin and a point on the first aspherical refractive surface,the said first curve is symmetric about the z-axis,a distance from the origin to a first point on the first curve with a zenith angle θ

is r(θ

),rectangular coordinates (x, z) and polar coordinates (θ

, r) of the first point in the x-z plane satisfy relations given in Eqs. 1 and 2,
x(θ

)=r(θ

)sin θ

(Eq.

1)
z(θ

)=r(θ

)cos θ

(Eq.

2)the distance r(θ

) is given as Eq. 3, $\begin{matrix} r (θ) = r (θ_{i}) \exp [\int_{θ_{i}}^{θ} \frac{- n_{1} \sin (δ - θ^{'})}{n_{1} \cos (δ - θ^{'}) - n_{2}} \partial θ^{'}] & (Eq . 3) \end{matrix}$ said θ

_iis a zenith angle of a second point on the first curve, said r(θ

_i) is a corresponding distance from the origin to the second point, said δ

is an arbitrary function of the zenith angle θ

of the first point (δ

=δ

(θ

)), and the zenith angle θ

ranges from a minimum θ

₁not smaller than zero to a maximum θ

₂smaller than π

/2.

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Abstract

An optical component including lens having at least one aspherical refractive surface capable of satisfying desired performance and characteristics is disclosed.

Citations

57 Claims

1. An optical component comprising:
- at least a first aspherical refractive surface, whereinthe first aspherical refractive surface constitute a part of a boundary between a first medium having a refractive index n₁and a second medium having a refractive index n₂,a first curve is defined as a collection of intersections between the x-z plane of a rectangular coordinate system and the first aspherical refractive surface, whereinthe origin of the rectangular coordinate system is located within the second medium, and the z-axis of the rectangular coordinate system passes through the origin and a point on the first aspherical refractive surface,the said first curve is symmetric about the z-axis,a distance from the origin to a first point on the first curve with a zenith angle θ
  
  is r(θ
  
  ),rectangular coordinates (x, z) and polar coordinates (θ
  
  , r) of the first point in the x-z plane satisfy relations given in Eqs. 1 and 2,
  x(θ
  
  )=r(θ
  
  )sin θ
  
  (Eq.
  
  1)
  z(θ
  
  )=r(θ
  
  )cos θ
  
  (Eq.
  
  2)the distance r(θ
  
  ) is given as Eq. 3, $\begin{matrix} r (θ) = r (θ_{i}) \exp [\int_{θ_{i}}^{θ} \frac{- n_{1} \sin (δ - θ^{'})}{n_{1} \cos (δ - θ^{'}) - n_{2}} \partial θ^{'}] & (Eq . 3) \end{matrix}$ said θ
  
  _iis a zenith angle of a second point on the first curve, said r(θ
  
  _i) is a corresponding distance from the origin to the second point, said δ
  
  is an arbitrary function of the zenith angle θ
  
  of the first point (δ
  
  =δ
  
  (θ
  
  )), and the zenith angle θ
  
  ranges from a minimum θ
  
  ₁not smaller than zero to a maximum θ
  
  ₂smaller than π
  
  /2.
- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17)
- - 2. The optical component of claim 1, wherein the refractive index n₁of the first medium is larger than the refractive index n₂of the second medium (n₁>
    - n₂), said δ
      
      is zero (δ
      
      =θ
      
      ),the optical component further comprises a second lens surface,a second curve is defined as a collection of intersections between the x-z plane and the second lens surface, and the second curve is a line segment perpendicular to the z-axis,the z-coordinate Z_Fof the second curve is not smaller than the maximum z-coordinate of the first points on the first curve (Z_F≧
      
      max(z(θ
      
      ))), andthe space between the first aspherical refractive surface and the second lens surface is filled with the first medium having the refractive index n₁.
  - 3. The optical component of claim 2, wherein the first aspherical refractive surface and the second lens surface are rotationally symmetric about the z-axis.
  - 4. The optical component of claim 2, wherein the first aspherical refractive surface and the second lens surface have translational symmetry along the y-axis of the rectangular coordinate system.
  - 5. The optical component of claim 2, wherein the first aspherical refractive surface and the second lens surface are rotationally symmetric about the x-axis of the rectangular coordinate system.
  - 6. The optical component of claim 1, wherein the refractive index n₁of the first medium is smaller than the refractive index n₂of the second medium (n₁<
    - n₂), said δ
      
      is zero (δ
      
      =θ
      
      ),the optical component further comprises a second lens surface,a second curve defined as a collection of intersections between the x-z plane and the second lens surface is a circular arc around the origin with a radius r_B,the radius r_Bof the circular arc is not larger than the shortest distance r(θ
      
      ) (r_E≦
      
      min(r(θ
      
      ))), andthe space between the first aspherical refractive surface and the second lens surface is filled with the second medium having the refractive index n₂.
  - 7. The optical component of claim 6, wherein the first aspherical refractive surface and the second lens surface are rotationally symmetric about the z-axis.
  - 8. The optical component of claim 6, wherein the first aspherical refractive surface and the second lens surface have translational symmetry along the y-axis of the rectangular coordinate system.
  - 9. The optical component of claim 6, wherein the first aspherical refractive surface and the second lens surface are rotationally symmetric about the x-axis of the rectangular coordinate system.
  - 10. The optical component of claim 1, wherein said θ
    - ₁is zero and said δ
      
      (θ
      
      ) has a relation given in Eq. 4,
11. The optical component of claim 1, wherein said θ
- ₁is zero, said δ
  
  (θ
  
  ) has a relation given in Eq. 5, $\begin{matrix} δ (θ) = (\frac{δ_{2}}{\tan θ_{2}}) \tan θ & (Eq . 5) \end{matrix}$ and δ
  
  ₂is a value of δ
  
  corresponding to the said θ
  
  ₂(δ
  
  ₂=δ
  
  (θ
  
  ₂)).
12. The optical component of claim 1, wherein said θ
- ₁is zero, said δ
  
  (θ
  
  ) has a relation given in Eq. 6, $\begin{matrix} δ (θ) = 2 \tan^{- 1} [\frac{\tan \frac{δ_{2}}{2}}{\tan θ_{2}} \tan θ] & ^{*} (Eq . 6) \end{matrix}$ and δ
  
  ₂is a value of δ
  
  corresponding to the said θ
  
  ₂(δ
  
  =δ
  
  (θ
  
  ₂)).
13. The optical component of claim 1, wherein said θ
- ₁is zero, said δ
  
  (θ
  
  ) has a relation given in Eq. 7, $\begin{matrix} δ (θ) = \sin^{- 1} [\frac{\sin δ_{2}}{\tan θ_{2}} \tan θ] & (Eq . 7) \end{matrix}$ and δ
  
  ₂is a value of δ
  
  corresponding to the said θ
  
  ₂(δ
  
  =δ
  
  (θ
  
  ₂)).
14. The optical component of claim 1, wherein the refractive index n₁of the first medium is smaller than the refractive index n₂of the second medium (n₁<
- n₂), the optical component further comprises a second lens surface,a second curve defined as a collection of intersections between the x-z plane and the second lens surface is a circular arc around the origin with a radius r_B,the radius r_Bof the circular arc is not larger than the shortest distance to the first points on the first curve (r_B≦
  
  min(r(θ
  
  ))) andthe space between the first aspherical refractive surface and the second lens surface is filled with the second medium with the refractive index n₂.
15. The optical component of claim 14, wherein the first aspherical refractive surface and the second lens surface are rotationally symmetric about the z-axis.
16. The optical component of claim 14, wherein the first aspherical refractive surface and the second lens surface have translational symmetry along the y-axis of the rectangular coordinate system.
17. The optical component of claim 14, wherein the first aspherical refractive surface and the second lens surface are rotationally symmetric about the x-axis of the rectangular coordinate system.

18. An optical component comprising:
- at least a first aspherical refractive surface, whereinthe first aspherical refractive surface constitute a part of a boundary between a first medium having a refractive index n₁and a second medium having a refractive index n₂,a first curve is defined as a collection of intersections between the x-z plane of a rectangular coordinate system and the first aspherical refractive surface, whereinthe origin of the rectangular coordinate system is located within the second medium, and the z-axis of the rectangular coordinate system passes through the origin and a point on the first aspherical refractive surface,the said first curve is symmetric about the z-axis,a distance from the origin to a first point on the first curve with a zenith angle θ
  
  is r(θ
  
  ),rectangular coordinates (x, z) and polar coordinates (θ
  
  , r) of the first point in the x-z plane satisfy relations given in Eqs. 8 and 9,
  x(θ
  
  )=r(θ
  
  )sin θ
  
  (Eq.
  
  8)
  z(θ
  
  )=r(θ
  
  )cos θ
  
  (Eq.
  
  9)the distance r(θ
  
  ) is given as the following Eq. 10, $\begin{matrix} r (θ) = r (θ_{i}) \exp [\int_{θ_{i}}^{θ} \frac{n_{2} \sin θ^{'}}{n_{2} \cos θ^{'} - n_{2}} \partial θ^{'}] & (Eq . 10) \end{matrix}$ wherein θ
  
  _iis the zenith angle of a second point on the first curve, r(θ
  
  _i) is the corresponding distance from the origin to the second point, and the zenith angle θ
  
  ranges from a minimum θ
  
  ₁not smaller than zero to a maximum η
  
  ₂smaller than λ
  
  /2.
- View Dependent Claims (19, 20, 21, 22, 23, 24, 25, 26)
- - 19. The optical component of claim 18, wherein the refractive index n₁of the first medium is larger than the refractive index n₂of the second medium (n₁>
    - n₂),the optical component further comprises a second lens surface,a second curve defined as a collection of intersections between the x-z plane and the second lens surface is a circular arc around the origin with a radius r_F,the radius r_Fof the circular arc is not smaller than the longest distance to the first points on the first curve (r_F≧
      
      max(r(θ
      
      ))), andthe space between the first aspherical refractive surface and the second lens surface is filled with the first medium having the refractive index n₁.
  - 20. The optical component of claim 19, wherein the first aspherical refractive surface and the second lens surface are rotationally symmetric about the z-axis.
  - 21. The optical component of claim 19, wherein the first aspherical refractive surface and the second lens surface have translational symmetry along the y-axis of the rectangular coordinate system.
  - 22. The optical component of claim 19, wherein the first aspherical refractive surface and the second lens surface are rotationally symmetric about the x-axis of the rectangular coordinate system.
  - 23. The optical component of claim 18, wherein the refractive index n₁of the first medium is smaller than the refractive index n₂of the second medium (n₁<
    - n₂), the optical component further comprises a second lens surface,a second curve defined as a collection of intersections between the x-z plane and the second lens surface is a straight line segment perpendicular to the z-axis,the z-coordinate z_Bof the second curve is not larger than the minimum z-coordinate of the first points on the first curve (z_B≦
      
      min(z(θ
      
      ))), andthe space between the first aspherical refractive surface and the second lens surface is filled with the second medium having the refractive index n₂.
  - 24. The optical component of claim 23, wherein the first aspherical refractive surface and the second lens surface are rotationally symmetric about the z-axis.
  - 25. The optical component of claim 23, wherein the first aspherical refractive surface and the second lens surface have translational symmetry along the y-axis of the rectangular coordinate system.
  - 26. The optical component of claim 23, wherein the first aspherical refractive surface and the second lens surface are rotationally symmetric about the x-axis of the rectangular coordinate system.

27. An optical component comprising:
- a first lens surface;
  
  a second lens surface;
  
  a third lens surface; and
  
  a fourth lens surface, whereinthe fourth lens surface constitute a part of a boundary between a fourth medium having a refractive index n₄and a fifth medium having a refractive index n₅, the refractive index n₄of the fourth medium is larger than the refractive index n₅of the fifth medium (n₄>
  
  n₅),a fourth curve is defined as a collection of intersections between the x-z plane of a rectangular coordinate system and the fourth lens surface, whereinan origin of the rectangular coordinate system is located within the fifth medium,and the z-axis of the rectangular coordinate system passes through the origin and a point on the fourth lens surface,the said fourth curve is symmetric about the z-axis,a distance from the origin to a first point on the fourth curve with a zenith angle θ
  
  is r(θ
  
  ),rectangular coordinates (x, z) and polar coordinates (θ
  
  , r) of the first point in the x-z plane satisfy relations given in the following Eqs. 11 and 12,
  x(θ
  
  )=r(θ
  
  )sin θ
  
  (Eq.
  
       11)
  z(θ
  
  )=r(θ
  
  )cos θ
  
  (Eq.
  
       12)the distance r(θ
  
  ) is given as Eq. 13 shown below, $\begin{matrix} r (θ) = r (θ_{i}) \exp [\int_{θ_{i}}^{θ} \frac{- n_{5} \sin θ^{'}}{n_{4} - n_{5} \cos θ^{'}} \partial θ^{'}] & (Eq . 13) \end{matrix}$ wherein θ
  
  _iis the zenith angle of a second point on the first curve, r(θ
  
  _i) is a corresponding distance from the origin to the second point, the zenith angle θ
  
  ranges from a minimum θ
  
  ₁not smaller than zero to a maximum θ
  
  ₂smaller than π
  
  /2, the first lens surface constitute a part of a boundary between a first medium having a refractive index n₁and a second medium having a refractive index n₂, the refractive index n₁of the first medium is smaller than the refractive index n₂of the second medium (n₁<
  
  n₂), a first curve defined as a collection of intersections between the x-z plane and the first lens surface is symmetric about the z-axis, a distance from the origin to a third point on the first curve having the zenith angle θ
  
  is R(θ
  
  ), rectangular coordinates (X, Z) and polar coordinates (θ
  
  , R) of the third point in the x-z plane satisfy the following relations given in Eqs. 14 and 15,
  X(θ
  
  )=R(θ
  
  )sin θ
  
  (Eq.
  
       14)
  Z(θ
  
  )=R(θ
  
  )cos θ
  
  (Eq.
  
       15) the distance R(θ
  
  ) is given as Eq. 16 shown below, $\begin{matrix} R (θ) = R (θ_{i}) \exp [\int_{θ_{i}}^{θ} \frac{- n_{1} \sin θ^{'}}{n_{2} - n_{1} \cos θ^{'}} \partial θ^{'}] & (Eq . 16) \end{matrix}$ said R(θ
  
  _i) is a distance from the origin to a fourth point on the first curve having the zenith angle θ
  
  _i, a second curve defined as a collection of intersections between the x-z plane and the second lens surface is a circular arc around the origin with a radius R_B, a third curve defined as a collection of intersections between the x-z plane and the third lens surface is a circular arc around the origin with a radius r_F, the radius R_Bof the second curve is not larger than the shortest distance to the third points on the first curve (R_B≦
  
  min(R(θ
  
  ))), the radius r_Fof the third curve is not smaller than the longest distance to the first points on the fourth curve (r_F≧
  
  max(r(θ
  
  ))), the radius R_Bof the second curve is not smaller than the radius r_Fof the third curve (R_B≧
  
  r_F), the space between the first lens surface and the second lens surface is filled with the second medium having the refractive index n₂, the space between the second lens surface and the third lens surface is filled with a third medium having a refractive index n₃, and the space between the third lens surface and the fourth lens surface is filled with a fourth medium having the refractive index n₄.
- View Dependent Claims (28, 29, 30, 31)
- - 28. The optical component of claim 27, wherein the refractive indices n₂, n₃and n₄of the second, the third and the fourth medium are all the same (n₂=n₃=n₄).
  - 29. The optical component of claim 27, wherein the first lens surface, the second lens surface, the third lens surface and the fourth lens surface are rotationally symmetric about the z-axis.
  - 30. The optical component of claim 27, wherein the first lens surface, the second lens surface, the third lens surface and the fourth lens surface have translational symmetry along the y-axis of the rectangular coordinate system.
  - 31. The optical component of claim 27, wherein the first aspherical refractive surface, the second lens surface, the third lens surface and the fourth lens surface are rotationally symmetric about the x-axis of the rectangular coordinate system.

32. An optical component comprising:
- a first lens surface; and
  
  a second lens surface, whereinthe first lens surface constitutes a part of a boundary between a first medium having a refractive index n₀and a second medium having a refractive index n₁,the second lens surface constitutes a part of a boundary between the second medium and a third medium having a refractive index n₂,a first curve is defined as a collection of intersections between the x-z plane of a rectangular coordinate system and the first lens surface, whereinan origin of the rectangular coordinate system is located within the third medium,and the z-axis of the rectangular coordinate system passes through the origin and a point on the first lens surface,the said first curve is symmetric about the z-axis,a second curve is defined as a collection of intersections between the x-z plane and the second lens surface, and the second curve is a straight line segment perpendicular to the z-axis,a distance from the origin to the second curve is f_B,rectangular coordinates (x, z) and polar coordinates (θ
  
  , r) of a first point on the second curve in the x-z plane with a zenith angle θ
  
  is given as Eqs. 17 and 18,
  x(θ
  
  )=f_Btan θ
  
  (Eq.
  
       17)
  z(θ
  
  )=f_B
  
  (Eq.
  
       18)the zenith angle θ
  
  ranges from a minimum θ
  
  ₁not smaller than zero to a maximum θ
  
  ₂smaller than π
  
  /2,rectangular coordinates (X, Z) of a second point on the first curve corresponding to the first point on the second curve satisfy relations given in Eqs. 19 and 20,
  X(θ
  
  )=f_Btan θ
  
  +L(θ
  
  )sin δ
  
  (θ
  
  )
  
  (Eq.
  
       19)
  Z(θ
  
  )=f_B+L(θ
  
  )cos δ
  
  (θ
  
  )
  
  (Eq.
  
       20)said L(θ
  
  ) is the distance from the first point to the second point, and said L(θ
  
  ) is given as Eq. 21, $\begin{matrix} L (θ) = \frac{1}{F (θ)} {L (θ_{i}) + \int_{θ_{i}}^{θ} F (θ^{'}) B (θ^{'}) \partial θ^{'}} & (Eq . 21) \end{matrix}$ said L(θ
  
  _i) is the distance from a third point on the second curve with θ
  
  =θ
  
  _ito the corresponding fourth point on the first curve, said F(θ
  
  ) is given as Eq. 22,
  F(θ
  
  )=exp[∫
  
  _θ_i^θA(θ
  
  ′
  
  )dθ
  
  ′
  
  ]
  
  (Eq.
  
       22) said A(θ
  
  ) is given as Eq. 23, $\begin{matrix} A (θ) = \frac{n_{o}}{\sqrt{n_{1}^{2} - n_{2}^{2} \sin^{2} θ}} \frac{n_{2}^{2} \sin θcos θ}{n_{1}^{2} - n_{o} \sqrt{n_{1}^{2} - n_{2}^{2} \sin^{2} θ}} & (Eq . 23) \end{matrix}$ said B(θ
  
  ) is given as Eq. 24, and $\begin{matrix} B (θ) = - \frac{f_{B}}{\cos^{2} θ} \frac{n_{1} n_{2} \sin θ}{n_{1}^{2} - n_{o} \sqrt{n_{1}^{2} - n_{2}^{2} \sin^{2} θ}} & (Eq . 24) \end{matrix}$ and said δ
  
  (θ
  
  ) is given as Eq. 25. $\begin{matrix} δ (θ) = \tan^{- 1} [\frac{n_{2} \sin θ}{\sqrt{n_{1}^{2} - n_{2}^{2} \sin^{2} θ}}] & (Eq . 25) \end{matrix}$
- View Dependent Claims (33, 34, 35)
- - 33. The optical component of claim 32, wherein the first lens surface and the second lens surface are rotationally symmetric about the z-axis.
  - 34. The optical component of claim 32, wherein the first lens surface and the second lens surface have translational symmetry along the y-axis of the rectangular coordinate system.
  - 35. The optical component of claim 32, wherein the first lens surface and the second lens surface are rotationally symmetric about the x-axis of the rectangular coordinate system.

36. An optical component comprising:
- a first lens surface; and
  
  a second lens surface, whereinthe first lens surface constitutes a part of a boundary between a first medium having a refractive index n₀and a second medium having a refractive index n₁,the second lens surface constitutes a part of a boundary between the second medium and a third medium having a refractive index n₂,a first curve is defined as a collection of intersections between the x-z plane of a rectangular coordinate system and the first lens surface, whereinthe origin of the rectangular coordinate system is located within the third medium, and the z-axis of the rectangular coordinate system passes through the origin and a point on the first lens surface,the said first curve is a straight line segment perpendicular to the z-axis,a second curve is defined as a collection of intersections between the x-z plane and the second lens surface, and the second curve is symmetric about the z-axis,the distance from the origin to the first curve is z_o,rectangular coordinates (x, z) and polar coordinates (θ
  
  , r) of a first point on the first curve in the x-z plane with a zenith angle θ
  
  satisfy relations given in Eqs. 26 and 27,
  x(θ
  
  )=z_otan θ
  
  (Eq.
  
       26)
  z(θ
  
  )=z(θ
  
  )≡
  
  z_o
  
  (Eq.
  
       27)the zenith angle θ
  
  ranges from the minimum θ
  
  ₁not smaller than zero to the maximum θ
  
  ₂smaller than π
  
  /2,rectangular coordinates (X, Z) of a second point on the second curve corresponding to the first point on the first curve satisfy relations given in Eqs. 28 and 29,
  X(θ
  
  )=z_otan θ
  
  −
  
  L(θ
  
  )sin δ
  
  (θ
  
  )
  
  (Eq.
  
       28)
  Z(θ
  
  )=z_o−
  
  L(θ
  
  )cos δ
  
  (θ
  
  )
  
  (Eq.
  
       29)said L(θ
  
  ) is the distance from the first point to the second point, and said L(θ
  
  ) is given as Eq. 30, $\begin{matrix} L (θ) = \frac{1}{F (θ)} {L (θ_{i}) + \int_{θ_{i}}^{θ} F (θ^{'}) B (θ^{'}) \partial θ^{'}} & (Eq . 30) \end{matrix}$ said L(θ
  
  _i) is the distance from a third point on the first curve with θ
  
  =θ
  
  _ito the corresponding fourth point on the second curve,said F(θ
  
  ) is given as Eq. 31,
  F(θ
  
  )=exp[∫
  
  _θ_i^θA(θ
  
  ′
  
  )dθ
  
  ′
  
  ]
  
  (Eq.
  
       31)said A(θ
  
  ) is given as Eq. 32, $\begin{matrix} A (θ) = \frac{n_{2}}{\sqrt{n_{1}^{2} - n_{o}^{2} \sin^{2} θ}} \frac{n_{o}^{2} \sin θ \cos θ}{n_{1}^{2} - n_{2} \sqrt{n_{1}^{2} - n_{o}^{2} \sin^{2} θ}} & (Eq . 32) \end{matrix}$ said B(θ
  
  ) is given as Eq. 33, $\begin{matrix} B (θ) = \frac{z_{o}}{\cos^{2} θ} \frac{n_{1} n_{o} \sin θ}{n_{1}^{2} - n_{2} \sqrt{n_{1}^{2} - n_{o}^{2} \sin^{2} θ}} & (Eq . 33) \end{matrix}$ and said δ
  
  (θ
  
  ) is given as Eq. 34. $\begin{matrix} δ (θ) = \tan^{- 1} [\frac{n_{o} \sin θ}{\sqrt{n_{1}^{2} - n_{o}^{2} \sin^{2} θ}}] & (Eq . 34) \end{matrix}$
- View Dependent Claims (37, 38, 39)
- - 37. The optical component of claim 36, wherein the first lens surface and the second lens surface are rotationally symmetric about the z-axis.
  - 38. The optical component of claim 36, wherein the first lens surface and the second lens surface have translational symmetry along the y-axis of the rectangular coordinate system.
  - 39. The optical component of claim 36, wherein the first lens surface and the second lens surface are rotationally symmetric about the x-axis of the rectangular coordinate system.

40. An optical component comprising:
- a first aspherical refractive surface; and
  
  a second aspherical refractive surface, whereinthe first aspherical refractive surface constitutes a part of a boundary between a first medium having a refractive index n₀and a second medium having a refractive index n₁,the second aspherical refractive surface constitutes a part of a boundary between the second medium and a third medium having a refractive index n₂,a second curve is defined as a collection of intersections between the x-z plane of a rectangular coordinate system and the second aspherical refractive surface, whereinthe origin of the rectangular coordinate system is located within the third medium, and the z-axis of the rectangular coordinate system passes through the origin and a point on the second aspherical refractive surface,the said first curve is symmetric about the z-axis,a distance from the origin to the first point on the second curve with a zenith angle θ
  
  is r(θ
  
  ),rectangular coordinates (x, z) and polar coordinates (θ
  
  , r) of the first point in the x-z plane satisfy relations shown in the following Eqs. 35 and 36,
  x(θ
  
  )=r(θ
  
  )sin θ
  
  (Eq.
  
  35)
  z(θ
  
  )=r(θ
  
  )cos θ
  
  (Eq.
  
  36)the distance r(θ
  
  ) is given as Eq. 37 below, $\begin{matrix} r (θ) = r (θ_{i}) \exp [\int_{θ_{i}}^{θ} \frac{- n_{1} \sin (δ - θ^{'})}{n_{1} \cos (δ - θ^{'})} \partial θ^{'}] & (Eq . 37) \end{matrix}$ said θ
  
  _iis a zenith angle of a second point on the first curve, said r(θ
  
  _i) is a distance from the origin to the second point, said δ
  
  is an arbitrary function of the zenith angle θ
  
  of the first point (δ
  
  =δ
  
  (θ
  
  )), the zenith angle θ
  
  ranges from a minimum θ
  
  ₁not smaller than zero to a maximum θ
  
  ₂smaller than π
  
  /2, *a first curve is defined as collection of intersections between the x-z plane and the first aspherical refractive surface, and the first curve is symmetric about the z-axis, rectangular coordinates (X, Z) of a third point on the first curve corresponding to the first point on the second curve satisfy relations shown in the following Eqs. 38 to 40, $\begin{matrix} X (θ) = r (θ) \sin θ + L (θ) \sin δ (θ) & (Eq . 38) \\ Z (θ) = r (θ) \cos θ + L (θ) \cos δ (θ) & (Eq . 39) \\ L (θ) = L (θ_{i}) + \int_{θ_{i}}^{θ} [\frac{n_{2} r (θ^{'}) \sin (δ - θ^{'})}{n_{1} \cos (δ - θ^{'}) - n_{2}}] \partial θ^{'} & (Eq . 40) \end{matrix}$ said L(θ
  
  ) is a distance from the first point to the third point, said L(θ
  
  _i) is a distance from the second point to a fourth point on the first curve corresponding to the second point.
- View Dependent Claims (41, 42, 43, 44, 45, 46, 47)
- - 41. The optical component of claim 40, wherein the first aspherical refractive surface and the second aspherical refractive surface are rotationally symmetric about the z-axis.
  - 42. The optical component of claim 40, wherein the first aspherical refractive surface and the second aspherical refractive surface have translational symmetry along the y-axis of the rectangular coordinate system.
  - 43. The optical component of claim 40, wherein the first aspherical refractive surface and the second aspherical refractive surface are rotationally symmetric about the x-axis of the rectangular coordinate system.
  - 44. The optical component of claim 40, wherein said θ
    - ₁is zero, said δ
      
      (θ
      
      ) has a relation shown in Eq. 41,
45. The optical component of claim 40, wherein said θ
- ₁is zero, said δ
  
  (θ
  
  ) has a relation shown in Eq. 42, $\begin{matrix} δ (θ) = (\frac{δ}{\tan θ_{2}}) \tan θ & (Eq . 42) \end{matrix}$ and said δ
  
  ₂is a value of δ
  
  corresponding to the said θ
  
  ₂(δ
  
  ₂=δ
  
  (θ
  
  ₂)).
46. The optical component of claim 40, wherein said θ
- ₁is zero and said δ
  
  (θ
  
  ) has a relation shown in Eq. 43, $\begin{matrix} δ (θ) = 2 \tan^{- 1} [\frac{\tan \frac{δ_{2}}{2}}{\tan θ_{2}} \tan θ] & (Eq . 43) \end{matrix}$ and said δ
  
  ₂is a value of δ
  
  corresponding to the said θ
  
  ₂(δ
  
  ₂=δ
  
  (θ
  
  ₂)).
47. The optical component of claim 40, wherein said θ
- ₁is zero, said δ
  
  (θ
  
  ) has a relation shown in Eq. 44, $\begin{matrix} δ (θ) = \sin^{- 1} [\frac{\sin δ_{2}}{\tan θ_{2}} \tan θ] & (Eq . 44) \end{matrix}$ and said δ
  
  ₂is a value of δ
  
  corresponding to the said δ
  
  ₂(δ
  
  ₂=δ
  
  (θ
  
  ₂)).

48. An optical component comprising:
- a first aspherical refractive surface; and
  
  a second aspherical refractive surface, whereinthe first aspherical refractive surface constitutes a part of a boundary between a first medium having a refractive index n₀and a second medium having a refractive index n₁,the second aspherical refractive surface constitutes a part of a boundary between the second medium and a third medium having a refractive index n₂,a second curve is defined as a collection of intersections between the x-z plane of a rectangular coordinate system and the second aspherical refractive surface, whereinthe origin of the rectangular coordinate system is located within the third medium, and a z-axis of the rectangular coordinate system passes through the origin and a point on the second aspherical refractive surface,the said second curve is symmetric about the z-axis,a distance from the origin to a first point on the second curve with a zenith angle θ
  
  is r(θ
  
  ),rectangular coordinates (x, z) and polar coordinates (θ
  
  , r) of the first point in the x-z plane satisfy relations shown in the following Eqs. 45 and 46,
  x(θ
  
  )=r(θ
  
  )sin θ
  
  (Eq.
  
       45)
  z(θ
  
  )=r(θ
  
  )cos θ
  
  (Eq.
  
       46)the distance r(θ
  
  ) is given as Eq. 47 below, $\begin{matrix} r (θ) = r (θ_{i}) \exp [\int_{θ_{i}}^{θ} \frac{- n_{1} \sin (δ - θ^{'})}{n_{1} \cos (δ - θ^{'}) - n_{2}} \partial θ^{'}] & (Eq . 47) \end{matrix}$ said θ
  
  _iis a zenith angle of a second point on the first curve, said r(θ
  
  _i) is a distance from the origin to the second point, the zenith angle θ
  
  ranges from a minimum θ
  
  ₁not smaller than zero to a maximum θ
  
  ₂smaller than π
  
  /2, a first curve is defined as a collection of intersections between the x-z plane and the first aspherical refractive surface, and the first curve is symmetric about the z-axis, rectangular coordinates (X, Z) of a third point on the first curve corresponding to the first point on the second curve satisfy relations shown in the following Eqs. 48 to 50, $\begin{matrix} X (θ) = r (θ) \sin θ + L (θ) \sin δ (θ) & (Eq . 48) \\ Z (θ) = r (θ) \cos θ + L (θ) \cos δ (θ) & (Eq . 49) \\ L (θ) = \frac{1}{F (θ)} {L (θ_{i}) + \int_{θ_{i}}^{θ} F (θ^{'}) B (θ^{'}) \partial θ^{'}} & (Eq . 50) \end{matrix}$ said L(θ
  
  ) is a distance from the first point to the third point, said L(θ
  
  _i) is a distance from the second point to a fourth point on the first curve corresponding to the second point, said F(θ
  
  ) is given as Eq. 51,
  F(θ
  
  )=exp[∂
  
  _θ_i^θA(θ
  
  ′
  
  )dθ
  
  ′
  
  ]
  
  (Eq.
  
       51) said A(θ
  
  ) is given as Eq. 52, $\begin{matrix} A (θ) = - \frac{n_{o} \sin (β - δ)}{n_{1} - n_{o} \cos (β - δ)} \frac{\partial δ}{\partial θ} & ^{*} (Eq . 52) \end{matrix}$ said B(θ
  
  ) is given as Eq. 53, $\begin{matrix} B (θ) = - \frac{\begin{matrix} n_{o} n_{1} \sin (β - δ) + \\ n_{1} n_{2} \sin (δ - θ) + n_{2} n_{o} \sin (θ - β) \end{matrix}}{{n_{1} \cos (δ - θ) - n_{2}} {n_{o} \cos (β - δ) - n_{1}}} r (θ) & (Eq . 53) \end{matrix}$ said β
  
  is an arbitrary function of the zenith angle θ
  
  (β
  
  =β
  
  (θ
  
  )), and said δ
  
  (θ
  
  ) takes an arbitrary value between θ and
  
  β
  
  (θ
  
  ).
- View Dependent Claims (49, 50, 51, 52, 53, 54, 55, 56, 57)
- - 49. The optical component of claim 48, wherein the first aspherical refractive surface and the second aspherical refractive surface are rotationally symmetric about the z-axis.
  - 50. The optical component of claim 48, wherein the first aspherical refractive surface and the second aspherical refractive surface have translational symmetry along the y-axis of the rectangular coordinate system.
  - 51. The optical component of claim 48, wherein the first aspherical refractive surface and the second aspherical refractive surface are rotationally symmetric about a x-axis of the rectangular coordinate system.
  - 52. The optical component of claim 48, wherein said η
    - ₁is zero, said β
      
      (θ
      
      ) has a relation shown in Eq. 54,
53. The optical component of claim 48, wherein said θ
- ₁is zero, said β
  
  (θ
  
  ) has a relation shown in Eq. 55, $\begin{matrix} β (θ) = (\frac{β_{2}}{\tan θ_{2}}) \tan θ & (Eq . 55) \end{matrix}$ and said β
  
  ₂is a value of β
  
  corresponding to the said β
  
  ₂(β
  
  ₁=β
  
  (θ
  
  ₂)).
54. The optical component of claim 48, wherein said θ
- ₁is zero, and the β
  
  (θ
  
  ) has a relation given as Eq. 56, $\begin{matrix} β (θ) = 2 \tan^{- 1} [\frac{\tan \frac{β_{2}}{2}}{\tan θ_{2}} \tan θ] & (Eq . 56) \end{matrix}$ and said β
  
  ₂is a value of β
  
  corresponding to the said θ
  
  ₂(β
  
  ₂=β
  
  (θ
  
  ₂)).
55. The optical component of claim 48, wherein said θ
- ₁is zero, said β
  
  (θ
  
  ) has a relation shown in Eq. 57, $\begin{matrix} β (θ) = \sin^{- 1} [\frac{\sin β_{2}}{\tan θ_{2}} \tan θ] & (Eq . 57) \end{matrix}$ and said β
  
  ₂is a value of β
  
  corresponding to the said θ
  
  ₂(β
  
  ₂=β
  
  (θ
  
  ₂)).
56. The optical component of claim 48, wherein said δ
- (θ
  
  ) is given as Eq. 58. $\begin{matrix} δ (θ) = \frac{θ + β (θ)}{2} & (Eq . 58) \end{matrix}$
57. The optical component of claim 48, wherein said δ
- (θ
  
  ) is given as Eq. 59,
  δ
  
  (θ
  
  )=θ
  
  +c{β
  
  (θ
  
  )−
  
  θ
  
  }
  
  (Eq.
  
  59)and said c is a real number larger than 0 and smaller than 1.

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Current Assignee
Nanophotonics Ltd.
Original Assignee
Nanophotonics Ltd.
Inventors
Kweon, Gyeong-Il

Granted Patent

US 7,830,617 B2
Time in Patent Office

Days
Field of Search
US Class Current

359/708
CPC Class Codes

G02B 3/02 with non-spherical faces G0...

OPTICAL COMPONENTS INCLUDING LENS HAVING AT LEAST ONE ASPHERICAL REFRACTIVE SURFACE

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OPTICAL COMPONENTS INCLUDING LENS HAVING AT LEAST ONE ASPHERICAL REFRACTIVE SURFACE

First Claim

1 Assignment

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0 Petitions

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Accused Products

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Abstract

Citations

57 Claims

Specification

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