Method of and systems for measuring eccentricity of an aspherical lens surface

• US 5,844,670 A
• Filed: 07/29/1996
• Issued: 12/01/1998
• Est. Priority Date: 07/28/1995
• Status: Expired due to Fees

• Current Assignee: Ricoh Company Limited
• Original Assignee: Ricoh Company Limited
• Inventors: Takai, Masayuki, Morita, Nobuhiro
• Primary Examiner(s): Font, Frank G.
• Assistant Examiner(s): Smith, Zandra V.
• Application Number:
  US08/681,822
• Time in Patent Office: 855 Days
• Field of Search: 356/124, 356/127
• US Class Current: 356/124
• CPC Class Codes: G01B 11/255 for measuring radius of curvature measuring diameter G01B11/08
• CPC Class Codes: G01M 11/0221 by determining the optical axis or position of lenses
• CPC Class Codes: G01M 11/0242 by measuring geometrical properties or aberrations
• CPC Class Codes: G01M 11/025 by determining the shape of the object to be tested measuring contours or curvatures by optical means G01B11/24

Abstract

Accurate yet cost-effective measurement methods and systems determine eccentricity at a particular location of the aspherical lens surface. Since an aspherical lens generally has varying degrees of curvature along the aspherical surface, the eccentricity at the selected location on the aspherical lens surface provides precise information in determining the quality of a certain type of an aspherical lens component. Furthermore, these improved methods and systems according to the current invention are applicable to measure eccentricity of a selected aspherical lens surface in a complex lens assembly containing a plurality of aspherical lens components.

Claims

1. A method of measuring eccentricity of an aspherical lens using an image-forming optical subsystem, the aspherical lens having a substantially spherical portion near a paraxial region and an aspherical portion, comprising the steps of:

a) placing the aspherical lens in a holder so that a first optical axis near the paraxial region of the aspherical lens is substantially in alignment with a predetermined central axis of the holder, said step a) further comprising;

1) measuring an amount of misalignment using said first image for correcting the alignment;

2) moving the aspherical lens according to said measured amount; and

3) repeating said steps

     1) and

     2) until a predetermined level of said alignment is reached;

b) forming a first image through the substantially spherical portion using the image-forming optical subsystem whose second optical axis substantially coincides with said first optical axis;

c) storing a first set of coordinates of a center of said first image formed in said step b);

d) forming a second image through a predetermined position in the aspherical portion using the image-forming optical subsystem,

e) storing a second set of coordinates of a center of said second image formed in said step d); and

f) determining an amount of eccentricity of the aspherical lens based upon said first set and said second set of said coordinates stored in said steps c) and e).

2. The method of measuring eccentricity of an aspherical lens according to claim 1 wherein the aspherical lens converges light rays.

3. The method of measuring eccentricity of an aspherical lens according to claim 1 wherein the aspherical lens diverges light rays.

4. The method of measuring eccentricity of an aspherical lens according to claim 1 wherein the aspherical lens has a first lens surface and a second lens surface, at least one of said first lens surface and said second lens surface being aspherical.

5. The method of measuring eccentricity of an aspherical lens according to claim 1 wherein said alignment is manually performed by minimizing a size of said first image formed in said step b).

6. The method of measuring eccentricity of an aspherical lens according to claim 1 wherein said alignment is manually performed by placing the aspherical lens at a predetermined location in the holder.

7. The method of measuring eccentricity of an aspherical lens according to claim 1 wherein said step b) is performed by placing a focal point of the image-forming optical subsystem at a para-axial curvature center of the substantially spherical portion of the aspherical lens, the image-forming optical subsystem projecting substantially parallel light rays towards the aspherical lens.

8. The method of measuring eccentricity of an aspherical lens according to claim 7 wherein said step d) further comprises steps of:

j) determining a first distance from said para-axial curvature center to an aspherical curvature center for said predetermined position of said aspherical portion; and

k) placing said focal point of the image-forming optical subsystem at said aspherical curvature center.

9. The method of measuring,eccentricity of an aspherical lens according to claim 8 wherein said first distance is designated by Δ

R and is determined by

Δ

R={1/Z'"'"'(H)}H+Z (H)-R₀ aspherical

where R₀ is a radius of the substantially spherical portion, Z'"'"'(H) being a derivative of Z(H), Z being a function expressing the aspherical lens surface, H being a constant indicating said predetermined location of said aspherical portion.

10. The method of measuring eccentricity of an aspherical lens according to claim 9 wherein said step k) is accomplished by moving the holder along said first optical axis by said first distance.

11. The method of measuring eccentricity of an aspherical lens according to claim 9 wherein said step k) is accomplished by moving at least a part of the image-forming optical subsystem along said second optical axis by said first distance.

12. The method of measuring eccentricity of an aspherical lens according to claim 9 wherein the image-forming optical subsystem includes a first lens having a first focal length of f₁, a second lens having a second focal length of f₂ and a CCD camera having a pixel size of γ

.

13. The method of measuring eccentricity of an aspherical lens according to claim 12 wherein said step f) further comprises additional steps of:

l) determining a second distance D between said first set of coordinates defined as (X₁, Y₁) and said second set of coordinates defined as (X₂, Y₂) based upon a following relation;

##EQU9## where R₀ is a first radius of the substantially spherical region of the aspherical lens surface whose eccentricity is to be determined, R₁ being a second radius of said curvature opposite to the aspherical lens surface, t being a thickness of the aspherical lens; and

m) determining said eccentricity in a shift amount radian θ

based upon a following relation;

space="preserve" listing-type="equation">θ

=sin.sup.-1 {(f.sub.1 ·

D·

γ

)/2·

f.sub.2 ·

Δ

R)}·

180·

60/π

.

14. The method of measuring eccentricity of an aspherical lens according to claim 13 wherein said eccentricity is also determined in a tilt amount φ

based upon a following relation;

space="preserve" listing-type="equation">φ

=tan.sup.-1 {Y.sub.2 -(R.sub.0 -R.sub.1 -t+Δ

R)·

Y.sub.1 /(R.sub.0 -R.sub.1 -t)}/{X.sub.2 -(R.sub.0 -R.sub.1 -t+Δ

R)·

X.sub.1 /(R.sub.0 -R.sub.1 -t)}.sup.2 !.

15.

15. The method of measuring eccentricity of an aspherical lens according to claim 12 wherein said step c) further comprises additional steps of:

n) rotating the aspherical lens about said predetermined central axis of the holder to a predetermined set of angles; and

o) storing a first additional set of coordinates of an image formed at each of said predetermined angles, said first additional sets of coordinates being designated as X_1i, Y_1i where i ranges from 0 through n-1;

wherein said step e) further comprises additional steps of;

p) rotating the aspherical lens about said predetermined central axis of the holder to said predetermined set of said angles; and

q) storing a second additional set of coordinates of an image formed at each of said predetermined angles, said second additional sets of coordinates being designated as x_2i, y_2i where i ranges from 0 through n-1; and

wherein said step f) further includes an additional step r) adjusting said eccentricity based upon said first additional sets and said second additional sets of said coordinates so as to substantially minimize an error component contributed by the placement of the aspherical lens during said step k).

16. The method of measuring eccentricity of an aspherical lens according to claim 15 wherein said step r) further comprises additional steps of:

s) determining a third distance T between said first additional sets of coordinates designated by (X_1i, Y_1i) and said second additional sets of coordinates designated by (X_2i, Y_2i) based upon said first distance designated by Δ

R and a following relation;

##EQU10## where the above as well as the following averaged values are taken from 0 to n-1, X_c1 =(Σ

X_1i)/n, X_C2 =(σ

X_2i)/n,Y_c1 =(σ

Y_1i)/n, Y_C2 =(σ

Y_2i)/n, R₀ is a first radius of the substantially spherical portion of the aspherical lens surface whose eccentricity is to be determined, R₁ is a second radius of the substantially spherical portion opposite to the aspherical lens surface, and t is a thickness of the aspherical lens; and

t) determining said eccentricity in a corrected shift amount radian θ

'"'"' based upon a following relation;

space="preserve" listing-type="equation">θ

'"'"'=sin.sup.-1 {(f.sub.1 ·

T·

γ

)/2·

f.sub.2 Δ

R)}·

180·

60/π

.

17. The method of measuring eccentricity of an aspherical lens according to claim 16 wherein said eccentricity is also determined in a corrected tilt amount φ

'"'"' based upon a following relation;

##EQU11##

18. The method of measuring eccentricity of an aspherical lens according to claim 12 wherein said step c) further comprises additional steps of:

u) marking one location on an edge of the aspherical lens;

v) rotating the aspherical lens to predetermined angles after said marked position is initially positioned at a predetermined starting angle;

w) storing a first additional set of coordinates of an image formed at each of said predetermined angles, said first additional sets of coordinates being-designated as X'"'"'_1i, Y'"'"'_1i where i ranging from 0 through n-1;

x) rotating the aspherical lens to said predetermined angles after said marked position is rotated 180 degrees from said predetermined starting angle;

y) storing a second additional set of coordinates of an image formed at each of said predetermined angles, said second additional sets of coordinates being designated as X"_1i, Y"_1i where i ranging from 0 through n-1;

wherein said step e) further comprises additional steps of;

I) rotating the aspherical lens to predetermined angles after said marked position is initially positioned at said predetermined starting angle;

II) storing a third additional set of coordinates of an image formed at each of said predetermined angles, said third additional sets of coordinates being designated as X'"'"'_2i, Y'"'"'_2i where i ranging from 0 through n-1;

III) rotating the aspherical lens to said predetermined angles after said marked position is rotated 180 degrees from said predetermined starting angle;

IV) storing a fourth additional set of coordinates of an image formed at each of said predetermined angles, said fourth additional sets of coordinates being designated as X"_2i, Y"_2i where i ranging from 0 through n-1; and

V) adjusting said eccentricity based upon said first additional sets, said second additional sets, said third additional sets and said fourth additional sets of said coordinates so as to substantially minimize an error component contributed by an misalignment between the holder and the image-forming optical subsystem.

19. The method of measuring eccentricity of an aspherical lens according to claim 18 wherein said step V) further comprises additional steps of:

VI) determining X_1i =(X'"'"'_1i -X"_1i)/2 and Y_1i =(Y'"'"'_1i-Y"1i) /2 for every i from 0 to n-1; and

VII) determining X_2i =(X'"'"'_2i -X"_2i)/2 and Y_2i =(Y'"'"'_2i -Y"_2i)/2 for every i from 0 to n-1.

20. The method of measuring eccentricity of an aspherical lens according to claim 19 wherein said step V) further comprises additional steps of:

VIII) determining a third distance T between (X_1i, Y_1i) and (X_2i, Y_2i) based upon said first distance designated by Δ

R and a following relation;

##EQU12## where the above as well as the following averaged values are taken from 0 to n-1, X_c1 =(Σ

X_1i)/n, X_C2 =(Σ

X_2i)/n, Y_c1 =(Σ

Y_1i)/n, Y_C2 =(Σ

Y_2i)/n, R₀ is a first radius of the substantial aspherical portion of the aspherical lens surface whose eccentricity is to be determined, R₁ is a second radius of the substantial aspherical portion opposite to the aspherical lens surface, and t is a thickness of the aspherical lens; and

IX) determining said eccentricity in a corrected shift amount radian θ

" based upon a following relation;

space="preserve" listing-type="equation">θ

"=sin.sup.-1 {(f.sub.1 ·

T·

γ

)/2·

f.sub.2 Δ

R)}·

180·

60/π

.

21. The method of measuring eccentricity of an aspherical lens according to claim 20 wherein said eccentricity is also determined in a corrected tilt amount φ

" based upon a following relation;

##EQU13##

22. The method of measuring eccentricity of an aspherical lens according to claim 1 wherein said steps b), c,) d) and e) are simultaneously performed.

23. The method of measuring eccentricity of an aspherical lens according to claim 1 wherein said steps b), c), d) and e) are sequentially performed.

24. The method of measuring eccentricity of an aspherical lens according to claim 1 wherein said eccentricity is determined in terms of a shift amount, the shift amount being an angle formed between said first optical axis and a light ray incident upon said predetermined portion of the aspherical portion.

25. The method of measuring eccentricity of an aspherical lens according to claim 24 wherein said eccentricity is determined in terms of a tilt amount, the tilt amount being a direction of said shift amount.

26. A method of measuring eccentricity of a plurality of aspherical lens surfaces in a lens assembly using an image-forming optical subsystem, each of said aspherical lens surfaces having a substantially spherical portion near a paraxial region and an aspherical region, comprising the steps of:

a) placing the lens assembly in a holder so that a first optical axis of a first aspherical lens surface is substantially in alignment with a predetermined central axis of the holder;

b) adjusting said first aspherical lens surface for aligning said first optical axis with a second optical axis of the image-forming optical subsystem;

c) forming a first image through a first predetermined location of said aspherical portion of said first aspherical lens surface using the image-forming optical subsystem;

d) storing a first set of coordinates of a center of said first image formed in said step c) rotating the aspherical lens assembly about said predetermined central axis of the holder to a predetermined set of angles;

storing a first additional set of coordinates of said first image formed at each of said predetermined angles, said first additional sets of coordinates being designated as X_1i, Y_1i where i ranges from 0 through n-1;

e) forming a second image through a second predetermined location of said aspherical portion of a second aspherical lens surface using the image-forming optical subsystem;

f) storing a second set of coordinates of a center of said second image formed in said step e), rotating the aspherical lens assembly about said predetermined central axis of the holder to said predetermined set of said angles, storing a second additional set of coordinates of said second image formed at each of said predetermined angles, said second additional sets of coordinates being designated as X_2i, Y_2i where i ranges from 0 through n-1;

g) determining first eccentricity of said first aspherical lens surface and second eccentricity of said second aspherical lens surface based upon said first set and said second set of said coordinates stored in said steps d) and f), and

h'"'"') of adjusting said eccentricity based upon said first additional sets and said second additional sets of said coordinates so as to substantially minimize an error component contributed by the placement of the aspherical lens assembly.

27. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 26 wherein the image-forming optical subsystem projects substantially parallel light rays towards the aspherical lens and includes a first object lens having a focal length f₁, a second lens having a focal length f₂, a CCD camera having a pixel size of γ

.

28. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 27 wherein said step b) is performed by placing a focal point of the image-forming optical subsystem at a para-axial curvature center of the substantially spherical portion near the paraxial region.

29. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 28 wherein said step c) further comprises the steps of:

h) determining a first distance from said para-axial curvature center to an aspherical curvature center of said predetermined position of said aspherical portion; and

i) placing said focal point of the image-forming optical subsystem at said aspherical curvature center.

30. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 29 wherein said first distance is designated by Δ

R and is determined by

space="preserve" listing-type="equation">Δ

R={1/Z'"'"'(H)}H+Z(H)-R.sub.0

where R₀ is a radius of the substantially spherical portion and Z'"'"'(H) is a derivative of Z(H), Z being a function of H expressing a surface of the aspherical lens surface, H being a constant specifying said predetermined location of said aspherical portion.

31. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 29 wherein said step i) is accomplished by moving the holder along said first optical axis by said first distance.

32. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 29 wherein said step i) is accomplished by moving along said second optical axis at least a part of the image-forming optical subsystem by said first distance.

33. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 30 wherein said step e) further comprises the steps of:

j) determining a second distance between the first aspherical lens surface and a center of the object lens of the image-forming optical subsystem; and

k) placing the first object lens and the first aspherical lens surface at said second distance apart.

34. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 33 wherein said second distance is designated by Z and is determined by

35. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 33 wherein said step k) is accomplished by moving along said second optical axis the first object lens of the image-forming optical subsystem by said second distance.

36. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 33 wherein said step k) is accomplished by moving the holder along said first optical axis by said second distance.

37. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 34 wherein said step g) further comprises the steps of:

l) determining a shift amount ε

b of said second eccentricity of said second aspherical lens surface based upon said second set of said coordinates designated by (X_b, Y_b) and the following relation;

##EQU14## where ;

β

=f₂ /f₁, m being a transmissivity magnification factor of the first aspherical lens surface, ξ

being a predetermined coefficient for determining a shift amount of the second aspherical lens surface; and

m) determining a tilt amount of said second eccentricity of said second aspherical lens surface designated by θ

_b based upon said second set of said coordinates designated by (X_b, Y_b) and the following relation;

space="preserve" listing-type="equation">θ

.sub.b =tan.sup.-1 (X.sub.b /Y.sub.b)·

180/π

.

38. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 37 wherein said step g) further comprises the steps of:

n) preparing first intermediate values α

_X and α

_Y based upon the following relations;

space="preserve" listing-type="equation">α

.sub.X =sin.sup.-1 γ

·

X.sub.b /{2β

·

m(R.sub.b -R.sub.a -t)}!

space="preserve" listing-type="equation">α

.sub.Y =cos.sup.-1 γ

·

X.sub.b /{2β

·

m(R.sub.b -R.sub.a -t)}!;

o) preparing second intermediate values X_a'"'"' and Y_a'"'"' based upon said first intermediate values α

_X and α

_Y ;

space="preserve" listing-type="equation">X.sub.a'"'"' ={γ

/(2β

)}X.sub.a ·

cos α

.sub.X -Δ

R·

sin α

.sub.X

space="preserve" listing-type="equation">Y.sub.a'"'"' ={γ

/(2β

)}Y.sub.a ·

cos α

.sub.Y -Δ

R·

sin α

.sub.Y ;

p) determining a shift amount of said first eccentricity of said first aspherical lens surface designated by ε

_a based upon said second intermediate values and the following relation;

space="preserve" listing-type="equation">ε

.sub.a =sin.sup.-1 {√

(X.sub.a'"'"'.sup.2 +Y.sub.a'"'"'.sup.2)/Δ

R};

and

q) determining a tilt amount of said first eccentricity of said first aspherical lens surface designated by ε

_a based upon said second intermediate values and the following relation;

space="preserve" listing-type="equation">θ

.sub.a =tan.sup.-1 (Y.sub.a'"'"' /X.sub.b'"'"')·

180/π

.

39.

39. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 26 said steps c,) d), e) and f) are simultaneously performed.

40. The method of measuring eccentricity of a plurality of aspherical lens surfaces according to claim 26 said steps c,) d), e) and f) are sequentially performed.

41. A system for measuring eccentricity of an aspherical lens having a substantially spherical portion near a paraxial region and an aspherical portion, the aspherical lens having a first optical axis, comprising:

a lens holder having a predetermined central axis for positioning the aspherical lens so that the first optical axis of the aspherical lens is substantially in alignment with the predetermined central axis of the holder;

an image-forming optical portion located near said lens holder for forming an image through the aspherical lens, said image-forming optical portion having a second optical axis and being positioned with respect to said lens holder so that said second optical axis substantially coincides with said first optical axis;

an optical distance controller for controlling an optical distance between said lens holder and said image-forming optical portion, a first distance allowing said image-forming optical portion to form a first image through the substantially spherical portion, a second distance allowing said image-forming optical portion to form a second image through a predetermined position in the aspherical portion of the aspherical lens; and

an image-analysis portion for storing information related to said first image and said second image and determining eccentricity of the aspherical lens based upon said stored information.

42. The system for measuring eccentricity of an aspherical lens according to claim 41 wherein the aspherical lens converges light rays.

43. The system for measuring eccentricity of an aspherical lens according to claim 41 wherein the aspherical lens diverges light rays.

44. The system for measuring eccentricity of an aspherical lens according to claim 41 wherein the aspherical lens has a first lens surface and a second lens surface, at least one of said first lens surface and said second lens surface being aspherical.

45. The system for measuring eccentricity of an aspherical lens according to claim 41 wherein said lens holder further comprises an adjustment unit for moving the aspherical lens held in said holder in a predetermined direction.

46. The system for measuring eccentricity of an aspherical lens according to claim 41 wherein said image-forming optical portion further comprises a light source and at least one objective lens for projecting substantially parallel light rays towards the aspherical lens.

47. The system for measuring eccentricity of an aspherical lens according to claim 46 wherein said optical distance controller places a focal point of said objective lens at a para-axial curvature center of the substantially spherical portion of the aspherical lens at said first distance.

48. The system for measuring eccentricity of an aspherical lens according to claim 47 wherein said optical distance controller determines Δ

R for said second distance and is determined by

space="preserve" listing-type="equation">Δ

R={1/Z'"'"'(H)}H+Z(H)-R.sub.0

where R₀ is a radius of the substantially spherical portion, Z'"'"'(H) being a derivative of Z(H), Z being a function expressing the aspherical lens surface, H being a constant indicating said predetermined location of said aspherical portion.

49. The system for measuring eccentricity of an aspherical lens according to claim 47 wherein the image-forming optical portion further comprises a first lens having a first focal length of f₁, a second lens having a second focal length of f₂ and a CCD camera having a pixel size of γ

.

50. The system for measuring eccentricity of an aspherical lens according to claim 49 wherein said image-analysis portion stores said information including said first set of coordinates defined as (X₁, Y₁) for said first image and said second set of coordinates defined as (X₂, Y₂) for said second image.

51. The system for measuring eccentricity of an aspherical lens according to claim 50 wherein said image-analysis portion determines said eccentricity in a shift amount radian θ

based upon a following relation;

space="preserve" listing-type="equation">θ

=sin.sup.-1 {(f.sub.1 ·

D·

γ

)/2·

f.sub.2 ·

Δ

R)}·

180·

60/π

where a distance D between (X₁, Y₁) and (X₂, Y₂) is determined based upon a following relation;

##EQU15## where R₀ is a first radius of the substantially spherical region of the aspherical lens surface whose eccentricity is to be determined, R₁ being a second radius of said curvature opposite to the aspherical lens surface, t being a thickness of the aspherical lens.

52. The system for measuring eccentricity of an aspherical lens according to claim 51 wherein said image-analysis portion determines said eccentricity in a tilt amount φ

based upon a following relation;

space="preserve" listing-type="equation">φ

=tan.sup.-1 {Y.sub.2 -(R.sub.0 -R.sub.1 -t+Δ

R)·

Y.sub.1 /(R.sub.0 -R.sub.1 -t)}/{X.sub.2 -(R.sub.0 -R.sub.1 -t+Δ

R)·

X.sub.1 /(R.sub.0 -R.sub.1 -t)}!.

53. The system for measuring eccentricity of an aspherical lens according to claim 41 wherein said optical distance controller moves said lens holder along said first optical axis.

54. The system for measuring,eccentricity of an aspherical lens according to claim 41 wherein said optical distance controller moves at least a part of the image-forming optical portion along said second optical axis.

55. The system for measuring eccentricity of an, aspherical lens according to claim 41 wherein said optical distance controller further comprises a plurality of reticules located at various predetermined distances for forming a plurality of said images.

56. The system for measuring eccentricity of an aspherical lens according to claim 55 wherein said images are sequentially formed.

57. The system for measuring eccentricity of an aspherical lens according to claim 55 wherein said images are simultaneously formed.

58. The system for measuring eccentricity of an aspherical lens according to claim 41 wherein said eccentricity is determined in terms of a shift amount, the shift amount being an angle formed between said first optical axis and a light ray incident upon said predetermined portion of the aspherical portion.

59. The system for measuring eccentricity of an aspherical lens according to claim 41 wherein said eccentricity is determined in terms of a tilt amount, the tilt amount being a direction of said shift amount.

60. The system for measuring eccentricity of an aspherical lens according to claim 41 wherein said lens holder further comprises a rotation unit for rotating the aspherical lens about said predetermined central axis of said lens holder to a predetermined set of angles.

61. The system for measuring eccentricity of an aspherical lens according to claim 60 wherein said image-analysis portion stores a first additional set of coordinates of said first image formed at each of said predetermined angles, said first additional sets of coordinates being designated as X_1i, Y_1i where i ranges from 0 through n-1, said image-analysis portion also storing a second additional set of coordinates of said second image formed at each of said predetermined angles, said second additional sets of coordinates being designated as X_2i, Y_2i where i ranges from 0 through n-1, said image-analysis portion correcting said eccentricity based upon said first additional sets and said second additional sets of said coordinates so as to substantially minimize an error component contributed by the placement of the aspherical lens.

62. The system for measuring eccentricity of an aspherical lens according to claim 61 wherein said image-analysis portion determines said eccentricity in a corrected shift amount radian θ

'"'"' based upon a following relation;

space="preserve" listing-type="equation">θ

'"'"'=sin.sup.-1 {(f.sub.1 ·

T·

γ

)/2·

f.sub.2 ·

Δ

R)}·

180·

60/π

where a third distance T between (X_1i, Y_1i) and (X_2i, Y_2i) is based upon Δ

R and a following relation;

##EQU16## where the above as well as the following averaged values are taken from 0 to n-1, X_C1 =(Σ

X_1i)/n, X_C2 =(Σ

X_2i)/n, Y_C1 =(Σ

Y_1i)/n, Y_C2 =(Σ

Y_2i)/n, R₀ is a first radius of the substantially spherical portion of the aspherical lens surface whose eccentricity is to be determined, R₁ is a second radius of the substantially spherical portion opposite to the aspherical lens surface, and t is a thickness of the aspherical lens.

63. The system for measuring eccentricity of an aspherical lens according to claim 62 wherein said image-analysis portion also determines eccentricity in a corrected tilt amount φ

'"'"' based upon a following relation;

##EQU17##

64. A system for measuring eccentricity of a plurality of aspherical lens surfaces in a lens assembly using an image-forming optical subsystem, each of said aspherical lens surfaces having a substantially spherical portion near a paraxial region and an aspherical region, comprising:

a lens assembly holder having a predetermined central axis for placing the lens assembly in a holder so that a first optical axis of a first aspherical lens surface is substantially in alignment with the predetermined central axis of the holder;

an image-forming optical portion located near said lens holder for forming an image through the aspherical lens, said image-forming optical portion having a second optical axis and being positioned with respect to said lens holder so that said second optical axis substantially coincides with said first optical axis;

an optical distance controller for controlling an optical distance between said lens holder and said image-forming optical portion, a first distance allowing said image-forming optical portion to form a first image through a predetermined position in the aspherical portion of the first aspherical lens surface, a second distance allowing said image-forming optical portion to form a second image through a predetermined position in the aspherical portion of the second aspherical lens surface, a third distance allowing said image-forming optical portion to form a third image through the substantially spherical portion of the first aspherical lens surface; and

an image-analysis portion operationally connected to said image-forming optical portion for receiving information related to said first image and said second image and determining eccentricity of the aspherical lens based upon said stored information.

65. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 64 wherein the image-forming optical portion projects substantially parallel light rays towards the aspherical lens and includes a first object lens having a focal length f₁, a second lens having a focal length f₂, a CCD camera having a pixel size of γ

.

66. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 64 wherein said optical distance controller places a focal point of the image-forming optical portion at a para-axial curvature center of the substantially spherical portion of the first aspherical surface at said third distance.

67. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 64 wherein said optical distance controller determines said first distance Δ

R based upon the following relation;

space="preserve" listing-type="equation">Δ

R={1/Z'"'"'(H)}H+Z(H)-R.sub.0

where R₀ is a radius of the substantially spherical portion and Z'"'"'(H) is a derivative of Z(H), Z being a function of H expressing a surface of the aspherical lens surface, H being a constant specifying said predetermined location of said aspherical portion.

68. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 64 wherein said optical distance controller moves said lens assembly holder along said first optical axis by said first distance.

69. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 64 wherein said optical distance controller moves along said second optical axis at least a part of said image-forming optical portion by said first distance.

70. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 64 wherein said optical distance controller determines said second distance which is designated by Z based upon

71. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 70 wherein said optical distance controller moves along said second optical axis a portion of said image-forming optical portion by said second distance.

72. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 71 wherein said optical distance controller moves said lens assembly holder along said first optical axis by said second distance.

73. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 70 wherein said image-analysis portion stores information on said second image including a second set of said coordinates designated by (X_b, Y_b).

74. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 73 wherein said image-analysis unit determines a shift amount ε

_b of said second eccentricity of said second aspherical lens surface based upon (X_b, Y_b) and the following relation;

##EQU18## where β

=f₂ /f₁, m being a transmissivity magnification factor of the first aspherical lens surface, ξ

being a predetermined coefficient for determining a shift amount of the second aspherical lens surface.

75. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 74 wherein said image-analysis unit determines a tilt amount θ

_b of said second eccentricity of said second aspherical lens surface based upon (X_b, Y_b) and the following relation;

space="preserve" listing-type="equation">θ

.sub.b =tan.sup.-1 (X.sub.b /Y.sub.b)·

180/π

.

76. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 75 wherein said image-analysis unit determines a shift amount ε

_a of said first eccentricity of said first aspherical lens surface based upon the following relation;

space="preserve" listing-type="equation">ε

.sub.a =sin.sup.-1 {√

(X.sub.a'"'"'.sup.2 +Y.sub.a'"'"'.sup.2)/Δ

R}

where

space="preserve" listing-type="equation">α

.sub.X =sin.sup.-1 γ

·

X.sub.b /{2β

·

m(R.sub.b -R.sub.a -t)}!

space="preserve" listing-type="equation">α

.sub.Y =cos.sup.-1 γ

·

X.sub.b /{2β

·

m(R.sub.b -R.sub.a -t)}!

space="preserve" listing-type="equation">X.sub.a'"'"' ={γ

/(2β

)}X.sub.a ·

cos α

.sub.X -Δ

R·

sin α

.sub.X

space="preserve" listing-type="equation">Y.sub.a'"'"' ={γ

/(2β

)}Y.sub.a ·

cos α

.sub.Y -Δ

R·

sin α

.sub.Y.

77. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 76 wherein said image-analysis unit determines a tilt amount θ

_a of said first eccentricity of said first aspherical lens surface based upon the following relation;

space="preserve" listing-type="equation">θ

.sub.a =tan.sup.-1 (Y.sub.a'"'"' /X.sub.b'"'"')·

180/π

.

78.

78. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 64 said optical distance controller further comprises a plurality of reticules located at various predetermined distances for forming a plurality of said images.

79. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 78 wherein said image-analysis unit simultaneously receives said images.

80. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 78 wherein said image-analysis unit sequentially receives said images.

81. The system for measuring eccentricity of a plurality of aspherical lens surfaces according to claim 64 wherein said lens assembly holder further comprises a rotation unit for rotating the aspherical lens assembly about said predetermined central axis of said lens assembly holder to a predetermined set of angles.