Imaging using a multifocal aspheric lens to obtain extended depth of field

• US 6,927,922 B2
• Filed: 12/18/2002
• Issued: 08/09/2005
• Est. Priority Date: 12/18/2001
• Status: Expired due to Term

• Current Assignee: University of Rochester
• Original Assignee: University of Rochester
• Inventors: George, Nicholas, Chi, Wanli
• Primary Examiner(s): Epps, Georgia
• Assistant Examiner(s): Harrington, Alicia M.
• Application Number:
  US10/324,255
• Publication Number:
  US 20030142877A1
• Time in Patent Office: 965 Days
• Field of Search: 359708-710, 359/721, 359/724, 359/725, 359742-743, 359558-560, 348/335, 348/360, 348/36, 348/207.1, 382/254, 382/255, 382/264
• US Class Current: 359/708
• CPC Class Codes: G02B 13/18 with lenses having one or more non-spherical faces, e.g. for reducing geometrical aberration G02B13/002 takes precedence
• CPC Class Codes: G02B 27/0075 with means for altering, e.g. increasing, the depth of field or depth of focus
• CPC Class Codes: G02B 3/04 with continuous faces that are rotationally symmetrical but deviate from a true sphere , e.g. so called "aspheric" lenses
• CPC Class Codes: G02B 3/10 Bifocal lenses; Multifocal lenses
• CPC Class Codes: H04N 23/55 Optical parts specially adapted for electronic image sensors; Mounting thereof
• CPC Class Codes: H04N 23/80 Camera processing pipelines; Components thereof

Abstract

A system for imaging with a circularly symmetric multifocal aspheric lens is provided for obtaining an extended depth of field. The system includes a camera for capturing an image of at least one object through a circularly symmetric multifocal aspheric lens to provide a blurred image, and a computer system for processing the captured blurred image to provide a recovered image of the object having an extended depth of field. The recovered image may be outputted to a display or other peripheral device. Processing of the blurred image utilizes one of inverse filtering, convolution matrix (e.g., edge sharpening matrix), or maximum entropy. The computer system performing image processing may be in the camera or represent a computer system external to the camera which receives the blurred image. The extended depth of field is characterized by the object being in focus over a range of distances in the recovered image.

Claims

1. A system for imaging one or more objects comprising:

means for capturing an image of at least one object through a circularly symmetric, multifocal aspheric lens which purposefully blurs the captured image; and

means for processing the captured blurred image in accordance with the blurring caused by said lens to provide a recovered image of the object having an extended depth of field.

2. The system according to claim 1 wherein said object represents a three-dimensional object which extends over a range of distance, and said extended depth of field is characterized by at least a substantial portion of the object being in focus in said recovered image over said range of distance.

3. The system according to claim 1 wherein said lens is characterized by the equation:

$\begin{array}{c}\mathrm{\varphi <br><br>}<br><br>\left(r\right)=<br><br>-\{\frac{2<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\left(\sqrt{r^2+t^2}-t\right)+\frac{\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\frac{R^2}{s_2-s_1}\\ <br><br>[\ln <br><br>\{2<br><br>\frac{s_2-s_1}{R^2}[\sqrt{r^2+{\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)}^2}+\\ <br><br>\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)]+1\}-\ln <br><br>\left(4<br><br>\frac{s_2-s_1}{R^2}<br><br>s_1+1\right)]\}\end{array}$

where, φ

(r) is the phase delay for radius r of the lens to within an arbitrary constant, said range is over distances s₁ through s₂, R is the outer radius of the lens, t is the distance from the plane where the lens is disposed to the plane of image capture by said capturing means, and λ

₀ is the free space wavelength.

4. The system according to claim 1 wherein said blurred image represents an array of pixel values, and said processing means applies a convolution matrix to said array of pixel values in accordance with the point spread function of said lens to provide said recovered image.

5. The system according to claim 4 wherein said convolution matrix is substantially an edge sharpening filter.

6. The system according to claim 1 wherein said means for processing the blurred image utilizes one of an inverse filter or maximum entropy to provide said recovered image.

7. The system according to claim 1 wherein said processing means is operative in accordance with the point spread function of the lens.

8. The system according to claim 1 wherein said processing means represents a computer system.

9. The system according to claim 1 further comprising means for outputting said recovered image.

10. The system according to claim 9 wherein said outputting means represents a display.

11. The system according to claim 1 wherein said lens is provided by one optical element.

12. The system according to claim 1 wherein said lens is provided by an optical system having multiple optical elements.

13. The system according to claim 1 wherein said capturing means comprises a camera which captures said blurred image through at least said lens, and said camera further comprises means for providing said blurred image to said processing means.

14. The system according to claim 13 wherein said providing means comprises removable memory in said camera for storing said blurred image, and said processing means comprises means for accessing said removable memory and retrieving said blurred image.

15. The system according to claim 13 wherein said providing means comprises one of a cable or optical connection between said camera and said processing means for transferring said blurred image to said processing means.

16. The system according to claim 13 wherein said camera represents a digital still or video camera.

17. The system according to claim 13 wherein said camera represents a digital video camera providing successive ones of said blurred images to said processing means, and said processing means processes each of said successive ones of said blurred images to provide corresponding successive recovered images.

18. The system according to claim 13 wherein said camera has at least one photodetector array to capture said blurred image through at least said lens.

19. The system according to claim 1 wherein said capturing means comprises a camera which captures said blurred image through at least said lens, and said camera further comprises said processing means to provide said recovered image from said blurred image.

20. The system according to claim 19 wherein said lens represents one or more optical elements.

21. The system according to claim 19 wherein said camera has a display for outputting said recovered image.

22. The system according to claim 19 wherein said camera represents a digital still or video camera.

23. The system according to claim 19 wherein said processing means represents a microprocessor-based system in said camera to provide said recovered image from said blurred image, and said camera has memory for storing said blurred image, said recovered image, or both said blurred image and recovered image.

24. The system according to claim 19 wherein said camera has at least one photodetector array to capture said blurred image through at least said lens.

25. The system according to claim 1 wherein said capturing means represents a camera for recording on film said blurred image captured through at least said lens, and means for digitizing one of a print or negative representing said blurred image recorded on said film to provided a digitized blurred image, in which said processing means operatives upon said digitized blurred image to provide said recovered image.

26. The system according to claim 1 wherein said capturing means comprises at least one CCD providing an array of pixels to record the blurred image, wherein each pixel has a size, and said imaging resolution of said system depends on said size of said pixel.

27. The system according to claim 1 wherein said lens is diffraction limited.

28. The system according to claim 1 wherein said lens provides two or more distances of operation of said system with respect to said capturing means.

29. The system according to claim 1 wherein said lens is characterized by a logarithmic phase function.

30. The system according to claim 1 wherein said means for processing the blurred image utilizes a Weiner Hellstrom inverse filter.

31. A system for imaging one or more objects comprising:

means for capturing an image of at least one object through a circularly symmetric, multifocal aspheric lens to provide a blurred image; and

means for processing the captured blurred image to provide a recovered image of the object having an extended depth of field, wherein said object represents a three-dimensional object which extends over a range of distance, and said extended depth of field is characterized by at least a substantial portion of the object being in focus in said recovered image over said range of distance, and said lens has a radius and annular portions of continuously varying focal length in accordance with said radius of the lens, in which said object at each distance in said range is in focus by at least one of said annular portions of said lens, and said object is blurred by other of said annular portions of said lens.

32. A system for imaging one or more objects comprising:

means for capturing an image of at least one object through a circularly symmetric, multifocal aspheric lens to provide a blurred image; and

means for processing the captured blurred image to provide a recovered image of the object having an extended depth of field, wherein said lens has a radius and said lens is multifocal by having a focal length which continuously varies with the radius of said lens.

33. A system for imaging one or more objects comprising:

means for capturing an image of at least one object through a circularly symmetric, multifocal aspheric lens to provide a blurred image; and

means for processing the captured blurred image to provide a recovered image of the object having an extended depth of field, wherein said lens is provided by an optical system having multiple optical elements, and said multiple optical elements represent a multi-focal phase plate and an objective lens.

34. The system according to claim 33 wherein angular field of view of capturing means is in accordance with the angular field of view of the objective lens.

35. A system for imaging one or more objects comprising:

means for capturing an image of at least one object through a circularly symmetric, multifocal aspheric lens to provide a blurred image; and

means for processing the captured blurred image to provide a recovered image of the object having an extended depth of field, wherein said lens is characterized by the equation;

$\hspace{1em}<br><br>\mathrm{\varphi <br><br>}<br><br>\left(r\right)=-\left\{\frac{2<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\left(\sqrt{r^2+t^2}-t\right)+\frac{\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\frac{R^2}{s_2-s_1}<br><br>\hspace{1em}<br><br>\hspace{1em}<br><br><br><br>\left[\ln <br><br>\left\{2<br><br>\frac{s_2-s_1}{R^2}\left[\sqrt{r^2+{\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)}^2}+\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)\right]+1\right\}-\ln <br><br>\left(4<br><br>\frac{s_2-s_1}{R^2}<br><br>s_1+1\right)\right]\right\}.$

where, φ

(r) is the phase delay for radius r of the lens to within an arbitrary constant, said range is over distances s₁ through s₂, R is the outer radius of the lens, t is the distance from the plane where the lens is disposed to the plane of image capture by said capturing means, and λ

₀ is the free space wavelength, and different ones of said lens characterized by φ

(r) are provided by changing the weighting of the ratio r/R to effect the rate of change of focal length of said lens with the radius of said lens.

36. A method for imaging one or more three-dimensional objects comprising the steps of:

imaging at least one object through a circularly symmetric aspheric lens to provide a blurred image purposefully blurred by said lens; and

processing said blurred image in accordance with the blurring caused by said lens to provide a recovered image of the object having an extended depth of field.

37. The method according to claim 36 wherein said object represents a three-dimensional object which extends over a range of distances, and said extended depth of field is characterized by at least a substantial portion of the object being in focus in said recovered image over said range of distances.

38. The method according to claim 36 wherein said lens is characterized by the equation:

$\mathrm{\varphi <br><br>}<br><br>\left(r\right)=-\left\{\frac{2<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\left(\sqrt{r^2+t^2}-t\right)+\frac{\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\frac{R^2}{s_2-s_1}[\text{\hspace{1em}<br><br>}<br><br>\ln <br><br>\left\{2<br><br>\frac{s_2-s_1}{R^2}\left[\sqrt{r^2+{\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)}^2}+\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)\right]+1\right\}-\ln <br><br>\left(4<br><br>\frac{s_2-s_1}{R^2}<br><br>s_1+1\right)]\right\}$

where, φ

(r) is the phase delay for radius r of the lens to within an arbitrary constant, said range is over distances s₁ through s₂, R is the outer radius of the lens, t is the distance from the plane where the lens is disposed to the plane of image capture by said capturing means, and λ

₀ is the free space wavelength.

39. The method according to claim 36 wherein said processing step utilizes a convolution matrix to provide the recovered image.

40. The method according to claim 39 wherein said convolution matrix represents an edge sharpening filter.

41. The method according to claim 36 wherein said processing step utilizes one of inverse filtering or maximum entropy to provide the recovered image.

42. The method according to claim 36 further comprising the step of displaying said recovered image.

43. The method according to claim 36 wherein said lens is provides by one or more optical elements.

44. The method according to claim 36 wherein said capturing step is carried out with the aid of a camera which records said blurred image through at least said lens.

45. The method according to claim 44 wherein said processing step is carried out in said camera.

46. The method according to claim 44 wherein said camera represents one of a digital still imaging camera or digital video camera.

47. The method according to claim 44 wherein said camera represents a digital video camera providing successive ones of said blurred images to said processing step, and said processing step processes each of said successive ones of said blurred images to provide corresponding successive recovered images.

48. The method according to claim 44 wherein said camera records on film said blurred image captured through at least said lens, and said method further comprises the step of digitizing one of a print or negative representing said blurred image recorded on said film to provided a digitized blurred image, in which said processing step is carried out using said digitized blurred image to provide said recovered image.

49. The method according to claim 44 wherein said lens provides two or more distances from said camera where said recovered image is in focus.

50. The method according to claim 36 wherein said processing step is carried out by a computer system.

51. The method according to claim 36 wherein said processing step is carried in accordance with the point spread function of the lens.

52. The method according to claim 36 wherein said capturing step utilizes at least one CCD providing an array of pixels to record the blurred image, wherein each pixel has a size, and said resolution of said system depends on said size of said pixel.

53. The method according to claim 36 wherein said lens is diffraction limited.

54. A method for imaging one or more three-dimensional objects comprising the steps of:

imaging at least one object through a circularly symmetric aspheric lens to provide a blurred image; and

processing said blurred image to provide a recovered image of the object having an extended depth of field, wherein said object represents a three-dimensional object which extends over a range of distances, and said extended depth of field is characterized by at least a substantial portion of the object being in focus in said recovered image over said range of distances, and said lens has a radius and annular portions of continuously varying focal length in accordance with said radius of the lens, in which said object at each distance in said range is in focus by at least one of said annular portions of said lens, and said object is blurred by other of said annular portions of said lens.

55. A method for imaging one or more three-dimensional objects comprising the steps of:

imaging at least one object through a circularly symmetric aspheric lens to provide a blurred image; and

processing said blurred image to provide a recovered image of the object having an extended depth of field, wherein said lens has a radius and said lens is multifocal by having a focal length which continuously varies with the radius of said lens.

56. A method for imaging one or more three-dimensional objects comprising the steps of:

imaging at least one object through a circularly symmetric aspheric lens to provide a blurred image; and

processing said blurred image to provide a recovered image of the object having an extended depth of field, wherein said lens represents an optical system having a multi-focal phase plate and an objective lens.

57. The method according to claim 56 wherein angular field of view of capturing means is in accordance with the angular field of view of the objective lens.

58. A smart camera comprising:

optics having circularly symmetric multiple focal lengths;

at least one detector array for capturing an image through said optics to provide a blurred image purposefully blurred by said optics; and

means for processing the captured blurred image in accordance with the blurring caused by said lens to provide a recovered image having an extended depth of field.

59. The camera according to claim 58 wherein said optics is provided by a circularly symmetric aspheric lens.

60. The camera according to claim 58 wherein said optics is provided by an objective lens and a circularly symmetric aspheric lens.

61. The camera according to claim 58 wherein said detector array represents one of a CCD array, CMOS array, or CID array.

62. The camera according to claim 58 wherein said lens has a point spread function, and said processing means operates upon said blurred image in accordance with said point spread function of said lens to provide said recovered image.

63. The camera accordingly to claim 62 wherein said lens is diffraction limited in accordance with said point spread function.

64. The camera according to claim 58 wherein said processing means utilizes one of an inverse filtering, convolution matrix, or maximum entropy upon the blurred image to provide the recovered image.

65. A smart camera comprising:

optics having circularly symmetric multiple focal lengths;

at least one detector array for capturing an image through said optics to provide a blurred image; and

means for processing the captured blurred image to provide a recovered image having an extended depth of field, wherein said optics is provided by an objective lens and a multi-focal phase plate.

66. An imaging system comprising:

means for capturing an image through a circularly symmetric, multifocal lens which purposefully blurs the image; and

means for processing the captured blurred image in accordance with the blurring caused by said lens to provide a recovered image having an extended depth of field.

67. A multifocal optical element comprising a body which is characterized by a logarithmic phase function, wherein said logarithm phase function is provided by φ

(r) in accordance with the equation;

$\mathrm{\varphi <br><br>}<br><br>\left(r\right)=-\left\{\frac{2<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\left(\sqrt{r^2+t^2}-t\right)+\frac{\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\frac{R^2}{s_2-s_1}[\text{\hspace{1em}<br><br>}<br><br>\ln <br><br>\left\{2<br><br>\frac{s_2-s_1}{R^2}\left[\sqrt{r^2+{\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)}^2}+\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)\right]+1\right\}-\ln <br><br>\left(4<br><br>\frac{s_2-s_1}{R^2}<br><br>s_1+1\right)]\right\}.$

where, φ

(r) is the phase delay for radius r of the lens to within an arbitrary constant, said range is over distances s₁ through s₂, R is the outer radius of the lens, t is the distance from the plane where the lens is disposed to the plane of image capture by said capturing means, and λ

₀ is the free space wavelength, and wherein different ones of said lens characterized by φ

(r) are provided by changing the weighting of the ratio r/R to effect the rate of change of focal length of said lens with the radius of said lens.

68. The optical element according to claim 67, wherein said body represents one of a lens and a phase-plate.

69. An imaging system comprising:

a circularly symmetric multifocal aspheric lens; and

means for capturing an image through said multifocal aspheric lens, wherein said lens has a radius and annular portions of continuously varying focal length in accordance with said radius of the lens.

70. An imaging system comprising:

a circularly symmetric multifocal aspheric lens; and

means for capturing an image through said multifocal aspheric lens, wherein said lens has a radius and said lens is multifocal by having a focal length which continuously varies with the radius of said lens.

71. The system according to claim 70 wherein said lens provides an extended depth of field.

72. The system according to claim 70 wherein said lens is characterized by the equation:

$\mathrm{\varphi <br><br>}<br><br>\left(r\right)=-\left\{\frac{2<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\left(\sqrt{r^2+t^2}-t\right)+\frac{\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\frac{R^2}{s_2-s_1}[\text{\hspace{1em}<br><br>}<br><br>\ln <br><br>\left\{2<br><br>\frac{s_2-s_1}{R^2}\left[\sqrt{r^2+{\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)}^2}+\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)\right]+1\right\}-\ln <br><br>\left(4<br><br>\frac{s_2-s_1}{R^2}<br><br>s_1+1\right)]\right\}.$

where, φ

(r) is the phase delay for radius r of the lens to within an arbitrary constant, said range is over distances s₁ through s₂, R is the outer radius of the lens, t is the distance from the plane where the lens is disposed to the plane of image capture by said capturing means, and λ

₀ is the free space wavelength.

73. The system according to claim 70 wherein said lens is provided by one optical element.

74. The system according to claim 70 wherein said lens is provided by an optical system having multiple optical elements.

75. The system according to claim 70 wherein said capturing means comprises at least one photodetector array to capture said image through at least said lens.

76. The system according to claim 70 wherein said lens is characterized by a logarithmic phase function.

77. An imaging system comprising:

a circularly symmetric multifocal aspheric lens; and

means for capturing an image through said multifocal aspheric lens, wherein said lens is characterized by the equation;

$\mathrm{\varphi <br><br>}<br><br>\left(r\right)=-\left\{\frac{2<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\left(\sqrt{r^2+t^2}-t\right)+\frac{\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\frac{R^2}{s_2-s_1}[\text{\hspace{1em}<br><br>}<br><br>\ln <br><br>\left\{2<br><br>\frac{s_2-s_1}{R^2}\left[\sqrt{r^2+{\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)}^2}+\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)\right]+1\right\}-\ln <br><br>\left(4<br><br>\frac{s_2-s_1}{R^2}<br><br>s_1+1\right)]\right\}.$

where, φ

(r) is the phase delay for radius r of the lens to within an arbitrary constant, said range is over distances s₁ through s₂, R is the outer radius of the lens, t is the distance from the plane where the lens is disposed to the plane of image capture by said capturing means, and λ

₀ is the free space wavelength, and wherein different ones of said lens characterized by φ

(r) are provided by changing the weighting of the ratio r/R to effect the rate of change of focal length of said lens with the radius of said lens.

78. An imaging system comprising:

a circularly symmetric multifocal aspheric lens; and

means for capturing an image through said multifocal aspheric lens, wherein said lens is provided by an optical system having multiple optical elements, and said multiple optical elements represent a multi-focal phase plate and an objective lens.

79. A method for imaging comprising the step of:

imaging through a circularly symmetric aspheric lens to provide an image having an extended depth of field, wherein said lens has a radius and annular portions of continuously varying focal length in accordance with said radius of the lens.

80. A method for imaging comprising the step of:

imaging through a circularly symmetric aspheric lens to provide an image having an extended depth of field, wherein said lens has a radius and said lens is multifocal by having a focal length which continuously varies with the radius of said lens.

81. The method according to claim 80 wherein said lens is characterized by the equation:

$\mathrm{\varphi <br><br>}<br><br>\left(r\right)=-\left\{\frac{2<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\left(\sqrt{r^2+t^2}-t\right)+\frac{\mathrm{\pi <br><br>}}{{\mathrm{\lambda <br><br>}}_0}<br><br>\frac{R^2}{s_2-s_1}[\text{\hspace{1em}<br><br>}<br><br>\ln <br><br>\left\{2<br><br>\frac{s_2-s_1}{R^2}\left[\sqrt{r^2+{\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)}^2}+\left(s_1+\frac{s_2-s_1}{R^2}<br><br>r^2\right)\right]+1\right\}-\ln <br><br>\left(4<br><br>\frac{s_2-s_1}{R^2}<br><br>s_1+1\right)]\right\}.$

where, φ

(r) is the phase delay for radius r of the lens to within an arbitrary constant, said range is over distances s₁ through s₂, R is the outer radius of the lens, t is the distance from the plane where the lens is disposed to the plane of image capture by said capturing means, and λ

₀ is the free space wavelength.