Abstract

An initial optical design method based on an iterative calculation of third-order aberration is presented to overcome the problems of the conventional method. The aberrations of each lens group in the optical system are calculated individually and iteratively under the constraint that aberrations of one group compensate for those of the other groups. The stabilities of initial design results have been confirmed and the iterative design method has been applied for the design of optical system with an external entrance pupil for imaging spectrometer. The designed lens corresponds to an objective lens with the aperture of F/1.5 and the focal length of 30 mm.

© 2014 Optical Society of America

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References

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  1. W. J. Smith, Modern Lens Design (McGraw-Hill, 1992).
  2. H. H. Hopkins, Wave Theory of Aberrations (Oxford University, 1950).
  3. R. Kingslake, Lens Design Fundamentals (Academic, 1978).
  4. H. A. Buchdahl, “Algebraic theory of the primary aberrations of the symmetrical optical system,” J. Opt. Soc. Am. A 38, 14–18 (1948).
    [CrossRef]
  5. H. H. Hopkins and V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
  6. L. N. Hazra, “Structural design of multicomponent lens systems,” Appl. Opt. 23, 4440–4443 (1984).
    [CrossRef]
  7. S. C. Park and J. U. Lee, “Rapid optical zoom system design using optimized lens modules,” J. Korean Phys. Soc. 32, 815–822 (1998).
  8. C. S. Rim, “Curvature linear equation of a two-mirror system with an infinite object distance,” J. Korean Phys. Soc. 46, 448–454 (2005).
  9. A. Miks, “Modification of the formulas for third-order aberration coefficients,” J. Opt. Soc. Am. A 19, 1867–1871 (2002).
    [CrossRef]
  10. K. M. Bystricky and P. R. Yoder, “An improved zoom lens with external entrance pupil,” Proc. SPIE 39, 299–304 (1973).
  11. H. W. Epps and S. S. Vogt, “Extremely achromatic f/1.0 all-spherical camera constructed for the high-resolution echelle spectrometer of the Keck telescope,” Appl. Opt. 32, 6270–6279 (1993).
    [CrossRef]
  12. D. J. Reiley and J. M. Sasian, “Optical design of a free-space photonic switching system,” Appl. Opt. 36, 4497–4504 (1997).
    [CrossRef]
  13. A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
    [CrossRef]
  14. R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
    [CrossRef]
  15. C. Feng and A. Ahmad, “Design and modeling of a compact imaging spectrometer,” Opt. Eng. 34, 3217–3221 (1995).
    [CrossRef]
  16. A. F. H. Goetz, J. B. Wellman, and W. L. Barnes, “Optical remote sensing of the Earth,” Proc. IEEE 73, 950–969 (1985).
    [CrossRef]
  17. C. T. Willoughby, M. A. Folkman, and M. A. Figueroa, “Application of hyperspectral imaging spectrometer systems to industrial inspection,” Proc. SPIE 2599, 264–272 (1996).
  18. F. D. Van Der Meer and S. M. De Jong, Imaging Spectrometry (Kluwer Academic, 2001).
  19. R. Glenn Sellar and G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. 44, 013602 (2005).
    [CrossRef]
  20. J. Choi, T. H. Kim, H. J. Kong, and J. U. Lee, “Zoom lens design for a novel imaging spectrometer that controls spatial and spectral resolution individually,” Appl. Opt. 45, 3430–3441 (2006).
    [CrossRef]
  21. W. J. Smith, “Objective of the petzval type with field flattener and three or more positive elements,” U. S. patent3,255,664 (14June1966).
  22. J. Tesar, “Using small glass catalogs,” Opt. Eng. 39, 1816–1821 (2000).
    [CrossRef]
  23. R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).
  24. CODE V Reference Manual, Version 9.40 (Optical Research Associates, 2003).

2006

2005

R. Glenn Sellar and G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. 44, 013602 (2005).
[CrossRef]

C. S. Rim, “Curvature linear equation of a two-mirror system with an infinite object distance,” J. Korean Phys. Soc. 46, 448–454 (2005).

2002

2000

J. Tesar, “Using small glass catalogs,” Opt. Eng. 39, 1816–1821 (2000).
[CrossRef]

1998

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

S. C. Park and J. U. Lee, “Rapid optical zoom system design using optimized lens modules,” J. Korean Phys. Soc. 32, 815–822 (1998).

1997

1996

C. T. Willoughby, M. A. Folkman, and M. A. Figueroa, “Application of hyperspectral imaging spectrometer systems to industrial inspection,” Proc. SPIE 2599, 264–272 (1996).

1995

C. Feng and A. Ahmad, “Design and modeling of a compact imaging spectrometer,” Opt. Eng. 34, 3217–3221 (1995).
[CrossRef]

1993

1985

A. F. H. Goetz, J. B. Wellman, and W. L. Barnes, “Optical remote sensing of the Earth,” Proc. IEEE 73, 950–969 (1985).
[CrossRef]

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef]

1984

1973

K. M. Bystricky and P. R. Yoder, “An improved zoom lens with external entrance pupil,” Proc. SPIE 39, 299–304 (1973).

1970

H. H. Hopkins and V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).

1948

H. A. Buchdahl, “Algebraic theory of the primary aberrations of the symmetrical optical system,” J. Opt. Soc. Am. A 38, 14–18 (1948).
[CrossRef]

Ahmad, A.

C. Feng and A. Ahmad, “Design and modeling of a compact imaging spectrometer,” Opt. Eng. 34, 3217–3221 (1995).
[CrossRef]

Aronsson, M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Barnes, W. L.

A. F. H. Goetz, J. B. Wellman, and W. L. Barnes, “Optical remote sensing of the Earth,” Proc. IEEE 73, 950–969 (1985).
[CrossRef]

Boreman, G. D.

R. Glenn Sellar and G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. 44, 013602 (2005).
[CrossRef]

Buchdahl, H. A.

H. A. Buchdahl, “Algebraic theory of the primary aberrations of the symmetrical optical system,” J. Opt. Soc. Am. A 38, 14–18 (1948).
[CrossRef]

Bystricky, K. M.

K. M. Bystricky and P. R. Yoder, “An improved zoom lens with external entrance pupil,” Proc. SPIE 39, 299–304 (1973).

Chippendale, B. J.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Choi, J.

Chovit, C. J.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Chrien, T. G.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

De Jong, S. M.

F. D. Van Der Meer and S. M. De Jong, Imaging Spectrometry (Kluwer Academic, 2001).

Eastwood, M. L.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Epps, H. W.

Faust, J. A.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Feng, C.

C. Feng and A. Ahmad, “Design and modeling of a compact imaging spectrometer,” Opt. Eng. 34, 3217–3221 (1995).
[CrossRef]

Figueroa, M. A.

C. T. Willoughby, M. A. Folkman, and M. A. Figueroa, “Application of hyperspectral imaging spectrometer systems to industrial inspection,” Proc. SPIE 2599, 264–272 (1996).

Fischer, R. E.

R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).

Folkman, M. A.

C. T. Willoughby, M. A. Folkman, and M. A. Figueroa, “Application of hyperspectral imaging spectrometer systems to industrial inspection,” Proc. SPIE 2599, 264–272 (1996).

Glenn Sellar, R.

R. Glenn Sellar and G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. 44, 013602 (2005).
[CrossRef]

Goetz, A. F. H.

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef]

A. F. H. Goetz, J. B. Wellman, and W. L. Barnes, “Optical remote sensing of the Earth,” Proc. IEEE 73, 950–969 (1985).
[CrossRef]

Green, R. O.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Hazra, L. N.

Hopkins, H. H.

H. H. Hopkins and V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).

H. H. Hopkins, Wave Theory of Aberrations (Oxford University, 1950).

Kim, T. H.

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, 1978).

Kong, H. J.

Lee, J. U.

J. Choi, T. H. Kim, H. J. Kong, and J. U. Lee, “Zoom lens design for a novel imaging spectrometer that controls spatial and spectral resolution individually,” Appl. Opt. 45, 3430–3441 (2006).
[CrossRef]

S. C. Park and J. U. Lee, “Rapid optical zoom system design using optimized lens modules,” J. Korean Phys. Soc. 32, 815–822 (1998).

Miks, A.

Olah, M. R.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Park, S. C.

S. C. Park and J. U. Lee, “Rapid optical zoom system design using optimized lens modules,” J. Korean Phys. Soc. 32, 815–822 (1998).

Pavri, B. E.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Rao, V. V.

H. H. Hopkins and V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).

Reiley, D. J.

Rim, C. S.

C. S. Rim, “Curvature linear equation of a two-mirror system with an infinite object distance,” J. Korean Phys. Soc. 46, 448–454 (2005).

Rock, B. N.

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef]

Sarture, C. M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Sasian, J. M.

Smith, W. J.

W. J. Smith, Modern Lens Design (McGraw-Hill, 1992).

W. J. Smith, “Objective of the petzval type with field flattener and three or more positive elements,” U. S. patent3,255,664 (14June1966).

Solis, M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Solomon, J. E.

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef]

Tadic-Galeb, B.

R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).

Tesar, J.

J. Tesar, “Using small glass catalogs,” Opt. Eng. 39, 1816–1821 (2000).
[CrossRef]

Van Der Meer, F. D.

F. D. Van Der Meer and S. M. De Jong, Imaging Spectrometry (Kluwer Academic, 2001).

Vane, G.

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef]

Vogt, S. S.

Wellman, J. B.

A. F. H. Goetz, J. B. Wellman, and W. L. Barnes, “Optical remote sensing of the Earth,” Proc. IEEE 73, 950–969 (1985).
[CrossRef]

Williams, O.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Willoughby, C. T.

C. T. Willoughby, M. A. Folkman, and M. A. Figueroa, “Application of hyperspectral imaging spectrometer systems to industrial inspection,” Proc. SPIE 2599, 264–272 (1996).

Yoder, P. R.

K. M. Bystricky and P. R. Yoder, “An improved zoom lens with external entrance pupil,” Proc. SPIE 39, 299–304 (1973).

Appl. Opt.

J. Korean Phys. Soc.

S. C. Park and J. U. Lee, “Rapid optical zoom system design using optimized lens modules,” J. Korean Phys. Soc. 32, 815–822 (1998).

C. S. Rim, “Curvature linear equation of a two-mirror system with an infinite object distance,” J. Korean Phys. Soc. 46, 448–454 (2005).

J. Opt. Soc. Am. A

H. A. Buchdahl, “Algebraic theory of the primary aberrations of the symmetrical optical system,” J. Opt. Soc. Am. A 38, 14–18 (1948).
[CrossRef]

A. Miks, “Modification of the formulas for third-order aberration coefficients,” J. Opt. Soc. Am. A 19, 1867–1871 (2002).
[CrossRef]

Opt. Acta

H. H. Hopkins and V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).

Opt. Eng.

C. Feng and A. Ahmad, “Design and modeling of a compact imaging spectrometer,” Opt. Eng. 34, 3217–3221 (1995).
[CrossRef]

R. Glenn Sellar and G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. 44, 013602 (2005).
[CrossRef]

J. Tesar, “Using small glass catalogs,” Opt. Eng. 39, 1816–1821 (2000).
[CrossRef]

Proc. IEEE

A. F. H. Goetz, J. B. Wellman, and W. L. Barnes, “Optical remote sensing of the Earth,” Proc. IEEE 73, 950–969 (1985).
[CrossRef]

Proc. SPIE

C. T. Willoughby, M. A. Folkman, and M. A. Figueroa, “Application of hyperspectral imaging spectrometer systems to industrial inspection,” Proc. SPIE 2599, 264–272 (1996).

K. M. Bystricky and P. R. Yoder, “An improved zoom lens with external entrance pupil,” Proc. SPIE 39, 299–304 (1973).

Remote Sens. Environ.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227–248 (1998).
[CrossRef]

Science

A. F. H. Goetz, G. Vane, J. E. Solomon, and B. N. Rock, “Imaging spectrometry for earth remote sensing,” Science 228, 1147–1153 (1985).
[CrossRef]

Other

W. J. Smith, Modern Lens Design (McGraw-Hill, 1992).

H. H. Hopkins, Wave Theory of Aberrations (Oxford University, 1950).

R. Kingslake, Lens Design Fundamentals (Academic, 1978).

F. D. Van Der Meer and S. M. De Jong, Imaging Spectrometry (Kluwer Academic, 2001).

R. E. Fischer and B. Tadic-Galeb, Optical System Design (McGraw-Hill, 2000).

CODE V Reference Manual, Version 9.40 (Optical Research Associates, 2003).

W. J. Smith, “Objective of the petzval type with field flattener and three or more positive elements,” U. S. patent3,255,664 (14June1966).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic diagram of a typical dispersive push broom imaging spectrometer.

Fig. 2.
Fig. 2.

Configuration of the desired Petzval lens. ci, ni, and d are the lens parameters: curvature, refractive index, and distance between groups, respectively. The subscript i denotes the ith surface.

Fig. 3.
Fig. 3.

(a) Curves of c5 versus c6 satisfying zero spherical aberration (black line) and zero astigmatism (gray line) of the rear group, in the first calculation step. (b) Curves of c1 versus c2 satisfying zero spherical aberration (black line) of the front group and compensating for the coma (gray line) of the rear group, in the first calculation step.

Fig. 4.
Fig. 4.

(a) Curves of c5 versus c6 and (b) curves of c1 versus c2 after fifth iterative calculation of third aberrations.

Fig. 5.
Fig. 5.

Convergence of iterative calculation of third order aberration in (a) linear scale and (b) its absolute value in log scale.

Fig. 6.
Fig. 6.

Stability test of astigmatism by external perturbation in (a) linear scale and (b) its absolute value in log scale. Arrow represents when the perturbation of external aberration is applied.

Fig. 7.
Fig. 7.

Ray tracing on the Petzval lens obtained from the aberration correction by using an iterative process.

Fig. 8.
Fig. 8.

Ray tracing on the optimized Petzval lens from initial design.

Fig. 9.
Fig. 9.

Modulation transfer function on the optimized design.

Fig. 10.
Fig. 10.

Field curves for the longitudinal spherical aberration, astigmatism, and distortion of the optimized design.

Tables (3)

Tables Icon

Table 1. Change in the Aberration Coefficients According to the Aberration Correction by Using an Iterative Process

Tables Icon

Table 2. Prescription Data of the Proposed Initial Designa

Tables Icon

Table 3. Prescription Data of the Optimized Objective Lens from the Initial Designa

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

SI=i(niIi)2hi(uiniui1ni1),
SII=i(niIi)(niI¯i)hi(uiniui1ni1),
SIII=i(niI¯i)2hi(uiniui1ni1),
SIV=H2ici(1ni11ni),
SV=i(I¯iIi)[{H2ci(1ni11ni)}+{(niI¯i)2hi(uiniui1ni1)}],
CL=i(niIi)hi(nsh,inl,ininsh,i1nl,i1ni1),
CT=i(niI¯i)hi(nsh,inl,ininsh,i1nl,i1ni1),
ni+1ui+1=niui+(nini+1)hi+1ci+1,
hi+1=hi+tiui,
niIi=niui+nihici,
ni+1u¯i+1=niu¯i+(nini+1)h¯i+1ci+1,
h¯i+1=h¯i+tiu¯i,
niI¯i=niu¯i+nih¯ici,

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