Abstract

Ghost image analysis is of interest for optical designers as ghost images may degrade image quality in imaging systems. In a previous paper by Abd El-Maksoud and Sasian [Appl. Opt. 50, 2305 (2011) [CrossRef]  ], ghost image analysis for incoherent systems was evaluated using geometrical optics. Some criteria were presented to identify focused ghost images at the nominal image plane. The main goal of this paper is to provide a conceptual understanding of ghost image formation and its impact on the performance of imaging systems using wave theory and Fourier optics. To achieve this goal, a methodology is developed to model ghost images after considering diffraction effects. Expressions for the ghost diffraction point spread function and the ghost transfer function are presented. These functions are used to construct effective point spread and effective transfer functions. To provide insights on the developed theory, some simulation examples are provided and discussed.

© 2012 Optical Society of America

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  1. M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
    [CrossRef]
  2. J. D. Rogers, T. S. Tkaczyk, M. R. Descour, A. H. Kärkkäinen, and R. Richards-Kortum, “Removal of ghost images by using tilted element optical systems with polynomial surfaces for aberration compensation,” Opt. Lett. 31, 504–506 (2006).
    [CrossRef]
  3. J. Buchheister and L. Mueller, “Reflex free double pass objective due to reflective freeform surfaces,” Proc. SPIE 7100, 71000N (2008).
    [CrossRef]
  4. J. Buchheister and C. Weth, “Lens design with suppressed first order reflections,” Proc. SPIE 7652, 76522V (2010).
    [CrossRef]
  5. R. E. English, J. Miller, and J. Schweyen, “Ghost reflection analysis for the main laser of the national ignition facility,” Proc. SPIE 3482, 748–753 (1998).
    [CrossRef]
  6. J. L. Hendrix, J. Schweyen, J. Rowe, and G. Beer, “Ghost analysis visualization techniques for complex systems from the NIF final optics assembly,” Proc. SPIE 3492, 306–320 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. J.-C. Perrin, “Methods for rapid evaluation of the stray light in optical systems,” Proc. SPIE 5249, 392–399 (2004).
    [CrossRef]
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    [CrossRef]
  13. R. H. Abd El-Maksoud, “Ghost image analysis for optical systems,” Ph.D. dissertation (University of Arizona, 2009).
  14. R. H. Abd El-Maksoud and J. M. Sasian, “Paraxial ghost image analysis,” Proc. SPIE 7428, 742807 (2009).
    [CrossRef]
  15. R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
    [CrossRef]
  16. J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).
  17. V. Mahajan, Aberration Theory Made Simple (SPIE, 1991).
  18. ZEMAX optical design software, http://www.radiantzemax.com .

2011

2010

J. Buchheister and C. Weth, “Lens design with suppressed first order reflections,” Proc. SPIE 7652, 76522V (2010).
[CrossRef]

2009

R. H. Abd El-Maksoud and J. M. Sasian, “Paraxial ghost image analysis,” Proc. SPIE 7428, 742807 (2009).
[CrossRef]

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

2008

J. Buchheister and L. Mueller, “Reflex free double pass objective due to reflective freeform surfaces,” Proc. SPIE 7100, 71000N (2008).
[CrossRef]

2006

2004

J.-C. Perrin, “Methods for rapid evaluation of the stray light in optical systems,” Proc. SPIE 5249, 392–399 (2004).
[CrossRef]

2002

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

1999

J. L. Hendrix, J. Schweyen, J. Rowe, and G. Beer, “Ghost analysis visualization techniques for complex systems from the NIF final optics assembly,” Proc. SPIE 3492, 306–320 (1999).
[CrossRef]

1998

R. E. English, J. Miller, and J. Schweyen, “Ghost reflection analysis for the main laser of the national ignition facility,” Proc. SPIE 3482, 748–753 (1998).
[CrossRef]

1971

G. Smith, “Veiling glare due to reflections from component surfaces: the paraxial approximation,” Mod. Opt. 18, 815–827 (1971).
[CrossRef]

1970

A. G. Naylor, “Veiling glare due to multiple reflections between surfaces,” Can. J. Phys. 48, 2720–2724 (1970).
[CrossRef]

1949

1947

Abd El-Maksoud, R. H.

R. H. Abd El-Maksoud and J. Sasian, “Modeling and analyzing ghost images for incoherent optical systems,” Appl. Opt. 50, 2305–2315 (2011).
[CrossRef]

R. H. Abd El-Maksoud and J. M. Sasian, “Paraxial ghost image analysis,” Proc. SPIE 7428, 742807 (2009).
[CrossRef]

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

R. H. Abd El-Maksoud, “Ghost image analysis for optical systems,” Ph.D. dissertation (University of Arizona, 2009).

Abraham, V.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Anslyn, E. V.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Beer, G.

J. L. Hendrix, J. Schweyen, J. Rowe, and G. Beer, “Ghost analysis visualization techniques for complex systems from the NIF final optics assembly,” Proc. SPIE 3492, 306–320 (1999).
[CrossRef]

Buchheister, J.

J. Buchheister and C. Weth, “Lens design with suppressed first order reflections,” Proc. SPIE 7652, 76522V (2010).
[CrossRef]

J. Buchheister and L. Mueller, “Reflex free double pass objective due to reflective freeform surfaces,” Proc. SPIE 7100, 71000N (2008).
[CrossRef]

Crabtree, K.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Czajkowski, A.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Dawsey, M.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

de Leon, E.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Descour, M. R.

J. D. Rogers, T. S. Tkaczyk, M. R. Descour, A. H. Kärkkäinen, and R. Richards-Kortum, “Removal of ghost images by using tilted element optical systems with polynomial surfaces for aberration compensation,” Opt. Lett. 31, 504–506 (2006).
[CrossRef]

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Dupuis, R. D.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

English, R. E.

R. E. English, J. Miller, and J. Schweyen, “Ghost reflection analysis for the main laser of the national ignition facility,” Proc. SPIE 3482, 748–753 (1998).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Hendrix, J. L.

J. L. Hendrix, J. Schweyen, J. Rowe, and G. Beer, “Ghost analysis visualization techniques for complex systems from the NIF final optics assembly,” Proc. SPIE 3492, 306–320 (1999).
[CrossRef]

Irvin, R.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Kärkkäinen, A. H.

Kärkkäinen, A. H. O.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Kilic, B.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Kim, J.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Kim, Y.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Koshel, R. J.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Kudenov, M.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Liang, C.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Liu, Ron

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Madenci, E.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Mahajan, V.

V. Mahajan, Aberration Theory Made Simple (SPIE, 1991).

Miller, J.

R. E. English, J. Miller, and J. Schweyen, “Ghost reflection analysis for the main laser of the national ignition facility,” Proc. SPIE 3482, 748–753 (1998).
[CrossRef]

Mueller, L.

J. Buchheister and L. Mueller, “Reflex free double pass objective due to reflective freeform surfaces,” Proc. SPIE 7100, 71000N (2008).
[CrossRef]

Murray, A. E.

Nakazawa, T.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Namnabat, S.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Naylor, A. G.

A. G. Naylor, “Veiling glare due to multiple reflections between surfaces,” Can. J. Phys. 48, 2720–2724 (1970).
[CrossRef]

Orr, R. M.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Perrin, J.-C.

J.-C. Perrin, “Methods for rapid evaluation of the stray light in optical systems,” Proc. SPIE 5249, 392–399 (2004).
[CrossRef]

Primeau, B.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Rantala, J. T.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Richards-Kortum, R.

Richards-Kortum, R. R.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Richardson, S.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Rogers, J. D.

J. D. Rogers, T. S. Tkaczyk, M. R. Descour, A. H. Kärkkäinen, and R. Richards-Kortum, “Removal of ghost images by using tilted element optical systems with polynomial surfaces for aberration compensation,” Opt. Lett. 31, 504–506 (2006).
[CrossRef]

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Rowe, J.

J. L. Hendrix, J. Schweyen, J. Rowe, and G. Beer, “Ghost analysis visualization techniques for complex systems from the NIF final optics assembly,” Proc. SPIE 3492, 306–320 (1999).
[CrossRef]

Sasian, J.

Sasian, J. M.

R. H. Abd El-Maksoud and J. M. Sasian, “Paraxial ghost image analysis,” Proc. SPIE 7428, 742807 (2009).
[CrossRef]

Schul, R. J.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Schweyen, J.

J. L. Hendrix, J. Schweyen, J. Rowe, and G. Beer, “Ghost analysis visualization techniques for complex systems from the NIF final optics assembly,” Proc. SPIE 3492, 306–320 (1999).
[CrossRef]

R. E. English, J. Miller, and J. Schweyen, “Ghost reflection analysis for the main laser of the national ignition facility,” Proc. SPIE 3482, 748–753 (1998).
[CrossRef]

Smith, G.

G. Smith, “Veiling glare due to reflections from component surfaces: the paraxial approximation,” Mod. Opt. 18, 815–827 (1971).
[CrossRef]

Tiggis, C. P.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Tkaczyk, T. S.

Tuckerman, L. B.

Wang, L.

R. J. Koshel, V. Abraham, J. Kim, Ron Liu, S. Richardson, S. Namnabat, A. Czajkowski, R. H. Abd El-Maksoud, R. Irvin, T. Nakazawa, M. Kudenov, M. Dawsey, E. de Leon, L. Wang, K. Crabtree, R. M. Orr, B. Primeau, and Y. Kim, “Illumination system design in a project-based course,” Proc. SPIE 7423, 742305 (2009).
[CrossRef]

Weinstein, R. S.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Weth, C.

J. Buchheister and C. Weth, “Lens design with suppressed first order reflections,” Proc. SPIE 7652, 76522V (2010).
[CrossRef]

Willison, C. G.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

Appl. Opt.

Can. J. Phys.

A. G. Naylor, “Veiling glare due to multiple reflections between surfaces,” Can. J. Phys. 48, 2720–2724 (1970).
[CrossRef]

IEEE J. Quantum Electron.

M. R. Descour, A. H. O. Kärkkäinen, J. D. Rogers, C. Liang, R. S. Weinstein, J. T. Rantala, B. Kilic, E. Madenci, R. R. Richards-Kortum, E. V. Anslyn, R. D. Dupuis, R. J. Schul, C. G. Willison, and C. P. Tiggis, “Toward the development of miniaturized imaging systems for detection of pre-cancer,” IEEE J. Quantum Electron. 38, 122–130 (2002).
[CrossRef]

J. Opt. Soc. Am.

Mod. Opt.

G. Smith, “Veiling glare due to reflections from component surfaces: the paraxial approximation,” Mod. Opt. 18, 815–827 (1971).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Figures (16)

Fig. 1.
Fig. 1.

An-axis point object is imaged into focused nominal and defocused ghost images.

Fig. 2.
Fig. 2.

Formation of ghost images by Nikon camera D5000 with AF-S DX Zoom-Nikkor lens.

Fig. 3.
Fig. 3.

The i th ghost system is reduced into its cardinal points, entrance pupil, and exit pupil.

Fig. 4.
Fig. 4.

(a) Nominal and ghost system with the same magnification. (b) Equivalent optical system (not to scale).

Fig. 5.
Fig. 5.

Nominal and possible ghost layouts for two 4 f optical systems.

Fig. 6.
Fig. 6.

(a) Nominal spot diagram and (b) ghost spot diagram.

Fig. 7.
Fig. 7.

Field curvature plot for three wavelengths.

Fig. 8.
Fig. 8.

Nominal and ghost image irradiances of bright and faint point objects. “E,” “b,” and “f” refer to irradiance, bright, and faint, respectively.

Fig. 9.
Fig. 9.

Focused ghost at the nominal Gaussian image plane formed by incoherent system. f / g = 15 . (a) Nominal ghost irradiance PSFs. (b) Nominal, ghost, and effective OTFs.

Fig. 10.
Fig. 10.

Focused ghost at the nominal Gaussian image plane formed by incoherent system. f / g = 5 . (a) Nominal and ghost irradiance PSFs. (b) Nominal, ghost, and effective OTFs.

Fig. 11.
Fig. 11.

Focused ghost at the nominal Gaussian image plane formed by coherent system. f / w , g = 15 . (a) Nominal, ghost, and effective PSFs. (b) Nominal and effective coherent transfer functions.

Fig. 12.
Fig. 12.

Focused ghost at the nominal Gaussian image plane formed by coherent system. f / w , g = 5 . (a) Nominal, ghost, and effective PSFs. (b) Nominal and effective coherent transfer functions.

Fig. 13.
Fig. 13.

Defocused ghost image at the nominal Gaussian image plane formed by incoherent system. f / w , g = 15 , and W 020 , g = 3 λ . (a) Nominal and ghost PSFs. (b) Nominal, ghost, and effective OTFs.

Fig. 14.
Fig. 14.

Defocused ghost image at the nominal Gaussian image plane formed by incoherent system. f / w , g = 5 , and W 020 , g = 3 λ . (a) Nominal and ghost PSFs. (b) Nominal, ghost, and effective OTFs.

Fig. 15.
Fig. 15.

Ghost f / w , g = 15 , W 020 , g = 3 λ , W 020 , g = 6 λ , W 020 , n = 0.05 λ , W 040 , n = 0.5 λ . (a) Ghost on-axis aberration function. (b) Nominal, ghost, and effective OTFs.

Fig. 16.
Fig. 16.

f / w , g = 5 , W 020 , g = 3 λ , W 040 , g = 6 λ , W 020 , n = 0.05 λ , W 040 , n = 0.5 λ . (a)  OTF n , OTF g , and OTF e across frequency range 0 100 c / mm . (b)  OTF n , OTF g , and OTF e across frequency range 100 200 c / mm .

Tables (3)

Tables Icon

Table 1. First Set of Parameters for the Nominal System ( N ) and the Ghost System( G 3 , 2 )

Tables Icon

Table 2. Second Set of Parameters for the Nominal System ( N ) and the Ghost System ( G 3 , 2 )

Tables Icon

Table 3. Parameters for the Nominal and the Ghost Systems

Equations (21)

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u g , i ( x , y ) = PSF g , i ( x , y ) O g , i ( x , y ) ,
O g , i ( x , y ) = 1 | m g , i | O ( x m g , i , y m g , i ) ,
PSF g , i ( x , y ) = A g , i exp ( j k 2 L g , i ( x 2 + y 2 ) ) λ L g , i 𝒫 g , i ( x p , y p ) exp ( j 2 π λ L g , i ( x p x + y p y ) ) d x p d y p ,
PSF g , i ( x , y ) = t g , i λ L g , i 𝒫 g , i ( x p , y p ) exp ( j 2 π λ L g , i ( x p x + y p y ) ) d x p d y p ,
𝒫 g , i ( x p , y p ) = P g , i ( x p , y p ) exp ( j 2 π λ W g , i ( x p , y p ) ) ,
U g , i ( f x , f y ) = H g , i ( f x , f y ) I [ O g , i ( x , y ) ] ,
H g , i ( f x , f y ) = ( A g , i λ L g , i ) 𝒫 g , i ( λ L g , i f x , λ L g , i f y ) .
ν g , i = 1 2 λ f / g , i , w .
| u g , i ( x , y ) | 2 = | PSF g , i ( x , y ) | 2 | O g , i ( x , y ) | 2 ,
U g , i ( f x , f y ) U g , i * ( f x , f y ) = OTF g , i ( f x , f y ) { I [ O g , i ( x , y ) ] I [ O g , i * ( x , y ) ] } ,
OTF g , i ( f x , f y ) = H g , i ( f x , f y ) H g , i * ( f x , f y ) .
OTF g , i , nor ( f x , f y ) = OTF g , i ( f x , f y ) OTF g , i ( 0 , 0 ) = MTF g , i ( f x , f y ) exp ( j ϕ g , i ( f x , f y ) ) OTF g , i ( 0 , 0 ) ,
ν g , i = 1 λ f / g , i , w .
| u e ( x , y ) | 2 = | u n ( x , y ) | 2 + i u n * ( x , y ) u g , i ( x , y ) + i u n ( x , y ) u g , i * ( x , y ) + i j u g , i ( x , y ) u g , i * ( x , y ) .
U e ( f x , f y ) = H n ( f x , f y ) I [ O n ( x , y ) ] + i H g , i ( f x , f y ) ) I [ O g , i ( x , y ) ] .
PSF e ( x , y ) = PSF n ( x , y ) + PSF g , i ( x , y ) .
H e ( f x , f y ) = H n ( f x , f y ) + H g , i ( f x , f y ) .
| u e ( x , y ) | 2 = | u n ( x , y ) | 2 + i | u g , i ( x , y ) | 2 .
U e ( f x , f y ) U e * ( f x , f y ) = OTF n ( f x , f y ) { I [ O n ( x , y ) ] I [ O n * ( x , y ) ] } + i OTF g , i ( f x , f y ) { I [ O g , i ( x , y ) ] I [ O g , i * ( x , y ) ] } .
PSF e ( x , y ) = | PSF n ( x , y ) | 2 + | PSF g , i ( x , y ) | 2 .
OTF e ( f x , f y ) = OTF n ( f x , f y ) + OTF g , i ( f x , f y ) .

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