Abstract

In a previous paper [Proc. SPIE PSISDG0277-786X 7428, 742807 (2009)], a methodology was developed to model and analyze incoherent ghosts that are formed by two reflections in the paraxial regime. In this paper, we extend the previously developed methodology to model and analyze ghost images that are formed by N (even) reflections. Rather than dealing with ghosts as spots of light, we apply the concept that each ghost has a structure in the nonparaxial regime that depends on the optical system parameters. A methodology to determine the fourth-order ghost aberration function is developed. We present new key parameters for ghost image formation, namely the ghost sagittal and tangential image surfaces. An expression for the paraxial ghost image irradiance distribution of the point object at the nominal image plane is derived. Since focused ghosts are the most bothersome ghosts, tools are proposed to identify potential problematic ghosts. Simulation examples are provided and are used to validate the developed methodology.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. H. Smith, Camera Lenses: From Box Camera to Digital (SPIE, 2006).
  2. L. B. Tuckerman, “On the intensity of the light reflected from or transmitted through a pile of plates,” J. Opt. Soc. Am. 37, 818–819 (1947).
    [CrossRef] [PubMed]
  3. G. Smith,“Veiling glare due to reflections from component surfaces: the paraxial approximation,” J. Mod. Opt. 18, 815–827(1971).
    [CrossRef]
  4. A. E. Murray, “Reflected light and ghosts in optical systems,” J. Opt. Soc. Am. 39, 30–31 (1949).
    [CrossRef]
  5. A. G. Naylor, “Veiling glare due to multiple reflections between surfaces,” Can. J. Phys. 48, 2720–2724 (1970).
    [CrossRef]
  6. 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]
  7. 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] [PubMed]
  8. J.-C. Perrin, “Methods for rapid evaluation of the stray light in optical systems,” Proc. SPIE 5249, 392–399 (2004).
    [CrossRef]
  9. OpTaliX optical design software, http://www.optenso.com/optix/ex_ghost.html.
  10. R. E. Fischer, B. Tedic-Galib, and P. R. Yoder, Optical System Design, 2nd ed. (McGraw-Hill, 2008), Chap 24.
  11. R. H. Abd El-Maksoud and J. M. Sasian, “Paraxial ghost image analysis,” Proc. SPIE 7428, 742807 (2009).
    [CrossRef]
  12. R. H. Abd El-Maksoud, “Ghost image analysis for optical systems,” Ph.D. dissertation (University of Arizona, 2009).
  13. J. M. Sasian, College of Optical Sciences, University of Arizona, Tucson, Arizona (Lens Design, OPTI 517 course notes, 2006).
  14. V. N. Mahajan, Optical Imaging and Aberrations (SPIE, 1998), Part 1.
    [CrossRef]
  15. E. D. Avetta and A. R. Phillips, “Wide angle mapping camera lens,” Tech. Rep. AFAL-TR-70-125 (1970).

2009 (1)

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

2006 (1)

2004 (1)

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

2002 (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]

1971 (1)

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

1970 (1)

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

1949 (1)

1947 (1)

Abd El-Maksoud, R. H.

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

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

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]

Avetta, E. D.

E. D. Avetta and A. R. Phillips, “Wide angle mapping camera lens,” Tech. Rep. AFAL-TR-70-125 (1970).

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] [PubMed]

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]

Fischer, R. E.

R. E. Fischer, B. Tedic-Galib, and P. R. Yoder, Optical System Design, 2nd ed. (McGraw-Hill, 2008), Chap 24.

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]

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]

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. N.

V. N. Mahajan, Optical Imaging and Aberrations (SPIE, 1998), Part 1.
[CrossRef]

Murray, A. E.

Naylor, A. G.

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

Phillips, A. R.

E. D. Avetta and A. R. Phillips, “Wide angle mapping camera lens,” Tech. Rep. AFAL-TR-70-125 (1970).

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]

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] [PubMed]

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]

Sasian, J. M.

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

J. M. Sasian, College of Optical Sciences, University of Arizona, Tucson, Arizona (Lens Design, OPTI 517 course notes, 2006).

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]

Smith, G.

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

Smith, G. H.

G. H. Smith, Camera Lenses: From Box Camera to Digital (SPIE, 2006).

Tedic-Galib, B.

R. E. Fischer, B. Tedic-Galib, and P. R. Yoder, Optical System Design, 2nd ed. (McGraw-Hill, 2008), Chap 24.

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.

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]

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]

Yoder, P. R.

R. E. Fischer, B. Tedic-Galib, and P. R. Yoder, Optical System Design, 2nd ed. (McGraw-Hill, 2008), Chap 24.

Can. J. Phys. (1)

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

IEEE J. Quantum Electron. (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]

J. Mod. Opt. (1)

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

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Proc. SPIE (2)

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

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

Other (7)

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

J. M. Sasian, College of Optical Sciences, University of Arizona, Tucson, Arizona (Lens Design, OPTI 517 course notes, 2006).

V. N. Mahajan, Optical Imaging and Aberrations (SPIE, 1998), Part 1.
[CrossRef]

E. D. Avetta and A. R. Phillips, “Wide angle mapping camera lens,” Tech. Rep. AFAL-TR-70-125 (1970).

OpTaliX optical design software, http://www.optenso.com/optix/ex_ghost.html.

R. E. Fischer, B. Tedic-Galib, and P. R. Yoder, Optical System Design, 2nd ed. (McGraw-Hill, 2008), Chap 24.

G. H. Smith, Camera Lenses: From Box Camera to Digital (SPIE, 2006).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (23)

Fig. 1
Fig. 1

(left) Photo with ghosts. (right) Photo without ghosts.

Fig. 2
Fig. 2

Ghost image formation by a thick lens. Odd and even ghost generations are shown.

Fig. 3
Fig. 3

Modeling and analyzing ghosts’ algorithms.

Fig. 4
Fig. 4

Ghost layout generation flowchart for ghosts that are formed by four reflections.

Fig. 5
Fig. 5

Ghost and nominal image planes with respect to the ghost exit pupil.

Fig. 6
Fig. 6

Ghost tangential image surface.

Fig. 7
Fig. 7

Ghost image of an off-axis point object at the nominal image plane.

Fig. 8
Fig. 8

Ghost irradiance by the simulation model (dotted curve) and FRED (solid curve). (a) Ghost G 3 , 2 , (b) ghost G 2 , 1 , (c) ghost G 4 , 1 , (d) ghost G 3 , 1 , (e) ghost G 4 , 2 , and (f) ghost G 4 , 3 .

Fig. 9
Fig. 9

Irradiance distribution for ghosts G 4 , 2 , G 4 , 1 , G 3 , 2 , G 3 , 1 , G 3 , 2 at the nominal image plane.

Fig. 10
Fig. 10

Ghost irradiance point spread function for a biconvex lens and a glass plate after it.

Fig. 11
Fig. 11

The y axis represents the ghost back focal distance, the ghost rear principal plane location with respect to the rear vertex, and the ghost rear focal length. The x axis represents the number of reflections.

Fig. 12
Fig. 12

Paraxial ghost irradiance distribution at the nominal image plane of a biconvex lens for (a) ghost G 2 R , (b) ghost G 4 R , (c) ghost G 6 R , (d) ghost G 8 R , (e) ghost G 10 R .

Fig. 13
Fig. 13

The ghost tangential image surface intersects the ghost Gaussian image nominal image plane.

Fig. 14
Fig. 14

G 14 , 13 ghost layout and the ghost spot at half field of views of 0 ° , 12 ° , and 21 ° .

Fig. 15
Fig. 15

Wavefront error for the G 14 , 13 ghost at half field of views of 0 ° , 12 ° , and 21 ° . Maximum scale is 200 waves (wavelength is 0.588 μm ).

Fig. 16
Fig. 16

Ghost ( G 14 , 13 ) spot diagrams at the nominal image plane for nine field angles. Units are in micrometers.

Fig. 17
Fig. 17

Ghost ( G 4 , 2 ) layout for four field angles ( 0 ° , 9.9 ° , 12.1 ° , and 20 ° ).

Fig. 18
Fig. 18

Ghost ( G 4 , 2 ) tangential and sagittal image surfaces intersecting the nominal image plane at two fields. The maximum field is 20 ° .

Fig. 19
Fig. 19

Ghost ( G 4 , 2 ) spot diagrams at the nominal image plane for four field angles. Units are in micrometers.

Fig. 20
Fig. 20

Ghost ( G 4 , 2 , 4 , 3 ) tangential and sagittal image surfaces intersecting the nominal image plane at two fields. The maximum field is 20 ° .

Fig. 21
Fig. 21

Ghost ( G 4 , 2 , 4 , 3 ) spot diagrams at the nominal image plane for four field angles. Units are in micrometers.

Fig. 22
Fig. 22

Ghost ( G 4 , 2 , 4 , 3 , 4 , 3 ) tangential and sagittal image surfaces. The maximum field is 20 ° .

Fig. 23
Fig. 23

Ghost ( G 4 , 2 , 4 , 3 , 4 , 3 ) spot diagrams at the nominal image plane for four field angles. Units are in micrometers.

Tables (1)

Tables Icon

Table 1 Nominal Layout Prescription

Equations (25)

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

First loop: k 1 = 2 , 3 , M , second loop:   k 2 = 1 , 2 , k 1 1.
First loop:   k 1 = 2 , 3 , M , second loop:   k 2 = 1 , 2 , k 1 1 , third loop:   k 3 = k 2 + 1 , k 2 + 2 , , M , fourth loop:   k 4 = 1 , 2 , , k 3 1.
First loop:   k 1 = 2 , 3 , M , second loop:   k 2 = 1 , 2 , k 1 1 , third loop:   k 3 = k 2 + 1 , k 2 + 2 , , M , fourth loop:   k 4 = 1 , 2 , , k 3 1 , fifth loop:   k 5 = k 4 + 1 , k 4 + 2 , , M , i th   loop:   k i = k i 1 + 1 , k i 1 + 2 , , M , ( i + 1 )   loop:   k i + 1 = 1 , 2 , k i 1 , ( N 1 )   loop:   k N 1 = k N 2 + 1 , k N 2 + 2 , , M , N th   loop:   k N = 1 , 2 , , k N - 1 - 1.
W g ( H g , ρ g , θ g ) = W g ( H g , ρ g , θ g ) + W 020 , g ( ρ g ) ,
W 020 , g = 1 2 ( 1 L g , n 1 L g ) a x p , g 2 .
W g ( H g , ρ g , θ g ) = W 040 , g ρ g 4 + W 131 , g H g ρ g 3 cos θ g + W 222 H g 2 ρ g 2 cos 2 θ g + W 220 , g H g 2 ρ g 2 + W 311 , g H g 3 ρ g cos θ g .
W g ( H g , ρ g , θ g ) = W 020 , g ρ g 2 + W 220 , g H g 2 ρ g 2 + W 222 , g H g 2 ρ g 2 cos 2 θ g .
ε y , g = 8 ( f / # w , g ) 2 [ 2 W 020 , g y p , g + 2 W 220 , g y p , g H g 2 + 2 W 222 , g y p , g H g 2 ] .
W 020 , g = W 220 , g H g 2 W 222 , g H g 2 .
δ Z t , g - 8 ( f / # w , g ) 2 ( W 220 , g + W 222 , g ) H g 2 ,
ε x , g = 8 ( f / # w , g ) 2 [ W 020 , g 2 x p , g + 2 W 220 , g x p , g H g 2 ] .
W 020 , g = W 220 , g H g 2 .
δ Z s , g - 8 ( f / # w , g ) 2 W 220 , g H g 2 .
ϕ en , g = I o Ω en , g ,
ϕ en , g = I o A en , g L g 2 ,
ϕ x p , g = T g ϕ en , g = T g I o A en L g 2 ,
E g , n ( y d ) = T g I o A en , g L g 2 A g , n rect ( y d y ¯ g , n | y g , n l y g , n u | ) ,
E g , n ( x d , y d ) = T g I o A en , g L g 2 A g , n circ ( ( x d x ¯ g , n ) 2 + ( y d y ¯ g , n ) 2 r g , n ) ,
IPSF g , n = g E g , n .
| y l g , n y u g , n | = 2 | y g , n | ,
IPSF g , n ( y d ) = g T g I o A en , g L g 2 A g , n rect ( y d y ¯ g , n 2 | y g , n | ) .
IPSF g , n ( x d , y d ) = g T g I o A en , g L g 2 A g , n circ ( ( x d x ¯ g , n ) 2 + ( y d y ¯ g , n ) 2 r g , n ) .
Δ Z g , n 8 ( f / # w , g ) 2 ( W 220 , g + W 222 , g ) H g 2 .
H g , t ± Δ Z g , n 8 ( f / # w , g ) 2 ( W 220 , g + W 222 , g ) .
H g , s ± Δ Z g , n 8 ( f / # w , g ) 2 W 220 , g .

Metrics