Abstract

We demonstrate an approach for improving the image quality for a projector system with a shape- programmable pupil, which could be generated by an illumination modular in which a digital micromirror device is embedded. Essentially, the shaped pupil from the illumination modulator is developed with a dynamically programmable approach to provide aberration compensation for the projection system. By analyzing the optical transfer function, the resolution limit of an imaging system with specific defocus, spherical aberration and coma are shown to be improved significantly with a binary-shaped pupil. It is found that the improvement of the projection quality could be characterized by the scale ratio of K=c/D, defined as the ratio between the resolution scale of structured light, c, and the size scale of the aperture stop, D. When K is equal to 0.05, the low-frequency components of the image could be improved, while if K is equal to 0.3, the imaging quality of the image at high-frequency components can be enhanced in a defocused system. Furthermore, as K ranges from 0.05 to 0.3, the imaging performance of the optical contrast could be enhanced in a projector system with large coefficients of defocused, spherical aberration and coma.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. H. Stupp and M. S. Brennesholtz, Projection Display(Wiley, 1999).
  2. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).
  3. M. Mino and Y. Okano, “Improvement in the OTF of a defocused optical system through the use of shaded apertures,” Appl. Opt. 10, 2219–2225 (1971).
    [CrossRef] [PubMed]
  4. J. Ojeda-Castaneda, P. Andrea, and A. Diaz, “Annular apodizers for low sensitivity to defocus and to spherical aberration,” Opt. Lett. 11, 487–489 (1986).
    [CrossRef] [PubMed]
  5. C. S. Chung and H. H. Hopkins, “Influence of nonuniform amplitude on the optical transfer function,” Appl. Opt. 28, 1244–1250 (1989).
    [CrossRef] [PubMed]
  6. J. A. Davis, J. C. Escalera, J. Campos, A. Marquez, and M. J. Yzuel, “Programmable axial apodizing and hyperresolving amplitude filters with a liquid-crystal spatial light modulator,” Opt. Lett. 24, 628–630 (1999).
    [CrossRef]
  7. A. Marquez, C. Iemmi, J. Campos, J. C. Escalera, and M. J. Yzuel, “Programmable apodizer to compensate chromatic aberration effects using a liquid-crystal spatial light modulator,” Opt. Express 13, 716–730 (2005).
    [CrossRef] [PubMed]
  8. J. van der Gracht and W. T. Rhodes, “Source sampling for incoherent imaging and spatial filtering,” J. Opt. Soc. Am. A 6, 1165–1167 (1989).
    [CrossRef]
  9. C. M. Cheng and J. L. Chern, “Programmable apodizer in incoherent imaging systems using a digital micromirror device,” Opt. Eng. 49, 023201 (2010).
    [CrossRef]
  10. D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) application,” Proc. SPIE 4985, 14–15(2003).
    [CrossRef]
  11. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103(1955).
    [CrossRef]
  12. C. M. Cheng and J.-L. Chern, “Design of a dual-F-number illumination system and its application to projection display with DMD™,” J. Soc. Inf. Display 14, 819–827 (2006).
    [CrossRef]
  13. Y. Kwak and L. MacDonald, “Characterisation of a desktop LCD projector,” Displays 21, 179–194 (2000).
    [CrossRef]
  14. Mathematica version 4, Wolfram Research, Incorporated, 100 Trade Center Drive, Champaign, Illinois 61820-7237, USA.
  15. See http://en.wikipedia.org/wiki/1951_USAF_resolution_test_chart.
  16. See http://www.eronn.net/camera/test-chart.
  17. V. N. Mahajan, Optical Imaging and Aberrations: Part II. Wave Diffraction Optics (SPIE, 2001).

2010 (1)

C. M. Cheng and J. L. Chern, “Programmable apodizer in incoherent imaging systems using a digital micromirror device,” Opt. Eng. 49, 023201 (2010).
[CrossRef]

2006 (1)

C. M. Cheng and J.-L. Chern, “Design of a dual-F-number illumination system and its application to projection display with DMD™,” J. Soc. Inf. Display 14, 819–827 (2006).
[CrossRef]

2005 (1)

2003 (1)

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) application,” Proc. SPIE 4985, 14–15(2003).
[CrossRef]

2000 (1)

Y. Kwak and L. MacDonald, “Characterisation of a desktop LCD projector,” Displays 21, 179–194 (2000).
[CrossRef]

1999 (1)

1989 (2)

1986 (1)

1971 (1)

1955 (1)

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103(1955).
[CrossRef]

Andrea, P.

Brennesholtz, M. S.

E. H. Stupp and M. S. Brennesholtz, Projection Display(Wiley, 1999).

Campos, J.

Cheng, C. M.

C. M. Cheng and J. L. Chern, “Programmable apodizer in incoherent imaging systems using a digital micromirror device,” Opt. Eng. 49, 023201 (2010).
[CrossRef]

C. M. Cheng and J.-L. Chern, “Design of a dual-F-number illumination system and its application to projection display with DMD™,” J. Soc. Inf. Display 14, 819–827 (2006).
[CrossRef]

Chern, J. L.

C. M. Cheng and J. L. Chern, “Programmable apodizer in incoherent imaging systems using a digital micromirror device,” Opt. Eng. 49, 023201 (2010).
[CrossRef]

Chern, J.-L.

C. M. Cheng and J.-L. Chern, “Design of a dual-F-number illumination system and its application to projection display with DMD™,” J. Soc. Inf. Display 14, 819–827 (2006).
[CrossRef]

Chung, C. S.

Davis, J. A.

Diaz, A.

Dudley, D.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) application,” Proc. SPIE 4985, 14–15(2003).
[CrossRef]

Duncan, W.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) application,” Proc. SPIE 4985, 14–15(2003).
[CrossRef]

Escalera, J. C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

Hopkins, H. H.

C. S. Chung and H. H. Hopkins, “Influence of nonuniform amplitude on the optical transfer function,” Appl. Opt. 28, 1244–1250 (1989).
[CrossRef] [PubMed]

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103(1955).
[CrossRef]

Iemmi, C.

Kwak, Y.

Y. Kwak and L. MacDonald, “Characterisation of a desktop LCD projector,” Displays 21, 179–194 (2000).
[CrossRef]

MacDonald, L.

Y. Kwak and L. MacDonald, “Characterisation of a desktop LCD projector,” Displays 21, 179–194 (2000).
[CrossRef]

Mahajan, V. N.

V. N. Mahajan, Optical Imaging and Aberrations: Part II. Wave Diffraction Optics (SPIE, 2001).

Marquez, A.

Mino, M.

Ojeda-Castaneda, J.

Okano, Y.

Rhodes, W. T.

Slaughter, J.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) application,” Proc. SPIE 4985, 14–15(2003).
[CrossRef]

Stupp, E. H.

E. H. Stupp and M. S. Brennesholtz, Projection Display(Wiley, 1999).

van der Gracht, J.

Yzuel, M. J.

Appl. Opt. (2)

Displays (1)

Y. Kwak and L. MacDonald, “Characterisation of a desktop LCD projector,” Displays 21, 179–194 (2000).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Soc. Inf. Display (1)

C. M. Cheng and J.-L. Chern, “Design of a dual-F-number illumination system and its application to projection display with DMD™,” J. Soc. Inf. Display 14, 819–827 (2006).
[CrossRef]

Opt. Eng. (1)

C. M. Cheng and J. L. Chern, “Programmable apodizer in incoherent imaging systems using a digital micromirror device,” Opt. Eng. 49, 023201 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Proc. R. Soc. London Ser. A (1)

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103(1955).
[CrossRef]

Proc. SPIE (1)

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) application,” Proc. SPIE 4985, 14–15(2003).
[CrossRef]

Other (6)

E. H. Stupp and M. S. Brennesholtz, Projection Display(Wiley, 1999).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

Mathematica version 4, Wolfram Research, Incorporated, 100 Trade Center Drive, Champaign, Illinois 61820-7237, USA.

See http://en.wikipedia.org/wiki/1951_USAF_resolution_test_chart.

See http://www.eronn.net/camera/test-chart.

V. N. Mahajan, Optical Imaging and Aberrations: Part II. Wave Diffraction Optics (SPIE, 2001).

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 (13)

Fig. 1
Fig. 1

Schematic diagram of the projector system with a Köhler illumination subsystem and a projection subsystem to illustrate the relationship between the aperture stop and the digital micromirror device. The dotted and solid lines indicate the optical path of the illumination rays in a Köhler illumination system. The dashed lines indicate the optical path of the imaging rays in a projection system.

Fig. 2
Fig. 2

Illustration of the binary amplitude transmittance T ( x , y ) for the normalized circular aperture, which is generated by the DMD. T ( x , y ) represents a specifically shaped aperture for a conventional annular apodizer.

Fig. 3
Fig. 3

Total aperture functions on the aperture stop, which are generated by the DMD in the conditions of (a) clear aper ture, (b) K = 0 , (c) K = 0.05 , (d) K = 0.3 , with fill factor 100%, (e) K = 0.3 with fill factor 90%, and (f) K = 0.3 with fill factor 80%.

Fig. 4
Fig. 4

Optical transfer functions in an aberration-free imaging system and a defocused projection system without spherical aberration ω 40 = 0 and coma aberration ω 31 = 0 , but with different defocus coefficients ω 20 = 0 , ω 20 = λ / π , ω 20 = 3 λ / π , ω 20 = 5 λ / π , ω 20 = 10 λ / π , ω 20 = 15 λ / π , and ω 20 = 20 λ / π for amplitude transmittances of the aperture functions for (a) clear aperture, (b) K = 0 , (c) K = 0.05 , and (d) K = 0.3 .

Fig. 5
Fig. 5

Computer-simulated images of resolution patterns for (a) a clear aperture and (b) a specifically shaped aperture with the scale ratio K = 0.05 , and (c) a specifically shaped aperture with the scale ratio K = 0.3 , obtained with different defocus coefficients: (1) ω 20 = 5 λ / π , (2) ω 20 = 10 λ / π , (3) ω 20 = 15 λ / π and (4) ω 20 = 20 λ / π .

Fig. 6
Fig. 6

Optical transfer functions in an aberration-free imaging system and a projection system without defocus aberration ω 20 = 0 and coma aberration ω 31 = 0 , but with different spherical aberration coefficients ω 40 = 0 , ω 40 = λ / π , ω 40 = 3 λ / π , ω 40 = 5 λ / π , ω 40 = 10 λ / π , ω 40 = 15 λ / π , and ω 40 = 20 λ / π for amplitude transmittances of the aperture functions for (a) clear aperture, (b) K = 0 , (c) K = 0.05 , and (d) K = 0.3 .

Fig. 7
Fig. 7

Computer-simulated images of resolution patterns for (a) a clear aperture, (b) a specifically shaped aperture with the scale ratio K = 0.05 , and (c) a specifically shaped aperture with the scale ratio K = 0.3 , obtained with different spherical aberration coefficients: (1) ω 40 = 5 λ / π , (2) ω 40 = 10 λ / π , (3) ω 40 = 15 λ / π , and (4) ω 40 = 20 λ / π .

Fig. 8
Fig. 8

Optical transfer functions in an aberration-free imaging system and a projection system without defocus aberration ω 20 = 0 and spherical aberration ω 40 = 0 , but with different coma aberration coefficients ω 31 = 0 , ω 31 = λ / π , ω 31 = 3 λ / π , ω 31 = 5 λ / π , ω 31 = 10 λ / π , ω 31 = 15 λ / π , and ω 31 = 20 λ / π for amplitude transmittances of the aperture functions for (a) clear aperture, (b) K = 0 , (c) K = 0.05 , and (d) K = 0.3 .

Fig. 9
Fig. 9

Computer-simulated images of resolution patterns for (a) a clear aperture, (b) a specifically shaped aperture with the scale ratio K = 0.05 , and (c) a specifically shaped aperture with the scale ratio K = 0.3 , obtained with different coma aberration coefficients: (1) ω 31 = 5 λ / π , (2) ω 31 = 10 λ / π , (3) ω 31 = 15 λ / π , and (4) ω 31 = 20 λ / π .

Fig. 10
Fig. 10

Optical transfer functions in an aberration-free imaging system and a projection system with different defocus coefficients ω 20 , different spherical aberration coefficients ω 41 , and different coma aberration coefficients ω 31 , when ω 20 = ω 40 = ω 31 = 0 , 5 λ / π , ω 31 = 10 λ / π , and ω 31 = 20 λ / π for amplitude transmittances of the aperture functions for (a) clear aperture, (b) K = 0 , (c) K = 0.05 , and (d) K = 0.3 .

Fig. 11
Fig. 11

Computer-simulated images of resolution patterns for (a) a clear aperture, (b) a specifically shaped aperture with the scale ratio K = 0.05 , and (c) a specifically shaped aperture with the scale ratio K = 0.3 , obtained with different defocus coefficients ω 20 , different spherical aberration coefficients ω 41 , and different coma aberration coefficients ω 31 , when ω 20 = ω 40 = ω 31 = (1) 5 λ / π , (2) 10 λ / π , and (3) 20 λ / π .

Fig. 12
Fig. 12

Optical transfer functions in a defocused system with amplitude transmittances of the aperture functions for a / D = 0.3 and the defocus coefficient ω 20 = 10 λ / π for different fill factors: 100%, 90%, and 80%.

Fig. 13
Fig. 13

Computer-simulated images of resolution patterns for a specific shaped aperture with the scale ratio a / D = 0.3 and different fill factors (a) 100%, (b) 90%, and (c) 80% in a defocus system with the defocus coefficient ω 20 = 10 λ / π .

Tables (1)

Tables Icon

Table 1 Optical Transfer Function Values of Clear Aperture and Two Specifically Shaped Pupils

Equations (11)

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

f ( x , y ) = T ( x , y ) exp { i k [ ω 20 ( x 2 + y 2 ) + ω 40 ( x 2 + y 2 ) 2 + ω 31 ( x 2 + y 2 ) × y ] } x 2 + y 2 1 = 0 x 2 + y 2 > 1 ,
T ( x , y ) = E ( x , y ) m n T ( x , y ) δ ( x 2 m c D ) δ ( y 2 n c D ) ,
0 | m | , | n | Int [ D / c 1 2 ] ,
K ( c / D ) .
T ( x , y ) = E ( x , y ) m n T ( x , y ) δ ( x 2 m a D ) δ ( y 2 n a D ) ,
0 | m | , | n | Int [ D / a 1 2 ] + 1 ,
τ ( s ) = g ( s , 0 ) g ( 0 , 0 ) = f ( x + s / 2 , y ) f * ( x s / 2 , y ) d x d y f ( x , y ) f * ( x , y ) d x d y ,
g ( s , 0 ) = [ 1 ( s / 2 ) 2 ] 1 / 2 [ 1 ( s / 2 ) 2 ] 1 / 2 [ ( 1 y 2 ) 1 / 2 s / 2 ] [ ( 1 y 2 ) 1 / 2 s / 2 ] T ( x + s 2 , y ) · T ( x s 2 , y ) × exp { i 2 k s x [ ω 20 + ω 40 ( 2 x 2 + 2 y 2 + s 2 2 ) + ω 31 y ] } d x d y ,
g ( 0 , 0 ) = 1 1 ( 1 y 2 ) 1 / 2 ( 1 y 2 ) 1 / 2 [ T ( x , y ) ] 2 d x d y .
g ( s , 0 ) = q = p p { [ ( 1 y 2 ) 1 / 2 s / 2 ] [ ( 1 y 2 ) 1 / 2 s / 2 ] T ( x + s 2 , y ) · T ( x s 2 , y ) × exp { i 2 k s x [ ω 20 + ω 40 ( 2 x 2 + 2 y 2 + s 2 2 ) + ω 31 y ] } d x } Δ y ,
g ( 0 , 0 ) = q = p p { ( 1 y 2 ) 1 / 2 ( 1 y 2 ) 1 / 2 [ T ( x , y ) ] 2 d x } · Δ y ,

Metrics