Abstract

Wavefront coding (WFC) is a kind of computational imaging technique that controls defocus and defocus related aberrations of optical systems by introducing a specially designed phase distribution to the pupil function. This technology has been applied in many imaging systems to improve performance and/or reduce cost. The application of WFC technology in an off-axis three mirror anastigmatic (TMA) system has been proposed, and the design and optimization of optics, the restoration of degraded images, and the manufacturing of wavefront coded elements have been researched in our previous work. In this paper, we describe the alignment, the imaging experiment, and the image restoration of the off-axis TMA system with WFC technology. The ideal wavefront map is set to be the system error of the interferometer to simplify the assembly, and the coefficients of certain Zernike polynomials are monitored to verify the result in the alignment process. A pinhole of 20 μm diameter and the third plate of WT1005-62 resolution patterns are selected as the targets in the imaging experiment. The comparison of the tail lengths of point spread functions is represented to show the invariance of the image quality in the extended depth of focus. The structure similarity is applied to estimate the relationship among the captured images with varying defocus. We conclude that the experiment results agree with the earlier theoretical analysis.

© 2012 Optical Society of America

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References

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    [CrossRef]
  2. S. Bradbum, W. T. Cathey, and E. R. Dowski, “Realizations of focus invariance in optical-digital systems with wave-front coding,” Appl. Opt. 36, 9157–9166 (1997).
    [CrossRef]
  3. R. Narayanswamy, A. E. Baron, V. Chumachenko, and A. Greengard, “Applications of wavefront coded imaging,” Proc. SPIE 5299, 163–174 (2004).
    [CrossRef]
  4. E. R. Dowski, R. H. Cormack, and S. D. Saramab, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000).
    [CrossRef]
  5. K. Kubala, E. R. Dowski, J. Kobus, and B. Brown, “Design and optimization of aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54–65 (2004).
    [CrossRef]
  6. R. Porras, S. Vázquez, and J. Castro, “Wavefront coding technology in the optical design of astronomical instruments,” Proc. SPIE 5622, 796–800 (2004).
    [CrossRef]
  7. S. Mezouari and A. R. Harvey, “Wavefront coding for aberration compensation in thermal imaging systems,” Proc. SPIE 4442, 34–42 (2001).
    [CrossRef]
  8. W. Chi and N. George, “Smart camera with extended depth of field,” Proc. SPIE 6024, 602424 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. F. Yan, L. G. Zheng, and X. J. Zhang, “Image restoration of an off-axis three mirror anastigmatic optical system with wavefront coding technology,” Opt. Eng. 47, 017006 (2008).
    [CrossRef]
  18. F. Yan, D. Fan, B. Z. Zhang, L. H. Yin, R. G. Li, and X. J. Zhang, “Manufacturing and testing of a cubic SiC surface,” Chin. Opt. Lett. 7, 534–536 (2009).
    [CrossRef]
  19. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
    [CrossRef]
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    [CrossRef]

2009

2008

P. Mouroulis, “Depth of field extension with spherical optics,” Opt. Express 16, 12995–13004 (2008).
[CrossRef]

S. H. Lee, N. C. Park, and Y. P. Park, “Breaking diffraction limit of a small f-number compact camera using wavefront coding,” Opt. Express 16, 13569–13578(2008).
[CrossRef]

F. Yan and X. J. Zhang, “A design of off-axis three mirror anastigmatic optical system with wavefront coding technology,” Opt. Eng. 47, 063001 (2008).
[CrossRef]

F. Yan, L. G. Zheng, and X. J. Zhang, “Image restoration of an off-axis three mirror anastigmatic optical system with wavefront coding technology,” Opt. Eng. 47, 017006 (2008).
[CrossRef]

2007

2005

W. Chi and N. George, “Smart camera with extended depth of field,” Proc. SPIE 6024, 602424 (2005).
[CrossRef]

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. Gracht, “Extended depth-of-field iris recognition system for a workstation environment,” Proc. SPIE 5779, 41–50 (2005).
[CrossRef]

2004

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

R. Narayanswamy, A. E. Baron, V. Chumachenko, and A. Greengard, “Applications of wavefront coded imaging,” Proc. SPIE 5299, 163–174 (2004).
[CrossRef]

K. Kubala, E. R. Dowski, J. Kobus, and B. Brown, “Design and optimization of aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54–65 (2004).
[CrossRef]

R. Porras, S. Vázquez, and J. Castro, “Wavefront coding technology in the optical design of astronomical instruments,” Proc. SPIE 5622, 796–800 (2004).
[CrossRef]

2003

G. A. Cirino and L. G. Neto, “Design of cubic-phase distribution lenses for passive infrared motion sensors,” Proc. SPIE 5073, 476–484 (2003).
[CrossRef]

2001

S. Mezouari and A. R. Harvey, “Wavefront coding for aberration compensation in thermal imaging systems,” Proc. SPIE 4442, 34–42 (2001).
[CrossRef]

2000

E. R. Dowski, R. H. Cormack, and S. D. Saramab, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000).
[CrossRef]

1997

1995

1981

1977

Baron, A. E.

R. Narayanswamy, A. E. Baron, V. Chumachenko, and A. Greengard, “Applications of wavefront coded imaging,” Proc. SPIE 5299, 163–174 (2004).
[CrossRef]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Bradbum, S.

Brown, B.

K. Kubala, E. R. Dowski, J. Kobus, and B. Brown, “Design and optimization of aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54–65 (2004).
[CrossRef]

Castro, J.

R. Porras, S. Vázquez, and J. Castro, “Wavefront coding technology in the optical design of astronomical instruments,” Proc. SPIE 5622, 796–800 (2004).
[CrossRef]

Cathey, W. T.

Chi, W.

W. Chi and N. George, “Smart camera with extended depth of field,” Proc. SPIE 6024, 602424 (2005).
[CrossRef]

Chumachenko, V.

R. Narayanswamy, A. E. Baron, V. Chumachenko, and A. Greengard, “Applications of wavefront coded imaging,” Proc. SPIE 5299, 163–174 (2004).
[CrossRef]

Cirino, G. A.

G. A. Cirino and L. G. Neto, “Design of cubic-phase distribution lenses for passive infrared motion sensors,” Proc. SPIE 5073, 476–484 (2003).
[CrossRef]

Cormack, R. H.

E. R. Dowski, R. H. Cormack, and S. D. Saramab, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000).
[CrossRef]

Dowski, E. R.

K. Kubala, E. R. Dowski, J. Kobus, and B. Brown, “Design and optimization of aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54–65 (2004).
[CrossRef]

E. R. Dowski, R. H. Cormack, and S. D. Saramab, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000).
[CrossRef]

S. Bradbum, W. T. Cathey, and E. R. Dowski, “Realizations of focus invariance in optical-digital systems with wave-front coding,” Appl. Opt. 36, 9157–9166 (1997).
[CrossRef]

E. R. Dowski and W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866(1995).
[CrossRef]

Fan, D.

Frieden, B. R.

George, N.

W. Chi and N. George, “Smart camera with extended depth of field,” Proc. SPIE 6024, 602424 (2005).
[CrossRef]

Gracht, J.

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. Gracht, “Extended depth-of-field iris recognition system for a workstation environment,” Proc. SPIE 5779, 41–50 (2005).
[CrossRef]

Greengard, A.

R. Narayanswamy, A. E. Baron, V. Chumachenko, and A. Greengard, “Applications of wavefront coded imaging,” Proc. SPIE 5299, 163–174 (2004).
[CrossRef]

Harvey, A. R.

S. Mezouari and A. R. Harvey, “Wavefront coding for aberration compensation in thermal imaging systems,” Proc. SPIE 4442, 34–42 (2001).
[CrossRef]

Kermisch, D.

Kobus, J.

K. Kubala, E. R. Dowski, J. Kobus, and B. Brown, “Design and optimization of aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54–65 (2004).
[CrossRef]

Kubala, K.

K. Kubala, E. R. Dowski, J. Kobus, and B. Brown, “Design and optimization of aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54–65 (2004).
[CrossRef]

Lee, S. H.

Li, R. G.

Mezouari, S.

S. Mezouari and A. R. Harvey, “Wavefront coding for aberration compensation in thermal imaging systems,” Proc. SPIE 4442, 34–42 (2001).
[CrossRef]

Mouroulis, P.

Narayanswamy, R.

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. Gracht, “Extended depth-of-field iris recognition system for a workstation environment,” Proc. SPIE 5779, 41–50 (2005).
[CrossRef]

R. Narayanswamy, A. E. Baron, V. Chumachenko, and A. Greengard, “Applications of wavefront coded imaging,” Proc. SPIE 5299, 163–174 (2004).
[CrossRef]

Neto, L. G.

G. A. Cirino and L. G. Neto, “Design of cubic-phase distribution lenses for passive infrared motion sensors,” Proc. SPIE 5073, 476–484 (2003).
[CrossRef]

Park, N. C.

Park, Y. P.

Pauca, V. P.

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. Gracht, “Extended depth-of-field iris recognition system for a workstation environment,” Proc. SPIE 5779, 41–50 (2005).
[CrossRef]

Porras, R.

R. Porras, S. Vázquez, and J. Castro, “Wavefront coding technology in the optical design of astronomical instruments,” Proc. SPIE 5622, 796–800 (2004).
[CrossRef]

Rutkowski, J.

Saramab, S. D.

E. R. Dowski, R. H. Cormack, and S. D. Saramab, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000).
[CrossRef]

Setty, H.

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. Gracht, “Extended depth-of-field iris recognition system for a workstation environment,” Proc. SPIE 5779, 41–50 (2005).
[CrossRef]

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Silveira, P. E. X.

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. Gracht, “Extended depth-of-field iris recognition system for a workstation environment,” Proc. SPIE 5779, 41–50 (2005).
[CrossRef]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Tamayo, I.

Tremblay, E. J.

Vázquez, S.

R. Porras, S. Vázquez, and J. Castro, “Wavefront coding technology in the optical design of astronomical instruments,” Proc. SPIE 5622, 796–800 (2004).
[CrossRef]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Yan, F.

F. Yan, D. Fan, B. Z. Zhang, L. H. Yin, R. G. Li, and X. J. Zhang, “Manufacturing and testing of a cubic SiC surface,” Chin. Opt. Lett. 7, 534–536 (2009).
[CrossRef]

F. Yan and X. J. Zhang, “Optimization of an off-axis three-mirror anastigmatic system with wavefront coding technology based on MTF invariance,” Opt. Express 17, 16809–16819 (2009).
[CrossRef]

F. Yan and X. J. Zhang, “A design of off-axis three mirror anastigmatic optical system with wavefront coding technology,” Opt. Eng. 47, 063001 (2008).
[CrossRef]

F. Yan, L. G. Zheng, and X. J. Zhang, “Image restoration of an off-axis three mirror anastigmatic optical system with wavefront coding technology,” Opt. Eng. 47, 017006 (2008).
[CrossRef]

Yin, L. H.

Zhang, B. Z.

Zhang, X. J.

F. Yan, D. Fan, B. Z. Zhang, L. H. Yin, R. G. Li, and X. J. Zhang, “Manufacturing and testing of a cubic SiC surface,” Chin. Opt. Lett. 7, 534–536 (2009).
[CrossRef]

F. Yan and X. J. Zhang, “Optimization of an off-axis three-mirror anastigmatic system with wavefront coding technology based on MTF invariance,” Opt. Express 17, 16809–16819 (2009).
[CrossRef]

F. Yan and X. J. Zhang, “A design of off-axis three mirror anastigmatic optical system with wavefront coding technology,” Opt. Eng. 47, 063001 (2008).
[CrossRef]

F. Yan, L. G. Zheng, and X. J. Zhang, “Image restoration of an off-axis three mirror anastigmatic optical system with wavefront coding technology,” Opt. Eng. 47, 017006 (2008).
[CrossRef]

Zheng, L. G.

F. Yan, L. G. Zheng, and X. J. Zhang, “Image restoration of an off-axis three mirror anastigmatic optical system with wavefront coding technology,” Opt. Eng. 47, 017006 (2008).
[CrossRef]

Appl. Opt.

Chin. Opt. Lett.

IEEE Trans. Image Process.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

J. Opt. Soc. Am.

Opt. Eng.

F. Yan and X. J. Zhang, “A design of off-axis three mirror anastigmatic optical system with wavefront coding technology,” Opt. Eng. 47, 063001 (2008).
[CrossRef]

F. Yan, L. G. Zheng, and X. J. Zhang, “Image restoration of an off-axis three mirror anastigmatic optical system with wavefront coding technology,” Opt. Eng. 47, 017006 (2008).
[CrossRef]

Opt. Express

Proc. SPIE

R. Narayanswamy, A. E. Baron, V. Chumachenko, and A. Greengard, “Applications of wavefront coded imaging,” Proc. SPIE 5299, 163–174 (2004).
[CrossRef]

E. R. Dowski, R. H. Cormack, and S. D. Saramab, “Wavefront coding: jointly optimized optical and digital imaging systems,” Proc. SPIE 4041, 114–120 (2000).
[CrossRef]

K. Kubala, E. R. Dowski, J. Kobus, and B. Brown, “Design and optimization of aberration and error invariant space telescope systems,” Proc. SPIE 5524, 54–65 (2004).
[CrossRef]

R. Porras, S. Vázquez, and J. Castro, “Wavefront coding technology in the optical design of astronomical instruments,” Proc. SPIE 5622, 796–800 (2004).
[CrossRef]

S. Mezouari and A. R. Harvey, “Wavefront coding for aberration compensation in thermal imaging systems,” Proc. SPIE 4442, 34–42 (2001).
[CrossRef]

W. Chi and N. George, “Smart camera with extended depth of field,” Proc. SPIE 6024, 602424 (2005).
[CrossRef]

R. Narayanswamy, P. E. X. Silveira, H. Setty, V. P. Pauca, and J. Gracht, “Extended depth-of-field iris recognition system for a workstation environment,” Proc. SPIE 5779, 41–50 (2005).
[CrossRef]

G. A. Cirino and L. G. Neto, “Design of cubic-phase distribution lenses for passive infrared motion sensors,” Proc. SPIE 5073, 476–484 (2003).
[CrossRef]

Other

W. B. Wetherell and D. A. Womble, “All-reflective three element objective,” U.S. patent 4,240,707 (23December1980).

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Figures (11)

Fig. 1.
Fig. 1.

Sketch and main parameters of the off-axis TMA system being researched, where PM is the primary mirror (ellipse), SM is the secondary mirror (WFC element), TM is the tertiary mirror (ellipse), and FM is the folded mirror (plane).

Fig. 2.
Fig. 2.

MTF curves of the optimized wavefront coding system with defocus varying from 1.25λ to 1.25λ with increments of 0.25λ defocus.

Fig. 3.
Fig. 3.

Graphical introduction of the alignment of the wavefront coding system.

Fig. 4.
Fig. 4.

(a) Ideal wavefront map of the wavefront coded system, (b) Actual wavefront map of the wavefront coded system obtained with the Phasecam 5030 interferometer of 4D Corp.

Fig. 5.
Fig. 5.

Sketch of the experiment setup.

Fig. 6.
Fig. 6.

Sketch of the CCD camera and its adjustment in the direction of incident chief rays.

Fig. 7.
Fig. 7.

PSF image of the system with defocus aberration from 1.25λ to 1.25λ and the ideal PSF image (bottom right).

Fig. 8.
Fig. 8.

Sketch of the length of the tail of the PSF in x direction and y direction.

Fig. 9.
Fig. 9.

Image of the third plate of WT1005-62 resolution patterns.

Fig. 10.
Fig. 10.

Original images of the 16th group resolution pattern with defocus aberration from 1.25λ to 1.25λ.

Fig. 11.
Fig. 11.

Restored images of the 16th group resolution pattern with defocus aberration from 1.25λ to 1.25λ.

Tables (4)

Tables Icon

Table 1. Coefficients of the 7th, 8th, 10th, and 11th Zernike Polynomials of the Measured Wavefront

Tables Icon

Table 2. Length of the Tail of the 11 PSF Images in x and y Directions

Tables Icon

Table 3. SSIM of the Images with Different Defocus

Tables Icon

Table 4. Comparison of RMSE and PSNR Among Captured Images and Restored Images

Equations (8)

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

Pusual={1for|x2+y2|10otherwisePWFC={12exp(jα(x3+y3))for|x2+y2|10otherwise,
H(u,W020)(π12αu)1/2exp(jαu34)exp(jkW0202u3α),u0.
z(x,y)=c(x2+y2)1+1(1+k)c2(x2+y2)+β(xn3+yn3),
x3+y3=12(Z2+Z3)+14(Z7+Z8+Z10Z11),
SSIM(x,y)=[l(x,y)]α[c(x,y)]β[s(x,y)]γα,β,γ>0,
l(x,y)=2μrμe+C1μr2+μe2+C1C1=(K1L)2K11,c(x,y)=2σrσe+C2σr2+σe2+C2C2=(K2L)2K21,s(x,y)=σre+C3σrσe+C3C3=C2/2,σr=[1N1i=1N(riμr)2]1/2σe=[1N1i=1N(eiμe)2]1/2,
σre=1N1i=1N(riμr)(eiμe),
RMSE=(1MNi=1Mj=1N(fi,jfmean)2)1/2LS=i=2M1j=2N1(8fi,ja=i1a=i+1b=j1b=j+1fa,b)(M2)(N2)whena=ib=j,fa,b=0IE=i=1Lp(gi)log2p(gi)(unit:bit/pix)

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