Abstract

Image-sharpness metrics can be used to optimize optical systems and to control wavefront sensorless adaptive optics systems. We show that for an aberrated system, the numerical value of an image-sharpness metric can be improved by adding specific aberrations. The optimum amplitudes of the additional aberrations depend on the power spectral density of the spatial frequencies of the object.

© 2019 Optical Society of America

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References

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  1. C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function (SPIE, 2002).
  2. V. N. Mahajan, Aberration Theory Made Simple, 2nd ed. (SPIE, 2011).
  3. O. H. Schade, “Image gradation, graininess and sharpness in television and motion picture systems: part II: the grain structure of motion picture images—an analysis of deviations and fluctuations of the sample number,” J. Soc. Motion Pict. Telev. Eng. 58, 181–222 (1952).
    [Crossref]
  4. P. Fellgett, “Concerning photographic grain, signal-to-noise ratio, and information,” J. Opt. Soc. Am. 43, 271–282 (1953).
    [Crossref]
  5. R. A. Muller and A. Buffington, “Real-time correction of atmospherically degraded telescope images through image sharpening,” J. Opt. Soc. Am. 64, 1200–1210 (1974).
    [Crossref]
  6. J. P. Hamaker, J. D. O’Sullivan, and J. E. Noordam, “Image sharpness, Fourier optics, and redundant-spacing interferometry,” J. Opt. Soc. Am. 67, 1122–1123 (1977).
    [Crossref]
  7. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  8. J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), vol. 11, chap. 1.
  9. W. B. King, “Dependence of the Strehl ratio on the magnitude of the variance of the wave aberration,” J. Opt. Soc. Am. 58, 655–661 (1968).
    [Crossref]
  10. E. H. Linfoot, Fourier Methods in Optical Image Evaluation (Focal, 1964).
  11. O. Kazasidis, S. Verpoort, and U. Wittrock, “Algorithm design for image-based wavefront control without wavefront sensing,” Proc. SPIE 10695, 1069502 (2018).
    [Crossref]
  12. O. Kazasidis, S. Verpoort, and U. Wittrock, “Image-based wavefront correction for space telescopes,” Proc. SPIE 11180, 111807Z (2019).
    [Crossref]
  13. S. Bonora and R. J. Zawadzki, “Wavefront sensorless modal deformable mirror correction in adaptive optics: optical coherence tomography,” Opt. Lett. 38, 4801–4804 (2013).
    [Crossref]
  14. James Webb Space Telescope User Documentation, “NIRCam detectors,” https://jwst-docs.stsci.edu/near-infrared-camera/nircam-instrumentation/nircam-detectors .
  15. NASA, “NASA captures “EPIC” Earth image,” https://www.nasa.gov/image-feature/nasa-captures-epic-earth-image .
  16. NASA, “The near side of the moon,” https://moon.nasa.gov/resources/77/the-near-side-of-the-moon/ .
  17. NASA, “Moon fact sheet,” https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html .

2019 (1)

O. Kazasidis, S. Verpoort, and U. Wittrock, “Image-based wavefront correction for space telescopes,” Proc. SPIE 11180, 111807Z (2019).
[Crossref]

2018 (1)

O. Kazasidis, S. Verpoort, and U. Wittrock, “Algorithm design for image-based wavefront control without wavefront sensing,” Proc. SPIE 10695, 1069502 (2018).
[Crossref]

2013 (1)

1977 (1)

1974 (1)

1968 (1)

1953 (1)

1952 (1)

O. H. Schade, “Image gradation, graininess and sharpness in television and motion picture systems: part II: the grain structure of motion picture images—an analysis of deviations and fluctuations of the sample number,” J. Soc. Motion Pict. Telev. Eng. 58, 181–222 (1952).
[Crossref]

Becklund, O. A.

C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function (SPIE, 2002).

Bonora, S.

Buffington, A.

Creath, K.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), vol. 11, chap. 1.

Fellgett, P.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Hamaker, J. P.

Kazasidis, O.

O. Kazasidis, S. Verpoort, and U. Wittrock, “Image-based wavefront correction for space telescopes,” Proc. SPIE 11180, 111807Z (2019).
[Crossref]

O. Kazasidis, S. Verpoort, and U. Wittrock, “Algorithm design for image-based wavefront control without wavefront sensing,” Proc. SPIE 10695, 1069502 (2018).
[Crossref]

King, W. B.

Linfoot, E. H.

E. H. Linfoot, Fourier Methods in Optical Image Evaluation (Focal, 1964).

Mahajan, V. N.

V. N. Mahajan, Aberration Theory Made Simple, 2nd ed. (SPIE, 2011).

Muller, R. A.

Noordam, J. E.

O’Sullivan, J. D.

Schade, O. H.

O. H. Schade, “Image gradation, graininess and sharpness in television and motion picture systems: part II: the grain structure of motion picture images—an analysis of deviations and fluctuations of the sample number,” J. Soc. Motion Pict. Telev. Eng. 58, 181–222 (1952).
[Crossref]

Verpoort, S.

O. Kazasidis, S. Verpoort, and U. Wittrock, “Image-based wavefront correction for space telescopes,” Proc. SPIE 11180, 111807Z (2019).
[Crossref]

O. Kazasidis, S. Verpoort, and U. Wittrock, “Algorithm design for image-based wavefront control without wavefront sensing,” Proc. SPIE 10695, 1069502 (2018).
[Crossref]

Williams, C. S.

C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function (SPIE, 2002).

Wittrock, U.

O. Kazasidis, S. Verpoort, and U. Wittrock, “Image-based wavefront correction for space telescopes,” Proc. SPIE 11180, 111807Z (2019).
[Crossref]

O. Kazasidis, S. Verpoort, and U. Wittrock, “Algorithm design for image-based wavefront control without wavefront sensing,” Proc. SPIE 10695, 1069502 (2018).
[Crossref]

Wyant, J. C.

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), vol. 11, chap. 1.

Zawadzki, R. J.

J. Opt. Soc. Am. (4)

J. Soc. Motion Pict. Telev. Eng. (1)

O. H. Schade, “Image gradation, graininess and sharpness in television and motion picture systems: part II: the grain structure of motion picture images—an analysis of deviations and fluctuations of the sample number,” J. Soc. Motion Pict. Telev. Eng. 58, 181–222 (1952).
[Crossref]

Opt. Lett. (1)

Proc. SPIE (2)

O. Kazasidis, S. Verpoort, and U. Wittrock, “Algorithm design for image-based wavefront control without wavefront sensing,” Proc. SPIE 10695, 1069502 (2018).
[Crossref]

O. Kazasidis, S. Verpoort, and U. Wittrock, “Image-based wavefront correction for space telescopes,” Proc. SPIE 11180, 111807Z (2019).
[Crossref]

Other (9)

James Webb Space Telescope User Documentation, “NIRCam detectors,” https://jwst-docs.stsci.edu/near-infrared-camera/nircam-instrumentation/nircam-detectors .

NASA, “NASA captures “EPIC” Earth image,” https://www.nasa.gov/image-feature/nasa-captures-epic-earth-image .

NASA, “The near side of the moon,” https://moon.nasa.gov/resources/77/the-near-side-of-the-moon/ .

NASA, “Moon fact sheet,” https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html .

E. H. Linfoot, Fourier Methods in Optical Image Evaluation (Focal, 1964).

C. S. Williams and O. A. Becklund, Introduction to the Optical Transfer Function (SPIE, 2002).

V. N. Mahajan, Aberration Theory Made Simple, 2nd ed. (SPIE, 2011).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, R. R. Shannon and J. C. Wyant, eds. (Academic, 1992), vol. 11, chap. 1.

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Figures (4)

Fig. 1.
Fig. 1. Color rendering plots of the merit function for pairs of Zernike modes when imaging a point object. The white contour lines near the global maximum are always circular or elliptical. The black contour lines for large aberration are circular or elliptical only in (a). (a) The pair Z4/Z5. For a constant amplitude of Z5, MF has a maximum always for Z4=0 (e.g., the X mark for Z5=0.7λ), and vice versa. (b) The pair Z3/Z4. When |Z4|0.4λ, MF has two maxima for opposite amplitudes of Z3 (e.g., the two X marks for Z4=0.7λ). (c) The pair Z4/Z11. When |Z11|0.25λ, MF has a maximum for a nonzero amplitude of Z4 (e.g., the X mark for Z11=0.7λ).
Fig. 2.
Fig. 2. (a) Color-rendering plot of the merit function for the pair Z4/Z11, when imaging the planet–moon object of Fig. 4(a). The white contour lines near the global maximum are elliptical. For a large aberration, the black contour lines are no longer elliptical. (b) The black dashed line plotted against the left y axis is a cut through the black dashed line in (a) when Z11=0.7λ. The red dotted line plotted against the right y axis corresponds to MF when imaging a point object and Z11=0.7λ. It is a cut through the plot in Fig. 1(c). The maxima of the two plots (the X marks) are obtained for different amplitudes of Z4.
Fig. 3.
Fig. 3. Simulated images with 0.7λ of secondary astigmatism 0° (Z11). (a) The amplitudes of all the other Zernike modes are zero. The moon is hidden in the halo of the planet. (b) Adding 0.6λ of primary astigmatism 0° (Z4), the moon is distinguished from the planet as a small blob. (c) Pixel profiles along the lines of (a) and (b). The moon appears as a secondary intensity peak for the dotted line that corresponds to (b). The image becomes sharper, although the wavefront variance increases by adding Z4.
Fig. 4.
Fig. 4. (a) Synthetic extended object, comprising a planet and its moon. (b) The simulated diffraction-limited image. The contrast of both images in (a) and (b) has been adjusted with γ=0.5 for illustration purposes only. (c) Pixel profiles along the lines of (a) and (b). The high-frequency spatial information of the planet–moon object (solid line) is not transmitted by the system. Nevertheless, the planet and the moon are clearly distinguishable in the diffraction-limited image (dotted line).

Equations (7)

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

S1I(x)2dx.
I^(s)=OTF(s)O^(s),
S1I(x)2dx|I^(s)|2ds|OTF(s)O^(s)|2dsMTF(s)2|O^(s)|2ds,
S10scutMTF(s)2|O^(s)|2ds.
S1,p0scutMTF(s)2ds,
MFI(x)2dx(I(x)dx)2dx.
MFdiscreteI2(I)2NxNy,