Abstract

The introduction of spherical aberration in a lens design can be used to extend the depth of field while preserving resolution up to half the maximum diffraction-limited spatial frequency. Two low-power microscope objectives are shown that achieve an extension of ±0.88 λ in terms of wavefront error, which is shown to be comparable to alternative techniques but without the use of special phase elements. The lens performance is azimuth-independent and achromatic over the visible range.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. G. Frédéric, "Advances in camera phone picture quality," Photonics Spectra, Nov. 2007, p. 50(no archival literature references found)
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. S. C. Tucker, W. T. Cathey and E. R. DowskiJr, "Extended depth of field and aberration control for inexpensive digital microscope systems," Opt. Express 4, 467-474 (1999). http://www.opticsexpress.org/abstract.cfm?uri=oe-4-11-467.
    [CrossRef] [PubMed]
  13. P. E. X. Silveira and R. Narayanswamy, "Signal-to-noise analysis of task-based imaging systems with defocus," Appl. Opt. 46, 2924-2934 (2006).
    [CrossRef]
  14. W. N. Charman and H. Whitefoot, "Pupil diameter and the depth-of-field of the human eye as measured by laser speckle," Optica Acta 24, 1211-1216 (1977).
    [CrossRef]
  15. S. Mezouari and A. R. Harvey, "Phase pupil functions for reduction of defocus and spherical aberrations," Opt. Lett. 28, 771-773 (2003).
    [CrossRef] [PubMed]
  16. V. N. Mahajan, Optical Imaging and Aberrations, Part II. Wave Diffraction Optics, Ch.2, SPIE Press, Bellingham, WA (2001).
  17. P. Mouroulis and J. Macdonald, Geometrical Optics and Optical Design, p. 324, Oxford University Press, New York/Oxford (1997).

2008

2007

Z. Zalevsky and S. Ben-Yaish, "Extended depth of focus imaging with birefringent plate," Opt. Express 15, 7204-7210 (2007), http://www.opticsexpress.org/abstract.cfm?uri=oe-15-12-7202.
[CrossRef]

G. Frédéric, "Advances in camera phone picture quality," Photonics Spectra, Nov. 2007, p. 50(no archival literature references found)

G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek, "Imaging with extended focal depth by means of lenses with radial and angular modulation," Opt. Express 15, 9184-9193 (2007), http://www.opticsexpress.org/abstract.cfm?uri=oe-15-15-9184.
[CrossRef] [PubMed]

2006

P. E. X. Silveira and R. Narayanswamy, "Signal-to-noise analysis of task-based imaging systems with defocus," Appl. Opt. 46, 2924-2934 (2006).
[CrossRef]

2005

2004

2003

N. George and W. Chi, "Extended depth of field using a logarithmic asphere," J. Opt. A: Pure Appl. Opt. 5, S157-S163 (2003).
[CrossRef]

S. Mezouari and A. R. Harvey, "Phase pupil functions for reduction of defocus and spherical aberrations," Opt. Lett. 28, 771-773 (2003).
[CrossRef] [PubMed]

2000

1999

1995

1984

1977

W. N. Charman and H. Whitefoot, "Pupil diameter and the depth-of-field of the human eye as measured by laser speckle," Optica Acta 24, 1211-1216 (1977).
[CrossRef]

1960

Bagheri, S.

Bartelt, H.

Ben-Eliezer, E.

Ben-Yaish, S.

Z. Zalevsky and S. Ben-Yaish, "Extended depth of focus imaging with birefringent plate," Opt. Express 15, 7204-7210 (2007), http://www.opticsexpress.org/abstract.cfm?uri=oe-15-12-7202.
[CrossRef]

Cathey, W. T.

Charman, W. N.

W. N. Charman and H. Whitefoot, "Pupil diameter and the depth-of-field of the human eye as measured by laser speckle," Optica Acta 24, 1211-1216 (1977).
[CrossRef]

Chi, W.

N. George and W. Chi, "Extended depth of field using a logarithmic asphere," J. Opt. A: Pure Appl. Opt. 5, S157-S163 (2003).
[CrossRef]

Dowski, E. R.

Frédéric, G.

G. Frédéric, "Advances in camera phone picture quality," Photonics Spectra, Nov. 2007, p. 50(no archival literature references found)

George, N.

N. George and W. Chi, "Extended depth of field using a logarithmic asphere," J. Opt. A: Pure Appl. Opt. 5, S157-S163 (2003).
[CrossRef]

Ghosh, A.

Harvey, A. R.

Jaroszewicz, Z.

Javidi, B.

Kolodziejczyk, A.

Konforti, N.

Marom, E.

Mezouari, S.

Mikula, G.

Narayanswamy, R.

P. E. X. Silveira and R. Narayanswamy, "Signal-to-noise analysis of task-based imaging systems with defocus," Appl. Opt. 46, 2924-2934 (2006).
[CrossRef]

Ojeda-Castañeda, J.

Petelczyc, K.

Sanyal, S.

Sherif, S. S.

Sicre, E. E.

Silveira, P. E. X.

P. E. X. Silveira and R. Narayanswamy, "Signal-to-noise analysis of task-based imaging systems with defocus," Appl. Opt. 46, 2924-2934 (2006).
[CrossRef]

Sypek, M.

Tucker, S. C.

Welford, W. T.

Whitefoot, H.

W. N. Charman and H. Whitefoot, "Pupil diameter and the depth-of-field of the human eye as measured by laser speckle," Optica Acta 24, 1211-1216 (1977).
[CrossRef]

Zalevsky, Z.

Appl. Opt.

J. Opt. A: Pure Appl. Opt.

N. George and W. Chi, "Extended depth of field using a logarithmic asphere," J. Opt. A: Pure Appl. Opt. 5, S157-S163 (2003).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Opt. Lett.

Optica Acta

W. N. Charman and H. Whitefoot, "Pupil diameter and the depth-of-field of the human eye as measured by laser speckle," Optica Acta 24, 1211-1216 (1977).
[CrossRef]

Photonics Spectra

G. Frédéric, "Advances in camera phone picture quality," Photonics Spectra, Nov. 2007, p. 50(no archival literature references found)

Other

V. N. Mahajan, Optical Imaging and Aberrations, Part II. Wave Diffraction Optics, Ch.2, SPIE Press, Bellingham, WA (2001).

P. Mouroulis and J. Macdonald, Geometrical Optics and Optical Design, p. 324, Oxford University Press, New York/Oxford (1997).

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Figures (8)

Fig. 1.
Fig. 1.

Two diffraction-limited low-power objectives, with NA=0.167 (top) and 0.08 (bottom) respectively. The image semi-diagonal shown is ~11 mm in both cases.

Fig. 2.
Fig. 2.

Re-optimized objectives with spherical aberration introduced. The Gaussian specifications are the same as those of the systems of Fig. 1. The spherical aberration is evident as ray aberration at the image plane.

Fig. 3.
Fig. 3.

MTF curves for the blue (486 nm) wavelength, at the distant extreme of focus for the two systems of Fig. 2. It can be seen that the curves show very little variation with field or orientation and are similar for the two systems after scaling the abscissa.

Fig. 4.
Fig. 4.

Axial MTF curves for the NA=0.167 system at three through focus positions and two wavelengths. The green wavelength shows an intermediate behavior between the two extremes. Also, the full-field MTFs are very similar to the corresponding axial ones.

Fig. 5.
Fig. 5.

Point spread functions for three focus positions and 586 nm wavelength, for the second SA system of NA=0.08.

Fig. 6.
Fig. 6.

Through focus images for the diffraction-limited system, and the SA system (raw and processed). The DOF range is 300 µm, shown on the right. The box size is approximately 200 µm. All images are normalized to a maximum intensity of one. The bottom two images show the ideal geometric image without aberrations or diffraction, and the same image re-sampled to the detector pitch.

Fig. 7.
Fig. 7.

MTF curves of a wavefront-coded system corresponding to the NA=0.167 lens for the center of the field only. The graph on the left shows three curves, one for each focus position, corresponding to the x (or y) direction of the phase function. The graph on the right shows curves corresponding to the directions at ±45°, labeled as T and S. Notice that the inherent asymmetry of the phase function means that different MTF curves are obtained along the two ±45° orientations even for the on-axis position.

Fig. 8.
Fig. 8.

Typical MTF curves for an annular aperture system with δ=0.86 and 0.81 linear obscuration ratio. These curves have been obtained using the NA=0.167 diffraction-limited system of Fig. 1. The legend shows the value of δ, and also the location within the DOF. Only the on-axis field point is shown, for a wavelength of 586 nm. Other locations, fields and wavelengths are omitted for clarity, but show similar behavior. The value of the lowermost curve at 80 c/mm is ~0.025.

Tables (1)

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Table 1. Design prescription for SA objective #2

Equations (1)

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δ W 20 = 0.5 ( NA ) 2 δ z

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