Abstract

Autofocus functions based on measurement of image resolution appear to be precise and robust for biological microscopy. However, the through-focus response of these functions previously exhibited unwanted local maxima, or side peaks. Here we report theoretical and experimental studies showing that side peaks are mainly a result of contrast reversals inherent in optical systems at mid-range frequencies. These contrast reversals are not present in frequencies near optical cutoff. Contrast reversals thus limit the lower cutoff for resolution measurement filters, whereas signal-to-noise limits the upper cutoff. These improved bandpass design criteria led to sharp, unimodal autofocus responses for all tested microscopy specimens.

© 1999 Optical Society of America

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References

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  1. M. Bravo-Zanoguera, B. V. Massenbach, A. L. Kellner, J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instruments 69, 3966–3977 (1998).
    [CrossRef]
  2. M. Bravo-Zanoguera, J. H. Price, “Analog autofocus circuit for scanning microscopy,” in Optical Diagnostics of Biological Fluids and Advanced Techniques in Analytical Cytology, A. V. Priezzhev, T. Asakura, R. C. Leif, eds., Proc. SPIE2982, 468–475 (1997).
    [CrossRef]
  3. F. R. Boddeke, L. J. van Vliet, H. Netten, I. T. Young, “Autofocusing in microscopy based on the OTF and sampling,” Bioimaging 2, 193–203 (1994).
    [CrossRef]
  4. J. H. Price, D. A. Gough, “Comparison of phase-contrast and fluorescence digital autofocus for scanning microscopy,” Cytometry 16, 283–297 (1994).
    [CrossRef] [PubMed]
  5. T. T. E. Yeo, S. H. Ong, Jayasooriah, R. Sinniah, “Autofocus for tissue microscopy,” Image Vision Comput. 11, 629–639 (1993).
  6. F. C. A. Groen, I. T. Young, G. Lighart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81–91 (1985).
    [CrossRef] [PubMed]
  7. E. Krotkov, “Focusing,” Int. J. Comput. Vision 1, 223–237 (1987).
    [CrossRef]
  8. S. B. Marapane, M. M. Trivedi, “Experiments in active vision with real and virtual robot heads,” Appl. Intelligence 5, 237–250 (1995).
    [CrossRef]
  9. S. Inoué, Video Microscopy (Plenum, New York, 1986).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989).
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988).
  15. P. A. Stokseth, “Properties of a defocused optical system,” J. Opt. Soc. Am. 59, 1314–1321 (1969).
    [CrossRef]
  16. D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Ann. Rev. Biophys. Bioeng. 13, 191–219 (1984).
    [CrossRef]
  17. M. Françon, Progress in Microscopy (Row, Peterson, Evanston, Ill., 1961).

1998 (1)

M. Bravo-Zanoguera, B. V. Massenbach, A. L. Kellner, J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instruments 69, 3966–3977 (1998).
[CrossRef]

1995 (1)

S. B. Marapane, M. M. Trivedi, “Experiments in active vision with real and virtual robot heads,” Appl. Intelligence 5, 237–250 (1995).
[CrossRef]

1994 (2)

F. R. Boddeke, L. J. van Vliet, H. Netten, I. T. Young, “Autofocusing in microscopy based on the OTF and sampling,” Bioimaging 2, 193–203 (1994).
[CrossRef]

J. H. Price, D. A. Gough, “Comparison of phase-contrast and fluorescence digital autofocus for scanning microscopy,” Cytometry 16, 283–297 (1994).
[CrossRef] [PubMed]

1993 (1)

T. T. E. Yeo, S. H. Ong, Jayasooriah, R. Sinniah, “Autofocus for tissue microscopy,” Image Vision Comput. 11, 629–639 (1993).

1987 (1)

E. Krotkov, “Focusing,” Int. J. Comput. Vision 1, 223–237 (1987).
[CrossRef]

1985 (1)

F. C. A. Groen, I. T. Young, G. Lighart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81–91 (1985).
[CrossRef] [PubMed]

1984 (2)

K. S. Park, R. Schowengerdt, M. A. Kaczynski, “Modulation-transfer-function analysis for sampled image systems,” Appl. Opt. 23, 2572–2582 (1984).
[CrossRef] [PubMed]

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Ann. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[CrossRef]

1969 (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]

Agard, D. A.

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Ann. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[CrossRef]

Boddeke, F. R.

F. R. Boddeke, L. J. van Vliet, H. Netten, I. T. Young, “Autofocusing in microscopy based on the OTF and sampling,” Bioimaging 2, 193–203 (1994).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989).

Bravo-Zanoguera, M.

M. Bravo-Zanoguera, B. V. Massenbach, A. L. Kellner, J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instruments 69, 3966–3977 (1998).
[CrossRef]

M. Bravo-Zanoguera, J. H. Price, “Analog autofocus circuit for scanning microscopy,” in Optical Diagnostics of Biological Fluids and Advanced Techniques in Analytical Cytology, A. V. Priezzhev, T. Asakura, R. C. Leif, eds., Proc. SPIE2982, 468–475 (1997).
[CrossRef]

Castleman, K. R.

K. R. Castleman, Digital Image Processing (Prentice-Hall, Upper Saddle River, N. J., 1996).

Françon, M.

M. Françon, Progress in Microscopy (Row, Peterson, Evanston, Ill., 1961).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988).

Gough, D. A.

J. H. Price, D. A. Gough, “Comparison of phase-contrast and fluorescence digital autofocus for scanning microscopy,” Cytometry 16, 283–297 (1994).
[CrossRef] [PubMed]

Groen, F. C. A.

F. C. A. Groen, I. T. Young, G. Lighart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81–91 (1985).
[CrossRef] [PubMed]

Hopkins, H. H.

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

Inoué, S.

S. Inoué, Video Microscopy (Plenum, New York, 1986).
[CrossRef]

Jayasooriah,

T. T. E. Yeo, S. H. Ong, Jayasooriah, R. Sinniah, “Autofocus for tissue microscopy,” Image Vision Comput. 11, 629–639 (1993).

Kaczynski, M. A.

Kellner, A. L.

M. Bravo-Zanoguera, B. V. Massenbach, A. L. Kellner, J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instruments 69, 3966–3977 (1998).
[CrossRef]

Krotkov, E.

E. Krotkov, “Focusing,” Int. J. Comput. Vision 1, 223–237 (1987).
[CrossRef]

Lighart, G.

F. C. A. Groen, I. T. Young, G. Lighart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81–91 (1985).
[CrossRef] [PubMed]

Marapane, S. B.

S. B. Marapane, M. M. Trivedi, “Experiments in active vision with real and virtual robot heads,” Appl. Intelligence 5, 237–250 (1995).
[CrossRef]

Massenbach, B. V.

M. Bravo-Zanoguera, B. V. Massenbach, A. L. Kellner, J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instruments 69, 3966–3977 (1998).
[CrossRef]

Netten, H.

F. R. Boddeke, L. J. van Vliet, H. Netten, I. T. Young, “Autofocusing in microscopy based on the OTF and sampling,” Bioimaging 2, 193–203 (1994).
[CrossRef]

Ong, S. H.

T. T. E. Yeo, S. H. Ong, Jayasooriah, R. Sinniah, “Autofocus for tissue microscopy,” Image Vision Comput. 11, 629–639 (1993).

Park, K. S.

Price, J. H.

M. Bravo-Zanoguera, B. V. Massenbach, A. L. Kellner, J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instruments 69, 3966–3977 (1998).
[CrossRef]

J. H. Price, D. A. Gough, “Comparison of phase-contrast and fluorescence digital autofocus for scanning microscopy,” Cytometry 16, 283–297 (1994).
[CrossRef] [PubMed]

M. Bravo-Zanoguera, J. H. Price, “Analog autofocus circuit for scanning microscopy,” in Optical Diagnostics of Biological Fluids and Advanced Techniques in Analytical Cytology, A. V. Priezzhev, T. Asakura, R. C. Leif, eds., Proc. SPIE2982, 468–475 (1997).
[CrossRef]

Schowengerdt, R.

Sinniah, R.

T. T. E. Yeo, S. H. Ong, Jayasooriah, R. Sinniah, “Autofocus for tissue microscopy,” Image Vision Comput. 11, 629–639 (1993).

Stokseth, P. A.

Trivedi, M. M.

S. B. Marapane, M. M. Trivedi, “Experiments in active vision with real and virtual robot heads,” Appl. Intelligence 5, 237–250 (1995).
[CrossRef]

van Vliet, L. J.

F. R. Boddeke, L. J. van Vliet, H. Netten, I. T. Young, “Autofocusing in microscopy based on the OTF and sampling,” Bioimaging 2, 193–203 (1994).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989).

Yeo, T. T. E.

T. T. E. Yeo, S. H. Ong, Jayasooriah, R. Sinniah, “Autofocus for tissue microscopy,” Image Vision Comput. 11, 629–639 (1993).

Young, I. T.

F. R. Boddeke, L. J. van Vliet, H. Netten, I. T. Young, “Autofocusing in microscopy based on the OTF and sampling,” Bioimaging 2, 193–203 (1994).
[CrossRef]

F. C. A. Groen, I. T. Young, G. Lighart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81–91 (1985).
[CrossRef] [PubMed]

Ann. Rev. Biophys. Bioeng. (1)

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Ann. Rev. Biophys. Bioeng. 13, 191–219 (1984).
[CrossRef]

Appl. Intelligence (1)

S. B. Marapane, M. M. Trivedi, “Experiments in active vision with real and virtual robot heads,” Appl. Intelligence 5, 237–250 (1995).
[CrossRef]

Appl. Opt. (1)

Bioimaging (1)

F. R. Boddeke, L. J. van Vliet, H. Netten, I. T. Young, “Autofocusing in microscopy based on the OTF and sampling,” Bioimaging 2, 193–203 (1994).
[CrossRef]

Cytometry (2)

J. H. Price, D. A. Gough, “Comparison of phase-contrast and fluorescence digital autofocus for scanning microscopy,” Cytometry 16, 283–297 (1994).
[CrossRef] [PubMed]

F. C. A. Groen, I. T. Young, G. Lighart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81–91 (1985).
[CrossRef] [PubMed]

Image Vision Comput. (1)

T. T. E. Yeo, S. H. Ong, Jayasooriah, R. Sinniah, “Autofocus for tissue microscopy,” Image Vision Comput. 11, 629–639 (1993).

Int. J. Comput. Vision (1)

E. Krotkov, “Focusing,” Int. J. Comput. Vision 1, 223–237 (1987).
[CrossRef]

J. Opt. Soc. Am. (1)

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]

Rev. Sci. Instruments (1)

M. Bravo-Zanoguera, B. V. Massenbach, A. L. Kellner, J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instruments 69, 3966–3977 (1998).
[CrossRef]

Other (6)

M. Bravo-Zanoguera, J. H. Price, “Analog autofocus circuit for scanning microscopy,” in Optical Diagnostics of Biological Fluids and Advanced Techniques in Analytical Cytology, A. V. Priezzhev, T. Asakura, R. C. Leif, eds., Proc. SPIE2982, 468–475 (1997).
[CrossRef]

S. Inoué, Video Microscopy (Plenum, New York, 1986).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1989).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1988).

K. R. Castleman, Digital Image Processing (Prentice-Hall, Upper Saddle River, N. J., 1996).

M. Françon, Progress in Microscopy (Row, Peterson, Evanston, Ill., 1961).

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Figures (10)

Fig. 1
Fig. 1

One-dimensional through-focus MTF, thin specimen.

Fig. 2
Fig. 2

One-dimensional through-focus spectra of a stage micrometer in phase contrast. The fundamental frequency of the micrometer is f m .

Fig. 3
Fig. 3

One-dimensional through-focus MTF, thick specimen.

Fig. 4
Fig. 4

One-dimensional through-focus spectra of a tilted stage micrometer in phase contrast.

Fig. 5
Fig. 5

One-dimensional through-focus spectra of a multicell field in phase contrast.

Fig. 6
Fig. 6

Focus function curve in which signal power from the fundamental frequency of the micrometer in phase contrast is used.

Fig. 7
Fig. 7

Frequency spectra of (a) 31-tap bandpass filter and (b) {1 0 -1}.

Fig. 8
Fig. 8

Focus function curves for nontilted micrometer images in phase contrast.

Fig. 9
Fig. 9

Focus function curves for tilted micrometer images in phase contrast.

Fig. 10
Fig. 10

Focus function curves for multicell field images in phase contrast.

Equations (9)

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fc=NAobj+NAcond/λ,
Fz=xyfxizx, yWx2xy izx, y2
Wa= zFzn/ Fzn,
izx, y=ox, yhzx, y,
Izfx, fy=Ofx, fyOTFzfx, fy,
OTFw, q=1π2β-sin 2βjinc8πwλ1-|q|fcqfc,
w=-df-Δz cos α+df2+2dfΔz+Δz2 cos2α1/2,
ix, y|z=j=- ox, y|jΔzhx, yz-jΔzΔz,
Ifx, fy|z=j=- Ofx, fy|jΔzOTFfx, fyz-jΔzΔz.

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