Abstract

Laser sources offer a possible solution to the problem of low light throughput in direct-view microscopes (DVMs). However, coherent source DVMs have been shown to suffer from problems such as increased sidelobes in the depth response because of coherent cross talk between neighboring apertures. We explore theoretically how source coherence affects the depth responses of DVMs by employing various aperture spacings and number of apertures. We show that, contrary to expectation, closely spaced apertures can result in decreased full width at half-maximum of the depth response curve. We explain this as an effect of destructive interference when cross talk between neighboring apertures occurs. Using apertures arranged in a square grid as an example, we move on to show that the use of aperture arrays that consist of regularly arranged apertures can accentuate the problematic sidelobes of the depth response. We show that arranging pinholes in a rectangular grid rather than a square grid can improve the optical sectioning strength significantly. Finally, by examination of the depth responses corresponding to the infinite-pinhole-array limit, we make some general statements about source coherence and the characteristics of arrays that are likely to perform well.

© 2002 Optical Society of America

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References

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  1. M. Minsky, “Microscopy apparatus,” U.S. patent3,013,467 (December19, 1961).
  2. M. D. Egger, M. Petráň, “New reflected-light microscope for viewing unstained brain and ganglion cells,” Science 157, 305–307 (1967).
    [CrossRef] [PubMed]
  3. M. Petráň, M. Hadravský, M. D. Egger, R. Galambos, “Tandem-scanning reflected-light microscope,” J. Opt. Soc. Am. 58, 90–93 (1968).
  4. A. Boyde, M. Petráň, M. Hadravský, “Tandem scanningreflected-light microscope of internal features in whole bone and tooth samples,” J. Microsc. (Oxford) 132, 1–7 (1983).
    [CrossRef]
  5. G. Q. Xiao, T. R. Corle, G. S. Kino, “Real-time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
    [CrossRef]
  6. E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, J. Hegarty, “Direct-view microscopy: optical sectioning strength for finite sized, multiple-pinhole arrays,” J. Microsc. (Oxford) 184, 95–105 (1996).
    [CrossRef]
  7. S. J. Hewlett, D. T. Fewer, E. M. McCabe, “Influence of source coherence and aperture distribution on the imaging properties in direct-view microscopy,” J. Opt. Soc. Am. A 14, 1066–1075 (1997).
    [CrossRef]
  8. D. T. Fewer, S. J. Hewlett, E. M. McCabe, “Laser sources in direct-view-scanning, tandem-scanning, or Nipkow-disk-scanning microscopy,” Appl. Opt. 37, 380–385 (1998).
    [CrossRef]
  9. C. J. R. Sheppard, T. Wilson, “The theory of the direct-view confocal microscope,” J. Microsc. (Oxford) 124, 107–117 (1981).
    [CrossRef]
  10. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).
  11. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London, Ser. A 231, 91–103 (1955).
    [CrossRef]
  12. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  13. T. Wilson, S. J. Hewlett, “Optical sectioning strength of the direct-view microscope employing finite-sized pin-hole arrays,” J. Microsc. (Oxford) 163, 131–150 (1991).
    [CrossRef]
  14. M. Liang, R. L. Stehr, A. W. Krause, “Confocal pattern period in multiple-aperture confocal imaging systems with coherent illumination,” Opt. Lett. 22, 751–753 (1997).
    [CrossRef] [PubMed]
  15. Q. S. Hanley, P. J. Verveer, M. J. Gemkow, T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. (Oxford) 196, 317–331 (1999).
    [CrossRef]
  16. H. Talbot, “Facts relating to optical science 4,” Philos. Mag. 9, 401–409 (1836).
  17. A. Egner, S. W. Hell, “Time multiplexing and parallelization in multifocal multiphoton microscopy,” J. Opt. Soc. Am. A 17, 1192–1201 (2000).
    [CrossRef]
  18. P. J. Smith, C. M. Taylor, A. J. Shaw, E. McCabe, “Programmable array microscopy using a ferroelectric liquid crystal SLM,” Appl. Opt. 39, 2664–2669 (2000).
    [CrossRef]
  19. C. M. Taylor, P. J. Smith, E. M. McCabe, “A programmable array microscope demonstrator: application of a ferroelectric liquid crystal SLM,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition Processing VII, J.-A. Conchello, C. J. Cogswell, T. Wilson, eds., Proc. SPIE3919, 21–29 (2000).
    [CrossRef]

2000

1999

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. (Oxford) 196, 317–331 (1999).
[CrossRef]

1998

1997

1996

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, J. Hegarty, “Direct-view microscopy: optical sectioning strength for finite sized, multiple-pinhole arrays,” J. Microsc. (Oxford) 184, 95–105 (1996).
[CrossRef]

1991

T. Wilson, S. J. Hewlett, “Optical sectioning strength of the direct-view microscope employing finite-sized pin-hole arrays,” J. Microsc. (Oxford) 163, 131–150 (1991).
[CrossRef]

1988

G. Q. Xiao, T. R. Corle, G. S. Kino, “Real-time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
[CrossRef]

1983

A. Boyde, M. Petráň, M. Hadravský, “Tandem scanningreflected-light microscope of internal features in whole bone and tooth samples,” J. Microsc. (Oxford) 132, 1–7 (1983).
[CrossRef]

1981

C. J. R. Sheppard, T. Wilson, “The theory of the direct-view confocal microscope,” J. Microsc. (Oxford) 124, 107–117 (1981).
[CrossRef]

1968

1967

M. D. Egger, M. Petráň, “New reflected-light microscope for viewing unstained brain and ganglion cells,” Science 157, 305–307 (1967).
[CrossRef] [PubMed]

1955

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

1836

H. Talbot, “Facts relating to optical science 4,” Philos. Mag. 9, 401–409 (1836).

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).

Boyde, A.

A. Boyde, M. Petráň, M. Hadravský, “Tandem scanningreflected-light microscope of internal features in whole bone and tooth samples,” J. Microsc. (Oxford) 132, 1–7 (1983).
[CrossRef]

Corle, T. R.

G. Q. Xiao, T. R. Corle, G. S. Kino, “Real-time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
[CrossRef]

Egger, M. D.

M. Petráň, M. Hadravský, M. D. Egger, R. Galambos, “Tandem-scanning reflected-light microscope,” J. Opt. Soc. Am. 58, 90–93 (1968).

M. D. Egger, M. Petráň, “New reflected-light microscope for viewing unstained brain and ganglion cells,” Science 157, 305–307 (1967).
[CrossRef] [PubMed]

Egner, A.

Fewer, D. T.

Galambos, R.

Gemkow, M. J.

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. (Oxford) 196, 317–331 (1999).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Hadravský, M.

A. Boyde, M. Petráň, M. Hadravský, “Tandem scanningreflected-light microscope of internal features in whole bone and tooth samples,” J. Microsc. (Oxford) 132, 1–7 (1983).
[CrossRef]

M. Petráň, M. Hadravský, M. D. Egger, R. Galambos, “Tandem-scanning reflected-light microscope,” J. Opt. Soc. Am. 58, 90–93 (1968).

Hanley, Q. S.

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. (Oxford) 196, 317–331 (1999).
[CrossRef]

Hegarty, J.

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, J. Hegarty, “Direct-view microscopy: optical sectioning strength for finite sized, multiple-pinhole arrays,” J. Microsc. (Oxford) 184, 95–105 (1996).
[CrossRef]

Hell, S. W.

Hewlett, S. J.

D. T. Fewer, S. J. Hewlett, E. M. McCabe, “Laser sources in direct-view-scanning, tandem-scanning, or Nipkow-disk-scanning microscopy,” Appl. Opt. 37, 380–385 (1998).
[CrossRef]

S. J. Hewlett, D. T. Fewer, E. M. McCabe, “Influence of source coherence and aperture distribution on the imaging properties in direct-view microscopy,” J. Opt. Soc. Am. A 14, 1066–1075 (1997).
[CrossRef]

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, J. Hegarty, “Direct-view microscopy: optical sectioning strength for finite sized, multiple-pinhole arrays,” J. Microsc. (Oxford) 184, 95–105 (1996).
[CrossRef]

T. Wilson, S. J. Hewlett, “Optical sectioning strength of the direct-view microscope employing finite-sized pin-hole arrays,” J. Microsc. (Oxford) 163, 131–150 (1991).
[CrossRef]

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]

Jovin, T. M.

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. (Oxford) 196, 317–331 (1999).
[CrossRef]

Kino, G. S.

G. Q. Xiao, T. R. Corle, G. S. Kino, “Real-time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
[CrossRef]

Krause, A. W.

Liang, M.

McCabe, E.

McCabe, E. M.

D. T. Fewer, S. J. Hewlett, E. M. McCabe, “Laser sources in direct-view-scanning, tandem-scanning, or Nipkow-disk-scanning microscopy,” Appl. Opt. 37, 380–385 (1998).
[CrossRef]

S. J. Hewlett, D. T. Fewer, E. M. McCabe, “Influence of source coherence and aperture distribution on the imaging properties in direct-view microscopy,” J. Opt. Soc. Am. A 14, 1066–1075 (1997).
[CrossRef]

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, J. Hegarty, “Direct-view microscopy: optical sectioning strength for finite sized, multiple-pinhole arrays,” J. Microsc. (Oxford) 184, 95–105 (1996).
[CrossRef]

C. M. Taylor, P. J. Smith, E. M. McCabe, “A programmable array microscope demonstrator: application of a ferroelectric liquid crystal SLM,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition Processing VII, J.-A. Conchello, C. J. Cogswell, T. Wilson, eds., Proc. SPIE3919, 21–29 (2000).
[CrossRef]

Minsky, M.

M. Minsky, “Microscopy apparatus,” U.S. patent3,013,467 (December19, 1961).

Ottewill, A. C.

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, J. Hegarty, “Direct-view microscopy: optical sectioning strength for finite sized, multiple-pinhole arrays,” J. Microsc. (Oxford) 184, 95–105 (1996).
[CrossRef]

Petrán, M.

A. Boyde, M. Petráň, M. Hadravský, “Tandem scanningreflected-light microscope of internal features in whole bone and tooth samples,” J. Microsc. (Oxford) 132, 1–7 (1983).
[CrossRef]

M. Petráň, M. Hadravský, M. D. Egger, R. Galambos, “Tandem-scanning reflected-light microscope,” J. Opt. Soc. Am. 58, 90–93 (1968).

M. D. Egger, M. Petráň, “New reflected-light microscope for viewing unstained brain and ganglion cells,” Science 157, 305–307 (1967).
[CrossRef] [PubMed]

Shaw, A. J.

Sheppard, C. J. R.

C. J. R. Sheppard, T. Wilson, “The theory of the direct-view confocal microscope,” J. Microsc. (Oxford) 124, 107–117 (1981).
[CrossRef]

Smith, P. J.

P. J. Smith, C. M. Taylor, A. J. Shaw, E. McCabe, “Programmable array microscopy using a ferroelectric liquid crystal SLM,” Appl. Opt. 39, 2664–2669 (2000).
[CrossRef]

C. M. Taylor, P. J. Smith, E. M. McCabe, “A programmable array microscope demonstrator: application of a ferroelectric liquid crystal SLM,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition Processing VII, J.-A. Conchello, C. J. Cogswell, T. Wilson, eds., Proc. SPIE3919, 21–29 (2000).
[CrossRef]

Stehr, R. L.

Talbot, H.

H. Talbot, “Facts relating to optical science 4,” Philos. Mag. 9, 401–409 (1836).

Taylor, C. M.

P. J. Smith, C. M. Taylor, A. J. Shaw, E. McCabe, “Programmable array microscopy using a ferroelectric liquid crystal SLM,” Appl. Opt. 39, 2664–2669 (2000).
[CrossRef]

C. M. Taylor, P. J. Smith, E. M. McCabe, “A programmable array microscope demonstrator: application of a ferroelectric liquid crystal SLM,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition Processing VII, J.-A. Conchello, C. J. Cogswell, T. Wilson, eds., Proc. SPIE3919, 21–29 (2000).
[CrossRef]

Verveer, P. J.

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. (Oxford) 196, 317–331 (1999).
[CrossRef]

Wilson, T.

T. Wilson, S. J. Hewlett, “Optical sectioning strength of the direct-view microscope employing finite-sized pin-hole arrays,” J. Microsc. (Oxford) 163, 131–150 (1991).
[CrossRef]

C. J. R. Sheppard, T. Wilson, “The theory of the direct-view confocal microscope,” J. Microsc. (Oxford) 124, 107–117 (1981).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).

Xiao, G. Q.

G. Q. Xiao, T. R. Corle, G. S. Kino, “Real-time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

G. Q. Xiao, T. R. Corle, G. S. Kino, “Real-time confocal scanning optical microscope,” Appl. Phys. Lett. 53, 716–718 (1988).
[CrossRef]

J. Microsc. (Oxford)

E. M. McCabe, D. T. Fewer, A. C. Ottewill, S. J. Hewlett, J. Hegarty, “Direct-view microscopy: optical sectioning strength for finite sized, multiple-pinhole arrays,” J. Microsc. (Oxford) 184, 95–105 (1996).
[CrossRef]

C. J. R. Sheppard, T. Wilson, “The theory of the direct-view confocal microscope,” J. Microsc. (Oxford) 124, 107–117 (1981).
[CrossRef]

T. Wilson, S. J. Hewlett, “Optical sectioning strength of the direct-view microscope employing finite-sized pin-hole arrays,” J. Microsc. (Oxford) 163, 131–150 (1991).
[CrossRef]

Q. S. Hanley, P. J. Verveer, M. J. Gemkow, T. M. Jovin, “An optical sectioning programmable array microscope implemented with a digital micromirror device,” J. Microsc. (Oxford) 196, 317–331 (1999).
[CrossRef]

A. Boyde, M. Petráň, M. Hadravský, “Tandem scanningreflected-light microscope of internal features in whole bone and tooth samples,” J. Microsc. (Oxford) 132, 1–7 (1983).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Philos. Mag.

H. Talbot, “Facts relating to optical science 4,” Philos. Mag. 9, 401–409 (1836).

Proc. R. Soc. London, Ser. A

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

Science

M. D. Egger, M. Petráň, “New reflected-light microscope for viewing unstained brain and ganglion cells,” Science 157, 305–307 (1967).
[CrossRef] [PubMed]

Other

C. M. Taylor, P. J. Smith, E. M. McCabe, “A programmable array microscope demonstrator: application of a ferroelectric liquid crystal SLM,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition Processing VII, J.-A. Conchello, C. J. Cogswell, T. Wilson, eds., Proc. SPIE3919, 21–29 (2000).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

M. Minsky, “Microscopy apparatus,” U.S. patent3,013,467 (December19, 1961).

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1997).

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Figures (12)

Fig. 1
Fig. 1

Image of a 1×3 pinhole array in the focal plane of an objective lens. Cross talk occurs between pinholes when the mirror is sufficiently displaced from the focal plane. The two types of interference that can occur are shown: (a) interference at X and (b) interference at Y.

Fig. 2
Fig. 2

Depth responses for DVMs employing 1×1 (□), 1×2 (○), and 1×5 (⋄) arrays of pinholes. The pinhole spacing was 30 μm, and the pinhole diameter was 15 μm. (a) Coherent source and (b) incoherent source. Overlayed on (a) are predicted cases of constructive and destructive interference resulting from cross talk in the cases of the 1×2 and 1×5 arrays. The axial position of occurrence of each instance of interference is plotted against its weight of occurrence (the vertical axis to the right). The legend for these is as follows: Cases of destructive interference for the 1×2 array, ▼; cases of destructive interference for the 1×5 array, ▲; cases of constructive interference for the 1×5 array, △.

Fig. 3
Fig. 3

Theoretical depth responses for DVMs employing 1×1, 2×2, and 5×5 pinhole arrays with pinhole diameters of 15 μm and pinhole spacings of 30 μm: (a) coherent source, (b) incoherent source.

Fig. 4
Fig. 4

Theoretical depth responses for DVMs employing 1×1 (solid curve with no symbols), 2×2 (□), 5×5 (○), 10×10 (△), and infinite (⋄) pinhole arrays with pinhole diameters of 15 μm and pinhole spacings of 60 μm. The depth responses have been vertically offset from each other so that each curve can be clearly distinguished. The series of dotted lines represents the zero reference for each of the offset curves. (a) Coherent source, (b) incoherent source.

Fig. 5
Fig. 5

Variation of the maximum sidelobe level in the depth responses (expressed as a fraction of the in-focus intensity) of coherent-source DVMs employing square 5×5 pinhole arrays as a function of the total number of pinholes, N, for pinhole spacings d of 30 μm (□), 45 μm (○), 60 μm (△), and 120 μm (⋄). The pinhole diameter was 15 μm.

Fig. 6
Fig. 6

Theoretical depth responses for DVMs employing 5×5 square pinhole arrays with pinhole diameters of 15 μm and center-to-center pinhole spacings of 15 μm (solid curve with no symbols), 30 μm (□), 60 μm (○), 120 μm (△), and 240 μm (⋄), and an infinitely spaced array (*). (a) Coherent source, (b) incoherent source.

Fig. 7
Fig. 7

Variation of the maximum sidelobe level in the depth response (expressed as a fraction of the in-focus intensity) of coherent-source DVMs employing 1×1, 2×2, and 5×5 pinhole arrays as a function of the pinhole spacing d. The pinhole diameter was 15 μm.

Fig. 8
Fig. 8

Theoretical depth responses for DVMs employing 5×5 pinhole arrays with pinhole diameters of 15 μm and pinhole spacings of 30 μm square (□), 45 μm square (○), and 30 μm × 45 μm rectangular (△). (a) Coherent source, (b) incoherent source.

Fig. 9
Fig. 9

Variation of the maximum sidelobe level in the depth response (expressed as a fraction of the in-focus intensity) as a function of (a) the number of pinholes, N, for pinhole spacings d of 30 μm square (solid curve with no symbols), 45 μm square (□), and 30 μm × 45 μm rectangular (○) and (b) the pinhole spacing d for a 5×5 square array with a pinhole spacing of 45 μm and a 5×5 rectangular array with a pinhole spacing of 30 μm × 45 μm.

Fig. 10
Fig. 10

Theoretical depth responses for coherent-source DVMs employing infinite pinhole arrays. The pinhole diameter was 15 μm. The solid curve represents the depth response of a square array with center-to-center pinhole spacing of 45 μm, the dashed curve is the depth response of a square array with center-to-center pinhole spacing of 60 μm, and the solid curve with Δs overlayed is the depth response of a rectangular array with center-to-center pinhole spacings of 45 μm (x direction) and 60 μm (y direction).

Fig. 11
Fig. 11

Theoretical depth responses for coherent-source DVMs employing infinite pinhole arrays. The pinhole diameter was 15 μm. The dashed curve represents the depth response of a square array with center-to-center pinhole spacing of 240 μm, and the solid curve is the depth response of a rectangular array with center-to-center pinhole spacings of 240 μm (x direction) and 225 μm (y direction).

Fig. 12
Fig. 12

Direct-view microscope employing a 1×5 pinhole array applied to a uniformly reflecting sample with a stepped profile.

Equations (22)

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

I(u)=i=1Nj=1N02FS1ρM2g(2u, ρ)×J0ρM|Ti-Tj|ρdρ.
u=8πnλ z sin2α2,
t=2πnλ r sin α.
FS1(ρ)=2 J1(ρvp)ρvp,
g(u, ρ)=(PP*)(u, ρ),
P(u, ρ)=exp(-12ju|ρ|2),|ρ|10,otherwise.
I(u)=j=1NS1(t)i=1N01P(2u, ρ)FS1ρM×J0ρM |Ti-Tj-t|ρdρ2d2t.
limNI(u)=klFS12πkRx, 2πlRy2×g2u, M2πkRx, M2πlRy,
kRx2+lRy21Mπ2.
limNI(u)=02π0vpklFS12πkRx, 2πlRy×P2u, M2πkRx, M2πlRy×exp2πjrkRxcos θ+lRysin θ2rdrdθ,
kRx2+lRy212Mπ2.
z=a24mλ-mλ4
z=m2λ216+14m2λ2 [(a2+b2)2-a2b2]-a2+b281/2
W=2(N-p).
P2u, M2πkRx, M2πlRy=exp-j4π2uM2R2 (k2+l2).
|u|(k2+l2)=R22πM2qintegersk,l
|u|=R22πM2q,
|z|=d2n cos2(α/2)λM2q,
|u|=R24πM2r,
P=exp[-jrπ(k2+l2)].
RxRy2=q2q1
u=Rx22πM2q1 or,equivalently,u=Ry22πM2q2,

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