Abstract

Oil-immersion microscope objective lenses have been designed and optimized for the study of thin, two-dimensional object sections that are mounted immediately below the coverslip in a medium that is index matched to the immersion oil. It has been demonstrated both experimentally and through geometrical- and physical-optics theory that, when the microscope is not used with the correct coverslip or immersion oil, when the detector is not located at the optimal plane in image space, or when the object does not satisfy specific conditions, aberration will degrade both the contrast and the resolution of the image. In biology the most severe aberration is introduced when an oil-immersion objective lens is used to study thick specimens, such as living cells and tissues, whose refractive indices are significantly different from that of the immersion oil. We present a model of the three-dimensional imaging properties of a fluorescence light microscope subject to such aberration and compare the imaging properties predicted by the model with those measured experimentally. The model can be used to understand and compensate for aberration introduced to a microscope system under nondesign optical conditions so that both confocal laser scanning microscopy and optical serial sectioning microscopy can be optimized.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Inoue, Video Microscopy (Plenum, New York, 1986).
  2. B. Herman, K. Jacobson, eds., Optical Microscopy for Biology (Wiley, New York, 1990).
  3. Y. Wang, D. L. Taylor, eds., Methods in Cell Biology, Fluorescence Microscopy of Living Cells in Culture (Academic, San Diego, Calif., 1989), Vol. 30, Part B.
  4. G. Brakenhoff, H. T. van der Voort, E. A. van Spronson, N. Nanninga, “3-dimensional imaging of biological structures by high resolution confocal scanning laser microscopy,” Scanning Microsc. 2, 33–40 (1988).
    [PubMed]
  5. T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).
  6. D. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984).
    [CrossRef] [PubMed]
  7. S. Frisken Gibson, F. Lanni, “Measured and analytical point-spread functions of the optical microscope for use in 3-D optical serial sectioning microscopy,” in Optical Microscopy for Biology, B. Herman, K. Jacobson, eds. (Wiley, New York, 1990), pp. 109–118.
  8. M. Born, E. Wolf, Principles of Optics, 8th ed. (Pergamon, New York, 1959).
  9. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. Phys. Soc. London Sect. A 231, 91–103 (1955).
    [CrossRef]
  10. P. A. Stokseth, “Properties of a defocused optical system,”J. Opt. Soc. Am. 59, 1314–1321 (1969).
    [CrossRef]
  11. F. S. Fay, W. Carrington, W. Fogarty, “Three-dimensional molecular distribution in single cells analyzed using the digital imaging microscope,” J. Microsc. (Oxford) Part 2 153, 133–149 (1989).
    [CrossRef]
  12. L. Tella, “The determination of a microscope’s three-dimensional transfer function for the use in image restoration,” master’s thesis (Worcester Polytechnic Institute, Worcester, Mass., 1985).
  13. D. Agard, Y. Hiraoka, P. Shaw, J. Sedat, “Fluorescence microscopy in three dimensions,” in Methods in Cell Biology, Fluorescence Microscopy of Living Cells in Culture, D. L. Taylor, Y. Wang, eds. (Academic, San Diego, Calif., 1989), Vol. 30, Part B, Chap. 13, pp. 353–377.
  14. Y. Hiraoka, J. W. Sedat, D. Agard, “Determination of the three-dimensional imaging properties of a light microscope system: partial confocal behavior in epifluorescence microscopy,” Biophys. J. 57, 325–333 (1990).
    [CrossRef] [PubMed]
  15. The accuracy of this assumption can easily be verified for a microscope lens system by the use of a planar diffraction grating object illuminated by a monochromatic, collimated laser and a telescope used to observe the back focal surface. We made these measurements on the microscope objective lenses described in this paper and found that the lenses produced compact images over the back focal surface of the individual diffraction orders formed by the grating and that this surface was planar to ±100 μm across the diameter of the back focal surface. The compact image of each order had the appearance of an Airy pattern, from which we conclude that each is a nearly stigmatic image of the incoming parallel rays. We also verified that the diffraction orders were equispaced in the focal plane, as is expected for a lens that obeys the sine condition. The results of this experiment verify the assumption that parallel rays entering a lens system will travel equal optical paths and cross in the back focal plane as well as the assumption that the back focal surface is planar.
  16. S. Frisken Gibson, “Modeling the 3-D imaging properties of the fluorescence light microscope,” Ph.D. dissertation (Carnegie Mellon University, Pittsburgh, Pa., 1990).
  17. R. J. Bracey, “I. The aberrations of microscope objectives and their variations with small departures from optimum working conditions,”J. R. Microsc. Soc. 72, 1–9 (1952).
    [CrossRef] [PubMed]
  18. B. Spinnel, R. Loveland, “V. Optics of the object space in microscopy,”J. R. Microsc. Soc. 79, 59–80 (1960).
    [CrossRef]
  19. R. Loveland, Photomicrography: A Comprehensive Treatise (Wiley, New York, 1981).
  20. H. Kraus, “Huygens–Fresnel–Kirchhoff wave-front diffraction formulation: spherical waves,” J. Opt. Soc. Am. A 6, 1196–1205 (1989).
    [CrossRef]
  21. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure in the image field of an aplanatic system,” Proc. R. Soc. London 253, 358–379 (1959).
    [CrossRef]
  22. H. van der Voort, G. Brakenhoff, “3D image formation in high-aperture fluorescence confocal microscopy: a numerical analysis,” J. Microsc. (Oxford) Part 2 158, 43–54 (1990).
    [CrossRef]
  23. Y. Hiraoka, J. W. Sedat, D. Agard, “The use of a charge-coupled device for quantitative optical microscopy of biological structures,” Science 238, 36–41 (1987).
    [CrossRef] [PubMed]
  24. Rayleigh’s quarter-wave rule states that the quality of the (2-D) image is not seriously affected when the wave-front error in the back aperture of the objective lens is less than 1/4 wavelength.8 However, Bracey17 states that this tolerance may be slightly high for the experienced microscopist and hence both λ/4 and λ/8 have been used as estimates of the maximum tolerable aberration.
  25. R. Barakat, “Computation of the transfer function of an optical system from the design data for rotationally symmetric aberrations,”J. Opt. Soc. Am. 52, 985–997 (1962).
    [CrossRef]
  26. R. Barakat, D. Lev, “Transfer function and total illuminance of high NA systems obeying the sine condition,”J. Opt. Soc. Am. 53, 324–332 (1963).
    [CrossRef]
  27. B. Nijboer, “The diffraction theory of optical aberration. Part II. Diffraction in the presence of small aberrations,” Physica 13, 605–620 (1943).
    [CrossRef]
  28. S. Wang, B. Frieden, “Effects of third order spherical aberration on the diffraction-limited 3-D incoherent optical transfer function,” Appl. Opt. 29, 2424–2432 (1990).
    [CrossRef] [PubMed]

1990 (3)

Y. Hiraoka, J. W. Sedat, D. Agard, “Determination of the three-dimensional imaging properties of a light microscope system: partial confocal behavior in epifluorescence microscopy,” Biophys. J. 57, 325–333 (1990).
[CrossRef] [PubMed]

H. van der Voort, G. Brakenhoff, “3D image formation in high-aperture fluorescence confocal microscopy: a numerical analysis,” J. Microsc. (Oxford) Part 2 158, 43–54 (1990).
[CrossRef]

S. Wang, B. Frieden, “Effects of third order spherical aberration on the diffraction-limited 3-D incoherent optical transfer function,” Appl. Opt. 29, 2424–2432 (1990).
[CrossRef] [PubMed]

1989 (2)

H. Kraus, “Huygens–Fresnel–Kirchhoff wave-front diffraction formulation: spherical waves,” J. Opt. Soc. Am. A 6, 1196–1205 (1989).
[CrossRef]

F. S. Fay, W. Carrington, W. Fogarty, “Three-dimensional molecular distribution in single cells analyzed using the digital imaging microscope,” J. Microsc. (Oxford) Part 2 153, 133–149 (1989).
[CrossRef]

1988 (1)

G. Brakenhoff, H. T. van der Voort, E. A. van Spronson, N. Nanninga, “3-dimensional imaging of biological structures by high resolution confocal scanning laser microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

1987 (1)

Y. Hiraoka, J. W. Sedat, D. Agard, “The use of a charge-coupled device for quantitative optical microscopy of biological structures,” Science 238, 36–41 (1987).
[CrossRef] [PubMed]

1984 (1)

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

1969 (1)

1963 (1)

1962 (1)

1960 (1)

B. Spinnel, R. Loveland, “V. Optics of the object space in microscopy,”J. R. Microsc. Soc. 79, 59–80 (1960).
[CrossRef]

1959 (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure in the image field of an aplanatic system,” Proc. R. Soc. London 253, 358–379 (1959).
[CrossRef]

1955 (1)

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

1952 (1)

R. J. Bracey, “I. The aberrations of microscope objectives and their variations with small departures from optimum working conditions,”J. R. Microsc. Soc. 72, 1–9 (1952).
[CrossRef] [PubMed]

1943 (1)

B. Nijboer, “The diffraction theory of optical aberration. Part II. Diffraction in the presence of small aberrations,” Physica 13, 605–620 (1943).
[CrossRef]

Agard, D.

Y. Hiraoka, J. W. Sedat, D. Agard, “Determination of the three-dimensional imaging properties of a light microscope system: partial confocal behavior in epifluorescence microscopy,” Biophys. J. 57, 325–333 (1990).
[CrossRef] [PubMed]

Y. Hiraoka, J. W. Sedat, D. Agard, “The use of a charge-coupled device for quantitative optical microscopy of biological structures,” Science 238, 36–41 (1987).
[CrossRef] [PubMed]

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

D. Agard, Y. Hiraoka, P. Shaw, J. Sedat, “Fluorescence microscopy in three dimensions,” in Methods in Cell Biology, Fluorescence Microscopy of Living Cells in Culture, D. L. Taylor, Y. Wang, eds. (Academic, San Diego, Calif., 1989), Vol. 30, Part B, Chap. 13, pp. 353–377.

Barakat, R.

Born, M.

M. Born, E. Wolf, Principles of Optics, 8th ed. (Pergamon, New York, 1959).

Bracey, R. J.

R. J. Bracey, “I. The aberrations of microscope objectives and their variations with small departures from optimum working conditions,”J. R. Microsc. Soc. 72, 1–9 (1952).
[CrossRef] [PubMed]

Brakenhoff, G.

H. van der Voort, G. Brakenhoff, “3D image formation in high-aperture fluorescence confocal microscopy: a numerical analysis,” J. Microsc. (Oxford) Part 2 158, 43–54 (1990).
[CrossRef]

G. Brakenhoff, H. T. van der Voort, E. A. van Spronson, N. Nanninga, “3-dimensional imaging of biological structures by high resolution confocal scanning laser microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

Carrington, W.

F. S. Fay, W. Carrington, W. Fogarty, “Three-dimensional molecular distribution in single cells analyzed using the digital imaging microscope,” J. Microsc. (Oxford) Part 2 153, 133–149 (1989).
[CrossRef]

Fay, F. S.

F. S. Fay, W. Carrington, W. Fogarty, “Three-dimensional molecular distribution in single cells analyzed using the digital imaging microscope,” J. Microsc. (Oxford) Part 2 153, 133–149 (1989).
[CrossRef]

Fogarty, W.

F. S. Fay, W. Carrington, W. Fogarty, “Three-dimensional molecular distribution in single cells analyzed using the digital imaging microscope,” J. Microsc. (Oxford) Part 2 153, 133–149 (1989).
[CrossRef]

Frieden, B.

Frisken Gibson, S.

S. Frisken Gibson, F. Lanni, “Measured and analytical point-spread functions of the optical microscope for use in 3-D optical serial sectioning microscopy,” in Optical Microscopy for Biology, B. Herman, K. Jacobson, eds. (Wiley, New York, 1990), pp. 109–118.

S. Frisken Gibson, “Modeling the 3-D imaging properties of the fluorescence light microscope,” Ph.D. dissertation (Carnegie Mellon University, Pittsburgh, Pa., 1990).

Hiraoka, Y.

Y. Hiraoka, J. W. Sedat, D. Agard, “Determination of the three-dimensional imaging properties of a light microscope system: partial confocal behavior in epifluorescence microscopy,” Biophys. J. 57, 325–333 (1990).
[CrossRef] [PubMed]

Y. Hiraoka, J. W. Sedat, D. Agard, “The use of a charge-coupled device for quantitative optical microscopy of biological structures,” Science 238, 36–41 (1987).
[CrossRef] [PubMed]

D. Agard, Y. Hiraoka, P. Shaw, J. Sedat, “Fluorescence microscopy in three dimensions,” in Methods in Cell Biology, Fluorescence Microscopy of Living Cells in Culture, D. L. Taylor, Y. Wang, eds. (Academic, San Diego, Calif., 1989), Vol. 30, Part B, Chap. 13, pp. 353–377.

Hopkins, H. H.

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

Inoue, S.

S. Inoue, Video Microscopy (Plenum, New York, 1986).

Kraus, H.

Lanni, F.

S. Frisken Gibson, F. Lanni, “Measured and analytical point-spread functions of the optical microscope for use in 3-D optical serial sectioning microscopy,” in Optical Microscopy for Biology, B. Herman, K. Jacobson, eds. (Wiley, New York, 1990), pp. 109–118.

Lev, D.

Loveland, R.

B. Spinnel, R. Loveland, “V. Optics of the object space in microscopy,”J. R. Microsc. Soc. 79, 59–80 (1960).
[CrossRef]

R. Loveland, Photomicrography: A Comprehensive Treatise (Wiley, New York, 1981).

Nanninga, N.

G. Brakenhoff, H. T. van der Voort, E. A. van Spronson, N. Nanninga, “3-dimensional imaging of biological structures by high resolution confocal scanning laser microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

Nijboer, B.

B. Nijboer, “The diffraction theory of optical aberration. Part II. Diffraction in the presence of small aberrations,” Physica 13, 605–620 (1943).
[CrossRef]

Richards, B.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure in the image field of an aplanatic system,” Proc. R. Soc. London 253, 358–379 (1959).
[CrossRef]

Sedat, J.

D. Agard, Y. Hiraoka, P. Shaw, J. Sedat, “Fluorescence microscopy in three dimensions,” in Methods in Cell Biology, Fluorescence Microscopy of Living Cells in Culture, D. L. Taylor, Y. Wang, eds. (Academic, San Diego, Calif., 1989), Vol. 30, Part B, Chap. 13, pp. 353–377.

Sedat, J. W.

Y. Hiraoka, J. W. Sedat, D. Agard, “Determination of the three-dimensional imaging properties of a light microscope system: partial confocal behavior in epifluorescence microscopy,” Biophys. J. 57, 325–333 (1990).
[CrossRef] [PubMed]

Y. Hiraoka, J. W. Sedat, D. Agard, “The use of a charge-coupled device for quantitative optical microscopy of biological structures,” Science 238, 36–41 (1987).
[CrossRef] [PubMed]

Shaw, P.

D. Agard, Y. Hiraoka, P. Shaw, J. Sedat, “Fluorescence microscopy in three dimensions,” in Methods in Cell Biology, Fluorescence Microscopy of Living Cells in Culture, D. L. Taylor, Y. Wang, eds. (Academic, San Diego, Calif., 1989), Vol. 30, Part B, Chap. 13, pp. 353–377.

Sheppard, C.

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

Spinnel, B.

B. Spinnel, R. Loveland, “V. Optics of the object space in microscopy,”J. R. Microsc. Soc. 79, 59–80 (1960).
[CrossRef]

Stokseth, P. A.

Tella, L.

L. Tella, “The determination of a microscope’s three-dimensional transfer function for the use in image restoration,” master’s thesis (Worcester Polytechnic Institute, Worcester, Mass., 1985).

van der Voort, H.

H. van der Voort, G. Brakenhoff, “3D image formation in high-aperture fluorescence confocal microscopy: a numerical analysis,” J. Microsc. (Oxford) Part 2 158, 43–54 (1990).
[CrossRef]

van der Voort, H. T.

G. Brakenhoff, H. T. van der Voort, E. A. van Spronson, N. Nanninga, “3-dimensional imaging of biological structures by high resolution confocal scanning laser microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

van Spronson, E. A.

G. Brakenhoff, H. T. van der Voort, E. A. van Spronson, N. Nanninga, “3-dimensional imaging of biological structures by high resolution confocal scanning laser microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

Wang, S.

Wilson, T.

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

Wolf, E.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure in the image field of an aplanatic system,” Proc. R. Soc. London 253, 358–379 (1959).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 8th ed. (Pergamon, New York, 1959).

Annu. Rev. Biophys. Bioeng. (1)

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

Appl. Opt. (1)

Biophys. J. (1)

Y. Hiraoka, J. W. Sedat, D. Agard, “Determination of the three-dimensional imaging properties of a light microscope system: partial confocal behavior in epifluorescence microscopy,” Biophys. J. 57, 325–333 (1990).
[CrossRef] [PubMed]

J. Microsc. (Oxford) Part 2 (2)

F. S. Fay, W. Carrington, W. Fogarty, “Three-dimensional molecular distribution in single cells analyzed using the digital imaging microscope,” J. Microsc. (Oxford) Part 2 153, 133–149 (1989).
[CrossRef]

H. van der Voort, G. Brakenhoff, “3D image formation in high-aperture fluorescence confocal microscopy: a numerical analysis,” J. Microsc. (Oxford) Part 2 158, 43–54 (1990).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

J. R. Microsc. Soc. (2)

R. J. Bracey, “I. The aberrations of microscope objectives and their variations with small departures from optimum working conditions,”J. R. Microsc. Soc. 72, 1–9 (1952).
[CrossRef] [PubMed]

B. Spinnel, R. Loveland, “V. Optics of the object space in microscopy,”J. R. Microsc. Soc. 79, 59–80 (1960).
[CrossRef]

Physica (1)

B. Nijboer, “The diffraction theory of optical aberration. Part II. Diffraction in the presence of small aberrations,” Physica 13, 605–620 (1943).
[CrossRef]

Proc. Phys. Soc. London Sect. A (1)

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

Proc. R. Soc. London (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure in the image field of an aplanatic system,” Proc. R. Soc. London 253, 358–379 (1959).
[CrossRef]

Scanning Microsc. (1)

G. Brakenhoff, H. T. van der Voort, E. A. van Spronson, N. Nanninga, “3-dimensional imaging of biological structures by high resolution confocal scanning laser microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

Science (1)

Y. Hiraoka, J. W. Sedat, D. Agard, “The use of a charge-coupled device for quantitative optical microscopy of biological structures,” Science 238, 36–41 (1987).
[CrossRef] [PubMed]

Other (12)

Rayleigh’s quarter-wave rule states that the quality of the (2-D) image is not seriously affected when the wave-front error in the back aperture of the objective lens is less than 1/4 wavelength.8 However, Bracey17 states that this tolerance may be slightly high for the experienced microscopist and hence both λ/4 and λ/8 have been used as estimates of the maximum tolerable aberration.

T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, New York, 1984).

S. Inoue, Video Microscopy (Plenum, New York, 1986).

B. Herman, K. Jacobson, eds., Optical Microscopy for Biology (Wiley, New York, 1990).

Y. Wang, D. L. Taylor, eds., Methods in Cell Biology, Fluorescence Microscopy of Living Cells in Culture (Academic, San Diego, Calif., 1989), Vol. 30, Part B.

S. Frisken Gibson, F. Lanni, “Measured and analytical point-spread functions of the optical microscope for use in 3-D optical serial sectioning microscopy,” in Optical Microscopy for Biology, B. Herman, K. Jacobson, eds. (Wiley, New York, 1990), pp. 109–118.

M. Born, E. Wolf, Principles of Optics, 8th ed. (Pergamon, New York, 1959).

R. Loveland, Photomicrography: A Comprehensive Treatise (Wiley, New York, 1981).

L. Tella, “The determination of a microscope’s three-dimensional transfer function for the use in image restoration,” master’s thesis (Worcester Polytechnic Institute, Worcester, Mass., 1985).

D. Agard, Y. Hiraoka, P. Shaw, J. Sedat, “Fluorescence microscopy in three dimensions,” in Methods in Cell Biology, Fluorescence Microscopy of Living Cells in Culture, D. L. Taylor, Y. Wang, eds. (Academic, San Diego, Calif., 1989), Vol. 30, Part B, Chap. 13, pp. 353–377.

The accuracy of this assumption can easily be verified for a microscope lens system by the use of a planar diffraction grating object illuminated by a monochromatic, collimated laser and a telescope used to observe the back focal surface. We made these measurements on the microscope objective lenses described in this paper and found that the lenses produced compact images over the back focal surface of the individual diffraction orders formed by the grating and that this surface was planar to ±100 μm across the diameter of the back focal surface. The compact image of each order had the appearance of an Airy pattern, from which we conclude that each is a nearly stigmatic image of the incoming parallel rays. We also verified that the diffraction orders were equispaced in the focal plane, as is expected for a lens that obeys the sine condition. The results of this experiment verify the assumption that parallel rays entering a lens system will travel equal optical paths and cross in the back focal plane as well as the assumption that the back focal surface is planar.

S. Frisken Gibson, “Modeling the 3-D imaging properties of the fluorescence light microscope,” Ph.D. dissertation (Carnegie Mellon University, Pittsburgh, Pa., 1990).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Paths of rays from an on-axis point source to the front element of a high-magnification oil-immersion objective lens. ABCD is a ray from a point source in a nondesign system that enters the front lens element at an angle θ when the object lies at a depth t s in a medium of refractive index n s , the coverslip has a thickness t g and refractive index n g , and the immersion oil has a thickness toil and refractive index noil. PQRS is the corresponding ray in the design system and enters the front lens element at an angle θ. In the design system the point-source object is located immediately below the coverslip, the coverslip has a thickness t g * and refractive index n g *, and the oil-immersion layer has a thickness toil* and refractive index noil*.

Fig. 2
Fig. 2

Meridional (xz) sections of the predicted PSF of an OSM microscope in which the coverslip refractive index differs from that of the design system, n g * = 1.522. In this and all other PSF’s displayed in this paper, the horizontal axis is in the plane of the 2-D detector, and the horizontal scale bar in these figures represents 120 μm measured in image space. The vertical axis is the optical axis and, as in all OSM PSF’s in this paper, is measured in object space as the distance of the point source from its in-focus plane. In all OSM PSF’s the vertical scale bar represents 3.2 μm of stage movement in object space. In all figures in this paper we have scaled the PSF’s by using the same logarithmic mapping in order to enhance low-intensity detail. The design conditions are satisfied in A: A, n g = 1.522; B, n g = 1.527; C, n g = 1.532; D, n g = 1.537.

Fig. 3
Fig. 3

Meridional sections of the PSF of an OSM microscope in which the immersion-oil refractive index differs from that of the design system, noil* = 1.515. The design conditions are satisfied in A: A, noil = 1.515; B, noil = 1.520; C, n g = 1.525; D, n g = 1.530.

Fig. 4
Fig. 4

Meridional sections of the PSF of an OSM microscope in which the point source is located at a depth t s into a specimen layer with a refractive index n s = 1.33, which is significantly different from that of the immersion oil. Note that the design conditions are satisfied in A, so that this is the aberration-free, diffraction-limited OSM PSF: A, t s = 0 μm; B, t s = 2 μm; C, t s = 4 μm; D, t s = 10 μm; E, t s = 20 μm; F, t s = 60 μm.

Fig. 5
Fig. 5

Meridional sections of the PSF of an OSM microscope in which the distance from the back focal plane to the detector is z d rather than the design distance z d * = 160 mm. The design conditions are satisfied in C: A, z d = 130 mm; B, z d = 150 mm; C, z d = 160 mm; D, z d = 170 mm; E, z d = 190 mm; F, z d = 210 mm.

Fig. 6
Fig. 6

Meridional sections of the 3-D image field produced by the light microscope when the point-source object is located at a depth t s into a specimen layer of refractive index n s = 1.33. The horizontal axis is in the plane of the detector, and the horizontal scale bar represents 120 μm measured in image space. The vertical axis lies along the optical axis and is measured as a function of the distance of the image plane from the back focal plane. The vertical scale bar represents a distance in image space along the optical axis of 50 μm: A, t s = 0 μm; B, t s = 4 μm; C, t s = 10 μm.

Fig. 7
Fig. 7

Layers separating a point source from the front element of the objective lens in experiments measuring the OSM PSF. A, The fluorescent microsphere is embedded immediately below the coverslip in optical cement. The effects of coverslip thickness, immersion-oil refractive index, and microscope tube length on the PSF are measured with this specimen. B, The fluorescent microspheres lie in a layer of 1% agarose gel between the coverslip and a glass slide. This specimen is used to measure the effect of specimen depth into a layer of refractive index mismatched to that of the immersion oil on the 3-D PSF of an OSM system.

Fig. 8
Fig. 8

Simplified circuit diagram of the feedback stage-height controller. The distance from the objective lens to the stage is measured with a capacitance gauge. This distance is converted to a voltage that is compared with a computer-controlled voltage that specifies the desired stage height. The difference between these two signals is used in a negative-feedback loop controlling the piezoelectric elements that contract or expand to decrease or increase the stage height as required.

Fig. 9
Fig. 9

Measured PSF’s for a system such as that shown in Fig. 7A in which only the thickness of the coverslip varies from the design conditions. This figure illustrates that with an oil-immersion objective lens, for coverslip thicknesses that differ reasonably from the design thickness t g * = 0.170 mm, the coverslip thickness has little effect on the PSF: A, t g = 0.110 mm; B, t g = 0.140 mm; C, t g = 0.150 mm; D, t g = 0.170 mm; E, t g = 0.180 mm; F, t g = 0.200 mm; G, t g = 0.230 mm.

Fig. 10
Fig. 10

Measured PSF’s for a system such as that shown in Fig. 7A in which only the refractive index of the immersion oil varies from the design conditions. The design immersion-oil refractive index is noil* = 1.515: A, noil = 1.500; B, noil = 1.505; C, noil = 1.510; D, noil = 1.513; E, noil = 1.515; F, noil = 1.517; G, noil = 1.520; H, noil = 1.525; I, noil = 1.530.

Fig. 11
Fig. 11

Measured PSF’s for a system such as that shown in Fig. 7B in which the depth of the point source into a 1% agarose layer is varied. The agarose has a refractive index close to that of water (1.33): A, t s = 0 μm; B, t s = 2 μm; C, t s = 4 μm; D, t s = 6 μm; E, t s = 8 μm; F, t s = 10 μm; G, t s = 20 μm; H, t s = 40 μm; I, t s = 60 μm; J, t s = 80 μm.

Fig. 12
Fig. 12

Measured PSF’s for a system such as that shown in Fig. 7A in which only the distance from the back focal plane to the detector varies from the design conditions. Since the exact design distance from the back focal plane to the detector is not known (it was assumed to be 160 mm in predicted PSF’s) these measured PSF’s are presented as a function of the distance, δz d , that the detector is moved from the fixed detector plane of our system: A, δz d = −10 mm; B, δz d = +20 mm; C, δz d = +30 mm; D, δz d = +50 mm; E, δz d = +70 mm.

Fig. 13
Fig. 13

Graphs of intensity profiles for measured and predicted PSF’s of Figs. 4 and 11 for points located at various depths into a specimen layer whose refractive index is significantly different from that of the immersion oil. The profiles are taken along the optical axis (A, predicted PSF’s; B, measured PSF’s) and taken in the detector plane perpendicular to the optical axis and through the brightest pixel (C, predicted PSF’s; D, measured PSF’s).

Fig. 14
Fig. 14

Log of the tolerances to various changes in the design system parameters versus log of the NA of the objective lens. These plots compare tolerances measured by Spinnel and Loveland18 with those calculated from Eq. (1) with the assumption that a phase aberration of either λ/4 or λ/8 causes observable degradation of an image: A, tolerances to changes in the immersion-oil refractive index versus NA; B, tolerances to changes in the microscope tube length versus NA; C, tolerances to changes in coverslip thickness versus NA; D, tolerances to depth of the point source into a watery layer versus NA.

Equations (5)

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

O P D = n s t s cos θ s + n g t g cos θ g + n oil t oil cos θ oil - ( n g * t g * cos θ g * + n oil * t oil * cos θ oil * + n γ ) ,
OPD n s t s [ 1 - ( NA ρ n s ) 2 ] 1 / 2 + n g t g [ 1 - ( NA ρ n g ) 2 ] 1 / 2 + n oil t oil [ 1 - ( NA ρ n oil ) 2 ] 1 / 2 - n g * t g * [ 1 - ( NA ρ n g * ) 2 ] 1 / 2 - n oil * t oil * [ 1 - ( NA ρ n oil * ) 2 ] 1 / 2
Δ z n oil t s n s + t g n g + t oil n oil - t g * n g * - t oil * n oil * ,
OPD n oil [ Δ z + ( z d * - z d ) a 2 n oil z d * z d NA 2 ] [ 1 - ( NA ρ n oil ) 2 ] 1 / 2 + a 2 ρ 2 ( z d * - z d ) 2 n oil z d * z d + n s t s { [ 1 - ( NA ρ n s ) 2 ] 1 / 2 - ( n oil n s ) 2 [ 1 - ( NA ρ n oil ) 2 ] 1 / 2 } + n g t g { [ 1 - ( NA ρ n g ) 2 ] 1 / 2 - ( n oil n g ) 2 [ 1 - ( NA ρ n oil ) 2 ] 1 / 2 } - n g * t g * { [ 1 - ( NA ρ n g * ) 2 ] 1 / 2 - ( n oil n g * ) 2 × [ 1 - ( NA ρ n oil ) 2 ] 1 / 2 } - n oil * t oil * { [ 1 - ( NA ρ n oil * ) 2 ] 1 / 2 - ( n oil n oil * ) 2 × [ 1 - ( NA ρ n oil ) 2 ] 1 / 2 } .
I ( x d , y d , z d ) = | C z d 0 1 J 0 [ k a ρ ( x d 2 + y d 2 ) 1 / 2 z d ] exp [ j W ( ρ ) ] ρ d ρ | 2 ,

Metrics