Abstract

Three methods for direct measurement of the intensity distribution in laser beams focused by microscope optics to waists of submicron width are described and compared. They use scans of the beam waist with (1) a knife-edge, (2) a submicroscopic point fluorescent source, and (3) convolution scans generated by the photobleached pattern of the focused beam. An indirect photographic technique is also evaluated. The laser beam is found to propagate ideally down to a minimum size usually limited by the aberrations of the optics.

© 1981 Optical Society of America

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  1. J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Claviere, E. A. Franke, J. M. Franke, Appl. Opt. 10, 2775 (1971).
    [Crossref] [PubMed]
  2. D. R. Skinner, R. E. Whitcher, J. Phys. E: 5, 237 (1972).
    [Crossref]
  3. J. Corcoran, Laser Focus 61 (June1973).
  4. Y. Suzaki, A. Tachibana, Appl. Opt. 14, 2809 (1975).
    [Crossref] [PubMed]
  5. A. H. Firester, M. E. Heller, P. Sheng, Appl. Opt. 16, 1971 (1977).
    [Crossref] [PubMed]
  6. D. Magde, E. L. Elson, W. W. Webb, Phys. Rev. Lett. 29, 705 (1972).
    [Crossref]
  7. E. L. Elson, D. Magde, Biopolymers 13, 1 (1974).
    [Crossref]
  8. D. Magde, E. L. Elson, W. W. Webb, Biopolymers 13, 19 (1974).
    [Crossref]
  9. D. Axelrod, D. E. Koppel, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1055 (1976).
    [Crossref] [PubMed]
  10. J. Schlessinger, D. E. Koppel, D. Axelrod, K. Jacobson, W. W. Webb, E. L. Elson, Proc. Natl. Acad. Sci. U.S.A. 73, 2409 (1976).
    [Crossref] [PubMed]
  11. W. W. Webb, Q. Rev. Biophys. 9, 49 (1976).
    [Crossref] [PubMed]
  12. P. F. Fahey, W. W. Webb, Biochemistry 17, 3046 (1978).
    [Crossref] [PubMed]
  13. H. H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).
  14. H. H. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966).
    [Crossref] [PubMed]
  15. L. D. Dickson, Appl. Opt. 9, 1854 (1970).
    [Crossref] [PubMed]
  16. A. Yoshida, T. Asakura, Optik 44, 281 (1974).
  17. E. Wolf, Proc. R. Soc. London Ser. A: 253, 349 (1959).
    [Crossref]
  18. Optical Systems for the Microscope (Carl Zeiss, Inc., Dept. of Microscopy, Oberkochen, West Germany, 1971), p. 18.
  19. P. J. Sims, A. S. Waggoner, C.-H. Wang, J. F. Hoffman, Biochemistry 13, 3315 (1974).
    [Crossref] [PubMed]
  20. D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1315 (1976).
    [Crossref] [PubMed]

1978 (1)

P. F. Fahey, W. W. Webb, Biochemistry 17, 3046 (1978).
[Crossref] [PubMed]

1977 (1)

1976 (4)

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1315 (1976).
[Crossref] [PubMed]

D. Axelrod, D. E. Koppel, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1055 (1976).
[Crossref] [PubMed]

J. Schlessinger, D. E. Koppel, D. Axelrod, K. Jacobson, W. W. Webb, E. L. Elson, Proc. Natl. Acad. Sci. U.S.A. 73, 2409 (1976).
[Crossref] [PubMed]

W. W. Webb, Q. Rev. Biophys. 9, 49 (1976).
[Crossref] [PubMed]

1975 (1)

1974 (4)

E. L. Elson, D. Magde, Biopolymers 13, 1 (1974).
[Crossref]

D. Magde, E. L. Elson, W. W. Webb, Biopolymers 13, 19 (1974).
[Crossref]

A. Yoshida, T. Asakura, Optik 44, 281 (1974).

P. J. Sims, A. S. Waggoner, C.-H. Wang, J. F. Hoffman, Biochemistry 13, 3315 (1974).
[Crossref] [PubMed]

1973 (1)

J. Corcoran, Laser Focus 61 (June1973).

1972 (2)

D. Magde, E. L. Elson, W. W. Webb, Phys. Rev. Lett. 29, 705 (1972).
[Crossref]

D. R. Skinner, R. E. Whitcher, J. Phys. E: 5, 237 (1972).
[Crossref]

1971 (1)

1970 (1)

1966 (1)

1965 (1)

H. H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

1959 (1)

E. Wolf, Proc. R. Soc. London Ser. A: 253, 349 (1959).
[Crossref]

Arnaud, J. A.

Asakura, T.

A. Yoshida, T. Asakura, Optik 44, 281 (1974).

Axelrod, D.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1315 (1976).
[Crossref] [PubMed]

D. Axelrod, D. E. Koppel, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1055 (1976).
[Crossref] [PubMed]

J. Schlessinger, D. E. Koppel, D. Axelrod, K. Jacobson, W. W. Webb, E. L. Elson, Proc. Natl. Acad. Sci. U.S.A. 73, 2409 (1976).
[Crossref] [PubMed]

Corcoran, J.

J. Corcoran, Laser Focus 61 (June1973).

de la Claviere, B.

Dickson, L. D.

Elson, E. L.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1315 (1976).
[Crossref] [PubMed]

J. Schlessinger, D. E. Koppel, D. Axelrod, K. Jacobson, W. W. Webb, E. L. Elson, Proc. Natl. Acad. Sci. U.S.A. 73, 2409 (1976).
[Crossref] [PubMed]

D. Axelrod, D. E. Koppel, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1055 (1976).
[Crossref] [PubMed]

D. Magde, E. L. Elson, W. W. Webb, Biopolymers 13, 19 (1974).
[Crossref]

E. L. Elson, D. Magde, Biopolymers 13, 1 (1974).
[Crossref]

D. Magde, E. L. Elson, W. W. Webb, Phys. Rev. Lett. 29, 705 (1972).
[Crossref]

Fahey, P. F.

P. F. Fahey, W. W. Webb, Biochemistry 17, 3046 (1978).
[Crossref] [PubMed]

Firester, A. H.

Franke, E. A.

Franke, J. M.

Heller, M. E.

Hoffman, J. F.

P. J. Sims, A. S. Waggoner, C.-H. Wang, J. F. Hoffman, Biochemistry 13, 3315 (1974).
[Crossref] [PubMed]

Hubbard, W. M.

Jacobson, K.

J. Schlessinger, D. E. Koppel, D. Axelrod, K. Jacobson, W. W. Webb, E. L. Elson, Proc. Natl. Acad. Sci. U.S.A. 73, 2409 (1976).
[Crossref] [PubMed]

Kogelnik, H. H.

H. H. Kogelnik, T. Li, Appl. Opt. 5, 1550 (1966).
[Crossref] [PubMed]

H. H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

Koppel, D. E.

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1315 (1976).
[Crossref] [PubMed]

D. Axelrod, D. E. Koppel, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1055 (1976).
[Crossref] [PubMed]

J. Schlessinger, D. E. Koppel, D. Axelrod, K. Jacobson, W. W. Webb, E. L. Elson, Proc. Natl. Acad. Sci. U.S.A. 73, 2409 (1976).
[Crossref] [PubMed]

Li, T.

Magde, D.

E. L. Elson, D. Magde, Biopolymers 13, 1 (1974).
[Crossref]

D. Magde, E. L. Elson, W. W. Webb, Biopolymers 13, 19 (1974).
[Crossref]

D. Magde, E. L. Elson, W. W. Webb, Phys. Rev. Lett. 29, 705 (1972).
[Crossref]

Mandeville, G. D.

Schlessinger, J.

J. Schlessinger, D. E. Koppel, D. Axelrod, K. Jacobson, W. W. Webb, E. L. Elson, Proc. Natl. Acad. Sci. U.S.A. 73, 2409 (1976).
[Crossref] [PubMed]

D. Axelrod, D. E. Koppel, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1055 (1976).
[Crossref] [PubMed]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1315 (1976).
[Crossref] [PubMed]

Sheng, P.

Sims, P. J.

P. J. Sims, A. S. Waggoner, C.-H. Wang, J. F. Hoffman, Biochemistry 13, 3315 (1974).
[Crossref] [PubMed]

Skinner, D. R.

D. R. Skinner, R. E. Whitcher, J. Phys. E: 5, 237 (1972).
[Crossref]

Suzaki, Y.

Tachibana, A.

Waggoner, A. S.

P. J. Sims, A. S. Waggoner, C.-H. Wang, J. F. Hoffman, Biochemistry 13, 3315 (1974).
[Crossref] [PubMed]

Wang, C.-H.

P. J. Sims, A. S. Waggoner, C.-H. Wang, J. F. Hoffman, Biochemistry 13, 3315 (1974).
[Crossref] [PubMed]

Webb, W. W.

P. F. Fahey, W. W. Webb, Biochemistry 17, 3046 (1978).
[Crossref] [PubMed]

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1315 (1976).
[Crossref] [PubMed]

D. Axelrod, D. E. Koppel, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1055 (1976).
[Crossref] [PubMed]

J. Schlessinger, D. E. Koppel, D. Axelrod, K. Jacobson, W. W. Webb, E. L. Elson, Proc. Natl. Acad. Sci. U.S.A. 73, 2409 (1976).
[Crossref] [PubMed]

W. W. Webb, Q. Rev. Biophys. 9, 49 (1976).
[Crossref] [PubMed]

D. Magde, E. L. Elson, W. W. Webb, Biopolymers 13, 19 (1974).
[Crossref]

D. Magde, E. L. Elson, W. W. Webb, Phys. Rev. Lett. 29, 705 (1972).
[Crossref]

Whitcher, R. E.

D. R. Skinner, R. E. Whitcher, J. Phys. E: 5, 237 (1972).
[Crossref]

Wolf, E.

E. Wolf, Proc. R. Soc. London Ser. A: 253, 349 (1959).
[Crossref]

Yoshida, A.

A. Yoshida, T. Asakura, Optik 44, 281 (1974).

Appl. Opt. (5)

Bell Syst. Tech. J. (1)

H. H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

Biochemistry (2)

P. F. Fahey, W. W. Webb, Biochemistry 17, 3046 (1978).
[Crossref] [PubMed]

P. J. Sims, A. S. Waggoner, C.-H. Wang, J. F. Hoffman, Biochemistry 13, 3315 (1974).
[Crossref] [PubMed]

Biophys. J. (2)

D. E. Koppel, D. Axelrod, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1315 (1976).
[Crossref] [PubMed]

D. Axelrod, D. E. Koppel, J. Schlessinger, E. L. Elson, W. W. Webb, Biophys. J. 16, 1055 (1976).
[Crossref] [PubMed]

Biopolymers (2)

E. L. Elson, D. Magde, Biopolymers 13, 1 (1974).
[Crossref]

D. Magde, E. L. Elson, W. W. Webb, Biopolymers 13, 19 (1974).
[Crossref]

J. Phys. E (1)

D. R. Skinner, R. E. Whitcher, J. Phys. E: 5, 237 (1972).
[Crossref]

Laser Focus (1)

J. Corcoran, Laser Focus 61 (June1973).

Optik (1)

A. Yoshida, T. Asakura, Optik 44, 281 (1974).

Phys. Rev. Lett. (1)

D. Magde, E. L. Elson, W. W. Webb, Phys. Rev. Lett. 29, 705 (1972).
[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. Schlessinger, D. E. Koppel, D. Axelrod, K. Jacobson, W. W. Webb, E. L. Elson, Proc. Natl. Acad. Sci. U.S.A. 73, 2409 (1976).
[Crossref] [PubMed]

Proc. R. Soc. London Ser. A (1)

E. Wolf, Proc. R. Soc. London Ser. A: 253, 349 (1959).
[Crossref]

Q. Rev. Biophys. (1)

W. W. Webb, Q. Rev. Biophys. 9, 49 (1976).
[Crossref] [PubMed]

Other (1)

Optical Systems for the Microscope (Carl Zeiss, Inc., Dept. of Microscopy, Oberkochen, West Germany, 1971), p. 18.

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Figures (9)

Fig. 1
Fig. 1

Envelope of ideal focused Gaussian beam with optic axis in the vertical (z) direction, waist w0 at z0, and cone angle θ.

Fig. 2
Fig. 2

(a) Optics schematic. Krypton- or argon-ion laser beam passes through spatial filter SF, is reflected by beam splitter quartz plate BS1, and then focused onto second shutter SHT. It passes through the second quartz plate BS2, is attenuated by neutral density filters NDF, and then steered onto focusing lens L3 of the system by two λ/20 flat mirrors M1 and M2. Beam enters vertical illuminator of Zeiss universal microscope and is reflected downward by dichroic mirror DM through objective OBJ onto fluorescent sample SAM in the object plane of the microscope. Fluorescence is collected by objective OBJ; it passes upward through dichroic mirror DM and barrier filter BF, which absorbs laser light, and is imaged on field diaphragm FD at the image plane of the microscope. Transmitted light is collected by dry ice-cooled photomultiplier tube PMT. The camera, CAM, is mounted to photograph the image plane of the microscope. (b) Scheme of λ/20 quartz plates which separate the weak monitor beam, (dashed line) from the strong bleaching beam (thick line). The monitor beam is attenuated to 0.03% of the bleaching beam by various interfaces of BS1 and BS2. MIR and AR are mirror and antireflection coatings, respectively. The two beams are recombined where the bleaching beam enters BS2. Very fast bleaching times (electronically controlled) are attained by pulling the first shutter (SHT 1) out of the bleaching beam path and then using the second shutter (SHT 2) to block the beam. MON 1 and MON 2 are PIN photodiode monitors which detect start and end of bleach. (The shutters were developed by J. A. Bloom at the suggestion of D. E. Koppel.)

Fig. 3
Fig. 3

Schematic diagram of the scanning device and Fabry-Perot interferometer for scan displacement measurement. Moving parts are shaded. An expanded H–N laser beam illuminates the partially transmitting parallel mirrors M1 and M2. A diaphragm D1 passes the central fringe of the interference pattern. The fringe amplitude is detected by the PIN photodiode, MON, and recorded on the chart recorder, CR. The piezoelectric ceramic PZ, driven by a linear voltage ramp LVR, moves the stage ST and sample SAM parallel to the interferometer axis. The sample is in the focal plane of microscope MS.

Fig. 4
Fig. 4

Typical convolution scan for a 40×/0.65-N.A. air objective, 531-nm Kr laser line: (top) fluorescence intensity (proportional to voltage); (center) transmitted interferometer intensity; and (bottom) voltage ramp; as functions of scan time. Left axis refers to the top curve only. Despite the linearity of the voltage ramp, the fringes are not uniformly spaced due to mechanical imperfections. Speed of translation is ~0.07 μm/sec. Bleaching time is 50 msec. A distance of 0.1 μm is indicated by the horizontal bar.

Fig. 5
Fig. 5

Point scan for 40×/0.65-N.A. air objective, 488-nm Ar laser line, using FITC labeled, 0.038-μm polystyrene beads. Left axis refers to the top curve only.

Fig. 6
Fig. 6

Gaussian fitting procedure plot of {0.5 ln[I0/(IB)]}1/2 vs displacement x (measured in half-fringes, 0.63/4 μm) for the data of Fig. 5. 2w0 can be read as the width of the graph a distance 1.0 above the point of intersection of the two lines, giving w0 = 6.5 × 0.63/4 μm. The beam is slightly asymmetric, as evidenced by different slopes of the two lines (the left one implies w0 = 6.3 × 0.63/4 μm, the right one implies w0 = 6.7 × 0.63/4 μm).

Fig. 7
Fig. 7

Least squares fit of data from Fig. 4 to Eq. (4), giving τF = 3.59 or w0 = 0.57 μm.

Fig. 8
Fig. 8

Expanded image scan: Joyce densitometer tracings of a photographic negative image of the focused laser beam and of the same beam attenuated to half-intensity. The 2 × 1.7 × w0 diameter is identified on the first scan by the peak height of the second scan.

Fig. 9
Fig. 9

Off-focus measurements for a 40×/0.75-N.A. water immersion objective, 531 Kr laser line. z is measured along the optic axis. (a) Filled circles are the 1/e2 intensity radii from the convolution scan. The line is fit to ideal Gaussian propagation formula [Eq. (1)]. The waist, at z = z0, is found to be 1.2 μm above the visually selected focal plane at z = 0. The paraxial focal plane is approximately at z = z1, the location of the image (shown, radius s0) of the field diaphragm (FD in Fig. 2). Due to the field diaphragm, the PMT sees a limited area (shaded) with 1/e2 intensity or more. Asymmetry about z = 0 is due to spherical aberration. (b) Test of out-of-plane collection efficiency formula [Eq. (5)] showing effect of spherical aberration: filled circles are normalized measurements of 1/E(z); thin lines are theoretical 1/E(z) for z1 = 0; thick lines are theoretical 1/E(z) for z1 = 3.0 μm. The numerical aperture was taken as 0.89 times the quoted numerical aperture. The improved fit for z1 = 3.0 μm suggests a range of focal plane positions spread over this distance by axial spherical aberration, in agreement with independent measurements.

Tables (1)

Tables Icon

Table I Results of Beam Radii Measurements

Equations (5)

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w 2 ( z ) = w 0 2 + tan 2 θ ( z z 0 ) 2 ,
tan θ = λ / ( n π w 0 ) ,
I ( x ) = B + I 0 exp [ 2 ( x x 0 ) 2 / w 0 2 ] .
F ( t ) = q P 0 C 0 A n = 0 ( K ) n ( n + 1 ) ! exp [ 2 n n + 1 ( t τ F ) 2 ] ,
1 E ( z ) = 1 + tan 2 α · ( z z 1 ) 2 2 s 0 2 + w 2 ( z ) 2 s 0 2 .

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