Abstract

The output from a linear diode array is used in a modified laser Doppler velocimeter to measure the size and shape of irregular particles. The sizing accuracy for transparent and opaque particles between 30 and 140 μm is better than 10%. The inaccuracy caused by trajectories that lay at angles of less than 24° to the axis of the array was less than +5%, and a further inaccuracy of ±5% was caused by defocusing of the particle from the center of the velocimeter measuring volume by up to ±500 μm. The advantages of the shadow Doppler technique over other techniques for sizing irregular particles, such as amplitude systems with pointer volumes, are that the shadow Doppler technique records shape, the optical arrangement is more robust, less precise alignment is required, and the equipment can be constructed at low cost.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Hishida, M. Maeda, J. Imaru, K. Hironaga, H. Kano, “Measurements of size and velocity of particle in two-phase flow by a three beam LDA system,” in Laser Velocimetry in Fluid Mechanics, R. J. Adrian, D. F. G. Duro, F. Durst, H. Mishina, J. H. Whitelaw, eds. (LADOAN, Lisbon, Portugal, 1984), Vol. 1, pp. 121–136.
  2. C. R. Negus, L. E. Drain, “Mie calculations of the scattered light from a spherical particle traversing a fringe pattern produced by two intersecting laser beams,” J. Phys. D 15, 375–402 (1982).
    [CrossRef]
  3. N. S. Hong, A. R. Jones, “A light scattering technique for particle sizing based on laser fringe velocimetry,” J. Phys. D 9, 1839–1848 (1976).
    [CrossRef]
  4. E. D. Hirleman, “Laser technique for simultaneous particle size and velocity measurement,” Opt. Lett. 3, 19–21 (1978).
    [CrossRef] [PubMed]
  5. D. J. Holve, S. Self, “Optical particle sizing for in siu measurements Parts 1 and 2,” Appl. Opt. 18, 1632–1652 (1979).
    [CrossRef] [PubMed]
  6. J. C. F. Wang, K. R. Hencken, “In situ particle size measurement using a two-color laser scattering technique,” Appl. Opt. 25, 653–657 (1986).
    [CrossRef] [PubMed]
  7. C. F. Hess, “A technique combining the visibility of a Doppler signal with the peak intensity of the pedestal to measure the size and velocity of droplets in spray,” Rep. AIAA-84-0203 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1984).
  8. G. Gréhan, G. Gouesbet, “Simultaneous measurement of velocities and sizes of particles in a flow using a combined system incorporating a top-hat technique,” Appl. Opt. 25, 3527–3538 (1986).
    [CrossRef] [PubMed]
  9. M. L. Yeoman, H. J. White, B. J. Azzopardi, C. J. Bates, P. J. Roberts, “Optical development and application of a two colour LDA system for the simultaneous measurement of particle size and particle velocity,” in Proceedings of the ASME Winter Symposium (American Society of Mechanical Engineers, New York, 1982), pp. 127–135.
  10. N. G. Orfanoudakis, A. M. K. P. Taylor, “The effect of particle shape on the amplitude of scattered light for a sizing instrument,” Part. Part. Syst. Charact. 9, 223–230 (1992).
    [CrossRef]
  11. N. G. Orfanoudakis, A. M. K. P. Taylor, “Evaluation of a anemometer and application to a small scale swirl coal burner,” presented at the Clean Air Conference, Lisbon, Spain, 19–22 July 1993.
  12. Y. Hardalupas, H. Morikita, A. M. K. P. Taylor, “Amplitude measurement of size of non-spherical particles: tolerances and validation schemes evaluated by scalar diffraction theory,” presented at the Third Congress on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.
  13. B. A. Weiss, P. Derov, D. DeBiase, H. C. Simmons, “Fluid particle sizing using a fully automated optical imaging system,” Opt. Eng. 23, 561–566 (1984).
  14. G. P. Bertollini, L. M. Oberdier, H. Y. Lee, “Image processing system to analyse droplet distributions,” Opt. Eng. 24, 464–469 (1985).
  15. K. D. Ahlers, D. R. Alexander, “Microcomputer based digital image processing system developed to count and size laser-generated small particle images,” Opt. Eng. 24, 1060–1065 (1985).
  16. G. Brenn, A. Frohn, “Collision and merging of two equal droplets of propanol,” Exp. Fluids 7, 441–446 (1989).
    [CrossRef]
  17. S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model of the laser imaging of small aerosols: applications to aerosol sizing,” Appl. Opt. 30, 4777–4784 (1991).
    [CrossRef] [PubMed]
  18. S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment,” Opt. Eng. 28, 565–571 (1989).
  19. K. Kobashi, K. Hishida, M. Maeda, “Measurement of fuel injector spray flow of I.C. Engine by FFT based phase Doppler anemometer,” in Applications of Laser Techniques to Fluid Mechanics: Fifth International Symposium (Springer-Verlag, Berlin, 1991), pp. 268–287.
    [CrossRef]

1992 (1)

N. G. Orfanoudakis, A. M. K. P. Taylor, “The effect of particle shape on the amplitude of scattered light for a sizing instrument,” Part. Part. Syst. Charact. 9, 223–230 (1992).
[CrossRef]

1991 (1)

1989 (2)

G. Brenn, A. Frohn, “Collision and merging of two equal droplets of propanol,” Exp. Fluids 7, 441–446 (1989).
[CrossRef]

S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment,” Opt. Eng. 28, 565–571 (1989).

1986 (2)

1985 (2)

G. P. Bertollini, L. M. Oberdier, H. Y. Lee, “Image processing system to analyse droplet distributions,” Opt. Eng. 24, 464–469 (1985).

K. D. Ahlers, D. R. Alexander, “Microcomputer based digital image processing system developed to count and size laser-generated small particle images,” Opt. Eng. 24, 1060–1065 (1985).

1984 (1)

B. A. Weiss, P. Derov, D. DeBiase, H. C. Simmons, “Fluid particle sizing using a fully automated optical imaging system,” Opt. Eng. 23, 561–566 (1984).

1982 (1)

C. R. Negus, L. E. Drain, “Mie calculations of the scattered light from a spherical particle traversing a fringe pattern produced by two intersecting laser beams,” J. Phys. D 15, 375–402 (1982).
[CrossRef]

1979 (1)

1978 (1)

1976 (1)

N. S. Hong, A. R. Jones, “A light scattering technique for particle sizing based on laser fringe velocimetry,” J. Phys. D 9, 1839–1848 (1976).
[CrossRef]

Ahlers, K. D.

K. D. Ahlers, D. R. Alexander, “Microcomputer based digital image processing system developed to count and size laser-generated small particle images,” Opt. Eng. 24, 1060–1065 (1985).

Alexander, D. R.

S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model of the laser imaging of small aerosols: applications to aerosol sizing,” Appl. Opt. 30, 4777–4784 (1991).
[CrossRef] [PubMed]

S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment,” Opt. Eng. 28, 565–571 (1989).

K. D. Ahlers, D. R. Alexander, “Microcomputer based digital image processing system developed to count and size laser-generated small particle images,” Opt. Eng. 24, 1060–1065 (1985).

Azzopardi, B. J.

M. L. Yeoman, H. J. White, B. J. Azzopardi, C. J. Bates, P. J. Roberts, “Optical development and application of a two colour LDA system for the simultaneous measurement of particle size and particle velocity,” in Proceedings of the ASME Winter Symposium (American Society of Mechanical Engineers, New York, 1982), pp. 127–135.

Barton, J. P.

S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model of the laser imaging of small aerosols: applications to aerosol sizing,” Appl. Opt. 30, 4777–4784 (1991).
[CrossRef] [PubMed]

S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment,” Opt. Eng. 28, 565–571 (1989).

Bates, C. J.

M. L. Yeoman, H. J. White, B. J. Azzopardi, C. J. Bates, P. J. Roberts, “Optical development and application of a two colour LDA system for the simultaneous measurement of particle size and particle velocity,” in Proceedings of the ASME Winter Symposium (American Society of Mechanical Engineers, New York, 1982), pp. 127–135.

Bertollini, G. P.

G. P. Bertollini, L. M. Oberdier, H. Y. Lee, “Image processing system to analyse droplet distributions,” Opt. Eng. 24, 464–469 (1985).

Brenn, G.

G. Brenn, A. Frohn, “Collision and merging of two equal droplets of propanol,” Exp. Fluids 7, 441–446 (1989).
[CrossRef]

DeBiase, D.

B. A. Weiss, P. Derov, D. DeBiase, H. C. Simmons, “Fluid particle sizing using a fully automated optical imaging system,” Opt. Eng. 23, 561–566 (1984).

Derov, P.

B. A. Weiss, P. Derov, D. DeBiase, H. C. Simmons, “Fluid particle sizing using a fully automated optical imaging system,” Opt. Eng. 23, 561–566 (1984).

Drain, L. E.

C. R. Negus, L. E. Drain, “Mie calculations of the scattered light from a spherical particle traversing a fringe pattern produced by two intersecting laser beams,” J. Phys. D 15, 375–402 (1982).
[CrossRef]

Frohn, A.

G. Brenn, A. Frohn, “Collision and merging of two equal droplets of propanol,” Exp. Fluids 7, 441–446 (1989).
[CrossRef]

Gouesbet, G.

Gréhan, G.

Hardalupas, Y.

Y. Hardalupas, H. Morikita, A. M. K. P. Taylor, “Amplitude measurement of size of non-spherical particles: tolerances and validation schemes evaluated by scalar diffraction theory,” presented at the Third Congress on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

Hencken, K. R.

Hess, C. F.

C. F. Hess, “A technique combining the visibility of a Doppler signal with the peak intensity of the pedestal to measure the size and velocity of droplets in spray,” Rep. AIAA-84-0203 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1984).

Hirleman, E. D.

Hironaga, K.

K. Hishida, M. Maeda, J. Imaru, K. Hironaga, H. Kano, “Measurements of size and velocity of particle in two-phase flow by a three beam LDA system,” in Laser Velocimetry in Fluid Mechanics, R. J. Adrian, D. F. G. Duro, F. Durst, H. Mishina, J. H. Whitelaw, eds. (LADOAN, Lisbon, Portugal, 1984), Vol. 1, pp. 121–136.

Hishida, K.

K. Hishida, M. Maeda, J. Imaru, K. Hironaga, H. Kano, “Measurements of size and velocity of particle in two-phase flow by a three beam LDA system,” in Laser Velocimetry in Fluid Mechanics, R. J. Adrian, D. F. G. Duro, F. Durst, H. Mishina, J. H. Whitelaw, eds. (LADOAN, Lisbon, Portugal, 1984), Vol. 1, pp. 121–136.

K. Kobashi, K. Hishida, M. Maeda, “Measurement of fuel injector spray flow of I.C. Engine by FFT based phase Doppler anemometer,” in Applications of Laser Techniques to Fluid Mechanics: Fifth International Symposium (Springer-Verlag, Berlin, 1991), pp. 268–287.
[CrossRef]

Holve, D. J.

Hong, N. S.

N. S. Hong, A. R. Jones, “A light scattering technique for particle sizing based on laser fringe velocimetry,” J. Phys. D 9, 1839–1848 (1976).
[CrossRef]

Imaru, J.

K. Hishida, M. Maeda, J. Imaru, K. Hironaga, H. Kano, “Measurements of size and velocity of particle in two-phase flow by a three beam LDA system,” in Laser Velocimetry in Fluid Mechanics, R. J. Adrian, D. F. G. Duro, F. Durst, H. Mishina, J. H. Whitelaw, eds. (LADOAN, Lisbon, Portugal, 1984), Vol. 1, pp. 121–136.

Jones, A. R.

N. S. Hong, A. R. Jones, “A light scattering technique for particle sizing based on laser fringe velocimetry,” J. Phys. D 9, 1839–1848 (1976).
[CrossRef]

Kano, H.

K. Hishida, M. Maeda, J. Imaru, K. Hironaga, H. Kano, “Measurements of size and velocity of particle in two-phase flow by a three beam LDA system,” in Laser Velocimetry in Fluid Mechanics, R. J. Adrian, D. F. G. Duro, F. Durst, H. Mishina, J. H. Whitelaw, eds. (LADOAN, Lisbon, Portugal, 1984), Vol. 1, pp. 121–136.

Kobashi, K.

K. Kobashi, K. Hishida, M. Maeda, “Measurement of fuel injector spray flow of I.C. Engine by FFT based phase Doppler anemometer,” in Applications of Laser Techniques to Fluid Mechanics: Fifth International Symposium (Springer-Verlag, Berlin, 1991), pp. 268–287.
[CrossRef]

Lee, H. Y.

G. P. Bertollini, L. M. Oberdier, H. Y. Lee, “Image processing system to analyse droplet distributions,” Opt. Eng. 24, 464–469 (1985).

Maeda, M.

K. Hishida, M. Maeda, J. Imaru, K. Hironaga, H. Kano, “Measurements of size and velocity of particle in two-phase flow by a three beam LDA system,” in Laser Velocimetry in Fluid Mechanics, R. J. Adrian, D. F. G. Duro, F. Durst, H. Mishina, J. H. Whitelaw, eds. (LADOAN, Lisbon, Portugal, 1984), Vol. 1, pp. 121–136.

K. Kobashi, K. Hishida, M. Maeda, “Measurement of fuel injector spray flow of I.C. Engine by FFT based phase Doppler anemometer,” in Applications of Laser Techniques to Fluid Mechanics: Fifth International Symposium (Springer-Verlag, Berlin, 1991), pp. 268–287.
[CrossRef]

Morikita, H.

Y. Hardalupas, H. Morikita, A. M. K. P. Taylor, “Amplitude measurement of size of non-spherical particles: tolerances and validation schemes evaluated by scalar diffraction theory,” presented at the Third Congress on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

Negus, C. R.

C. R. Negus, L. E. Drain, “Mie calculations of the scattered light from a spherical particle traversing a fringe pattern produced by two intersecting laser beams,” J. Phys. D 15, 375–402 (1982).
[CrossRef]

Oberdier, L. M.

G. P. Bertollini, L. M. Oberdier, H. Y. Lee, “Image processing system to analyse droplet distributions,” Opt. Eng. 24, 464–469 (1985).

Orfanoudakis, N. G.

N. G. Orfanoudakis, A. M. K. P. Taylor, “The effect of particle shape on the amplitude of scattered light for a sizing instrument,” Part. Part. Syst. Charact. 9, 223–230 (1992).
[CrossRef]

N. G. Orfanoudakis, A. M. K. P. Taylor, “Evaluation of a anemometer and application to a small scale swirl coal burner,” presented at the Clean Air Conference, Lisbon, Spain, 19–22 July 1993.

Roberts, P. J.

M. L. Yeoman, H. J. White, B. J. Azzopardi, C. J. Bates, P. J. Roberts, “Optical development and application of a two colour LDA system for the simultaneous measurement of particle size and particle velocity,” in Proceedings of the ASME Winter Symposium (American Society of Mechanical Engineers, New York, 1982), pp. 127–135.

Schaub, S. A.

S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model of the laser imaging of small aerosols: applications to aerosol sizing,” Appl. Opt. 30, 4777–4784 (1991).
[CrossRef] [PubMed]

S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment,” Opt. Eng. 28, 565–571 (1989).

Self, S.

Simmons, H. C.

B. A. Weiss, P. Derov, D. DeBiase, H. C. Simmons, “Fluid particle sizing using a fully automated optical imaging system,” Opt. Eng. 23, 561–566 (1984).

Taylor, A. M. K. P.

N. G. Orfanoudakis, A. M. K. P. Taylor, “The effect of particle shape on the amplitude of scattered light for a sizing instrument,” Part. Part. Syst. Charact. 9, 223–230 (1992).
[CrossRef]

N. G. Orfanoudakis, A. M. K. P. Taylor, “Evaluation of a anemometer and application to a small scale swirl coal burner,” presented at the Clean Air Conference, Lisbon, Spain, 19–22 July 1993.

Y. Hardalupas, H. Morikita, A. M. K. P. Taylor, “Amplitude measurement of size of non-spherical particles: tolerances and validation schemes evaluated by scalar diffraction theory,” presented at the Third Congress on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

Wang, J. C. F.

Weiss, B. A.

B. A. Weiss, P. Derov, D. DeBiase, H. C. Simmons, “Fluid particle sizing using a fully automated optical imaging system,” Opt. Eng. 23, 561–566 (1984).

White, H. J.

M. L. Yeoman, H. J. White, B. J. Azzopardi, C. J. Bates, P. J. Roberts, “Optical development and application of a two colour LDA system for the simultaneous measurement of particle size and particle velocity,” in Proceedings of the ASME Winter Symposium (American Society of Mechanical Engineers, New York, 1982), pp. 127–135.

Yeoman, M. L.

M. L. Yeoman, H. J. White, B. J. Azzopardi, C. J. Bates, P. J. Roberts, “Optical development and application of a two colour LDA system for the simultaneous measurement of particle size and particle velocity,” in Proceedings of the ASME Winter Symposium (American Society of Mechanical Engineers, New York, 1982), pp. 127–135.

Appl. Opt. (4)

Exp. Fluids (1)

G. Brenn, A. Frohn, “Collision and merging of two equal droplets of propanol,” Exp. Fluids 7, 441–446 (1989).
[CrossRef]

J. Phys. D (2)

C. R. Negus, L. E. Drain, “Mie calculations of the scattered light from a spherical particle traversing a fringe pattern produced by two intersecting laser beams,” J. Phys. D 15, 375–402 (1982).
[CrossRef]

N. S. Hong, A. R. Jones, “A light scattering technique for particle sizing based on laser fringe velocimetry,” J. Phys. D 9, 1839–1848 (1976).
[CrossRef]

Opt. Eng. (4)

B. A. Weiss, P. Derov, D. DeBiase, H. C. Simmons, “Fluid particle sizing using a fully automated optical imaging system,” Opt. Eng. 23, 561–566 (1984).

G. P. Bertollini, L. M. Oberdier, H. Y. Lee, “Image processing system to analyse droplet distributions,” Opt. Eng. 24, 464–469 (1985).

K. D. Ahlers, D. R. Alexander, “Microcomputer based digital image processing system developed to count and size laser-generated small particle images,” Opt. Eng. 24, 1060–1065 (1985).

S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment,” Opt. Eng. 28, 565–571 (1989).

Opt. Lett. (1)

Part. Part. Syst. Charact. (1)

N. G. Orfanoudakis, A. M. K. P. Taylor, “The effect of particle shape on the amplitude of scattered light for a sizing instrument,” Part. Part. Syst. Charact. 9, 223–230 (1992).
[CrossRef]

Other (6)

N. G. Orfanoudakis, A. M. K. P. Taylor, “Evaluation of a anemometer and application to a small scale swirl coal burner,” presented at the Clean Air Conference, Lisbon, Spain, 19–22 July 1993.

Y. Hardalupas, H. Morikita, A. M. K. P. Taylor, “Amplitude measurement of size of non-spherical particles: tolerances and validation schemes evaluated by scalar diffraction theory,” presented at the Third Congress on Optical Particle Sizing, Yokohama, Japan, 23–26 August 1993.

C. F. Hess, “A technique combining the visibility of a Doppler signal with the peak intensity of the pedestal to measure the size and velocity of droplets in spray,” Rep. AIAA-84-0203 (American Institute of Aeronautics and Astronautics, Washington, D.C., 1984).

K. Hishida, M. Maeda, J. Imaru, K. Hironaga, H. Kano, “Measurements of size and velocity of particle in two-phase flow by a three beam LDA system,” in Laser Velocimetry in Fluid Mechanics, R. J. Adrian, D. F. G. Duro, F. Durst, H. Mishina, J. H. Whitelaw, eds. (LADOAN, Lisbon, Portugal, 1984), Vol. 1, pp. 121–136.

M. L. Yeoman, H. J. White, B. J. Azzopardi, C. J. Bates, P. J. Roberts, “Optical development and application of a two colour LDA system for the simultaneous measurement of particle size and particle velocity,” in Proceedings of the ASME Winter Symposium (American Society of Mechanical Engineers, New York, 1982), pp. 127–135.

K. Kobashi, K. Hishida, M. Maeda, “Measurement of fuel injector spray flow of I.C. Engine by FFT based phase Doppler anemometer,” in Applications of Laser Techniques to Fluid Mechanics: Fifth International Symposium (Springer-Verlag, Berlin, 1991), pp. 268–287.
[CrossRef]

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 (16)

Fig. 1
Fig. 1

Schematic of the collection optics of the shadow Doppler velocimeter, the axis of which is horizontal. The particle is travelling vertically downward in the plane that contains the two incident beams from the transmission optics. The axis of the photodiode array is horizontal. AOM, acousto-optic modulator.

Fig. 2
Fig. 2

Image of the stationary shadow, of a 90-μm opaque Flowbead sphere recorded by a CCD camera and frame grabber system, as a function of defocus distance x from the center of the measuring volume.

Fig. 3
Fig. 3

Idealized representation of the output from a photodiode that recorded the passage of a particle for three trajectories defined in Fig. 4, below. Note that the signal of trajectory C shows the characteristics of the halo shown in Fig. 2 for particles that are out of focus, and the halo is called the outer ring structure in Fig. 4, below.

Fig. 4
Fig. 4

Definition of the trajectories considered in Fig. 3.

Fig. 5
Fig. 5

Representation of areas S L and S U , the areas of the shadow below and above the lower and upper threshold levels defined in the text, respectively, in an out-of-focus shadow.

Fig. 6
Fig. 6

Circuit of a transient recorder used to capture the output from the 16 channels of the photodiode array. I/O, input–output.

Fig. 7
Fig. 7

Sequence of the digitization times of the outputs of the photodiodes.

Fig. 8
Fig. 8

Output and normalized output from the photodiodes, the construction of the eight-level pseudoimage, and the pseudoimage after tristate thresholding.

Fig. 9
Fig. 9

Averaging of digitized output from photodiodes to provide the pixel average.

Fig. 10
Fig. 10

Sizing error, referred to a CCD camera image, of the shadow Doppler area-based size measurement of an in-focus 90-μm opaque Flowbead rotated at 0.74 m/s as a function of the setting of the upper and lower threshold levels.

Fig. 11
Fig. 11

CCD camera image for (a)–(c) a nonspherical 140-μm copper particle and (d)–(f) an 87-μm glass bead: (b) and (d) corresponding shadow Doppler pseudoimages, (c) and (f) corresponding images converted to the tristate.

Fig. 12
Fig. 12

Comparison of the area-based size taken from the shadow Doppler with that taken from microscope observation for four in-focus Flowbead spheres and two in-focus spheroidal copper particles. A single optimized pair of threshold levels was used.

Fig. 13
Fig. 13

Sizing error and rms rerror of diameter of the shadow Doppler results as a function of particle trajectory angle with particle velocity normal to the axis of the diode array as a parameter.

Fig. 14
Fig. 14

Sizing error from CCD camera inspection of the shadow as a function of the defocus distance.

Fig. 15
Fig. 15

(a) Sizing error as a function of the defocus distance with the setting of the threshold levels as a parameter. The shapes are the results from a single measurement. (b) Sizing error as a function of the defocus distance for high and low threshold levels, 0.85 and 0.5, respectively. The open circles are averages over 100 measurements.

Fig. 16
Fig. 16

Distance separating the centers of the circular images of the two beams as a function of the defocus distance. The linear dependence can be used to measure the defocus distance.

Equations (2)

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

d a = ( S proj 4 π ) 1 / 2 ,             S proj = 2 S L + S U 2 ,
r norm ( i , t ) = r ( i , t ) - r min ( i ) r max ( i ) - r min ( i ) ,

Metrics