Abstract

Photographs of clouds taken with a camera with a large aperture ratio must have a short depth of focus to resolve small droplets. Hence the sampling volume is small, which limits the number of droplets and gives rise to a large statistical error on the number counted. However, useful signals can be obtained with a small aperture ratio, which allows for a sample volume large enough for counting cloud droplets at aircraft speeds with useful spatial resolution. The signal is sufficient to discriminate against noise from a sunlit cloud as background, provided the bandwidth of the light source and camera are restricted, and against readout noise. Hence, in principle, an instrument to sample the size distribution of cloud droplets from aircraft in daylight can be constructed from a simple TV camera and an array of laser diodes, without any components or screens external to the aircraft window.

© 1999 Optical Society of America

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References

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  1. R. G. Knollenberg, “The optical array: an alternative to scattering or extinction for airborne particle size determination,” J. Appl. Meteorol. 9, 86–103 (1970).
    [CrossRef]
  2. A. J. Heymsfield, J. L. Parrish, “A computational technique for increasing the effective volume of the PMS two-dimensional particle size spectrometer,” J. Appl. Meteorol. 17, 1566–1572 (1978).
    [CrossRef]
  3. P. D. Jonas, UMIST, Manchester, UK (personal communication, 1996).
  4. R. Greenler, Rainbows, Haloes, and Glories (Cambridge U. Press, Cambridge, UK, 1980), pp. 1–2.
  5. B. I. Bleaney, B. Bleaney, Electricity and Magnetism, 2nd ed. (Oxford U. Press, London, 1965), p. 275.
  6. H. C. van de Hulst, “Light Scattering by Small Particles” (Dover, New York, 1981).
  7. R. A. R. Tricker, Introduction to Meterological Optics (Elsevier, New York, 1970).
  8. H. K. Roscoe, W. H. Taylor, J. D. Evans, A. M. Tait, R. A. Freshwater, D. J. Fish, E. K. Strong, R. L. Jones, “Automated ground-based star-pointing UV–visible spectrometer for stratospheric measurements,” Appl. Opt. 36, 6069–6975 (1997).
    [CrossRef] [PubMed]
  9. C. D. Mackay, “Charge-coupled devices in astronomy,” Ann. Rev. Astron. Astrophys. 24, 255–283 (1986).
    [CrossRef]
  10. J. T. Houghton, The Physics of Atmospheres (Cambridge U. Press, Cambridge, UK, 1977), pp. 177–178.

1997 (1)

1986 (1)

C. D. Mackay, “Charge-coupled devices in astronomy,” Ann. Rev. Astron. Astrophys. 24, 255–283 (1986).
[CrossRef]

1978 (1)

A. J. Heymsfield, J. L. Parrish, “A computational technique for increasing the effective volume of the PMS two-dimensional particle size spectrometer,” J. Appl. Meteorol. 17, 1566–1572 (1978).
[CrossRef]

1970 (1)

R. G. Knollenberg, “The optical array: an alternative to scattering or extinction for airborne particle size determination,” J. Appl. Meteorol. 9, 86–103 (1970).
[CrossRef]

Bleaney, B.

B. I. Bleaney, B. Bleaney, Electricity and Magnetism, 2nd ed. (Oxford U. Press, London, 1965), p. 275.

Bleaney, B. I.

B. I. Bleaney, B. Bleaney, Electricity and Magnetism, 2nd ed. (Oxford U. Press, London, 1965), p. 275.

Evans, J. D.

Fish, D. J.

Freshwater, R. A.

Greenler, R.

R. Greenler, Rainbows, Haloes, and Glories (Cambridge U. Press, Cambridge, UK, 1980), pp. 1–2.

Heymsfield, A. J.

A. J. Heymsfield, J. L. Parrish, “A computational technique for increasing the effective volume of the PMS two-dimensional particle size spectrometer,” J. Appl. Meteorol. 17, 1566–1572 (1978).
[CrossRef]

Houghton, J. T.

J. T. Houghton, The Physics of Atmospheres (Cambridge U. Press, Cambridge, UK, 1977), pp. 177–178.

Jonas, P. D.

P. D. Jonas, UMIST, Manchester, UK (personal communication, 1996).

Jones, R. L.

Knollenberg, R. G.

R. G. Knollenberg, “The optical array: an alternative to scattering or extinction for airborne particle size determination,” J. Appl. Meteorol. 9, 86–103 (1970).
[CrossRef]

Mackay, C. D.

C. D. Mackay, “Charge-coupled devices in astronomy,” Ann. Rev. Astron. Astrophys. 24, 255–283 (1986).
[CrossRef]

Parrish, J. L.

A. J. Heymsfield, J. L. Parrish, “A computational technique for increasing the effective volume of the PMS two-dimensional particle size spectrometer,” J. Appl. Meteorol. 17, 1566–1572 (1978).
[CrossRef]

Roscoe, H. K.

Strong, E. K.

Tait, A. M.

Taylor, W. H.

Tricker, R. A. R.

R. A. R. Tricker, Introduction to Meterological Optics (Elsevier, New York, 1970).

van de Hulst, H. C.

H. C. van de Hulst, “Light Scattering by Small Particles” (Dover, New York, 1981).

Ann. Rev. Astron. Astrophys. (1)

C. D. Mackay, “Charge-coupled devices in astronomy,” Ann. Rev. Astron. Astrophys. 24, 255–283 (1986).
[CrossRef]

Appl. Opt. (1)

J. Appl. Meteorol. (2)

R. G. Knollenberg, “The optical array: an alternative to scattering or extinction for airborne particle size determination,” J. Appl. Meteorol. 9, 86–103 (1970).
[CrossRef]

A. J. Heymsfield, J. L. Parrish, “A computational technique for increasing the effective volume of the PMS two-dimensional particle size spectrometer,” J. Appl. Meteorol. 17, 1566–1572 (1978).
[CrossRef]

Other (6)

P. D. Jonas, UMIST, Manchester, UK (personal communication, 1996).

R. Greenler, Rainbows, Haloes, and Glories (Cambridge U. Press, Cambridge, UK, 1980), pp. 1–2.

B. I. Bleaney, B. Bleaney, Electricity and Magnetism, 2nd ed. (Oxford U. Press, London, 1965), p. 275.

H. C. van de Hulst, “Light Scattering by Small Particles” (Dover, New York, 1981).

R. A. R. Tricker, Introduction to Meterological Optics (Elsevier, New York, 1970).

J. T. Houghton, The Physics of Atmospheres (Cambridge U. Press, Cambridge, UK, 1977), pp. 177–178.

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Figures (6)

Fig. 1
Fig. 1

Rays with one internal or external reflection from a droplet. Rays with more than one internal reflection have, in general, much weaker intensity if the refractive index is small. The backscatter angle (β) used throughout this work is equal to 180° minus the scattering angle. At the small backscatter angles discussed, two internally reflected rays are observed, one near the center of the drop and one near its edge.

Fig. 2
Fig. 2

Photograph of the light from a small-aperture lamp, reflected from a polished steel ball bearing, as the lamp is moved around the ball bearing at the same distance from it, so that the image moves closer to the edge of the ball bearing. Note that the area of the illuminated image stays the same as it moves closer to the edge—the geometric factor is independent of backscatter angle.

Fig. 3
Fig. 3

Photograph of the glass and steel spheres used for test measurements, at ∼10° backscatter angle. The externally reflected ray, and the center and edge internally reflected rays, can be seen clearly in the glass sphere. The reflected ray in the steel sphere was used as the lamp calibration in the measurements in Table 2. The contrast in diameters of the two spheres was important for preventing the otherwise more intense reflection from the steel sphere from saturating the TV camera.

Fig. 4
Fig. 4

Sketch of a possible airborne system for photographing cloud droplets in sunlight, without any components external to the aircraft window.

Fig. 5
Fig. 5

Constructions for deriving the geometric factor for an external reflection from a sphere illuminated by a beam of parallel light, for beam displacements in (a) the radial plane containing the incoming and outgoing rays and (b) the circumferential plane perpendicular to (a). The plane of the output ray in (b) is that of the y axis and the dashed line, thus allowing us to derive the relationship between z/ a and δα.

Fig. 6
Fig. 6

Constructions for deriving the geometric factor for one internal reflection from a sphere illuminated by a beam of parallel light, for beam displacements in (a) the radial plane containing the incoming and outgoing rays and (b) the circumferential plane perpendicular to (a). The plane of the output ray in (b) is that of the two dashed lines, thus allowing us to derive the relationship between z/ a and δα.

Tables (5)

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Table 1 Comparison of Our Calculated Intensities of the Internally Reflected Ray from a Large Spherical Water Droplet to Those Calculated by van de Hulst (1981)a

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Table 2 Comparison of Our Calculations of the Intensities of the Reflected Rays from a Large Glass Sphere to our Measurementsa

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Table 3 Calculated Intensity Reflected from a Large Water Droplet: Ratios of the Minimum Intensity Due to Interference to the Intensity without Interferencea

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Table 4 Variables and Equations Used in the Calculation of Instrument Feasibility

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Table 5 Values of the Variables for a Typical Calculation for an Airborne Instrument

Equations (2)

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§=Γ/Ω, by definition;  Γ=x * z/π * a2, by definition;§=x * z/π * a2 * Ω;  Ω=δβ * δα, by definition;§=x * z/π * a2 * δβ * δα;  x=δβ * a * cosβ/2/2 from Fig. 5a;§=z * cosβ/2/2 * π * a * δα;  z=a * δα/2 * cosβ/2from Fig. 5b;§=1/4π.
§=Γ/Ω, by definition;   Γ=x * z/π * a2, by definition;§=x * z/π * a2 * Ω;   Ω=δβ * δα, by definition;§=x * z/π * a2 * δβ * δα;   x=δï * a * cosï from Fig. 6a;§=δï * z * cosï/π * a * δβ * δα;   z=a * δα * sinï/sinβ from Fig. 6b;§=δï * sinï * cosï/π * δβ * sinβ;  β/2=2 * ıˆ-ï;      sinıˆ=sinï/ñ;   β=4 * sin-1sinï/ñ-2 * ï; differentiating   δβ=(4 * cosï/1-sin2ï/ñ1/2 * ñ-2) * δıˆ;      sinï/ñ=sinıˆ;   δβ=(4 * cosï/1-sin2ıˆ1/2 * ñ-2) * δıˆ;      1-sin2ı˜=cos2ıˆ;   δβ=4 * cosï/ñ * cosıˆ]-2δıˆ;§=cosï * sinï/(π * sinβ * 4 * cosï/ñ * cosı˜-2);      cosï * sinï=sin2 * ï/2;§=sin(2 * ï/(2 * π * sinβ * 4 * cosï/n * cosıˆ-2).

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