PDI: Phase Doppler Interferometer
Droplet size and velocity measurements
Theory of Operation
In a basic PDI optical system, the laser beam is split into two beams of equal intensity. The beams are then focused and made to intersect using a transmitter lens. Frequency shifting is used to compress the frequency dynamic range and resolve the directional ambiguity that would occur for drops passing in a reverse direction. This makes the measurements of droplet size completely independent of droplet velocity (magnitude and angle of trajectory). Particles passing through the beam intersection will scatter light that is collected by the receiver lens. A single aperture is used in the receiver to allow only light scattered by particles crossing a small region of the beam intersection to reach the photodetectors. This aperture is easily changed via computer control and software so the sample volume size can be automatically adjusted to optimize the instrument for the prevailing droplet number density conditions without experiencing significant coincidence rejections and associated measurement uncertainty.
Measurement of the spacing of the interference fringes produced by the scattered light is accomplished in a straightforward manner using pairs of detectors. For this approach, pairs of detectors are located in the fringe pattern or an image of it, and the effective separations S12 and S13 between the detectors are measured and calibrated. When the particle or drop is moving, the usual Doppler difference frequency of the scattered light occurs. The difference in the Doppler frequency shift between the light scattered from beam 1 and beam 2 causes the fringe pattern to appear to move.
As the pattern sweeps past the detectors at the Doppler difference frequency, each detector produces a signal that is similar in frequency but shifted in phase. The phase shift is related to the spacing of the scattered fringe pattern through the following relationship:
where S is the detector spacing and f is the phase shift between the measured electronic signals. The wavelength L is the spacing of the interference fringes formed by the scattered light and is inversely proportional to the drop diameter. Typically, three detectors are used to avoid ambiguity in the measurements, to provide redundant measurements of the pattern, and to improve the resolution for the small particles. The ambiguity could occur when the fringe spacing, L is less than the detector separation. In this case, the phase shift would be greater than 360 degrees but is reported as f – 360.
The unique three-detector separation arrangement originally invented by Bachalo (US Patent 4,540,283) and first reported in 1982 (NASA Technical Report) is shown below. The phase versus diameter curves that correspond to these detector separations are also shown. With this configuration, the phase shift between the signals from the closely spaced detectors, D1 and D2 follow the smaller slope on the phase-diameter plot indicated by the dotted lines. The phase between the signals for the detectors with the larger spacing, D1 and D3, follow the curves with the greater slope. With this arrangement, the phase may be measured for detector separations that extend over several fringes (1 fringe corresponds to a measured phase shift of 360°) when placed in the field of the scattered light. More recently, we use three pairs of detectors (f12, f13, and f23) to in the measurement as shown in the updated diagram of phase versus diameter. This provides some greater flexibility in optimizing for different drop size ranges.
Configuration of a basic phase Doppler interferometer (PDI) system.
Interference fringe pattern projected onto a plane surface and showing a preferred location of the receiver lens in the off-axis forward scatter (30 degree) location.
Calculated interference fringe pattern with the segmented receiver placed over the pattern showing how the fringe spacing can be measured using the phase shift information.
Response of the phase shift to spherical droplet size showing that with three detectors, the phase shift can be measured unambiguously over several cycles. The response is linear over the full size range.