Phase Doppler Interferometry (PDI) is an extension of Laser Doppler Velocimetry (LDV) for measuring the size of spherical droplets in addition to its velocity. Like the LDV, the PDI uses two coherent laser beams to intersect and form a measurement probe volume. Particles passing through the beam intersection region will scatter light that is collected by a receiver placed at a suitable angle, typically in the forward scatter direction. However, unlike an LDV system, the receiver lens of a phase Doppler system is partitioned into four segments and the scattered light collected by these segments are directed to separate photodetectors. The Doppler difference frequency observed by each of the photodetectors will be identical and any one of them can be used to infer the particle velocity as in a traditional LDV. In addition, since the phase difference between any two Doppler burst signals can be shown to bear a nearly monotonic, linear relationship with the particle or droplet diameter, in PDI, the phase is measured and used to infer the diameter of a spherical particle. Non-spherical particles will also produce a Doppler signal but will be rejected based on proprietary phase validation logic that is incorporated into the system software.

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.

Click Here for an animated explanation of the Phase Doppler Interferometry system (requires Adobe ShockWave plug-in).

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.

  • Measurements are based on the wavelength of light that is known to high accuracy and does not change due to environmental conditions
  • The size of the sample volume can be easily controlled and made as small as the largest droplet to be measured (or even smaller)
  • Response is to ballistic or singly-scattered photons; secondary light scattering is not detected
  • Signals have a unique sinusoidal character making them easily detectable with high reliability using digital techniques
  • Simultaneously measures the size, velocity, and time-of-arrival of every drop and forms a direct measurement of the size distribution
  • Droplet size range capability of 0.5 μm to 2000 μm or greater
  • LWC capability from 0 to 100g/m3 or larger
  • Measures in droplet number densities to 100,000/cc, depending on droplet size
  • High data rate capability of >100,000 drops/second without loss of readings
  • In situ measurements of the sample volume size allowing determination of droplet number density, flux and LWC
  • Reliable detection and rejection of ice particles from the droplet size measurement

Artium’s PDI system consists of an optical transmitter, an optical receiver, ASA Signal Processors, the instrument control computer, and the AIMS System Software. Artium offers a variety of optical designs to meet different spray applications. Systems capable of measuring droplet size and 1-, 2-, or 3-components of velocity are available either in a modular or self-contained design configurations. The laser wavelengths and power can be customized based on the application and user needs.

The Artium PDI design incorporates several features aimed at ease-of-use and data accuracy. A key feature is the ability to change the droplet size measurement range without requiring the user to change lenses or realign the optics. This can be accomplished by changing the laser beam separation and selecting different masks in the receiver via software. A software controlled aperture module also allows for the selection of a variety of apertures and tilts. A new version of the ASA is now available for improved data accuracy at high speeds in dense environment. The AIMS software includes an auto-setup feature that automatically selects the processor and optics settings for optimal performance in complex sprays.

Key features that are unique to Artium’s PDI include:

  • Built-in, high-powered DPSS lasers to enable backscatter measurements through contaminated windows.
  • Automated instrument setup features to simplify instrument operation in difficult environments (U.S. Patent 7,564,564, 2009)
  • Digital signal detection and full complex Fourier transform signal processing for frequency and phase
  • Automatic selection of size range through computer selection of beam intersection angle and beam expansion
  • Automatic selection of size range through computer controlled mask selection in the receiver covering at least three size ranges
  • Signal intensity validation logic
  • Three phase measurements for improved particle measurement reliability and accuracy and rejection of trajectory errors
  • Option fourth phase measurement for improved measurement accuracy in dense spray application
  • Full complex Fourier transform signal processing with up to 100,000 samples in the signals
  • Advanced signal validation logic including tests for variations in frequency and phase over the duration of the Doppler signals (U.S. Patent Pending)
  • Computer selectable sample volume size to minimize coincidence errors
Artium Competition

· Unique built in compact diode pumped solid state (DPSS) laser design

· Turn-key lasers

· High coherence length >100m

· High beam quality and pointing stability

· Very long lifetime >10,000 hours

· High power at probe volume (up to 1 watt)

· Three widely separated wavelengths available for 3D LDV and PDI systems

· Very low power consumption

· No water cooling or air cooling required


· Now have followed Artium’s lead and use low power DPSS lasers

· Still use inefficient and troublesome single mode polarization preserving fibers to couple the beam to the probe head.

Modular Optics

· Stable alignment

· Computer/software selectable beam expansion for size range selection

· Easily adjustable to accommodate thick windows

· Interchangeable optics

· Computer controlled size range

Fiber Optics-Based

· Fiber optics need frequent alignment

· Approximately 40% loss in laser power in fibers

· Fibers degrade with age, reduced signal quality

High Spray Density Capability

· Computer controlled beam expansion in transmitter

· Computer controlled selection of six apertures (15, 25, 50, 100, 250, and 500 μm or 50, 100, 200, 400, 800, and 1600 μm)

· Computer selectable masks in receiver to change size range

· System alignment not affected by change in apertures or masks


· Manual selection of apertures

· Apertures exposed where they can be damaged or contaminated

· Changing masks in receiver requires disassembly of the receiver and realignment after the change

Phase Calibration

· Laser diode in receiver produces simulated Doppler signals

· Automatic phase calibration


· Built in signal simulator

· Automatic phase calibration

Signal Processing

· Artium’s Automated Instrument Management System (AIMS) software automatically selects the instrument setup based on the incoming signals (U.S. Patent 7,788,067)

· New signal processor using FPGA’s for reliability and compactness

· Sampling frequency 160 MHz Quadrature, equivalent to 320 MHz

· Continuously selectable bandwidths

· Fixed and variable down-mixing

· Ethernet cable connection to computer interface

· Full complex (real and imaginary signal sampled and processed) using complex FFT

· Variable record length for recording the signals with up to 100,000 ADC samples in the record

· FFT’s with up to 16,000 frequencies for very high resolution measurements

· Signal processors transfers the sampled signals, transit time, arrival time, signal amplitude and other important information to the computer where it is saved

· Sampled signals can be easily re-processed using, for example, different validation criteria

· Processing signals in the software allows application of advanced methods and proprietary signal validation methods

· 12 bit sampling of signals available

· High speed transfer of signals to the computer (>100,000/second)


· Older electronics system requires selecting a velocity range (center frequency and band width)· BSA signal processor was developed over 20 years ago

· Hard-wired FFT using only the real signals which limits the phase measurement accuracy

· Sampling frequency 300 MHz

· 28 selectable bandwidths with different center frequencies

· Fixed down-mix frequencies

· Fixed record length of only 64 samples in the FFT

· Protection is needed to avoid PMT signal amplitude overload

· Signal processor transfers only the final results (size, velocity, arrival time, etc.)

· Ethernet connection to the computer

· Signals are not saved and only the reduced results are available during measurements

· Digital multi-bit sampling to only 8 bits. Signal amplitudes for sizing will vary over a range of 2000 to one so 8 bits (256 levels) isn’t enough

· Fast transfer to the computer of only reduced measurements

Signal Detection

· Signal Amplitude and digital detection based on Signal to Noise Ratio


· Burst detection based on amplitude threshold and SNR

Size Validation

· SNR evaluation on each of the three size channels

· Frequency variation over the signal duration (U.S. Patent 7,788,067)

· Phase variation over the signal duration

· Size range validation

· Velocity range validation

· Size based on the weighted average over the three phase pair measurements, figure 4 and 5.

· Intensity validation


· SNR on single signal for the sizing channel· Dual PDA comparison of the normal and planar values

· Sphericity check

· Size based on only one phase measurement

Sphericity Check

· Validate signals based on the comparison between three phase measurements, AB, AC ,and BC. Optional, fourth phase measurement is also offered for custom applications.

· Relies on random orientation of drops, average leads to a close approximation of the true spherical diameter


· Only a single phase measurement pair used for size measurement· Sphericity check and rejection leads to missing the largest particles in a distribution and significant measurement errors on higher moments (D32, D30)

· Dual PDA loses capability of testing every signal by comparing to two or three valid phase measurements for each droplet