Particle sizing by forward lobe scattered intensity-ratio technique: errors introduced by applying diffraction theory...

Area of Science:

• Optical Physics
• Particle Metrology

Background:

• Fraunhofer diffraction theory offers an approximation to Mie theory for particle size measurement using forward lobe scattering intensity ratios.
• Previous estimations of theoretical errors in this approximation were limited.

Purpose of the Study:

• To develop and describe a technique for quantifying the theoretical errors inherent in using Fraunhofer diffraction as an approximation to Mie theory.
• To assess the magnitude and behavior of these errors for specific particle types and measurement conditions.

Main Methods:

• Theoretical error quantification technique developed.
• Calculations performed for monodisperse latex spheres in air and water.
• Evaluated specific angle pairs: 5°/2.5°, 10°/5°, and 20°/10°.

Main Results:

• Theoretical errors were computed and found to oscillate with particle size.
• Oscillations correlate with particle extinction coefficient variations.
• Errors generally fall within +/-40%, exceeding previous estimates.
• Errors are consistently stronger and larger in air compared to water.

Conclusions:

• The Fraunhofer diffraction approximation to Mie theory for particle size measurement introduces significant, oscillating theoretical errors.
• Error magnitudes are dependent on the medium (air vs. water) and measurement angles.
• These findings necessitate careful consideration of the approximation's limitations in practical applications.