Measurement of three dimensional position of particles by single CCD image including lens aberration

A new technique using a single CCD image through a lens system with large aberration is proposed in the present study for measurement of the three dimensional position of particles, in which a thick laser light source and a forward-scattering light from particles are processed. This optical system could be very compact and applicable to various flow measurements. The particle image detected by a CCD sensor is distorted in the present system due to lens aberrations. A transformation function of the optical system, which is the relationship between the reference particle with unit luminosity in the measuring volume and the corresponding distorted particle image detected by a CCD sensor through symmetric-convex lenses, is constructed theoretically based on the image formation optics of small particles. In order to obtain a high accuracy in the measurement, it is important to remove the background noise and the light intensity non-uniformity in the measuring volume from the CCD particle image by using a low-pass filtering technique based on the FFT analysis. By calculating the cross-correlation coefficient between the measured particle image and the data base images prepared by the above transformation function, the three dimensional position of the particle is determined as the position at which the largest cross-correlation coefficient is obtained. It is verified experimentally that this compact measuring system is useful for measurement of the three dimensional position of the particle with a good accuracy.