Reconstruction of the Sizes of Spherical Particles from Their Shadow Images. Part I: Theoretical Considerations

Imaging optical array probes (OAPs) have become conventional instruments in studies of cloud microphysics. Previous works have shown that the error particle sizing in OAPs may reach 100%. Correcting the particle size measurements is not a trivial task, since the error depends on its size and distance from the object plane. A new technique for the size reconstruction of spherical particles from its measured image is introduced here. This technique also enables the retrieval of the particle position along the depth of field in the sample volume. The essence of the algorithm consists in the deduction of size and position from the relationships between the size of the Poisson spots and the geometrical dimensions of the image. The retrieval technique has been tested on the simulated discrete binary diffraction images of spherical particles, similar to those produced by OAPs. The images were modeled using the Fresnel diffraction approximation. It is demonstrated that the new algorithm can be applied to discrete binary images of spherical particles consisting of more than three pixels in size. An important feature of the retrieval technique is that it does not depend on the pixel resolution, and it can be applied for any type of OAPs that use a monochromatic coherent source of illumination.