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The effects of the individual scattering process on the formations of both the particle hologram and its corresponding reconstructed three-dimensional particle image are investigated using the Debye series. A particle hologram model using the Debye series decomposes the object wave into different scattering modes and thus permits evaluating the effects of the individual scattering process [diffraction, reflection, transmission, refractions with (p-1) internal reflections] on the particle holography quantitatively. In the Gabor inline holography of a transparent droplet, the transmission light causes small discrepancies between the hologram fringes of an opaque particle (diffraction) and a transparent particle near the zero point of the Bessel-like modulation function, eventually giving rise to the glory spot in the center of the reconstructed dark particle image. For off-axis holography, this paper reveals the effects of reflection, particularly total reflection by bubbles, transmission, and refractions with (p-1) internal reflections of the scattered light on the formation and the reconstructed glory spot images of typical forward and backward off-axis holography.

On the basis of generalized Lorenz-Mie theory, the Debye series expansion (DSE) for radiation pressure forces (RPF) exerted on a multilayered sphere induced by focused beams is introduced. The DSE can isolate the contribution of each scattering process to RPF, and give a physical explanation of RPF. Typically, the RPF induced by a Gaussian beam is studied. The DSE is employed to the simulation of RPF corresponding to different scattering processes (diffraction, reflection, refraction, etc.) in detail, and gives the physical mechanism of RPF. The effects of various parameters, such as scattering mode p, beam position, and radius of core for coated spheres, to RPF is researched.

By means of geometrical optics we present an approximation method for acceleration of the computation of the scattering intensity distribution within a forward angular range (0-60 degrees ) for gradient-index spheres illuminated by a plane wave. The incident angle of reflected light is determined by the scattering angle, thus improving the approximation accuracy. The scattering angle and the optical path length are numerically integrated by a general-purpose integrator. With some special index models, the scattering angle and the optical path length can be expressed by a unique function and the calculation is faster. This method is proved effective for transparent particles with size parameters greater than 50. It fails to give good approximation results at scattering angles whose refractive rays are in the backward direction. For different index models, the geometrical-optics approximation is effective only for forward angles, typically those less than 60 degrees or when the refractive-index difference of a particle is less than a certain value.

We derive the formula of the Debye-series decomposition for normally incident plane-wave scattering by an infinite multilayered cylinder. A comparison of the scattering diagrams calculated by the Debye series and Mie theory for a graded-index polymer optical fiber is given and the agreement is found to be satisfied. This approach permits us to simulate the rainbow intensity distribution of any single order and the interference of several orders, which is of good use to the study of the scattering characteristics of an inhomogeneous cylinder and to the measurement of the refractive index profile of an inhomogeneous cylinder.