Differential Fourier transform technique for the inverse scattering problem

Area of Science:

• Physics
• Optics
• Materials Science

Background:

• Characterizing the size distribution of randomly distributed tenuous scatterers is crucial in various scientific fields.
• Existing methods often require matrix inversion or prior knowledge of the scatterer size distribution, limiting their applicability.

Purpose of the Study:

• To develop a novel inversion technique for determining the size distribution of tenuous scatterers from forward scattering data.
• To create a method that is versatile, applicable to 1-D, 2-D, and 3-D scatterers, and does not require a priori information.

Main Methods:

• The technique utilizes spectral analysis, incorporating fast Fourier transform (FFT) and digital filtering.
• It processes the forward scattering pattern to retrieve the size distribution without matrix inversion.
• A 1024-point FFT was employed for analysis, demonstrating robustness against noise.

Main Results:

• The developed inversion technique accurately estimates the size distribution of scatterers.
• Even with 10% noise, the estimation error for a Gaussian size distribution was within a few percent.
• The method proved effective in practical experiments involving latex spheres and bacteria.

Conclusions:

• The novel inversion technique offers an efficient and accurate means to determine scatterer size distributions.
• Its independence from matrix inversion and prior knowledge makes it a broadly applicable tool.
• Experimental validation confirms the technique's practical utility in characterizing biological and synthetic scatterers.