Signal reconstruction algorithm based on a single intensity in the Fresnel domain

Area of Science:

• Optics and Photonics
• Signal Processing
• Computational Imaging

Background:

• Signal reconstruction typically requires multiple intensity measurements.
• Existing methods for Fresnel transform-based signal recovery are often computationally intensive.

Purpose of the Study:

• To develop a novel algorithm for reconstructing symmetrical signals (amplitude and phase) from a single Fresnel transform intensity.
• To introduce an efficient complex-convolution method for this reconstruction task.

Main Methods:

• A new algorithm based on a single Fresnel transform intensity is proposed.
• A complex-convolution method is introduced as a key component of the algorithm.
• Properties of the discrete Fresnel transform are analyzed and presented.

Main Results:

• The proposed method successfully reconstructs the signal using only one intensity measurement.
• Numerical simulations validate the algorithm's effectiveness.
• The new method demonstrates superior speed and efficiency compared to conventional techniques.

Conclusions:

• A single-intensity Fresnel transform reconstruction is feasible with the proposed algorithm.
• The complex-convolution approach offers significant advantages in speed and efficiency for signal reconstruction.