Double-lens extended fractional Fourier transform

Area of Science:

• Optics and Photonics
• Fourier Optics
• Wave Phenomena

Background:

• The fractional Fourier transform (FRT) is a powerful tool in optical signal processing.
• Extended fractional Fourier transforms (EFRTs) generalize FRT to arbitrary orders.
• Existing single-lens systems for EFRT have limitations in flexibility and order control.

Purpose of the Study:

• To propose and validate a double-lens optical system for performing extended fractional Fourier transforms (EFRTs).
• To demonstrate the capability of the double-lens system to execute arbitrary-order EFRTs, including complex orders.
• To compare the performance and characteristics of the double-lens EFRT with the single-lens EFRT.

Main Methods:

• Development of a double-lens optical configuration for EFRT.
• Theoretical analysis of the double-lens system for real and complex orders.
• Numerical simulations to verify the system's functionality.
• Optical experiments to validate the simulation results and system performance.

Main Results:

• The proposed double-lens system successfully performs arbitrary-order EFRTs.
• Numerical simulations and optical experiments confirm the equivalence between single-lens and double-lens EFRT systems.
• The double-lens EFRT system demonstrates consistency with the single-lens EFRT for both real and complex orders.
• The double-lens setup is established as a viable basic optical configuration.

Conclusions:

• The double-lens EFRT system provides a flexible and effective method for implementing arbitrary-order fractional Fourier transforms.
• The double-lens configuration offers advantages over single-lens systems, enhancing its utility in optical applications.
• This work establishes a new fundamental optical setup for advanced Fourier optics manipulations.