Fresnel diffractograms from pure-phase wave fields under perfect spatio-temporal coherence: Non-linear/non-local...

Area of Science:

• Wave optics
• Diffraction theory
• Image analysis

Background:

• The diffractogram, a Fourier transform of wave field intensity contrast after propagation, has been studied for Gaussian phase profiles.
• A critical low-frequency zero in the diffractogram emerges at small Fresnel numbers, dependent on phase-scaling and Fresnel number.
• Understanding S-scaling behavior is crucial for non-perturbative analysis of wave propagation.

Purpose of the Study:

• To investigate the S-scaling behavior of the entire diffractogram across various Fresnel numbers.
• To identify conditions for maximum S-scaling linearity and universal physical frequencies.
• To analyze the transition between oscillatory and non-oscillatory diffractogram behaviors and its implications.

Main Methods:

• Non-perturbative analysis of diffractograms with varying phase-scaling factors (S) and Fresnel numbers (F).
• Identification of linearity valleys in the F-σ plane.
• Simulation of diffractograms using a complex phase map (Lena).
• Experimental validation using X-ray imaging.

Main Results:

• A valley of maximum S-scaling linearity was found, corresponding to a universal physical frequency.
• Near-field (large F) diffractograms show S-scaling linearity only at low spatial frequencies (σ).
• Far-field (small F) diffractograms exhibit distinct bands of S-scaling linearity (damped oscillatory).
• The transition from damped oscillatory to overdamped non-oscillatory diffractograms is a critical phenomenon.

Conclusions:

• S-scaling analysis provides insights into wave propagation and phase information.
• The identified universal frequency and scaling behaviors are significant for optical metrology.
• The critical transition phenomenon is observable in both simulations and experiments, including X-ray imaging.