Reconstruction of gratings from noisy reflection data.

Area of Science:

• Optics and Photonics
• Materials Science
• Inverse Problems

Background:

• Grating characterization from reflection spectra is crucial for optical device design.
• Error amplification during reconstruction limits accuracy, particularly for strong gratings.
• Understanding the relationship between grating strength and reconstruction fidelity is essential.

Purpose of the Study:

• To quantify the worst-case error amplification in grating reconstruction from complex reflection spectra.
• To investigate the impact of grating strength (kappaL) on reconstruction accuracy.
• To propose a method for stabilizing grating reconstruction for moderately strong gratings.

Main Methods:

• Analysis of error amplification factor in relation to minimum transmissivity (Tmin).
• Derivation of error amplification for uniform gratings as exp(2kappaL).
• Development of a regularization technique for inverse-scattering problems.

Main Results:

• Worst-case error amplification is proportional to 1/Tmin.
• Error amplification grows exponentially with the grating strength product (kappaL).
• Spatial characterization is impossible for sufficiently strong gratings.
• The proposed regularization technique stabilizes solutions for moderately strong gratings.

Conclusions:

• Strong gratings pose significant challenges for accurate spatial reconstruction from reflection spectra.
• The exponential error amplification highlights the limitations of direct reconstruction methods.
• Regularization provides a viable approach for analyzing moderately strong gratings, enabling practical applications.