Limits of diffractometric reconstruction of line gratings when using scalar diffraction theory

Area of Science:

• Optics and Photonics
• Metrology
• Diffraction Theory

Background:

• Scalar diffraction theory is widely used for optical element design.
• Computer-generated holograms (CGHs) demand high phase accuracy for testing aspheres and free-form surfaces.
• Line gratings with periods below 10 μm are critical components in advanced CGHs.

Purpose of the Study:

• To investigate the geometric and phase reconstruction errors of scalar diffraction theory for sub-10 μm line gratings.
• To determine the failure limits of scalar diffraction theory in this regime.
• To identify significant error mechanisms impacting high-precision optical metrology.

Main Methods:

• Rigorous electromagnetic simulations were employed as a reference.
• Analysis of grating geometry and phase reconstruction accuracy.
• Comparison between scalar theory predictions and rigorous simulation results.

Main Results:

• Scalar diffraction theory exhibits significant errors for line gratings with periods below 10 μm.
• The study quantifies the deviation from rigorous predictions.
• Specific error mechanisms related to grating geometry and phase reconstruction were identified.

Conclusions:

• Scalar diffraction theory is insufficient for accurately modeling sub-10 μm line gratings in demanding applications.
• Understanding these limitations is essential for achieving error budgets in the range of λ/100 for interferometric testing.
• Rigorous methods are necessary for accurate design and simulation in advanced optical metrology.