Interferometric Phase Calculation with Bandwidth and Numerical Aperture Correction
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Solution Overview
Problem
Existing interferometric measurement techniques, such as phase-shifting interferometry, are ineffective in accounting for modulation variations caused by narrowband wavelengths and high numerical apertures, leading to inaccurate surface topography measurements due to factors like mechanical vibrations and environmental perturbations.
Innovation Solution
The development of an equation that expresses intensity as a function of scan position, initial phase, and parameters dependent on bandwidth and numerical aperture, allowing for a global error function minimization to correct for these variations, thereby improving the precision of phase and height calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional phase-shifting interferometry algorithms are used, then the measurement process is simple and fast, but the measurement precision deteriorates due to unaccounted modulation variations from narrowband wavelengths and high numerical apertures
Solution Approach 1:
The patent modifies the traditional PSI algorithm by introducing new parameters that account for modulation variations. Specifically, it incorporates bandwidth-dependent and numerical-aperture-dependent parameters into the intensity equation, transforming the simple PSI model into a more complex but accurate model that reflects real-world conditions. This parameter expansion allows the algorithm to compensate for practical limitations while maintaining computational feasibility.
Solution Approach 2:
The patent replaces the assumption of ideal interferometric conditions with a corrected mathematical model that accounts for real-world deviations. Instead of relying on perfect single-wavelength and zero-numerical-aperture conditions, the invention substitutes these idealized assumptions with corrected equations that incorporate actual system parameters, thereby achieving accurate measurements under practical conditions.
2Adaptability or versatility
If ideal single-wavelength and zero numerical aperture conditions are assumed, then the algorithm performance is optimized, but these conditions are not achievable in practice
Solution Approach 1:
The patent transforms the algorithm from being sensitive to wavelength and numerical aperture variations to being robust by explicitly incorporating these parameters into the intensity equation. The modified model includes bandwidth-dependent modulation terms and numerical-aperture-dependent cosine factors, allowing the algorithm to adapt to actual system conditions rather than requiring idealized assumptions.
Solution Approach 2:
The patent introduces intermediate correction terms in the intensity equation that mediate between the ideal interferometric model and real-world conditions. These intermediate terms account for the effects of finite bandwidth and non-zero numerical aperture, serving as corrective factors that bridge the gap between theoretical assumptions and practical implementation.
3Measurement precision
If fixed scanning step size is used, then the algorithm is simple to implement, but random changes in step size due to vibrations produce non-uniform profiles
Solution Approach 1:
The patent implements a feedback mechanism where the algorithm iteratively refines the scanning step size based on the actual interference data. By comparing measured intensities with predicted intensities from the corrected model, the algorithm adjusts the step size parameters to minimize errors, thereby compensating for random variations caused by vibrations and other environmental factors.
Solution Approach 2:
The patent transitions from a static fixed step size approach to a dynamic step size determination method. The scanning step size becomes a variable that is optimized based on the actual measurement conditions and data quality, allowing the system to adapt to vibrations and environmental perturbations rather than relying on rigid predetermined values.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly reduces the impact of mechanical vibrations, scanner nonlinearities, and environmental factors, enhancing the accuracy of interferometric measurements by accounting for practical conditions like narrowband light and non-zero numerical apertures.
Implementation Method 1
phase-shifting interferometry (PSI) and related techniques are based on changing the phase difference between two coherent interfering beams
Data Source
AI summary
An interferometric intensity equation includes parameters that depend on bandwidth and numerical aperture. An error function based on the difference between actual intensities produced by interferometry and the intensities predicted by the equation is minimized iteratively with respect to the parameters. The scan positions (i.e., the step sizes between frames) that minimized the error function are then used to calculate the phase for each pixel, from which the height can also be calculated in conventional manner. As a result, the phase map generated by the procedure is corrected to a degree of precision significantly better than previously possible.