White Light Interferometry Non-Linear Phase Calibration

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Solution Overview

Problem

White light phase shifting interferometry struggles to measure objects with complex surface properties, such as bulk surfaces and multi-layer film stacks, due to non-linear phase shifts caused by material properties like piezoelectric transducers, leading to errors in sampling the temporal interferometric signal and deteriorating measurement accuracy.

Innovation Solution

Combining signal modeling techniques with non-linear phase shift calibration, which directly obtains non-linear phase shift information from interferograms to account for error sources and ensure a uniform phase shifting speed, allowing for accurate measurement of objects with complex surface properties without additional hardware or processor circuits.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If signal modeling techniques are used with PZT pushers to measure objects with complex surface properties, then measurement capability is improved, but non-linear phase shifts occur causing sampling errors and deteriorating measurement accuracy

Engineering Contradiction:

Improvemeasurement capabilityVSAvoidmeasurement accuracy

Core Design Contradiction:

Adaptability or versatilityVSMeasurement precision

Solution Approach 1:

The patent transforms the non-linear phase shift problem by changing the parameter representation from time-domain to frequency-domain. By applying Fourier transform to the temporal interferometric signal, the non-linear phase shift becomes a linear phase term in the frequency domain, which can be accurately modeled and corrected. This parameter transformation resolves the contradiction by maintaining measurement capability while eliminating sampling errors.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces the mechanical assumption of linear phase shift with a mathematical model that accounts for non-linear phase shifts. Instead of relying on the mechanical linearity of PZT pushers, the invention uses spectral analysis and frequency-domain processing to model and correct the non-linear phase behavior, thereby maintaining measurement accuracy despite the non-linear mechanical system.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Measurement precision

If constant phase shift calibration is applied to multiple overlapping interferograms, then phase extraction accuracy is improved, but the non-linear phase shift from PZT materials causes sampling errors

Engineering Contradiction:

Improvephase extraction accuracyVSAvoidsampling accuracy

Core Design Contradiction:

Measurement precisionVSReliability

Solution Approach 1:

The patent performs preliminary calibration to determine the non-linear phase shift characteristics before processing the interferograms. By characterizing the non-linear phase shift behavior in advance and incorporating it into the signal model, the system can accurately sample and process interferograms despite the non-linear PZT behavior, thereby maintaining both phase extraction accuracy and sampling reliability.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent implements a feedback mechanism where the non-linear phase shift information is continuously refined through iterative processing. The spectral analysis results are used to update and refine the phase shift model, which then feeds back into the signal processing to improve sampling accuracy and phase extraction precision in a closed-loop manner.

Inventive Principle:

Principle #23Feedback

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 improves the ability to extract information from phase-shifted white light interferograms, enhancing measurement precision and accuracy for objects with complex surface properties by correcting non-linear phase shifts and maintaining consistent phase shifting speed.

Implementation Method 1

Signal modeling techniques may acquire a set of white light phase-shifted interferograms with piezoelectric transducer (PZT) pushers of either the reference flat or the test object

Methodology Applied

Scientific EffectPiezoelectric effect: Piezoelectric Effect

Implementation Method 2

The fundamental concept of PSI is that the phase of an interferogram can be extracted by acquiring a set of a few sequentially phase-shifted interferograms

Methodology Applied

Scientific EffectInterference: Interference

Data Source

PatentUS7538887B1Temporal interferometric signal modeling with constant phase shift in white light interferometry

Publication Date: 2009.05.26 KLA CORP

AI summary

A method for determining the surface topography of an object with various surface properties in white light interferometry first generates a set of interferograms, produced by a phase shift driving mechanism supplied with known inputs, obtained from a single reflective surface at the location of the test piece. The sequence of interferograms from the test piece then is used to calibrate a sequence of inputs to the phase shift driving mechanism to compensate for non-linear characteristics of the phase shifting mechanism. The temporal interferometric signal or its transform at each pixel of a set of subsequently acquired interferograms from a test piece then is compared with signals or their transforms modeled with different properties of the measuring surface. The measured surface properties which generate a best match to the modeling surface properties are selected as the desired signal.