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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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Errors in phase-measurement interferometry with high numerical apertures.

G Schulz, K E Elssner

    Applied Optics
    |August 19, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Phase-measurement interferometry (PMI) errors arise with high numerical aperture (NA) optics, invalidating simple height correction factors. These errors, dependent on NA and illumination, can reach 17% for specific configurations.

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    Area of Science:

    • Optical Metrology
    • Interferometry
    • Surface Characterization

    Background:

    • Phase-measurement interferometry (PMI) is a technique used for precise surface height measurements.
    • High numerical aperture (NA) objectives in microscopy can introduce optical aberrations and measurement errors.
    • The linear relationship between measured phase and surface height is assumed in standard PMI analysis.

    Purpose of the Study:

    • To investigate the occurrence and nature of errors in phase-measurement interferometry (PMI) when applied with high numerical aperture (NA).
    • To demonstrate that a constant NA scaling factor is insufficient for accurate height measurements under high NA conditions.
    • To analyze the impact of different pupil illuminations on PMI accuracy at high NA.

    Main Methods:

    • Theoretical analysis of phase variations in PMI for high NA.
    • Modeling of phase shifts considering different pupil illumination profiles (e.g., intensity proportional to cos(2) alpha, cos alpha, or constant).
    • Calculation of correction factors for height measurements under varying surface heights and illumination conditions.

    Main Results:

    • The phase variation no longer exhibits a linear relationship with the surface height difference at high NA.
    • A universal, constant correction factor for NA scaling does not exist for high NA PMI.
    • For a specific example (NA=0.9, constant pupil illumination), the correction factor varied by 17% (from 1.20 to 1.37) across a height difference of approximately lambda;/4.

    Conclusions:

    • High NA significantly impacts PMI accuracy, necessitating advanced correction methods beyond simple scaling factors.
    • The choice of pupil illumination critically affects the magnitude of errors in high NA PMI.
    • Accurate height measurements with high NA PMI require considering the specific NA and illumination conditions.