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Updated: Jul 6, 2026

Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging
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Multilayer-coating-induced aberrations in extreme-ultraviolet lithography optics.

C Liang, M R Descour, J M Sasian

    Applied Optics
    |March 22, 2008
    PubMed
    Summary
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    This study introduces a mathematical framework to analyze how multilayer coatings affect light wave front phase. Graded coatings significantly reduce wave-front aberrations compared to uniform coatings.

    Area of Science:

    • Optics
    • Materials Science
    • Surface Science

    Background:

    • Multilayer coatings modify reflected wave front amplitude and phase.
    • Amplitude effects are well-understood, but phase effects require further mathematical description.

    Purpose of the Study:

    • To develop a general mathematical formalism for coating-induced phase effects.
    • To create an analytical method for estimating wave-front aberrations from multilayer coatings.
    • To investigate field-independent and field-dependent aberrations in uniform and graded coatings.

    Main Methods:

    • Developed a mathematical formalism for coating phase effects.
    • Derived an analytical method to estimate wave-front aberrations.
    • Analyzed aberrations for uniform and graded coatings under tilted mirror conditions.

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    Multi-step Variable Height Photolithography for Valved Multilayer Microfluidic Devices
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    Multi-step Variable Height Photolithography for Valved Multilayer Microfluidic Devices

    Published on: January 27, 2017

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    Last Updated: Jul 6, 2026

    Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging
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    Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging

    Published on: September 8, 2017

    Multi-step Variable Height Photolithography for Valved Multilayer Microfluidic Devices
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    Multi-step Variable Height Photolithography for Valved Multilayer Microfluidic Devices

    Published on: January 27, 2017

  • Applied analysis to a specific case of a tilted plane mirror with a converging beam.

    • Main Results:

    • Identified second-order aberrations: field-dependent piston, field-squared-dependent piston, defocus, field-independent tilt, field-independent astigmatism, and anamorphic magnification.
    • Graded coatings showed field-independent aberration coefficients approximately ten times smaller than uniform coatings.
    • Demonstrated that coatings can introduce anamorphic magnification.

    Conclusions:

    • The developed formalism accurately describes coating-induced phase effects and aberrations.
    • Graded multilayer coatings offer superior performance in minimizing wave-front aberrations compared to uniform coatings.
    • Multilayer coatings can introduce complex aberrations, including anamorphic magnification, which must be considered in optical system design.