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Defocus transfer function for circularly symmetric pupils.

A R Fitzgerrell, E R Dowski, W T Cathey

    Applied Optics
    |August 10, 1997
    PubMed
    Summary
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    We introduce the defocus transfer function (DTF), a 2D tool visualizing how defocus impacts optical transfer functions (OTFs) for circular pupils. This DTF aids in analyzing optical systems affected by defocus.

    Area of Science:

    • Optics
    • Image Science

    Background:

    • Optical systems performance is often limited by aberrations, particularly defocus.
    • Analyzing the impact of defocus on the optical transfer function (OTF) is crucial for understanding image quality.
    • Existing methods for visualizing OTF variations due to defocus can be limited, especially for circularly symmetric systems.

    Purpose of the Study:

    • To introduce a novel two-dimensional function, the defocus transfer function (DTF).
    • To graphically illustrate the effects of defocus on the OTF for circularly symmetric pupil functions.
    • To demonstrate the utility of the DTF in analyzing optical systems with defocus.

    Main Methods:

    • Development of a new two-dimensional function, the defocus transfer function (DTF).
    • Comparison of the DTF with the ambiguity function for defocused separable pupil functions.

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  • Application of the DTF to analyze systems with clear, bifocal, and annular pupil functions.

    • Main Results:

    • The DTF provides a graphical representation of defocus effects on the OTF for circularly symmetric pupils.
    • The DTF is analogous to the ambiguity function for separable pupil functions.
    • The DTF's properties are useful for analyzing OTF variations as a function of defocus.

    Conclusions:

    • The defocus transfer function (DTF) is a valuable tool for optical system analysis.
    • The DTF simplifies the visualization and understanding of defocus effects in systems with circular symmetry.
    • The DTF is applicable to various pupil types, including clear, bifocal, and annular.