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    Area of Science:

    • Optics and Photonics
    • Interferometry
    • Astronomical Instrumentation

    Background:

    • Shearing interferometers measure wavefront derivatives.
    • Rotationally shearing interferometers (RSI) are used in optical testing.
    • Previous assumptions suggested increased sensitivity with larger shear angles.

    Purpose of the Study:

    • To investigate the range of validity for the derivative function in RSIs.
    • To challenge the prevailing belief about RSI sensitivity and shear angle.
    • To propose methods for improving aberration measurement accuracy.

    Main Methods:

    • Mathematical analysis of the aberration polynomial in RSIs.
    • Examination of the multiplicative factor involving the sine of the half-shear angle and polynomial order.
    • Series expansion for small and specific large shear angles.

    Main Results:

    • RSI sensitivity is inversely proportional to the shear angle, not directly.
    • Aberration polynomial terms are multiplied by a factor dependent on shear angle and aberration order.
    • A method to evaluate and minimize errors in aberration magnitude determination is presented.

    Conclusions:

    • The study reveals a counterintuitive relationship between RSI sensitivity and shear angle.
    • Findings provide a framework for accurate aberration analysis in optical systems.
    • The results have direct implications for high-precision applications like planet detection.