Foucault test: shadowgram modeling from the physical theory for quantitative evaluations

Area of Science:

• Optics and Optical Engineering
• Metrology

Background:

• The Foucault test is a common method for evaluating optical aberrations.
• Existing theories primarily address nearly diffraction-limited systems, limiting their applicability.

Purpose of the Study:

• To develop a more comprehensive physical theory for the Foucault test applicable to devices with large aberrations.
• To derive closed-form expressions for complex amplitude and irradiance in the presence of significant wavefront errors.

Main Methods:

• The study extends the physical theory of the Foucault test beyond the paraxial approximation.
• It utilizes properties of the Hilbert transform to derive new expressions.
• The complex amplitude and irradiance are represented in terms of wavefront error.

Main Results:

• New closed-form expressions for complex amplitude and irradiance are derived for optical devices with large aberrations.
• The irradiance is shown to be simply related to the partial derivatives of the wavefront error.
• This represents a significant advancement over previous treatments.

Conclusions:

• The derived expressions provide a more precise interpretation of the Foucault test for a wider range of optical devices.
• The methodology offers a new perspective for quantitative analysis of the Foucault test.
• This work removes limitations of previous studies on diffraction-limited systems.