Classification scheme and properties of schlieren techniques

Area of Science:

• Optics and Photonics
• Image Processing
• Mathematical Physics

Background:

• Spatial filtering is crucial for visualizing subtle phase variations in transparent media.
• Schlieren techniques (ST) are widely used for flow visualization and optical testing.
• A unified mathematical framework for ST is lacking.

Purpose of the Study:

• To formulate the phase-contrast function (PhCF) using mathematical symmetry.
• To define, analyze, and classify various schlieren techniques (ST) based on their PhCF.
• To elucidate the optical filtering behavior of ST under different illumination conditions.

Main Methods:

• Mathematical formulation of the phase-contrast function (PhCF) leveraging symmetry properties.
• Analysis of the PhCF to classify different schlieren techniques (ST).
• Investigation of the PhCF's behavior under coherent and noncoherent illumination.

Main Results:

• All schlieren techniques (ST) can be represented by a single, unified phase-contrast function (PhCF).
• The PhCF acts as a passband Hilbert transformer under coherent illumination.
• The PhCF functions as a differential filter when noncoherent illumination is used.

Conclusions:

• A unified mathematical description of schlieren techniques (ST) is achieved through the phase-contrast function (PhCF).
• The PhCF provides a versatile framework for understanding ST's filtering characteristics.
• This work offers a new perspective on the fundamental principles of schlieren imaging.