Response of quadrant detectors to structured beams via convolution integrals.

Area of Science:

• Optics and Photonics
• Optical Metrology
• Instrumentation

Background:

• Quadrant detectors are crucial for optical alignment and beam analysis.
• Existing methods for calculating detector response can be complex and computationally intensive.

Purpose of the Study:

• To introduce a novel, simplified expression for quadrant detector response using convolution integrals.
• To derive analytical forms for detector response and sensitivity to various optical beams.

Main Methods:

• Utilized convolution integrals to formulate a new expression for quadrant detector response.
• Derived analytical solutions for Gaussian and Hermite-Gaussian beams.
• Performed comparisons with existing approximations and simulation results.
• Calculated detector sensitivity for Bessel beams to demonstrate computational ease.

Main Results:

• A new, easily evaluable expression for quadrant detector response was derived.
• Analytical expressions for the response to Gaussian and Hermite-Gaussian beams were obtained.
• The new method showed good agreement with simulations and previous approximations for Gaussian beams.
• Analytical sensitivity expressions were derived, showcasing computational efficiency.

Conclusions:

• The proposed convolution integral method offers a simplified and computationally practical approach for analyzing quadrant detector performance.
• This new expression facilitates the derivation of analytical solutions for various beam types, enhancing optical system analysis.
• The method is versatile and efficient for calculating detector sensitivity, as demonstrated with Bessel beams.