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Related Experiment Video

Updated: Jun 13, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Published on: August 12, 2013

Differentiation of a noninteger order and its optical implementation.

¹Technical University of Wroclaw, Institute of Physics, Wroclaw, Wybrzeze Wyspianskiego 27, Poland.

|April 17, 2010

Summary

This study defines arbitrary order differentiation using Fourier transform properties. Researchers physically implemented this generalized differentiation with a coherent processing system and binary synthetic filters, demonstrating 1-D and 2-D filter models and results.

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Area of Science:

Mathematics
Signal Processing
Optics

Background:

Generalized differentiation extends calculus concepts to non-integer orders.
Fourier transform is a powerful tool for analyzing frequency components of signals.
Optical processing offers a physical implementation pathway for complex mathematical operations.

Purpose of the Study:

To define and provide examples of arbitrary order differentiation.
To physically implement generalized differentiation using optical methods.
To demonstrate the effectiveness of binary synthetic filters in this application.

Main Methods:

Utilized properties of the Fourier transform for defining arbitrary order differentiation.
Employed a coherent processing system for physical implementation.
Designed and tested 1-D and 2-D binary synthetic filters.

Main Results:

Successfully defined arbitrary order differentiation.
Demonstrated physical implementation of generalized differentiation.
Presented models and experimental results for 1-D and 2-D binary filters.

Conclusions:

Arbitrary order differentiation can be effectively defined using Fourier transform properties.
Coherent optical systems with binary synthetic filters are suitable for implementing generalized differentiation.
Experimental validation confirms the feasibility of the proposed method.