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Applied Optics

Applied Optics


  • Vol. 40, Iss. 32 — Nov. 10, 2001
  • pp: 5943–5948

Fractional derivatives—analysis and experimental implementation

Jeffrey A. Davis, David A. Smith, Dylan E. McNamara, Don M. Cottrell, and Juan Campos  »View Author Affiliations

Applied Optics, Vol. 40, Issue 32, pp. 5943-5948 (2001)

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The fractional derivative spatial-filtering operator is useful for image-processing applications, particularly for examination of phase objects. Experimental implementation is difficult because the mask function combines both amplitude and phase. We present a simple one-dimensional analysis of the fractional derivative operation and note similarities with the fractional Hilbert transform. We demonstrate how to encode these amplitude and phase masks using a phase-only liquid-crystal spatial light modulator and present experimental results. Finally, we introduce a radially symmetric extension of this operation that is more useful for objects having an arbitrary shape.

© 2001 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(100.0100) Image processing : Image processing
(120.2440) Instrumentation, measurement, and metrology : Filters
(200.3050) Optics in computing : Information processing
(230.3720) Optical devices : Liquid-crystal devices
(230.6120) Optical devices : Spatial light modulators

Original Manuscript: March 13, 2001
Revised Manuscript: August 13, 2001
Published: November 10, 2001

Jeffrey A. Davis, David A. Smith, Dylan E. McNamara, Don M. Cottrell, and Juan Campos, "Fractional derivatives—analysis and experimental implementation," Appl. Opt. 40, 5943-5948 (2001)

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  11. J. Campos, A. Marquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only filters,” Appl. Opt. 39, 5965–5970 (2000). [CrossRef]
  12. A. Marquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. Davis, M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator,” Appl. Opt. 40, 2316–2322 (2001). [CrossRef]
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