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8 June 2005 Scaled optical Fourier transform in cylindrical coordinates
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In Optical Signal Processing (OSP) one of the most important operations is the Optical Fourier Transform (OFT). Many different optical arrangements exist which allow implementation of the OFT, however one of the more popular is the Scaled Optical Fourier Transform (SOFT) because, as the name implies, this arrangement allows control over the scale of the output Fourier distribution. Using cylindrical coordinates we examine some of the practical limits introduced by the use of an illuminating spherical lens of finite aperture in the implementation of the SOFT. By deriving simple rules of thumb, based on examining phase and intensity deviations from the ideal unapertured case, we define a volume inside the geometric shadow, which we refer to as a sub-geometric shadow. Inside this sub-geometric shadow we show that the worst case errors in the resulting SOFT, arising due to diffraction, can be quantified and avoided.
© (2005) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Damien P. Kelly, John T. Sheridan, and William T. Rhodes "Scaled optical Fourier transform in cylindrical coordinates", Proc. SPIE 5827, Opto-Ireland 2005: Photonic Engineering, (8 June 2005);


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