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Early in 1960, the impulse response or the point spread function (PSF) was computed for circular and annular apertures in many articles (Minsky in Scanning 10:128–138, 1988; Goodman, Introduction to Fourier Optics, McGraw Hill Series, 1996; Sheppard and Choudhary in Opt Acta 24:1051–1059, 1977; Cox et al. in Appl Opt 21:778–781, 1982) using uniform illumination. The conventional microscope resolution is based on the resolution limit of the sole objective lens, while the resolution is improved for the confocal scanning laser microscope (Cox and Sheppard in Microscopic Res Tech 63:18–22, 2004; Sheppard and Shotton in Image formation in the confocal laser scanning microscope, Springer-Verlag, New York, 1997; Hamed, The point spread function for some modulated apertures application on speckle and interferometry images, Lambert Academic Publishing (LAP), 2017; Hamed, Modulated apertures and resolution in Microscopy, Springer, 2023) since the two microscope objectives play equal roles in the resolution and the effective PSF is the multiplication of the PSF corresponding to each objective lens. Later, the resolution was further improved by investigating the PSF in the case of conical and linear (Clair and Hamed in Optik 64:133–141, 1983; Hamed and Clair in Optik 64:277–284, 1983), quadratic and higher-order apertures (Hamed and Clair in Optik 65:209–218, 1983). In addition, twofold symmetry and fourfold symmetry apertures (Hamed in Opt Laser Technol 16:93–96, 1984) are proposed, and the PSF is computed and compared with a circular aperture. Recently, different modulated apertures have been suggested, e.g., elliptical apertures, some deformed apertures (Hamed in Opt Eng 50:1–7, 2011), and graded index apertures (Hamed in Precis Instr Mech 3:144–152, 2014), and the PSF has been computed in all cases. In addition, Hamming (Hamed and Al-Saeed in J Mod Opt 62:801–810, 2015), linear quadratic (Hamed in Optik 131:838–849, 2017), and longitudinal strips (Hamed in Int J Photon Opt Technol 3:1–9, 2017) have been investigated. The computations of the PSF corresponding to all the modulated apertures assume coherent uniform illumination.

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Fourier Transform and Convolution Operations in Optical Diffraction

  • 章节

  • 发表日期：

    2025年

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  • Abdallah Hamed

摘要

Early in 1960, the impulse response or the point spread function (PSF) was computed for circular and annular apertures in many articles (Minsky in Scanning 10:128–138, 1988; Goodman, Introduction to Fourier Optics, McGraw Hill Series, 1996; Sheppard and Choudhary in Opt Acta 24:1051–1059, 1977; Cox et al. in Appl Opt 21:778–781, 1982) using uniform illumination. The conventional microscope resolution is based on the resolution limit of the sole objective lens, while the resolution is improved for the confocal scanning laser microscope (Cox and Sheppard in Microscopic Res Tech 63:18–22, 2004; Sheppard and Shotton in Image formation in the confocal laser scanning microscope, Springer-Verlag, New York, 1997; Hamed, The point spread function for some modulated apertures application on speckle and interferometry images, Lambert Academic Publishing (LAP), 2017; Hamed, Modulated apertures and resolution in Microscopy, Springer, 2023) since the two microscope objectives play equal roles in the resolution and the effective PSF is the multiplication of the PSF corresponding to each objective lens. Later, the resolution was further improved by investigating the PSF in the case of conical and linear (Clair and Hamed in Optik 64:133–141, 1983; Hamed and Clair in Optik 64:277–284, 1983), quadratic and higher-order apertures (Hamed and Clair in Optik 65:209–218, 1983). In addition, twofold symmetry and fourfold symmetry apertures (Hamed in Opt Laser Technol 16:93–96, 1984) are proposed, and the PSF is computed and compared with a circular aperture. Recently, different modulated apertures have been suggested, e.g., elliptical apertures, some deformed apertures (Hamed in Opt Eng 50:1–7, 2011), and graded index apertures (Hamed in Precis Instr Mech 3:144–152, 2014), and the PSF has been computed in all cases. In addition, Hamming (Hamed and Al-Saeed in J Mod Opt 62:801–810, 2015), linear quadratic (Hamed in Optik 131:838–849, 2017), and longitudinal strips (Hamed in Int J Photon Opt Technol 3:1–9, 2017) have been investigated. The computations of the PSF corresponding to all the modulated apertures assume coherent uniform illumination.