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Examples of image blurring
Published in Mario Bertero, Patrizia Boccacci, Christine De Mol, Introduction to Inverse Problems in Imaging, 2021
Mario Bertero, Patrizia Boccacci, Christine De Mol
For monochromatic light with wavelength λ and in the absence of aberrations, i.e. in the case of a system consisting of perfectly corrected lenses, the PSF is, through a change of variable, the inverse FT of the pupil function, which is the characteristic function χP(x) of the exit pupil P of the instrument. Therefore an ideal diffraction-limited system is a bandlimited system which behaves like a perfect low-pass Fourier filter.
Examples of image blurring
Published in Bertero Mario, Boccacci Patrizia, Introduction to Inverse Problems in Imaging, 2020
Bertero Mario, Boccacci Patrizia
For monochromatic light with wavelength X and in the absence of aberrations, i.e. in the case of a system consisting of perfectly corrected lenses, the PSF is, through a change of variable, the inverse FT of the pupil function, which is the characteristic function Xv(x) of the exit pupil V of the instrument. Therefore an ideal diffraction-limited system is a bandlimited system which behaves like a perfect low-pass Fourier filter.
Lithography, Etch, and Silicon Process Technology
Published in Bruce W. Smith, Kazuaki Suzuki, Microlithography, 2020
Matthew Colburn, Derren N. Dunn, Michael A. Guillorn
One of the important defining characteristics of a diffraction-limited system that follows Abbe imaging is the concept of numerical aperture. Figure 1.8 shows a magnified area of the object illuminated in Figure 1.7.
Liquid crystal technology for vergence-accommodation conflicts in augmented reality and virtual reality systems: a review
Published in Liquid Crystals Reviews, 2021
Instead of correcting the refractive error of the eyes, another strategy for enhancing the image sharpness and solving the VAC challenge is to lower the spatial resolutions of the virtual image and the real object, which leads to the magnification of the virtual image and the image of the real object (optical zoom-in). An optical imaging system is said to be diffraction-limited when a point-source object is converted to an ideal point in the image plane thus, perfectly spherical waves propagate in the optical image system without wavefront aberrations (e.g. no refractive errors) [38]. In a diffraction-limited system, an object with fine details can be resolved. The typical contrast of the optical image system (equivalent to the resolving capability) as a function of spatial resolution is illustrated in Figure 23. The black solid line represents the contrast versus spatial resolution in a diffraction-limited image system. We consider the eyes as an example of a system with aberration (i.e. refractive errors), the contrast curve drops quickly, especially for the location of the high spatial resolution (green line in Figure 23). This means that an eye can see a blurred image when the image contains exquisite details. The typical engineering strategy for correcting the refractive error of the eye is to add corrected lenses or prescription lenses (i.e. compensation of focusing error) so that the green line is close to the black line. Another engineering strategy is to magnify the image or lower the spatial resolution of the images. Researchers have demonstrated this by implementing an optical zoom function in the AR system using two tunable LC lenses [43,44]. Two LC lenses are separated by a certain distance to achieve the optical zoom function (Figure 24). When the two LC lenses are turned off, the virtual image is set to coincide with a real object, as shown in Figure 24(a). When two LC lenses are operated together, the virtual image plane can be fixed, and the size of the virtual image is magnified, as shown in Figure 24(b). The experimental demonstrations in the literature are shown in Figure 24(c,d). This concept is also applicable for magnifying real objects when LC lenses are placed at appropriate locations. Furthermore, this concept can be transformed into a time-multiplexing foveated display with two virtual images at different magnifications.