Abstract:Diffraction is a natural phenomenon, which occurs when waves propagate or encounter an obstacle. Diffraction is also a fundamental aspect of modern optics: all imaging systems are diffraction systems. However, like a coin has two sides, diffraction also leads to some unfavorable effects, such as an increase in the size of a beam during propagation, and a limited minimal beam size after focusing. To overcome these disadvantages set by diffraction, many techniques have been developed by various groups, including… Show more
“…Improving resolution by modifying the pupil of the optical system (apodization) following the path broken by Toraldo di Francia has been traditionally referred to as 'super-resolution' [34,35]. Recently, efforts in this direction have been intensified [14,36,37,38], taking advantage of the progress achieved in nanofabrication.…”
The concept of the diffraction limit put forth by Ernst Abbe and others has been an important guiding principle limiting our ability to tightly focus classical waves, such as light and sound, in the far field. In the past decade, numerous reports have described focusing or imaging with light and sound 'below the diffraction limit'. We argue that the diffraction limit defined in a reasonable way, for example in terms of the upper bound on the wave numbers corresponding to the spatial Fourier components of the intensity profile, or in terms of the spot size into which at least 50% of the incident power can be focused, still stands unbroken to this day. We review experimental observations of 'subwavelength' or 'sub-diffraction-limit' focusing, which can be principally broken down into three broad categories: (i) 'super-resolution', i.e. the technique based on the modification of the pupil of the optical system to reduce the width of the central maximum in the intensity distribution at the expense of increasing side bands; (ii) solid immersion lenses, making use of metamaterials with a high effective index; (iii) concentration of intensity by a subwavelength structure such as an antenna. Even though a lot of interesting work has been done along these lines, none of the hitherto performed experiments violated the sensibly defined diffraction limit.
“…Improving resolution by modifying the pupil of the optical system (apodization) following the path broken by Toraldo di Francia has been traditionally referred to as 'super-resolution' [34,35]. Recently, efforts in this direction have been intensified [14,36,37,38], taking advantage of the progress achieved in nanofabrication.…”
The concept of the diffraction limit put forth by Ernst Abbe and others has been an important guiding principle limiting our ability to tightly focus classical waves, such as light and sound, in the far field. In the past decade, numerous reports have described focusing or imaging with light and sound 'below the diffraction limit'. We argue that the diffraction limit defined in a reasonable way, for example in terms of the upper bound on the wave numbers corresponding to the spatial Fourier components of the intensity profile, or in terms of the spot size into which at least 50% of the incident power can be focused, still stands unbroken to this day. We review experimental observations of 'subwavelength' or 'sub-diffraction-limit' focusing, which can be principally broken down into three broad categories: (i) 'super-resolution', i.e. the technique based on the modification of the pupil of the optical system to reduce the width of the central maximum in the intensity distribution at the expense of increasing side bands; (ii) solid immersion lenses, making use of metamaterials with a high effective index; (iii) concentration of intensity by a subwavelength structure such as an antenna. Even though a lot of interesting work has been done along these lines, none of the hitherto performed experiments violated the sensibly defined diffraction limit.
“…Another method which has been proposed to extend the depth of focus is by dividing the lens pupil in rings and modulate the phase and amplitude of each ring [3]. These and other methods are discussed in more detail in [4][5][6][7][8][9][10].…”
Abstract:In several optical systems, a specific Point Spread Function (PSF) needs to be generated. This can be achieved by shaping the complex field at the pupil. The Extended Nijboer-Zernike (ENZ) theory relates complex Zernike modes on the pupil directly to functions in the focal region. In this paper, we introduce a method to engineer a PSF using the ENZ theory. In particular, we present an optimization algorithm to design an extended depth of focus with high lateral resolution, while keeping the transmission of light high (over 60%). We also have demonstrated three outcomes of the algorithm using a Spatial Light Modulator (SLM). 145-148 (1965). 6. G. Toraldo di Francia, "Super-gain antennas and optical resolving power," Nuovo Cimento 9, 426-438 (1952). 7. H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001). 8. C. J. R. Sheppard, "Synthesis of filters for specified axial properties," J. Mod. Opt. 43, 525-536 (1996)
“…One inspired idea was to reshape the PSF of the focal spot to decrease the FWHM: the apodization method. 13 Proposed in 1952 by Di Francia,14 this method had the advantage of sharpening the central maximum of the focal spot at the expense of larger side lobes. This defect made it unsuitable for widefield optical microscopes, creating artifacts and blurring the image.…”
The resolution of conventional optical equipment is always restricted by the diffraction limit, and improving on this was previously considered improbable. Optical super-resolution imaging, which has recently experienced rapid growth and attracted increasing global interest, will result in applications in many domains, benefiting fields such as biology, medicine and material research. This review discusses the contributions of different researchers who identified the diffractive barrier and attempted to realize optical super-resolution. This is followed by a personal viewpoint of the development of optical nanoscopy in recent decades and the road towards the next generation of optical nanoscopy.
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