Superresolution

Although image acquisition systems improve their spatial resolution, there are instrumental limits related to this parameter. Superresolution strategies are mathematical procedures devoted to obtain spatial descriptions of the sample surface that go beyond the limits of the instrumental spatial resolution [135,136]. 

The natural expansion of the superresolution concept to hyperspectral images would imply applying the algorithm to each of the spectral channels registered with the consequent complexity and computation time, and the outcome would only be a raw superresolved image that would need further analysis. Therefore, working with compressed hyperspectral image representations is a clear need. 

Each of these images was shifted from the closest one by a motion step of 0.6 pm in the x- ory-direction. Shifts in the x- andy-direction with respect to the original image went from 1 to 6 times 0.6 pm. After resolution of the multiset formed by the 36 images, three contributions were modeled with clear spectral signatures. By application of the superresolution postprocessing to the three sets of low spatial 

As a general conclusion, the strategy combining multiset image analysis and superresolution postprocessing simultaneously saves computation time and, above all, provides unmixed, spatially detailed, constituent-specific interpretable information on the sample analyzed. 

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The most spectacular applications of ECLs are the possibiUty of direct overwrite (DOW) with laser modulation (79,80) and of magnetically iaduced superresolution (81,82). The stacks comprise at least a storage layer s and a bias layer b. For both appHcations, the storage layer s has the lower and the higher at room temperature when compared to the bias layer b. At room temperature, b is homogeneously magnetized (initialized) by an external permanent magnet is about 400 kA/m (5 kOe)). 

When used for superresolution, the laser beam is incident on b, which hides the domains in s. During read-out, b is heated and the domains in s are copied to b. The optical system sees only the overlap area between the laser spot and the temperature profile which is lagging behind, so that the effective resolution is increased. Experimentally it is possible to double the linear read-out resolution, so that a four times higher area density of the domains can be achieved when the higher resolution is also exploited across the tracks. At a domain distance of 0.6 pm, corresponding to twice the optical cutoff frequency, a SNR of 42 dB has been reached (82). 

In the quest for optimal FRET resolution in three dimensions [48, 49], one requires sophisticated algorithms for analyzing complex distributions [48, 50, 51], An issue of particular relevance when multiple probes [52-54] and multiparametric detection [26, 55] are employed. Strategies for spatial superresolution [56] have spawned a family of acronyms RESOLFT, STED, STORM, astigmatic STORM, PALM, fPALM, sptPALM, PALMIRA ([57-59] and other references), some of which involve systematic photoconversion or destruction. Undoubtedly, these techniques will be applied systematically to FRET imaging, and, conversely, one can anticipate that FRET mechanisms will be exploited for achieving superresolution. 

Schemes for achieving 3D spatial superresolution (see Section 12.4) will continue to proliferate, and at the same time microscopes...

Lidke K, Rieger B, Jovin T, Heintzmann R (2005) Superresolution by localization of quantum dots using blinking statistics. Opt Express 13 7052-7062... 

The Fourier frequency bandpass of the spectrometer is determined by the diffraction limit. In view of this fact and the Nyquist criterion, the data in the aforementioned application were oversampled. Although the Nyquist sampling rate is sufficient to represent all information in the data, it is not sufficient to represent the estimates o(k) because of the bandwidth extension that results from information implicit in the physical-realizability constraints. Although it was not shown in the original publication, it is clear from the quality of the restoration, and by analogy with other similarly bounded methods, that Fourier bandwidth extrapolation does indeed occur. This is sometimes called superresolution. The source of the extrapolation should be apparent from the Fourier transform of Eq. (13) with r(x) specified by Eq. (14). 

Fig. 5 Object (shaded) used in computer simulations Its diffraction image is the solid curve The data image (dashed curve) is the diffraction image plus 4% amplitude random noise All plotted points are spaced by one-half the Nyquist interval. Hence to resolve the central dip in the object would require superresolution.

The image data were formed by adding 4% (of peak image value) Gaussian noise to the signal image. Sampling was at one-half the Nyquist interval so as to permit superresolution of the central dip in the object. 

In Fig. 6(a), Qm was made constant, corresponding to prior knowledge of a flat spectrum. This is a rather conservative guess at the object. Both restorations exhibit resolution of the central object dip, indicating superresolution. 

Until the advent of superresolution microscopes the only way to observe the minute world was based on the common Fourier-type microscopes. The maximum theoretical resolution limit for these apparatuses was established by Abbe, applying the Rayleigh-Fourier diffraction resolution rule [28]. The basic principle underlying the operational working of these ordinary microscopes is, in the eyes of Niels Bohr, a textbook example of Heisenberg uncertainty relations. 

The superresolution optical microscope shown in Fig. 28 is basically made up of a sensor or light detector, a scanning system, (not shown in the sketch), designed to control the position of the probe over the sample, and a computer with a display device. Naturally it also has, as does any conventional... 

For this type of superresolution optical microscope, experiments have shown that it is possible to have spatial resolutions of the order of X/50. It is believed that the technique can be improved so to allow spatial resolutions of over X/100. 

Let us now consider the well-known Heisenberg microscope experiment, with both the common Fourier microscope and the new-generation superresolution optical microscope. 

Figure 29. Detection region of the two microscopes (a) usual Fourier microscope (b) superresolution microscope.

Some may argued that these superresolution optical microscopes work only with a large number of photons and, consequently, are no good, that is, appropriate, when only a single photon is diffused. If this claim had any grounds, then it should also be applied to the common Fourier microscope. Nevertheless, it can easily be shown that, in principle, these two types of microscopes can... 

The superresolution microscope, in essence, just like the common microscope, is no more than a device for measurement of position, for the mapping of material points. Essentially both types work in the following way. The point forming the object are illuminated, generating diffused light that is eventually captured by the microscope. In this conceptual analysis, the microscope must be treated like a blackbox, since there is no need to go into the particulars of its working. 

What is true is that, in any case, whether with the common microscope, or with the superresolution microscope, in order to be observed, the object points must be submitted to some kind of interaction. Since we are dealing with optical microscopes, the interaction occurs with photons. In such circumstances the photon, on interacting with the microparticle, is diffused by it. As a result of this interaction, which is fundamental in all direct concrete quantum measurements, a certain amount of momentum is transferred from the photon to the microparticle, leading to an uncertainty in the momentum of the microparticle. 

The product of these uncertainties in momentum and in position, lies in the case of the common Fourier microscopes in the Heisenberg uncertainty measurement space, while for the superresolution optical microscope, the same product lies in the more general wavelet uncertainty measurement space. 

A. Photon-Mode Superresolution by Transient Bleaching of Phthalocyanines... 

Figure 26 (a) Schematic representation of photon-mode superresolution using transi-... 

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