Editing Diffraction-limited system (section)

==Obtaining higher resolution==
{{See also|Super-resolution microscopy}}
Using special optical systems and [[digital image processing]], it is possible to produce images that have higher resolution (in some specific aspects of the subject, such as color or shape) than would be allowed by simple use of diffraction-limited optics.<ref name="U2">{{cite journal
| url=http://www.opfocus.org/index.php?topic=story&v=4&s=1
| author=Niek van Hulst
| title=Many photons get more out of diffraction
| journal=[[Optics & Photonics Focus]]
| volume=4
| issue=1
| year=2009
}}</ref> These largely computational methods offer advantages over other workarounds such as electron microscopy, and have been used to produce reasonably accurate images of individual molecules.<ref name="j702">{{cite web | title=True/Functional Techniques and Technology | website=MicroscopeMaster | url=https://www.microscopemaster.com/super-resolution-microscopy.html | access-date=2025-05-01}}</ref><ref name="h720">{{cite journal | last=Galbraith | first=Catherine G. | last2=Galbraith | first2=James A. | title=Super-resolution microscopy at a glance | journal=Journal of Cell Science | publisher=The Company of Biologists | volume=124 | issue=10 | date=2011-05-15 | issn=1477-9137 | doi=10.1242/jcs.080085 | doi-access=free | pages=1607–1611| pmc=3085433 }}</ref> Although these techniques improve some aspect of resolution, they generally come at an enormous increase in cost and complexity compared to using a simple light microscope. Usually the technique is only appropriate for a small subset of imaging problems, with several general approaches outlined below.

===Extending numerical aperture===

The effective resolution of a microscope can be improved by illuminating from the side. 

In conventional microscopes such as bright-field or [[Differential_interference_contrast_microscopy|differential interference contrast]], this is achieved by using a condenser. Under spatially incoherent conditions, the image is understood as a composite of images illuminated from each point on the condenser, each of which covers a different portion of the object's spatial frequencies.<ref>{{cite journal |first=Norbert |last=Streibl |title=Three-dimensional imaging by a microscope |journal=Journal of the Optical Society of America A |volume=2 |issue=2 |date=February 1985 |pages=121–127 |doi=10.1364/JOSAA.2.000121 |bibcode=1985JOSAA...2..121S}}</ref> This effectively improves the resolution by, at most, a factor of two. 

Simultaneously illuminating from all angles (fully open condenser) drives down interferometric contrast. In conventional microscopes, the maximum resolution (fully open condenser, at N&nbsp;=&nbsp;1) is rarely used. Further, under partially coherent conditions, the recorded image is often non-linear with object's scattering potential—especially when looking at non-self-luminous (non-fluorescent) objects.<ref>{{cite journal |first1=C.J.R. |last1=Sheppard |author-link1=Colin Sheppard |first2=X.Q. |last2=Mao |title=Three-dimensional imaging in a microscope |journal=Journal of the Optical Society of America A |volume=6 |issue=9 |date=September 1989 |pages=1260–1269 |doi=10.1364/JOSAA.6.001260 |bibcode=1989JOSAA...6.1260S }}</ref> To boost contrast, and sometimes to linearize the system, unconventional microscopes (with [[Structured light|structured illumination]]) synthesize the condenser illumination by acquiring a sequence of images with known illumination parameters. Typically, these images are composited to form a single image with data covering a larger portion of the object's spatial frequencies when compared to using a fully closed condenser (which is also rarely used).

Another technique, [[4Pi microscope|4Pi microscopy]], uses two opposing objectives to double the effective numerical aperture, effectively halving the diffraction limit, by collecting the forward and backward scattered light. When imaging a transparent sample, with a combination of incoherent or structured illumination, as well as collecting both forward, and backward scattered light it is possible to image the complete [[Ewald's sphere|scattering sphere]].

Unlike methods relying on [[Super-resolution microscopy#Localization microscopy|localization]], such systems are still limited by the diffraction limit of the illumination (condenser) and collection optics (objective), although in practice they can provide substantial resolution improvements compared to conventional methods.

===Near-field techniques===

The diffraction limit is only valid in the far field as it assumes that no [[evanescent field]]s reach the detector. Various [[Near and far field|near-field]] techniques that operate less than ≈1 wavelength of light away from the image plane can obtain substantially higher resolution. These techniques exploit the fact that the evanescent field contains information beyond the diffraction limit which can be used to construct very high resolution images, in principle beating the diffraction limit by a factor proportional to how well a specific imaging system can detect the near-field signal. For scattered light imaging, instruments such as [[near-field scanning optical microscope]]s and [[nano-FTIR]], which are built atop [[Atomic force microscopy|atomic force microscope]] systems, can be used to achieve up to 10-50&nbsp;nm resolution. The data recorded by such instruments often requires substantial processing, essentially solving an optical inverse problem for each image.

[[Metamaterial]]-based [[superlens]]es can image with a resolution better than the diffraction limit by locating the [[objective lens]] extremely close (typically hundreds of nanometers) to the object.

In fluorescence microscopy the excitation and emission are typically on different wavelengths. In [[total internal reflection fluorescence microscopy]] a thin portion of the sample located immediately on the cover glass is excited with an evanescent field, and recorded with a conventional diffraction-limited objective, improving the axial resolution.

However, because these techniques cannot image beyond 1 wavelength, they cannot be used to image into objects thicker than 1 wavelength which limits their applicability.

===Far-field techniques===

Far-field imaging techniques are most desirable for imaging objects that are large compared to the illumination wavelength but that contain fine structure. This includes nearly all biological applications in which cells span multiple wavelengths but contain structure down to molecular scales. In recent years several techniques have shown that sub-diffraction limited imaging is possible over macroscopic distances. These techniques usually exploit optical [[Nonlinear optics|nonlinearity]] in a material's reflected light to generate resolution beyond the diffraction limit.

Among these techniques, the [[STED microscope]] has been one of the most successful. In STED, multiple laser beams are used to first excite, and then quench [[fluorescent]] dyes. The nonlinear response to illumination caused by the quenching process in which adding more light causes the image to become less bright generates sub-diffraction limited information about the location of dye molecules, allowing resolution far beyond the diffraction limit provided high illumination intensities are used.