SherbyNet - /page/wikibook/entry.mu

Micron Document

<!DOCTYPE html>

<title>Diffraction-limited system</title>

</head>

<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Diffraction-limited system</span></span>

</h1>

</header>

<p>In <a href="Optics" title="Optics">optics</a>, any <a href="Optical_instrument" title="Optical instrument">optical instrument or system</a> – a <a href="Microscope" title="Microscope">microscope</a>, <a href="Telescope" title="Telescope">telescope</a>, or <a href="Camera" title="Camera">camera</a> – has a principal limit to its <a href="Optical_resolution" title="Optical resolution">resolution</a> due to the <a href="Physics" title="Physics">physics</a> of <a href="Diffraction" title="Diffraction">diffraction</a>. An optical instrument is said to be <b>diffraction-limited</b> if it has reached this limit of resolution performance. Other factors may affect an optical system's performance, such as lens imperfections or <a href="Optical_aberration" title="Optical aberration">aberrations</a>, but these are caused by errors in the manufacture or <a href="Paraxial_approximation" title="Paraxial approximation">calculation</a> of a lens, whereas the diffraction limit is the maximum resolution possible for a theoretically perfect, or ideal, optical system.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p><p>The diffraction-limited <a href="Angular_resolution" title="Angular resolution">angular resolution</a>, in radians, of an instrument is proportional to the <a href="Wavelength" title="Wavelength">wavelength</a> of the light being observed, and inversely proportional to the diameter of its <a href="Objective_(optics)" title="Objective (optics)">objective</a>'s <a href="Entrance_pupil" title="Entrance pupil">entrance aperture</a>. For telescopes with circular apertures, the size of the smallest feature in an image that is diffraction limited is the size of the <a href="Airy_disk" title="Airy disk">Airy disk</a>. As one decreases the size of the aperture of a telescopic <a href="Lens_(optics)" class="mw-redirect" title="Lens (optics)">lens</a>, diffraction proportionately increases. At small apertures, such as <a href="F-stop" class="mw-redirect" title="F-stop">f/22</a>, most modern lenses are limited only by diffraction and not by aberrations or other imperfections in the construction.

</p><p>For microscopic instruments, the diffraction-limited <a href="Spatial_resolution" title="Spatial resolution">spatial resolution</a> is proportional to the light wavelength, and to the <a href="Numerical_aperture" title="Numerical aperture">numerical aperture</a> of either the objective or the object illumination source, whichever is smaller.

</p><p>In <a href="Astronomy" title="Astronomy">astronomy</a>, a <b>diffraction-limited</b> observation is one that achieves the resolution of a theoretically ideal objective in the size of instrument used. However, most observations from Earth are <a href="Astronomical_seeing" title="Astronomical seeing">seeing</a>-limited due to <a href="Atmosphere_of_Earth" title="Atmosphere of Earth">atmospheric</a> effects. Optical telescopes on the <a href="Earth" title="Earth">Earth</a> work at a much lower resolution than the diffraction limit because of the distortion introduced by the passage of light through several kilometres of <a href="Turbulence" title="Turbulence">turbulent</a> atmosphere. Advanced observatories have started using <a href="Adaptive_optics" title="Adaptive optics">adaptive optics</a> technology, resulting in greater image resolution for faint targets, but it is still difficult to reach the diffraction limit using adaptive optics.

</p><p><a href="Radio_telescope" title="Radio telescope">Radio telescopes</a> are frequently diffraction-limited, because the wavelengths they use (from millimeters to meters) are so long that the atmospheric distortion is negligible. Space-based telescopes (such as <a href="Hubble_Space_Telescope" title="Hubble Space Telescope">Hubble</a>, or a number of non-optical telescopes) always work at their diffraction limit, if their design is free of <a href="Optical_aberration" title="Optical aberration">optical aberration</a>.

</p><p>The beam from a <a href="Laser" title="Laser">laser</a> with near-ideal beam propagation properties may be described as being diffraction-limited. A diffraction-limited laser beam, passed through diffraction-limited optics, will remain diffraction-limited, and will have a spatial or angular extent essentially equal to the resolution of the optics at the wavelength of the laser.

</p>

<div class="mw-heading mw-heading2"><h2 id="Calculation_of_diffraction_limit">Calculation of diffraction limit</h2></div>

<div class="mw-heading mw-heading3"><h3 id="The_Abbe_diffraction_limit_for_a_microscope">The Abbe diffraction limit for a microscope</h3></div>

<p>The observation of sub-wavelength structures with microscopes is difficult because of the <b>Abbe diffraction limit</b>. <a href="Ernst_Abbe" title="Ernst Abbe">Ernst Abbe</a> first mentioned the diffraction limit in his 1873 paper, page 466: „[…] die physikalische Unterscheidungsgrenze […] hängt allein vom Oeffnungswinkel ab und ist dem Sinus seines halben Betrages proportional“, or "[…] the physical limit of resolution […] depends solely on the aperture angle and is proportional to the sine of half its magnitude".<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Abbe wrote it in form of a formula in his 1882 paper, page 461: "The smallest dimensions which are within the reach of a given aperture are indicated with sufficient accuracy by taking the limit of the resolving or separating power of that aperture for periodic or regular structures, i.e. the minimum distance apart at which given elements can be delineated separately with the aperture in question. The numerical expression of that minimum distance is" <sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d={\frac {\lambda }{2n\sin \theta }}={\frac {\lambda }{2\mathrm {NA} }}}</annotation>

</semantics>

</math></span><img src="./2a4dfa1f30e4a718d5c4573d5bdac3fd96e248fb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:21.011ex; height:5.509ex;" alt="{\displaystyle d={\frac {\lambda }{2n\sin \theta }}={\frac {\lambda }{2\mathrm {NA} }}}" loading="lazy"></span>,</dd></dl>

<p>where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation>

</semantics>

</math></span><img src="./b43d0ea3c9c025af1be9128e62a18fa74bedda2a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }" loading="lazy"></span> is the wavelength, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle n}</annotation>

</semantics>

</math></span><img src="./a601995d55609f2d9f5e233e36fbe9ea26011b3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" loading="lazy"></span> is the refractive index of the medium, and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \theta }</annotation>

</semantics>

</math></span><img src="./6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"></span> is the semi-angle of the light focused by the optical system. The same formula had been proven by Hermann von Helmholtz in 1874.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The portion of the denominator <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\sin \theta }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle n\sin \theta }</annotation>

</semantics>

</math></span><img src="./d5aa19edc6faa4080d8fd0c33f2ec7b358ad2e4f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.115ex; height:2.176ex;" alt="{\displaystyle n\sin \theta }" loading="lazy"></span> is called the <a href="Numerical_aperture" title="Numerical aperture">numerical aperture</a> (NA) and can reach about 1.4–1.6 in modern optics, hence the Abbe limit is <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d={\frac {\lambda }{2.8}}}">

<mfrac>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d={\frac {\lambda }{2.8}}}</annotation>

</semantics>

</math></span><img src="./ddec9babc0db5bbe3c93318af9d71ee8780af7d9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.122ex; height:5.343ex;" alt="{\displaystyle d={\frac {\lambda }{2.8}}}" loading="lazy"></span>.

</p><p>Considering green light around 500 nm and a NA of 1, the Abbe limit is roughly <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d={\frac {\lambda }{2}}=250{\text{ nm}}}">

<mfrac>

</mfrac>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d={\frac {\lambda }{2}}=250{\text{ nm}}}</annotation>

</semantics>

</math></span><img src="./ab11aacf0fcc3bda0d3f8d22ae4e3df6158bf0ae.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.901ex; height:5.343ex;" alt="{\displaystyle d={\frac {\lambda }{2}}=250{\text{ nm}}}" loading="lazy"></span> (0.25 μm), which is small compared to most biological cells (1 μm to 100 μm), but large compared to viruses (100 nm), proteins (10 nm) and less complex molecules (1 nm). To increase the resolution, shorter wavelengths can be used such as UV and X-ray microscopes. These techniques offer better resolution but are expensive, suffer from lack of contrast in biological samples and may damage the sample.

</p>

<div class="mw-heading mw-heading3"><h3 id="Digital_photography">Digital photography</h3></div>

<p>In a digital camera, diffraction effects interact with the effects of the regular pixel grid. The combined effect of the different parts of an optical system is determined by the <a href="Convolution" title="Convolution">convolution</a> of the <a href="Point_spread_function" title="Point spread function">point spread functions</a> (PSF). The point spread function of a diffraction limited circular-aperture lens is simply the <a href="Airy_disk" title="Airy disk">Airy disk</a>. The point spread function of the camera, otherwise called the instrument response function (IRF) can be approximated by a rectangle function, with a width equivalent to the pixel pitch. A more complete derivation of the modulation transfer function (derived from the PSF) of image sensors is given by Fliegel.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Whatever the exact instrument response function, it is largely independent of the f-number of the lens. Thus at different f-numbers a camera may operate in three different regimes, as follows:

</p>

<ol><li>In the case where the spread of the IRF is small with respect to the spread of the diffraction PSF, in which case the system may be said to be essentially diffraction limited (so long as the lens itself is diffraction limited).</li>

<li>In the case where the spread of the diffraction PSF is small with respect to the IRF, in which case the system is instrument limited.</li>

<li>In the case where the spread of the PSF and IRF are similar, in which case both impact the available resolution of the system.</li></ol>

<p>The spread of the diffraction-limited PSF is approximated by the diameter of the first null of the <a href="Airy_disk" title="Airy disk">Airy disk</a>,

</p>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle d/2=1.22\lambda N,\,}</annotation>

</semantics>

</math></span><img src="./4326f003ae0f09137175c60b1296ae36ce5e8193.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.226ex; height:2.843ex;" alt="{\displaystyle d/2=1.22\lambda N,\,}" loading="lazy"></span><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></dd></dl>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation>

</semantics>

</math></span><img src="./b43d0ea3c9c025af1be9128e62a18fa74bedda2a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }" loading="lazy"></span> is the wavelength of the light and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle N}</annotation>

</semantics>

</math></span><img src="./f5e3890c981ae85503089652feb48b191b57aae3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}" loading="lazy"></span> is the <a href="F-number" title="F-number">f-number</a> of the imaging optics, i.e., <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2NA\rightarrow (2.44N)^{-1}}">

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 2NA\rightarrow (2.44N)^{-1}}</annotation>

</semantics>

</math></span><img src="./958b53bbc61bbbe75ae3340efb1fca7494218eff.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.923ex; height:3.176ex;" alt="{\displaystyle 2NA\rightarrow (2.44N)^{-1}}" loading="lazy"></span> in the Abbe diffraction limit formula. For instance, for an f/8 lens (<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=8}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle N=8}</annotation>

</semantics>

</math></span><img src="./558afd5d04eca060444da01dd32e67f9675253b7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.325ex; height:2.176ex;" alt="{\displaystyle N=8}" loading="lazy"></span> and <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle NA\approx 2.5\%}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle NA\approx 2.5\%}</annotation>

</semantics>

</math></span><img src="./e540aec7a18bd98f388995a28e056f85e4b3ed51.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.813ex; height:2.343ex;" alt="{\displaystyle NA\approx 2.5\%}" loading="lazy"></span> ) and for green light (<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda _{g}=}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lambda _{g}=}</annotation>

</semantics>

</math></span><img src="./9e314ee71a0fe68ff60413bb237b16e4d5df1a03.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.83ex; height:2.843ex;" alt="{\displaystyle \lambda _{g}=}" loading="lazy"></span> 0.5 μm wavelength) light, the focusing spot diameter will be d = 9.76 μm or 19.5<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda _{g}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lambda _{g}}</annotation>

</semantics>

</math></span><img src="./bb316d397662f2d3ba0d0abff10317bcd22de130.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.377ex; height:2.843ex;" alt="{\displaystyle \lambda _{g}}" loading="lazy"></span>. This is similar to the pixel size for the majority of commercially available 'full frame' (43mm sensor diagonal) cameras and so these will operate in regime 3 for f-numbers around 8 (few lenses are close to diffraction limited at f-numbers smaller than 8).

</p><p>Cameras with smaller sensors will tend to have smaller pixels, but their lenses will be designed for use at smaller f-numbers and it is likely that they will also operate in regime 3 for those f-numbers for which their lenses are diffraction limited. Given the same field of view, pixel count, <a href="Shutter_speed" title="Shutter speed">shutter speed</a> and <a href="Shot_noise" title="Shot noise">shot noise</a> SNR (i.e. the same amount of light collected per pixel), a small sensor and a large sensor of equivalent quality will produce the same digital image, with the same amount of blur due to both diffraction and <a href="Depth_of_field" title="Depth of field">depth of field</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The larger sensors do have an advantage in that the lenses for them tend to have larger maximum <a href="Entrance_pupil" title="Entrance pupil">entrance pupils</a>, which allows, to a larger extent, trading depth of field for less diffraction blur and either more SNR or higher shutter speeds.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Obtaining_higher_resolution">Obtaining higher resolution</h2></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}

/* end https://en.wikipedia.org/ */

</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="Super-resolution_microscopy" title="Super-resolution microscopy">Super-resolution microscopy</a></div>

<p>Using special optical systems and <a href="Digital_image_processing" title="Digital image processing">digital image processing</a>, 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.<sup id="cite_ref-U2_9-0" class="reference"><a href="#cite_note-U2-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> 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.<sup id="cite_ref-j702_10-0" class="reference"><a href="#cite_note-j702-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-h720_11-0" class="reference"><a href="#cite_note-h720-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> 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.

</p>

<div class="mw-heading mw-heading3"><h3 id="Extending_numerical_aperture">Extending numerical aperture</h3></div>

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

</p><p>In conventional microscopes such as bright-field or <a href="Differential_interference_contrast_microscopy" title="Differential interference contrast microscopy">differential interference contrast</a>, 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.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> This effectively improves the resolution by, at most, a factor of two.

</p><p>Simultaneously illuminating from all angles (fully open condenser) drives down interferometric contrast. In conventional microscopes, the maximum resolution (fully open condenser, at N = 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.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> To boost contrast, and sometimes to linearize the system, unconventional microscopes (with <a href="Structured_light" title="Structured light">structured illumination</a>) 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).

</p><p>Another technique, <a href="4Pi_microscope" title="4Pi microscope">4Pi microscopy</a>, 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 <a href="Ewald's_sphere" title="Ewald's sphere">scattering sphere</a>.

</p><p>Unlike methods relying on <a href="Super-resolution_microscopy#Localization_microscopy" title="Super-resolution microscopy">localization</a>, 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.

</p>

<div class="mw-heading mw-heading3"><h3 id="Near-field_techniques">Near-field techniques</h3></div>

<p>The diffraction limit is only valid in the far field as it assumes that no <a href="Evanescent_field" title="Evanescent field">evanescent fields</a> reach the detector. Various <a href="Near_and_far_field" title="Near and far field">near-field</a> 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 <a href="Near-field_scanning_optical_microscope" title="Near-field scanning optical microscope">near-field scanning optical microscopes</a> and <a href="Nano-FTIR" title="Nano-FTIR">nano-FTIR</a>, which are built atop <a href="Atomic_force_microscopy" title="Atomic force microscopy">atomic force microscope</a> systems, can be used to achieve up to 10-50 nm resolution. The data recorded by such instruments often requires substantial processing, essentially solving an optical inverse problem for each image.

</p><p><a href="Metamaterial" title="Metamaterial">Metamaterial</a>-based <a href="Superlens" title="Superlens">superlenses</a> can image with a resolution better than the diffraction limit by locating the <a href="Objective_lens" class="mw-redirect" title="Objective lens">objective lens</a> extremely close (typically hundreds of nanometers) to the object.

</p><p>In fluorescence microscopy the excitation and emission are typically on different wavelengths. In <a href="Total_internal_reflection_fluorescence_microscopy" class="mw-redirect" title="Total internal reflection fluorescence microscopy">total internal reflection fluorescence microscopy</a> 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.

</p><p>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.

</p>

<div class="mw-heading mw-heading3"><h3 id="Far-field_techniques">Far-field techniques</h3></div>

<p>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 <a href="Nonlinear_optics" title="Nonlinear optics">nonlinearity</a> in a material's reflected light to generate resolution beyond the diffraction limit.

</p><p>Among these techniques, the <a href="STED_microscope" class="mw-redirect" title="STED microscope">STED microscope</a> has been one of the most successful. In STED, multiple laser beams are used to first excite, and then quench <a href="Fluorescent" class="mw-redirect" title="Fluorescent">fluorescent</a> 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.

</p>

<div class="mw-heading mw-heading2"><h2 id="Laser_beams">Laser beams</h2></div>

<p>The limits on focusing or collimating a laser beam are very similar to the limits on imaging with a microscope or telescope. The only difference is that laser beams are typically soft-edged beams. This non-uniformity in light distribution leads to a coefficient slightly different from the 1.22 value familiar in imaging. However, the scaling with wavelength and aperture is exactly the same.

</p><p>The beam quality of a laser beam is characterized by how well its propagation matches an ideal <a href="Gaussian_beam" title="Gaussian beam">Gaussian beam</a> at the same wavelength. The beam quality factor <a href="M_squared" title="M squared">M squared</a> (M<sup>2</sup>) is found by measuring the size of the beam at its waist, and its divergence far from the waist, and taking the product of the two, known as the <a href="Beam_parameter_product" title="Beam parameter product">beam parameter product</a>. The ratio of this measured beam parameter product to that of the ideal is defined as M<sup>2</sup>, so that M<sup>2</sup>=1 describes an ideal beam. The M<sup>2</sup> value of a beam is conserved when it is transformed by diffraction-limited optics.

</p><p>The outputs of many low and moderately powered lasers have M<sup>2</sup> values of 1.2 or less, and are essentially diffraction-limited.

</p>

<div class="mw-heading mw-heading2"><h2 id="Other_waves">Other waves</h2></div>

<p>The same equations apply to other wave-based sensors, such as radar and the human ear.

</p><p>As opposed to light waves (i.e., photons), massive particles have a different relationship between their quantum mechanical wavelength and their energy. This relationship indicates that the effective <a href="De_Broglie_wavelength" class="mw-redirect" title="De Broglie wavelength">"de Broglie" wavelength</a> is inversely proportional to the momentum of the particle. For example, an electron at an energy of 10 keV has a wavelength of 0.01 nm, allowing the electron microscope (<a href="Scanning_electron_microscope" title="Scanning electron microscope">SEM</a> or <a href="Transmission_electron_microscopy" title="Transmission electron microscopy">TEM</a>) to achieve high resolution images. Other massive particles such as helium, neon, and gallium ions have been used to produce images at resolutions beyond what can be attained with visible light. Such instruments provide nanometer scale imaging, analysis and fabrication capabilities at the expense of system complexity.

</p>

<ul><li><a href="Angular_resolution#The_Rayleigh_criterion" title="Angular resolution">Rayleigh criterion</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}

/* end https://en.wikipedia.org/ */

</style><div class="reflist">

/* start https://en.wikipedia.org/ */

.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("./mw/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}

/* end https://en.wikipedia.org/ */

</style><cite id="CITEREFBornEmil_Wolf1997" class="citation book cs1">Born, Max; Emil Wolf (1997). <i><a href="Principles_of_Optics" title="Principles of Optics">Principles of Optics</a></i>. <a href="Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-521-63921-2</bdi>.</cite></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFAbbe1873" class="citation journal cs1">Abbe, Ernst (1873). <a rel="nofollow" class="external text" href="https://doi.org/10.1007/BF02956173">"Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung"</a>. <i>Archiv für mikroskopische Anatomie</i>. <b>9</b>: <span class="nowrap">413–</span>468. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF02956173">10.1007/BF02956173</a>.</cite></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFAbbe1882" class="citation journal cs1">Abbe, Ernst (1882). <span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://doi.org/10.1111/j.1365-2818.1882.tb04805.x">"The Relation of Aperture and Power in the Microscope (continued)"</a></span>. <i>Journal of the Royal Microscopical Society</i>. <b>2</b> (4): <span class="nowrap">460–</span>473. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1111%2Fj.1365-2818.1882.tb04805.x">10.1111/j.1365-2818.1882.tb04805.x</a>.</cite></span>

</li>

<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFvon_Helmholtz1874" class="citation journal cs1">von Helmholtz, Hermann (1874). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=b4gEAAAAYAAJ">"Die theoretische Grenze für die Leistungsfähigkeit der Mikroskope"</a> [The Theoretical Limit of the Efficiency of Microscopes)]. <i>Annalen der Physik und Chemie: Jubelband dem Herausgeber Johann Christian Poggendorff zur Feier fünfzigjährigen Wirkens gewidmet</i>: <span class="nowrap">557–</span>584.</cite></span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite id="CITEREFFliegel2004" class="citation journal cs1">Fliegel, Karel (December 2004). <a rel="nofollow" class="external text" href="http://www.radioeng.cz/fulltexts/2004/04_04_27_34.pdf">"Modeling and Measurement of Image Sensor Characteristics"</a> <span class="cs1-format">(PDF)</span>. <i>Radioengineering</i>. <b>13</b> (4).</cite></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFGoodman2005" class="citation book cs1">Goodman, Joseph W. (2005). "4.4.2 Example of Fraunhofer Diffraction Patterns for Circular Aperture". <i>Introduction to Fourier Optics</i>. Englewood, Colorado: Roberts and Company Publishers. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-9747077-2-4</bdi>.</cite></span>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><cite id="CITEREFClark2017" class="citation web cs1">Clark, Roger N. (2017-03-18). <a rel="nofollow" class="external text" href="https://clarkvision.com/articles/dof_myth/">"The Depth-of-Field Myth and Digital Cameras"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2025-06-13</span></span>.</cite></span>

</li>

<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite id="CITEREFClark2006" class="citation web cs1">Clark, Roger N. (2006-09-10). <a rel="nofollow" class="external text" href="https://clarkvision.com/articles/f-ratio_myth/index.html">"The f/ratio Myth and Digital Cameras"</a>.</cite></span>

</li>

<li id="cite_note-U2-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-U2_9-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFNiek_van_Hulst2009" class="citation journal cs1">Niek van Hulst (2009). <a rel="nofollow" class="external text" href="http://www.opfocus.org/index.php?topic=story&v=4&s=1">"Many photons get more out of diffraction"</a>. <i>Optics & Photonics Focus</i>. <b>4</b> (1).</cite></span>

</li>

<li id="cite_note-j702-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-j702_10-0">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.microscopemaster.com/super-resolution-microscopy.html">"True/Functional Techniques and Technology"</a>. <i>MicroscopeMaster</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2025-05-01</span></span>.</cite></span>

</li>

<li id="cite_note-h720-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-h720_11-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFGalbraithGalbraith2011" class="citation journal cs1">Galbraith, Catherine G.; Galbraith, James A. (2011-05-15). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3085433">"Super-resolution microscopy at a glance"</a>. <i>Journal of Cell Science</i>. <b>124</b> (10). The Company of Biologists: <span class="nowrap">1607–</span>1611. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1242%2Fjcs.080085">10.1242/jcs.080085</a></span>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1477-9137">1477-9137</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3085433">3085433</a></span>.</cite></span>

</li>

<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><cite id="CITEREFStreibl1985" class="citation journal cs1">Streibl, Norbert (February 1985). "Three-dimensional imaging by a microscope". <i>Journal of the Optical Society of America A</i>. <b>2</b> (2): <span class="nowrap">121–</span>127. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1985JOSAA...2..121S">1985JOSAA...2..121S</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1364%2FJOSAA.2.000121">10.1364/JOSAA.2.000121</a>.</cite></span>

</li>

<li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><cite id="CITEREFSheppardMao1989" class="citation journal cs1"><a href="Colin_Sheppard" title="Colin Sheppard">Sheppard, C.J.R.</a>; Mao, X.Q. (September 1989). "Three-dimensional imaging in a microscope". <i>Journal of the Optical Society of America A</i>. <b>6</b> (9): <span class="nowrap">1260–</span>1269. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1989JOSAA...6.1260S">1989JOSAA...6.1260S</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1364%2FJOSAA.6.001260">10.1364/JOSAA.6.001260</a>.</cite></span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><cite id="CITEREFPuts2003" class="citation web cs1">Puts, Erwin (September 2003). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20081217074256/http://en.leica-camera.com/assets/file/download.php?filename=file_1864.pdf">"Chapter 3: 180 mm and 280 mm lenses"</a> <span class="cs1-format">(PDF)</span>. <i>Leica R-Lenses</i>. <a href="Leica_Camera" title="Leica Camera">Leica Camera</a>. Archived from <a rel="nofollow" class="external text" href="http://en.leica-camera.com/assets/file/download.php?filename=file_1864.pdf">the original</a> <span class="cs1-format">(PDF)</span> on December 17, 2008.</cite> Describes the Leica APO-Telyt-R 280mm f/4, a diffraction-limited photographic lens.</li></ul>

/* start https://en.wikipedia.org/ */

.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}

/* end https://en.wikipedia.org/ */

</style><style data-mw-deduplicate="TemplateStyles:r1236075235">

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}

/* end https://en.wikipedia.org/ */

</style></div><div role="navigation" class="navbox" aria-labelledby="Optical_microscopy454" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><style data-mw-deduplicate="TemplateStyles:r1239400231">

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}

/* end https://en.wikipedia.org/ */

</style><div id="Optical_microscopy454" style="font-size:114%;margin:0 4em"><a href="Microscopy" title="Microscopy">Optical microscopy</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3"><div>

<ul><li><b><a href="Microscope" title="Microscope">Microscope</a></b></li>

<li><b><a href="Optical_microscope" title="Optical microscope">Optical microscopy</a></b></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Illumination and<br>contrast methods</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bright-field_microscopy" title="Bright-field microscopy">Bright-field microscopy</a></li>

<li><a href="K%C3%B6hler_illumination" title="Köhler illumination">Köhler illumination</a></li>

<li><a href="Dark-field_microscopy" title="Dark-field microscopy">Dark-field microscopy</a></li>

<li><a href="Phase-contrast_microscopy" title="Phase-contrast microscopy">Phase contrast</a></li>

<li><a href="Quantitative_phase-contrast_microscopy" title="Quantitative phase-contrast microscopy">Quantitative phase-contrast microscopy</a></li>

<li><a href="Differential_interference_contrast_microscopy" title="Differential interference contrast microscopy">Differential interference contrast (DIC)</a></li>

<li><a href="Dispersion_staining" title="Dispersion staining">Dispersion staining</a></li>

<li><a href="Second-harmonic_imaging_microscopy" title="Second-harmonic imaging microscopy">Second harmonic imaging (SHIM)</a></li>

<li><a href="4Pi_microscope" title="4Pi microscope">4Pi microscope</a></li>

<li><a href="Microscopy#Structured_illumination" title="Microscopy">Structured illumination</a></li>

<li><a href="Sarfus" title="Sarfus">Sarfus</a></li>

<li><a href="Interference_reflection_microscopy" title="Interference reflection microscopy">Interference reflection microscopy (IRM/RICM)</a></li>

<li><a href="Raman_microscope" title="Raman microscope">Raman</a></li></ul>

</div></td><td class="noviewer navbox-image" rowspan="3" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Fluorescence methods</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Fluorescence_microscope" title="Fluorescence microscope">Fluorescence microscopy</a></li>

<li><a href="Confocal_microscopy" title="Confocal microscopy">Confocal microscopy</a></li>

<li><a href="Two-photon_excitation_microscopy" title="Two-photon excitation microscopy">Multiphoton microscopy</a> (<a href="Two-photon_excitation_microscopy" title="Two-photon excitation microscopy">Two-photon</a>, <a href="Three_photon_microscopy" class="mw-redirect" title="Three photon microscopy">Three-photon</a>)</li>

<li><a href="Deconvolution#Optics_and_other_imaging" title="Deconvolution">Image deconvolution</a></li>

<li><a href="Total_internal_reflection_fluorescence_microscope" title="Total internal reflection fluorescence microscope">Total internal reflection fluorescence microscopy (TIRF)</a></li>

<li><a href="Light_sheet_fluorescence_microscopy" title="Light sheet fluorescence microscopy">Lightsheet microscopy (LSFM/SPIM)</a></li>

<li><a href="Lattice_light-sheet_microscopy" title="Lattice light-sheet microscopy">Lattice light-sheet microscopy</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sub-diffraction<br>limit techniques</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul>

<li><a href="STED_microscopy" title="STED microscopy">Stimulated emission depletion (STED)</a></li>

<li><a href="Photoactivated_localization_microscopy" title="Photoactivated localization microscopy">Photo-activated localization microscopy (PALM/STORM)</a></li>

<li><a href="Near-field_scanning_optical_microscope" title="Near-field scanning optical microscope">Near-field (NSOM/SNOM)</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3"><div>

<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> <b>Category</b></li>

<li><span class="noviewer" typeof="mw:File"><span title="Commons page"></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Optical_microscopy" class="extiw external" title="commons:Category:Optical microscopy">Commons</a></b></li></ul>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-07-16" href="https://en.wikipedia.org/wiki/?title=Diffraction-limited_system&oldid=1300812628">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

</div>

</div></div>

</div>

</main>

</div>

</body></html>