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<h1 id="firstHeading" class="firstHeading mw-first-heading">
<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Spectral resolution</span></span>
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<p>The <b>spectral resolution</b> of a <a href="Spectrograph" class="mw-redirect" title="Spectrograph">spectrograph</a>, or, more generally, of a <a href="Frequency_spectrum" class="mw-redirect" title="Frequency spectrum">frequency spectrum</a>, is a measure of its ability to resolve features in the <a href="Electromagnetic_spectrum" title="Electromagnetic spectrum">electromagnetic spectrum</a>. It is usually denoted by <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 \Delta \lambda }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>λ<!-- λ --></mi>
</mstyle>
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<annotation encoding="application/x-tex">{\displaystyle \Delta \lambda }</annotation>
</semantics>
</math></span><img src="./905140cc6559a946172b382a0da12bbc82096801.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.291ex; height:2.176ex;" alt="{\displaystyle \Delta \lambda }" loading="lazy"></span>, and is closely related to the <b>resolving power</b> of the spectrograph, defined as
<span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R={\frac {\lambda }{\Delta \lambda }},}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>R</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>λ<!-- λ --></mi>
<mrow>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>λ<!-- λ --></mi>
</mrow>
</mfrac>
</mrow>
<mo>,</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R={\frac {\lambda }{\Delta \lambda }},}</annotation>
</semantics>
</math></span></span>
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 \Delta \lambda }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>λ<!-- λ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Delta \lambda }</annotation>
</semantics>
</math></span><img src="./905140cc6559a946172b382a0da12bbc82096801.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.291ex; height:2.176ex;" alt="{\displaystyle \Delta \lambda }" loading="lazy"></span> is the smallest difference in <a href="Wavelength" title="Wavelength">wavelengths</a> that can be distinguished at a wavelength of <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 }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>λ<!-- λ --></mi>
</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>. For example, the <a href="Space_Telescope_Imaging_Spectrograph" title="Space Telescope Imaging Spectrograph">Space Telescope Imaging Spectrograph</a> (STIS) can distinguish features 0.17 <a href="Nanometre" title="Nanometre">nm</a> apart at a wavelength of 1000 nm, giving it a resolution of 0.17 nm and a resolving power of about 5,900. An example of a high resolution spectrograph is the <i>Cryogenic High-Resolution <a href="Infrared" title="Infrared">IR</a> <a href="Echelle_grating" title="Echelle grating">Echelle Spectrograph</a></i> (CRIRES+) installed at <a href="ESO" class="mw-redirect" title="ESO">ESO</a>'s <a href="Very_Large_Telescope" title="Very Large Telescope">Very Large Telescope</a>, which has a spectral resolving power of up to 100,000.<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>
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<div class="mw-heading mw-heading2"><h2 id="Doppler_effect">Doppler effect</h2></div>
<p>The spectral resolution can also be expressed in terms of physical quantities, such as velocity; then it describes the difference between velocities <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 \Delta v}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>v</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Delta v}</annotation>
</semantics>
</math></span><img src="./e18b43e4225eeaafeeb25aefc4ee90bd86f004dc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.063ex; height:2.176ex;" alt="{\displaystyle \Delta v}" loading="lazy"></span> that can be distinguished through the <a href="Doppler_effect" title="Doppler effect">Doppler effect</a>. Then, the resolution 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 \Delta v}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>v</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Delta v}</annotation>
</semantics>
</math></span><img src="./e18b43e4225eeaafeeb25aefc4ee90bd86f004dc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.063ex; height:2.176ex;" alt="{\displaystyle \Delta v}" loading="lazy"></span> and the resolving power is
<span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R={\frac {c}{\Delta v}},}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>R</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>c</mi>
<mrow>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mi>v</mi>
</mrow>
</mfrac>
</mrow>
<mo>,</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle R={\frac {c}{\Delta v}},}</annotation>
</semantics>
</math></span></span>
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 c}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>c</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle c}</annotation>
</semantics>
</math></span><img src="./86a67b81c2de995bd608d5b2df50cd8cd7d92455.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}" loading="lazy"></span> is the <a href="Speed_of_light" title="Speed of light">speed of light</a>. The STIS example above then has a spectral resolution of 51 <a href="Kilometres_per_second" class="mw-redirect" title="Kilometres per second">km/s</a>.
</p>
<div class="mw-heading mw-heading2"><h2 id="IUPAC_definition">IUPAC definition</h2></div>
<p><a href="International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a> defines resolution in optical spectroscopy as the minimum wavenumber, wavelength or frequency difference between two lines in a spectrum that can be distinguished.<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> Resolving power, <i>R</i>, is given by the transition wavenumber, wavelength or frequency, divided by the resolution.<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>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Angular_resolution" title="Angular resolution">Angular resolution</a></li>
<li><a href="Resolution_(mass_spectrometry)" title="Resolution (mass spectrometry)">Resolution (mass spectrometry)</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<div class="mw-references-wrap"><ol class="references">
<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.eso.org/instruments/crires/">- CRIRES Instrument page at ESO</a></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"><a href="International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a>, <i><a href="IUPAC_books" class="mw-redirect" title="IUPAC books">Compendium of Chemical Terminology</a></i>, 5th ed. (the "Gold Book") (2025). Online version: (2006–) "<a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/R05319.html">resolution in optical spectroscopy</a>". <style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.R05319">10.1351/goldbook.R05319</a></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"><a href="International_Union_of_Pure_and_Applied_Chemistry" title="International Union of Pure and Applied Chemistry">IUPAC</a>, <i><a href="IUPAC_books" class="mw-redirect" title="IUPAC books">Compendium of Chemical Terminology</a></i>, 5th ed. (the "Gold Book") (2025). Online version: (2006–) "<a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/R05322.html">resolving power, R, in optical spectroscopy</a>". <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1351%2Fgoldbook.R05322">10.1351/goldbook.R05322</a></span>
</li>
</ol></div></div>
<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>
<ul><li>Kim Quijano, J., et al. (2003), <i>STIS Instrument Handbook</i>, Version 7.0, (Baltimore: STScI)</li>
<li>Frank L. Pedrotti, S.J. (2007), <i>Introduction to optics</i>, 3rd version, (San Francisco)</li></ul></div><!--htdig_noindex--><div><div class="zim-footer">
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