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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Digital imaging calibration technique</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.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}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Field_flattener_lens" title="Field flattener lens">Field flattener lens</a>, which improves focus uniformity.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Woy_Woy_Channel_-_Vignetted.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Woy_Woy_Channel_-_Vignetted.jpg/220px-Woy_Woy_Channel_-_Vignetted.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Woy_Woy_Channel_-_Vignetted.jpg/330px-Woy_Woy_Channel_-_Vignetted.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Woy_Woy_Channel_-_Vignetted.jpg/440px-Woy_Woy_Channel_-_Vignetted.jpg 2x" data-file-width="2048" data-file-height="1536" /></a><figcaption>This picture is darker at the edges. This variation is called <a href="/wiki/Vignetting" title="Vignetting">vignetting</a>, and can be corrected by selectively brightening the perimeter of the image.</figcaption></figure> <p><b>Flat-field correction</b> (<b>FFC</b>) is a <a href="/wiki/Digital_imaging" title="Digital imaging">digital imaging</a> technique to mitigate the <a href="/wiki/Image_detector" class="mw-redirect" title="Image detector">image detector</a> pixel-to-pixel sensitivity and distortions in the <a href="/wiki/Optical_path" title="Optical path">optical path</a>. It is a standard calibration procedure in everything from personal <a href="/wiki/Digital_camera" title="Digital camera">digital cameras</a> to large telescopes. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flat-field_correction&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Flat fielding refers to the process of compensating for different <a href="/wiki/Gain_(electronics)" title="Gain (electronics)">gains</a> and <a href="/wiki/Dark_current_(physics)" title="Dark current (physics)">dark currents</a> in a detector. Once a detector has been appropriately flat-fielded, a uniform signal will create a uniform output (hence flat-field). This then means any further signal is due to the phenomenon being detected and not a <a href="/wiki/Systematic_error" class="mw-redirect" title="Systematic error">systematic error</a>. </p><p>A flat-field image is acquired by imaging a uniformly-illuminated screen, thus producing an image of uniform color and brightness across the frame. For handheld cameras, the screen could be a piece of paper at arm's length, but a telescope will frequently image a clear patch of sky at twilight, when the illumination is uniform and there are few, if any, stars visible.<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> Once the images are acquired, processing can begin. </p><p>A flat-field consists of two numbers for each pixel, the pixel's gain and its dark current (or <a href="/wiki/Dark_frame" class="mw-redirect" title="Dark frame">dark frame</a>). The pixel's gain is how the amount of signal given by the detector varies as a function of the amount of light (or equivalent). The gain is almost always a linear variable, as such the gain is given simply as the ratio of the input and output signals. The dark-current is the amount of signal given out by the detector when there is no incident light (hence dark frame). In many detectors this can also be a function of time, for example in astronomical telescopes it is common to take a dark-frame of the same time as the planned light exposure. The gain and dark-frame for optical systems can also be established by using a series of <a href="/wiki/Neutral_density_filter" class="mw-redirect" title="Neutral density filter">neutral density filters</a> to give input/output signal information and applying a least squares fit to obtain the values for the dark current and gain. <span class="mwe-math-element"><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 C={\frac {(R-D)\times m}{(F-D)}}=(R-D)\times G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>R</mi> <mo>−</mo> <mi>D</mi> <mo stretchy="false">)</mo> <mo>×</mo> <mi>m</mi> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>F</mi> <mo>−</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mo stretchy="false">(</mo> <mi>R</mi> <mo>−</mo> <mi>D</mi> <mo stretchy="false">)</mo> <mo>×</mo> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C={\frac {(R-D)\times m}{(F-D)}}=(R-D)\times G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/983e7475fc666f7b7e0b53e3f8b8d80a378ae9ed" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:35.023ex; height:6.509ex;" alt="{\displaystyle C={\frac {(R-D)\times m}{(F-D)}}=(R-D)\times G}"></span> where: </p> <ul><li><i>C</i> = corrected image</li> <li><i>R</i> = raw image</li> <li><i>F</i> = flat field image</li> <li><i>D</i> = dark frame image</li> <li><i>m</i> = image-averaged value of (<i>F</i>−<i>D</i>)</li> <li><i>G</i> = Gain = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m \over (F-D)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> <mrow> <mo stretchy="false">(</mo> <mi>F</mi> <mo>−</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle m \over (F-D)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2e9d7198f93e87b3555c6745b8fdf361f5fdb08" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:9.151ex; height:5.509ex;" alt="{\displaystyle m \over (F-D)}"></span><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></li></ul> <p>In this equation, capital letters are 2D matrices, and lowercase letters are scalars. All matrix operations are performed element-by-element. </p><p>In order for an astrophotographer to capture a light frame, they must place a light source over the imaging instrument's objective lens such that the light source emanates evenly through the users optics. The photographer must then adjust the exposure of their imaging device (<a href="/wiki/Charge-coupled_device" title="Charge-coupled device">charge-coupled device</a> (CCD) or <a href="/wiki/Digital_single-lens_reflex_camera" title="Digital single-lens reflex camera">digital single-lens reflex camera</a> (DSLR) ) so that when the histogram of the image is viewed, a peak reaching about 40–70% of the dynamic range (maximum range of pixel values) of the imaging device is seen. The photographer typically takes 15–20 light frames and performs median stacking. Once the desired light frames are acquired, the objective lens is covered so that no light is allowed in, then 15–20 dark frames are taken, each of equal exposure time as a light frame. These are called Dark-Flat frames. </p> <div class="mw-heading mw-heading2"><h2 id="In_X-ray_imaging">In X-ray imaging</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flat-field_correction&action=edit&section=2" title="Edit section: In X-ray imaging"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In X-ray imaging, the acquired projection images generally suffer from fixed-pattern noise, which is one of the limiting factors of image quality. It may stem from beam inhomogeneity, gain variations of the detector response due to inhomogeneities in the photon conversion yield, losses in charge transport, charge trapping, or variations in the performance of the readout. Also, the scintillator screen may accumulate dust and/or scratches on its surface, resulting in systematic patterns in every acquired X-ray projection image. In <a href="/wiki/X-ray_computed_tomography" class="mw-redirect" title="X-ray computed tomography">X-ray computed tomography</a> (CT), fixed-pattern noise is known to significantly degrade the achievable spatial resolution and generally leads to ring or band artifacts in the reconstructed images. Fixed pattern noise can be easily removed using flat field correction. In conventional flat field correction, projection images without sample are acquired with and without the X-ray beam turned on, which are referred to as flat fields (F) and dark fields (D). Based on the acquired flat and dark fields, the measured projection images (P) with sample are then normalized to new images (N) according to:<sup id="cite_ref-VanNieuwenhove_3-0" class="reference"><a href="#cite_note-VanNieuwenhove-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><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 N={\frac {(P-D)}{(F-D)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>P</mi> <mo>−</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>F</mi> <mo>−</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N={\frac {(P-D)}{(F-D)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6af260b940222b552c77a42c0a89c13588045f0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:14.318ex; height:6.509ex;" alt="{\displaystyle N={\frac {(P-D)}{(F-D)}}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Dynamic_flat_field_correction">Dynamic flat field correction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flat-field_correction&action=edit&section=3" title="Edit section: Dynamic flat field correction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While conventional flat field correction is an elegant and easy procedure that largely reduces fixed-pattern noise, it heavily relies on the stationarity of the X-ray beam, scintillator response and CCD sensitivity. In practice, however, this assumption is only approximately met. Indeed, detector elements are characterized by intensity dependent, nonlinear response functions and the incident beam often shows time dependent non-uniformities, which render conventional FFC inadequate. In synchrotron X-ray tomography, many factors may cause flat field variations: instability of the bending magnets of the synchrotron, temperature variations due to the water cooling in mirrors and the monochromator, or vibrations of the scintillator and other beamline components. The latter is responsible for the biggest variations in the flat fields. To deal with such variations, a <i><b>dynamic</b></i> <b>flat field correction</b> procedure can be employed that estimates a flat field for each individual projection. Through principal component analysis of a set of flat fields, which are acquired prior and/or posterior to the actual scan, eigen flat fields can be computed. A linear combination of the most important eigen flat fields can then be used to individually normalize each X-ray projection:<sup id="cite_ref-VanNieuwenhove_3-1" class="reference"><a href="#cite_note-VanNieuwenhove-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><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 N_{j}={\frac {P_{j}-{\bar {D}}}{{\bar {F}}+\sum _{k}w_{jk}u_{k}-{\bar {D}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>+</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munder> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>k</mi> </mrow> </msub> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{j}={\frac {P_{j}-{\bar {D}}}{{\bar {F}}+\sum _{k}w_{jk}u_{k}-{\bar {D}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3291cbc01839b06e6763d2f49216f3558a5a8e7d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:25.899ex; height:7.176ex;" alt="{\displaystyle N_{j}={\frac {P_{j}-{\bar {D}}}{{\bar {F}}+\sum _{k}w_{jk}u_{k}-{\bar {D}}}}}"></span> where </p> <ul><li><span class="mwe-math-element"><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_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e42efe207e17a74b4c17b1aa0cced7a84501bec9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.776ex; height:2.843ex;" alt="{\displaystyle N_{j}}"></span> = intensity normalized X-ray projection</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{j}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{j}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a5da6c3564a2129f714ef11acd8ba649d18e604" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.402ex; height:2.843ex;" alt="{\displaystyle P_{j}}"></span> = raw X-ray projection</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d00c359ac2602692ea5da2b035f86d6ce2455bc1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.805ex; height:2.509ex;" alt="{\displaystyle {\bar {F}}}"></span> = mean flat field image (average of flat fields)</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9837644700489d04d977da272524cd5fda36f3d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.418ex; height:2.009ex;" alt="{\displaystyle u_{k}}"></span> = k-th eigen flat field</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle w_{jk}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w_{jk}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3441353011a63d150bf9466a970d5a3f0222a75c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.43ex; height:2.343ex;" alt="{\displaystyle w_{jk}}"></span> = weight of the eigen flat field <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{k}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{k}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9837644700489d04d977da272524cd5fda36f3d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.418ex; height:2.009ex;" alt="{\displaystyle u_{k}}"></span></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {D}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>D</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {D}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a899b65dfb3ab3073b4f7f257be4491141bee64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.509ex;" alt="{\displaystyle {\bar {D}}}"></span> = mean dark field (average of dark fields)</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flat-field_correction&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Bias_frame" title="Bias frame">Bias frame</a></li> <li><a href="/wiki/Dark_frame" class="mw-redirect" title="Dark frame">Dark frame</a></li> <li><a href="/wiki/Fixed-pattern_noise" title="Fixed-pattern noise">Fixed-pattern noise</a></li> <li><a href="/wiki/Vignetting" title="Vignetting">Vignetting</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flat-field_correction&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.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}</style><div class="reflist"> <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"><style data-mw-deduplicate="TemplateStyles:r1238218222">.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("//upload.wikimedia.org/wikipedia/commons/6/65/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("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/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}}</style><cite id="CITEREFFrederic_V._HessmanEckart_Modrow2006" class="citation web cs1">Frederic V. Hessman; Eckart Modrow (2006-11-21). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20161130155351/http://www.astronomie-und-internet.de/docs/Creating%20a%20Flatfield%20Calibrating%20Image.pdf">"Creating a Flatfield Calibration Image"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://www.astronomie-und-internet.de/docs/Creating%20a%20Flatfield%20Calibrating%20Image.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2016-11-30<span class="reference-accessdate">. Retrieved <span class="nowrap">2019-10-14</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Creating+a+Flatfield+Calibration+Image&rft.date=2006-11-21&rft.au=Frederic+V.+Hessman&rft.au=Eckart+Modrow&rft_id=http%3A%2F%2Fwww.astronomie-und-internet.de%2Fdocs%2FCreating%2520a%2520Flatfield%2520Calibrating%2520Image.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlat-field+correction" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130407013841/http://www.princetoninstruments.com/cms/index.php/ccd-primer/152-flat-field-correction">"Flat Field Correction"</a>. <i>Princeton Instruments</i>. Archived from <a rel="nofollow" class="external text" href="http://www.princetoninstruments.com/cms/index.php/ccd-primer/152-flat-field-correction">the original</a> on 7 April 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">12 January</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Princeton+Instruments&rft.atitle=Flat+Field+Correction&rft_id=http%3A%2F%2Fwww.princetoninstruments.com%2Fcms%2Findex.php%2Fccd-primer%2F152-flat-field-correction&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlat-field+correction" class="Z3988"></span></span> </li> <li id="cite_note-VanNieuwenhove-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-VanNieuwenhove_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-VanNieuwenhove_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#DynFFC">Van Nieuwenhove 2015.</a></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flat-field_correction&action=edit&section=6" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Olsen, Doug.; Dou, Changyong.; Zhang, Xiaodong.; Hu, Lianbo.; Kim, Hojin.; Hildum, Edward. <a rel="nofollow" class="external text" href="http://www.mdpi.com/2072-4292/2/2/464/pdf">Radiometric Calibration for AgCam</a>; Remote Sens. 2010, 2, 464-477</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="DynFFC" class="citation journal cs1">V. Van Nieuwenhove; J. De Beenhouwer; F. De Carlo; L. Mancini; F. Marone; J. Sijbers (2015). <a rel="nofollow" class="external text" href="https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A7681">"Dynamic intensity normalization using eigen flat fields in X-ray imaging"</a>. <i>Optics Express</i>. <b>23</b> (21): 27975–27989. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2015OExpr..2327975V">2015OExpr..2327975V</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1364%2FOE.23.027975">10.1364/OE.23.027975</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/10067%2F1302930151162165141">10067/1302930151162165141</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26480456">26480456</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Optics+Express&rft.atitle=Dynamic+intensity+normalization+using+eigen+flat+fields+in+X-ray+imaging&rft.volume=23&rft.issue=21&rft.pages=27975-27989&rft.date=2015&rft_id=info%3Ahdl%2F10067%2F1302930151162165141&rft_id=info%3Apmid%2F26480456&rft_id=info%3Adoi%2F10.1364%2FOE.23.027975&rft_id=info%3Abibcode%2F2015OExpr..2327975V&rft.au=V.+Van+Nieuwenhove&rft.au=J.+De+Beenhouwer&rft.au=F.+De+Carlo&rft.au=L.+Mancini&rft.au=F.+Marone&rft.au=J.+Sijbers&rft_id=https%3A%2F%2Fwww.dora.lib4ri.ch%2Fpsi%2Fislandora%2Fobject%2Fpsi%253A7681&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFlat-field+correction" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Flat-field_correction&action=edit&section=7" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20210621124449/frigg.physastro.mnsu.edu/spect_flat.html">Flat-Field Correction</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Flat-field_correction&oldid=1256950218">https://en.wikipedia.org/w/index.php?title=Flat-field_correction&oldid=1256950218</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Optics" title="Category:Optics">Optics</a></li><li><a href="/wiki/Category:Computer_graphic_techniques" title="Category:Computer graphic techniques">Computer graphic techniques</a></li><li><a href="/wiki/Category:Astrophotography" title="Category:Astrophotography">Astrophotography</a></li><li><a href="/wiki/Category:Image_processing" title="Category:Image processing">Image processing</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 12 November 2024, at 11:13<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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