Flat-field correction - Revision history

InternetArchiveBot: Rescuing 1 sources and tagging 0 as dead.) #IABot (v2.0.9.5

2024-04-15T10:40:33Z

Rescuing 1 sources and tagging 0 as dead.) #IABot (v2.0.9.5

← Previous revision		Revision as of 10:40, 15 April 2024
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	Flat fielding refers to the process of compensating for different [[Gain (electronics)\|gains]] and [[dark current (physics)\|dark currents]] 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 [[systematic error]].		Flat fielding refers to the process of compensating for different [[Gain (electronics)\|gains]] and [[dark current (physics)\|dark currents]] 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 [[systematic error]].

	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.<ref>{{Cite web\|url=http://www.astronomie-und-internet.de/docs/Creating%20a%20Flatfield%20Calibrating%20Image.pdf\|title=Creating a Flatfield Calibration Image \|author=Frederic V. Hessman \|author2=Eckart Modrow \|date=2006-11-21\|website=\|access-date=2019-10-14}}</ref> Once the images are acquired, processing can begin.		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.<ref>{{Cite web\|url=http://www.astronomie-und-internet.de/docs/Creating%20a%20Flatfield%20Calibrating%20Image.pdf\|title=Creating a Flatfield Calibration Image\|author=Frederic V. Hessman\|author2=Eckart Modrow\|date=2006-11-21\|website=\|access-date=2019-10-14\|archive-date=2016-11-30\|archive-url=https://web.archive.org/web/20161130155351/http://www.astronomie-und-internet.de/docs/Creating%20a%20Flatfield%20Calibrating%20Image.pdf\|url-status=dead}}</ref> Once the images are acquired, processing can begin.

	A flat-field consists of two numbers for each pixel, the pixel's gain and its dark current (or [[dark frame]]). 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 [[neutral density filter]]s to give input/output signal information and applying a least squares fit to obtain the values for the dark current and gain.		A flat-field consists of two numbers for each pixel, the pixel's gain and its dark current (or [[dark frame]]). 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 [[neutral density filter]]s to give input/output signal information and applying a least squares fit to obtain the values for the dark current and gain.

Trappist the monk: cite repair;

2023-09-14T15:39:58Z

cite repair;

JimRenge: moved source

2023-09-09T16:27:36Z

moved source

← Previous revision		Revision as of 16:27, 9 September 2023
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	==References==		==References==
	{{reflist}}		{{reflist}}
⚫	*Olsen, Doug.; Dou, Changyong.; Zhang, Xiaodong.; Hu, Lianbo.; Kim, Hojin.; Hildum, Edward. [http://www.mdpi.com/2072-4292/2/2/464/pdf Radiometric Calibration for AgCam]; Remote Sens. 2010, 2, 464-477

	==Further reading==		==Further reading==
		⚫	*Olsen, Doug.; Dou, Changyong.; Zhang, Xiaodong.; Hu, Lianbo.; Kim, Hojin.; Hildum, Edward. [http://www.mdpi.com/2072-4292/2/2/464/pdf Radiometric Calibration for AgCam]; Remote Sens. 2010, 2, 464-477
	*{{cite journal \| authors = V. Van Nieuwenhove, J. De Beenhouwer, F. De Carlo, L. Mancini, F. Marone, and J. Sijbers \| doi = 10.1364/OE.23.027975 \| pmid = 26480456 \| title = Dynamic intensity normalization using eigen flat fields in X-ray imaging \| journal = Optics Express \| volume = 23 \| issue = 21 \| date = 2015 \| pages = 27975–27989 \|ref=DynFFC\|bibcode = 2015OExpr..2327975V \| url = https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A7681 \| hdl = 10067/1302930151162165141 \| hdl-access = free }}		*{{cite journal \| authors = V. Van Nieuwenhove, J. De Beenhouwer, F. De Carlo, L. Mancini, F. Marone, and J. Sijbers \| doi = 10.1364/OE.23.027975 \| pmid = 26480456 \| title = Dynamic intensity normalization using eigen flat fields in X-ray imaging \| journal = Optics Express \| volume = 23 \| issue = 21 \| date = 2015 \| pages = 27975–27989 \|ref=DynFFC\|bibcode = 2015OExpr..2327975V \| url = https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A7681 \| hdl = 10067/1302930151162165141 \| hdl-access = free }}

JimRenge: Restored revision 1168347175 by OlliverWithDoubleL (talk): I see no improvement

2023-08-24T17:25:29Z

Restored revision 1168347175 by OlliverWithDoubleL (talk): I see no improvement

← Previous revision		Revision as of 17:25, 24 August 2023
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	<math display="block"> N = \frac{(P-D)}{(F-D)}</math>		<math display="block"> N = \frac{(P-D)}{(F-D)}</math>

	== Dynamic flat field correction ~~method~~ ==		== Dynamic flat field correction ==

	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, ~~but~~, 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 '''''dynamic''''' '''flat field correction''' 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:<ref name="VanNieuwenhove" />		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 '''''dynamic''''' '''flat field correction''' 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:<ref name="VanNieuwenhove" />
	<math display="block">N_j = \frac{P_j - \bar D}{\bar F + \sum_k w_{jk}u_k - \bar D}</math>		<math display="block">N_j = \frac{P_j - \bar D}{\bar F + \sum_k w_{jk}u_k - \bar D}</math>
	where		where

212.174.75.78: /* Dynamic flat field correction */

2023-08-24T10:51:15Z

Dynamic flat field correction

← Previous revision		Revision as of 10:51, 24 August 2023
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	<math display="block"> N = \frac{(P-D)}{(F-D)}</math>		<math display="block"> N = \frac{(P-D)}{(F-D)}</math>

	== Dynamic flat field correction ==		== Dynamic flat field correction method ==

	While ~~coventional~~ 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 '''''dynamic''''' '''flat field correction''' 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:<ref name="VanNieuwenhove" />		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, but, 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 '''''dynamic''''' '''flat field correction''' 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:<ref name="VanNieuwenhove" />
	<math display="block">N_j = \frac{P_j - \bar D}{\bar F + \sum_k w_{jk}u_k - \bar D}</math>		<math display="block">N_j = \frac{P_j - \bar D}{\bar F + \sum_k w_{jk}u_k - \bar D}</math>
	where		where

212.174.75.78: /* Dynamic flat field correction */

2023-08-24T10:50:29Z

Dynamic flat field correction

← Previous revision		Revision as of 10:50, 24 August 2023
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	== Dynamic flat field correction ==		== Dynamic flat field correction ==

	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 '''''dynamic''''' '''flat field correction''' 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:<ref name="VanNieuwenhove" />		While coventional 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 '''''dynamic''''' '''flat field correction''' 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:<ref name="VanNieuwenhove" />
	<math display="block">N_j = \frac{P_j - \bar D}{\bar F + \sum_k w_{jk}u_k - \bar D}</math>		<math display="block">N_j = \frac{P_j - \bar D}{\bar F + \sum_k w_{jk}u_k - \bar D}</math>
	where		where

OlliverWithDoubleL at 07:17, 2 August 2023

2023-08-02T07:17:41Z

← Previous revision		Revision as of 07:17, 2 August 2023
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			{{Short description\|Digital imaging calibration technique}}
	{{Distinguish\|text=[[Field flattener lens]], which improves focus uniformity}}		{{Distinguish\|text=[[Field flattener lens]], which improves focus uniformity}}
	[[File:Woy Woy Channel - Vignetted.jpg\|thumb\|This picture is darker at the edges. This variation is called [[vignetting]], and can be corrected by selectively brightening the perimeter of the image.]]		[[File:Woy Woy Channel - Vignetted.jpg\|thumb\|This picture is darker at the edges. This variation is called [[vignetting]], and can be corrected by selectively brightening the perimeter of the image.]]

Fgnievinski at 01:20, 1 August 2023

2023-08-01T01:20:05Z

← Previous revision		Revision as of 01:20, 1 August 2023
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	{{Distinguish\|text=[[~~Petzval~~ ~~field~~ ~~curvature~~]], which ~~refers to~~ focus uniformity}}		{{Distinguish\|text=[[Field flattener lens]], which improves focus uniformity}}
	[[File:Woy Woy Channel - Vignetted.jpg\|thumb\|This picture is darker at the edges. This variation is called [[vignetting]], and can be corrected by selectively brightening the perimeter of the image.]]		[[File:Woy Woy Channel - Vignetted.jpg\|thumb\|This picture is darker at the edges. This variation is called [[vignetting]], and can be corrected by selectively brightening the perimeter of the image.]]

	'''Flat-field correction''' (FFC) is a ~~technique used to improve quality in~~ [[digital imaging]]. It ~~cancels~~ the ~~effects of~~ image ~~artifacts caused by variations in the~~ pixel-to-pixel sensitivity ~~of the detector~~ and by distortions in the optical path. It is a standard calibration procedure in everything from personal [[digital camera]]s to large telescopes.		'''Flat-field correction''' ('''FFC''') is a [[digital imaging]] technique to mitigate the [[image detector]] pixel-to-pixel sensitivity and distortions in the [[optical path]]. It is a standard calibration procedure in everything from personal [[digital camera]]s to large telescopes.

	==Overview==		==Overview==

JimRenge: + Further reading section

2023-07-21T12:26:52Z

+ Further reading section

← Previous revision		Revision as of 12:26, 21 July 2023
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	{{reflist}}		{{reflist}}
	*Olsen, Doug.; Dou, Changyong.; Zhang, Xiaodong.; Hu, Lianbo.; Kim, Hojin.; Hildum, Edward. [http://www.mdpi.com/2072-4292/2/2/464/pdf Radiometric Calibration for AgCam]; Remote Sens. 2010, 2, 464-477		*Olsen, Doug.; Dou, Changyong.; Zhang, Xiaodong.; Hu, Lianbo.; Kim, Hojin.; Hildum, Edward. [http://www.mdpi.com/2072-4292/2/2/464/pdf Radiometric Calibration for AgCam]; Remote Sens. 2010, 2, 464-477

			==Further reading==
	*{{cite journal \| authors = V. Van Nieuwenhove, J. De Beenhouwer, F. De Carlo, L. Mancini, F. Marone, and J. Sijbers \| doi = 10.1364/OE.23.027975 \| pmid = 26480456 \| title = Dynamic intensity normalization using eigen flat fields in X-ray imaging \| journal = Optics Express \| volume = 23 \| issue = 21 \| date = 2015 \| pages = 27975–27989 \|ref=DynFFC\|bibcode = 2015OExpr..2327975V \| url = https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A7681 \| hdl = 10067/1302930151162165141 \| hdl-access = free }}		*{{cite journal \| authors = V. Van Nieuwenhove, J. De Beenhouwer, F. De Carlo, L. Mancini, F. Marone, and J. Sijbers \| doi = 10.1364/OE.23.027975 \| pmid = 26480456 \| title = Dynamic intensity normalization using eigen flat fields in X-ray imaging \| journal = Optics Express \| volume = 23 \| issue = 21 \| date = 2015 \| pages = 27975–27989 \|ref=DynFFC\|bibcode = 2015OExpr..2327975V \| url = https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A7681 \| hdl = 10067/1302930151162165141 \| hdl-access = free }}

193.62.223.243 at 08:27, 21 July 2023

2023-07-21T08:27:43Z

← Previous revision		Revision as of 08:27, 21 July 2023
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	{{Distinguish\|text=[[Petzval field curvature]], which refers to focus uniformity}}		{{Distinguish\|text=[[Petzval field curvature]], which refers to focus uniformity}}
	[[File:Woy Woy Channel - Vignetted.jpg\|thumb\|~~The~~ ~~brightness~~ variation ~~due~~ to [[vignetting]], ~~as shown here,~~ can be corrected by selectively brightening the perimeter of the image.]]		[[File:Woy Woy Channel - Vignetted.jpg\|thumb\|This picture is darker at the edges. This variation is called [[vignetting]], and can be corrected by selectively brightening the perimeter of the image.]]

	'''Flat-field correction''' (FFC) is a technique used to improve quality in [[digital imaging]]. It cancels the effects of image artifacts caused by variations in the pixel-to-pixel sensitivity of the detector and by distortions in the optical path. It is a standard calibration procedure in everything from personal [[digital camera]]s to large telescopes.		'''Flat-field correction''' (FFC) is a technique used to improve quality in [[digital imaging]]. It cancels the effects of image artifacts caused by variations in the pixel-to-pixel sensitivity of the detector and by distortions in the optical path. It is a standard calibration procedure in everything from personal [[digital camera]]s to large telescopes.

← Previous revision		Revision as of 07:17, 2 August 2023
Line 1:		Line 1:
			{{Short description\|Digital imaging calibration technique}}
	{{Distinguish\|text=[[Field flattener lens]], which improves focus uniformity}}		{{Distinguish\|text=[[Field flattener lens]], which improves focus uniformity}}
	[[File:Woy Woy Channel - Vignetted.jpg\|thumb\|This picture is darker at the edges. This variation is called [[vignetting]], and can be corrected by selectively brightening the perimeter of the image.]]		[[File:Woy Woy Channel - Vignetted.jpg\|thumb\|This picture is darker at the edges. This variation is called [[vignetting]], and can be corrected by selectively brightening the perimeter of the image.]]

← Previous revision		Revision as of 15:39, 14 September 2023
Line 8:		Line 8:
	Flat fielding refers to the process of compensating for different [[Gain (electronics)\|gains]] and [[dark current (physics)\|dark currents]] 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 [[systematic error]].		Flat fielding refers to the process of compensating for different [[Gain (electronics)\|gains]] and [[dark current (physics)\|dark currents]] 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 [[systematic error]].

	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.<ref>{{Cite web\|url=http://www.astronomie-und-internet.de/docs/Creating%20a%20Flatfield%20Calibrating%20Image.pdf\|title=Creating a Flatfield Calibration Image\|~~last~~=Hessman & Modrow\|date=2006-11-21\|website~~=\|url-status=live\|archive-url=\|archive-date~~=\|access-date=2019-10-14}}</ref> Once the images are acquired, processing can begin.		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.<ref>{{Cite web\|url=http://www.astronomie-und-internet.de/docs/Creating%20a%20Flatfield%20Calibrating%20Image.pdf\|title=Creating a Flatfield Calibration Image \|author=Frederic V. Hessman \|author2=Eckart Modrow \|date=2006-11-21\|website=\|access-date=2019-10-14}}</ref> Once the images are acquired, processing can begin.

	A flat-field consists of two numbers for each pixel, the pixel's gain and its dark current (or [[dark frame]]). 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 [[neutral density filter]]s to give input/output signal information and applying a least squares fit to obtain the values for the dark current and gain.		A flat-field consists of two numbers for each pixel, the pixel's gain and its dark current (or [[dark frame]]). 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 [[neutral density filter]]s to give input/output signal information and applying a least squares fit to obtain the values for the dark current and gain.
Line 18:		Line 18:
	* ''D'' = dark field or dark frame		* ''D'' = dark field or dark frame
	* ''m'' = image-averaged value of (''F''−''D'')		* ''m'' = image-averaged value of (''F''−''D'')
	* ''G'' = Gain = <math>m\over(F-D)</math><ref>{{cite web \|url=http://www.princetoninstruments.com/cms/index.php/ccd-primer/152-flat-field-correction \|~~title~~=Princeton Instruments ~~\|~~ Flat Field Correction ~~\|website=www.princetoninstruments.com~~ \|access-date=12 January 2022 \|archive-url=https://web.archive.org/web/20130407013841/http://www.princetoninstruments.com/cms/index.php/ccd-primer/152-flat-field-correction \|archive-date=7 April 2013 ~~\|url-status=dead~~}}</ref>		* ''G'' = Gain = <math>m\over(F-D)</math><ref>{{cite web \|url=http://www.princetoninstruments.com/cms/index.php/ccd-primer/152-flat-field-correction \|website=Princeton Instruments \|title=Flat Field Correction \|access-date=12 January 2022 \|archive-url=https://web.archive.org/web/20130407013841/http://www.princetoninstruments.com/cms/index.php/ccd-primer/152-flat-field-correction \|archive-date=7 April 2013 }}</ref>

	In this equation, capital letters are 2D matrices, and lowercase letters are scalars. All matrix operations are performed element-by-element.		In this equation, capital letters are 2D matrices, and lowercase letters are scalars. All matrix operations are performed element-by-element.
Line 52:		Line 52:
	==Further reading==		==Further reading==
	*Olsen, Doug.; Dou, Changyong.; Zhang, Xiaodong.; Hu, Lianbo.; Kim, Hojin.; Hildum, Edward. [http://www.mdpi.com/2072-4292/2/2/464/pdf Radiometric Calibration for AgCam]; Remote Sens. 2010, 2, 464-477		*Olsen, Doug.; Dou, Changyong.; Zhang, Xiaodong.; Hu, Lianbo.; Kim, Hojin.; Hildum, Edward. [http://www.mdpi.com/2072-4292/2/2/464/pdf Radiometric Calibration for AgCam]; Remote Sens. 2010, 2, 464-477
	*{{cite journal \| ~~authors~~ = V. Van Nieuwenhove, J. De Beenhouwer, F. De Carlo, L. Mancini, F. Marone~~, and~~ J. Sijbers \| doi = 10.1364/OE.23.027975 \| pmid = 26480456 \| title = Dynamic intensity normalization using eigen flat fields in X-ray imaging \| journal = Optics Express \| volume = 23 \| issue = 21 \| date = 2015 \| pages = 27975–27989 \|ref=DynFFC\|bibcode = 2015OExpr..2327975V \| url = https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A7681 \| hdl = 10067/1302930151162165141 \| hdl-access = free }}		*{{cite journal \|author=V. Van Nieuwenhove \|author2=J. De Beenhouwer \|author3=F. De Carlo \|author4=L. Mancini \|author5=F. Marone \|author6=J. Sijbers \| doi = 10.1364/OE.23.027975 \| pmid = 26480456 \| title = Dynamic intensity normalization using eigen flat fields in X-ray imaging \| journal = Optics Express \| volume = 23 \| issue = 21 \| date = 2015 \| pages = 27975–27989 \|ref=DynFFC\|bibcode = 2015OExpr..2327975V \| url = https://www.dora.lib4ri.ch/psi/islandora/object/psi%3A7681 \| hdl = 10067/1302930151162165141 \| hdl-access = free }}

	== External links ==		== External links ==