Diagnostic and quality-assurance tools for low-contrast images obtained from array detectors

D. Brooke Hatfield; Bill R. Sandel

doi:10.1364/AO.32.005056

Applied Optics
Vol. 32,
Issue 26,
pp. 5056-5070
(1993)
•https://doi.org/10.1364/AO.32.005056

Diagnostic and quality-assurance tools for low-contrast images obtained from array detectors

D. Brooke Hatfield and Bill R. Sandel

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D. Brooke Hatfield and Bill R. Sandel, "Diagnostic and quality-assurance tools for low-contrast images obtained from array detectors," Appl. Opt. 32, 5056-5070 (1993)

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Abstract

We investigate methods of estimating a background image frame for subtraction from a data frame for use when a more suitable measured background frame is not available. We define background as any signal component that is not attributable to the phenomenon currently under investigation. We describe a technique that is based on pixel-by-pixel least-squares regression of images for computing a background frame from available data. We argue that the same technique can be a useful quality-assurance tool for evaluating instrument performance. For example, it can help to separate image structure resulting from the reading process from structure resulting from the characteristics of the detector itself. We demonstrate that background estimation can be nontrivial by comparing the results of different background estimation procedures by using data obtained from a CCD array detector. We investigate the temperature-dependent contributions of the detector and readout electronics to the total signal as a demonstration of the diagnostic capabilities of least-squares image regression.

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A0 _ij , b0 _ij	Y intercept of the (i, j)th pixel.
a1 _ij , b1 _ij	Slope of the (i, j)th pixel.
bias	Region of the image created by overscanning of the detector beyond the defined number of pixels.
column	Vertical axis of a gray-scale plot; parallel transport axis.
f _ijk:k _′	Scalar factor for the (i, j)th pixel, found by division of image k by image k′.
fixed pattern	Component(s) that are invariant in pixel coordinates.
i, j	Pixel coordinates for a row and a column (serial and parallel), respectively.
k	Index of a given image in a set of images.
row	Horizontal axis of a gray-scale plot; serial trans port axis.
signal	Data or contribution to data obtained from a detector or detector–readout train that may be at tributable to one or more components, which may be described by the following:
analytical	Component(s) attributable to the phenomenon under investigation.
background	Component(s) not attributable to the phenomenon under investigation.
dark	Component(s) attributable to effects independent of illumination, which are usually reproducible under dark conditions.
induced	Component(s) that are induced by external influences such as strong electromagnetic fields.
offset	Invariant, or constant, component(s).
readout	Component(s) attributable to the electronics associated with transduction, amplification, and digitization of the signal obtained from the detector.
S _ijk	Residual signal component(s) of the (i, j)th pixel of image k after subtraction of the estimated background signal.
t _k	Exposure time in seconds of image k.
X _k	Independent variable in the regression for image k.
Y _ijk	Dependent variable in the regression for the(i, j)th pixel of image k.

Image	Pixels N	Method A		Method B

		Mean	σ	Mean	σ
32-s exposure
Raw	229,320	196.7	4.2	196.7	4.2
Raw	100	193.7	2.5	193.7	2.5
−a0 _ij	229,320			94.8	6.6
−a0 _ij	100			92.1	4.6
f _ijk:k _′	229,320	1.19	0.02	1.50	0.10
	100	1.19	0.02	1.50	0.06
S _ijk	299,320	−0.04	25.4	5.99	27.5
	100	−13.9	18.5	5.62	19.4
42-s exposure
Raw	229,320	219.3	16.4	219.3	16.4
Raw	100	215.6	2.77	215.6	2.77
−a0 _ij	229,320			117.4	21.4
−a0 _ij	100			114.0	5.0
f _ijk:k _′	229,320	1.33	0.10	1.85	0.34
f _ijk:k _′	100	1.32	0.02	1.85	0.06
S _ijk	299,320	1.56	113	12.00	79.6
S _ijk	100	−25.5	19.1	8.09	20.5

A0 _ij , b0 _ij	Y intercept of the (i, j)th pixel.
a1 _ij , b1 _ij	Slope of the (i, j)th pixel.
bias	Region of the image created by overscanning of the detector beyond the defined number of pixels.
column	Vertical axis of a gray-scale plot; parallel transport axis.
f _ijk:k _′	Scalar factor for the (i, j)th pixel, found by division of image k by image k′.
fixed pattern	Component(s) that are invariant in pixel coordinates.
i, j	Pixel coordinates for a row and a column (serial and parallel), respectively.
k	Index of a given image in a set of images.
row	Horizontal axis of a gray-scale plot; serial trans port axis.
signal	Data or contribution to data obtained from a detector or detector–readout train that may be at tributable to one or more components, which may be described by the following:
analytical	Component(s) attributable to the phenomenon under investigation.
background	Component(s) not attributable to the phenomenon under investigation.
dark	Component(s) attributable to effects independent of illumination, which are usually reproducible under dark conditions.
induced	Component(s) that are induced by external influences such as strong electromagnetic fields.
offset	Invariant, or constant, component(s).
readout	Component(s) attributable to the electronics associated with transduction, amplification, and digitization of the signal obtained from the detector.
S _ijk	Residual signal component(s) of the (i, j)th pixel of image k after subtraction of the estimated background signal.
t _k	Exposure time in seconds of image k.
X _k	Independent variable in the regression for image k.
Y _ijk	Dependent variable in the regression for the(i, j)th pixel of image k.

Image	Pixels N	Method A		Method B

		Mean	σ	Mean	σ
32-s exposure
Raw	229,320	196.7	4.2	196.7	4.2
Raw	100	193.7	2.5	193.7	2.5
−a0 _ij	229,320			94.8	6.6
−a0 _ij	100			92.1	4.6
f _ijk:k _′	229,320	1.19	0.02	1.50	0.10
	100	1.19	0.02	1.50	0.06
S _ijk	299,320	−0.04	25.4	5.99	27.5
	100	−13.9	18.5	5.62	19.4
42-s exposure
Raw	229,320	219.3	16.4	219.3	16.4
Raw	100	215.6	2.77	215.6	2.77
−a0 _ij	229,320			117.4	21.4
−a0 _ij	100			114.0	5.0
f _ijk:k _′	229,320	1.33	0.10	1.85	0.34
f _ijk:k _′	100	1.32	0.02	1.85	0.06
S _ijk	299,320	1.56	113	12.00	79.6
S _ijk	100	−25.5	19.1	8.09	20.5

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Equations (21)

Applied Optics