Chemistry Reference
In-Depth Information
where F(x, y) is the flux (photons/s) intercepted by the pixel and B is the brightness of
the source (photons/s per mrad
2
). The ratio of the flux in pixel P(x, y) to the
center pixel P(0, 0) is then given as
D
3
R
3
¼
D
3
Fðx
;
yÞ
3=2
¼ cos
3
w
0Þ
¼
ð4
:
33Þ
Fð0
;
ðD
2
þx
2
þ y
2
Þ
where w is the angle between the X-rays to the pixel P(x, y) and the line from S to the
detector in perpendicular direction. It can be seen that the greater the sample-
to-detector distance, the smaller the difference between the center pixel and the
edge pixel in terms of the flux from the homogeneous source. This is the major reason
that the data frame collected at short sample-to-detector distance has a higher contrast
between the edge and center.
Geometric distortion may also appear with an area detector in which the detector
gain varies from pixel-to-pixel or a pixel position deviates from the specified pixel
position (spatial distortion). The detector gain variation can be corrected by a flood
field correction with a homogeneous radiation source. The flood field algorithm is
dependent on the type of detector. After the flood field correction, all pixels should
have the same counts when exposed to same radiation. The spatial distortion can be
corrected by applying the inverse distortion field to the raw data frame. Geometric
distortion is also referred to as the spatial linearity, which should not be confused
with the linearity of the counting curve of the detector or a pixel. The relationship
between measured pixel position and the true pixel position can be determined by
measuring the centroid position of all pinholes on a fiducial plate to generate a
lookup tables so that the accurate position of each pixel can be calculated. More
details on the flood field correction and spatial correction are covered in Chapter 6 on
data treatment.
4.5.2 Spatial Resolution of Area Detectors
The spatial resolution of an area detector is determined by two parameters. One is
the pixel size. A pixel is a single point information element in a digital graphic
image. The term“pixel” is an abbreviation of “pix” and “el” frompicture element. In
principle, each pixel is not really a dot, nor a square, but an abstract sample point. For
example, in a picture image, a pixel is determined by its position in the image and the
content of the pixel can be a single variable, such as the brightness in a black-white
image, or three variables, such as red, green, and blue in a color image. In a two-
dimensional X-ray diffraction frame, which is equivalent to a picture image, each
pixel contains the X-ray intensity collected by the detector corresponding to the
pixel element. The pixel size of an area detector can be determined or related to the
actual feature sizes of the detector structure or artificially determined by the readout
electronics or data acquisition software. Many detector techniques allow multiple
settings for variable pixel size. In the diffraction frame, the pixel size is given by the
actual detector active area and the number of pixels in the frame. For example, when
a Hi-Star (MWPC) detector of 10.5 cm in diameter is used to collect a diffraction
