UofO- Geology 619
Electron Beam MicroAnalysisTheory and Application
Electron Probe MicroAnalysis (EPMA)
Imaging:
(Analog imaging and X-ray
mapping)
Modified from Fournelle, 2006)
“A picture is worth a thousand words”
The more we know about how images are
acquired and processed, the better we can
present research results graphically.
Additionally, 2 or 3 dimensional
information about specimens can be
extracted from some images.
Image Acquisition
• Secondary electron images
• Backscatter electron images
• X-ray maps (WDS, EDS)
– Dot maps
– Counter (pulse count) maps
• Cathodo-luminescence images
• Microscope (camera) images
Image Processing & Analysis
• Image acquisition
• Image storage
• Image defects/correction
• Image enhancement
• Segmentation and thresholding
• Processing in frequency space
• Processing binary images
• Image measurements
• Image presentation
Resources:
Software
• MicroImage (interfaces with SX51) or Probe Image (interfaces with SX100)
• Probe for EPMA (SX51/SX100 and JEOL 8900/8200 and 8500)
• Matrox Frame grabber (interfaces with SX100 video display)
• NIH/Scion Image
rsb.info.nih.gov/nih-image/more-docs/Tutorial/Contents.html
• Image-Pro and Adobe Photoshop
•Books
• The Image Processing Handbook by John C. Russ, 3rd Ed, 1999, CRC Press
(he teaches a week-long short course at North Carolina State University)
• Quick Photoshop for Research, A guide to digital imaging for Photoshop 4xd,
5x,6x,7x by Jerry Sedgewick, 2002, Kluwer Academic/Plenum Publishers
Optical scanning (Nikon slide scanner)
Use the Nikon slide scanner to scan
your entire section for:
•1. Documentation
•2. Identify regions of interest
•3. Use Click and Move feature
(image registration)
Secondary electron images
SE imaging: the signal is
from the top 5 nm in metals,
and the top 50 nm in
insulators. Thus, fine scale
surface features are imaged.
The detector is located to
one side, so there is a
shadow effect – one side is
brighter than the opposite.
Everhart-Thornley detector: low-energy
secondary electrons are attracted by +200 V
on grid and accelerated onto scintillator by
+10 kV bias; light produced by scintillator
(phosphor surface) passes along light pipe to
external photomultiplier (PM) which converts
light to electric signal. Back scattered
electrons also detected but less efficiently
because they have higher energy and are not
significantly deflected by grid potential.
(image and text from Reed, 1996, p. 37)
BSE images
BSE imaging: the signal
comes from the top ~.1 um
surface; solid-state detector is
sensitive to light (and red
LEDs). Above, 5 phases stand
out in a volcanic ash fragment
A solid-state (semi-conductor) backscattered
electron detector (a) is energized by incident high
energy electrons (~90% E0), wherein electron-hole
pairs are generated and swept to opposite poles by
an applied bias voltage. This charge is collected
and input into an amplifier (gain of ~1000). (b) It
is positioned directly above the specimen,
surrounding the opening through the polepiece. In
our BSE detector, we can modify the amplifier
gain: BSE GMIN or BSE GMAX.
Goldstein et al, 1992, Fig 4.24, p. 184
Variations on a theme
There are several alternative type SEM images sometimes found in BSE or SE
imaging: (left) channeling (BSE) and (right) magnetic contrast (SE). Fournelle has
found BSE images of single phase metals with crystalline structure shown by the
first effect, and suspect the second effect may be the cause of problems with some
Mn-Ni phases.
Crystal lattice shown above, with 2
beam-crystal orientations: (a) nonchanneling, and (b) channelling.Less
BS electrons get out in B, so darker.
From Newbury et al, 1986, Advanced Scanning Electron
Microscopy and X-ray Microanalysis, Plenum, p. 88 and 159.
EBSD*
Electron backscatter diffraction is a relatively new and specialized application
whereby a specimen (say single crystal) is tilted acutely (~70°) in an SEM with a
special detector (‘camera’). The electron beam interacts with the crystal lattice
and the lattice planes will diffract the beam, with the backscattered electrons
striking the detector, yielding sets of intersecting lines, which then can be
indexed and crystallographic data deduced.
* Also referred
to as Kossel
X-ray
diffraction,
and Kikuchi
patterns.
(Left) EBSD pattern from marcasite (FeS2) crystal. (Right) Diagram showing
formation of cone of diffracted electrons formed from a divergent point source
within a specimen.
Dingley and Baba-Kishi, 1990, Electron backscatter diffraction in the scanning electron microscope, Microscopy and Analysis, May.
BSE and SE Detectors on our
SX51/SX100
Annular
BSE
detectors
Plates for
+voltage
for SE
detector
View from inside, looking up obliquely
(image taken by handheld digital camera)
Cathodo-luminescence
This is an optical phenomenon. CL occurs in semiconductors, be they man-made
or natural (i.e., some minerals). Electrons in the valence band of these
materials are excited into the conduction band for a brief time; subsequently
these electrons recombine with the holes left in the valence band. The
energy difference is released as a photon of wavelength of light.
Two commonly used applications are
•
Locating strain (lattice mismatch) in semiconductors, and
•
Evaluating minerals for heterogeneous growth (complex history,
overgrowths, dissolution, crack infilling)
There are two distinct methods to image this effect: by SEM or microprobe, or by
a small attachment to an optical microscope (static cold cathode electron
source). Additionally, the light spectra can be quantified by a scanning
monochronometer (spectrometer).
CL captured on
color film:
CL: in living color
A
B
C
D
A: Casserite, SnO2
B: Crinoidal limestone
C: Red = dolomite,
orange = calcite; dark
grey = baddeleyite
(ZrO2)
D: St Peter Sandstone;
mature quartz with zoned
authigenic quartz
overgrowths
(from Marshall,1988, CL
of Geological Materials)
The CL emitted is of varying wavelengths (=colors), and can be captured with
the right equipment. Various “CL microscope attachments” have been built that
fit on the stage of a regular microscope; one model is the Luminoscope.
CL Microscope Attachments
Cold cathode
gun
CMAs are relatively inexpensive attachments to microscopes. A
high voltage (10-30 keV) cold cathode gun discharges electrons
in a low vacuum chamber (rough pump only). A plasma results
that provides charge neutralization (no carbon coating
necessary). A camera and/or monochrometer are attached to
acquire images and/or wavelength scans of the light.
(From Marshall, 1993,The present stat of CL attachments for optical microscopes, Scanning Microscopy, Vol 7, p. 861)
CL: colors and eV
The figure on the left demonstrates several different mechanisms
whereby photons are emitted in the process of high voltage
electrons promoting valence electrons to conduction band. The
various band gap energies with their respective wavelengths and
colors is shown to the right.
(Right image from Marshall, 1988, Fig 1.4, p. 4)
CL: defects in GaAs
These and the following
CL images are monochromatic: only the total
light intensity at each
pixel is recorded by a
photomultiplier. This is a
common (simple/cheap)
attachment for an SEM or
microprobe.
GaAs on Si for opto-electronic devices can have defects due to lattice
mismatch between the film and Si substrate. The defects are not seen in SE
image (top left). However, a CL image (bottom left) shows the areas of
reduced strain, where a monochronometer collected 800 nm light. The right
figure shows the CL spectra of strained (top) vs unstrained (bottom) material.
Peter Heard, 1996, Cathodoluminescence--Interesting phenomenon or useful technique? Microscopy and Analysis, January, p. 25-27.
CL: quartz, zircon
CL
BSE
CL
Images acquired with the Cameca CL (PM) detector. Left: quartz from Skye with
complex history of growth or re-equilibration with hydrothermal system. Trace
amounts of Al, Ti or Mn may be involved. Right: CL image of zircon from
Yellowstone tuff (false color); adjacent BSE image (no zonation obvious).
(from research of Valley, and Bindeman and Valley)
X-ray maps
Counter Maps
Dot Maps
Mg Ka (Olivines in basalt lava)
WDS (TAP)
There are two modes
of X-ray mapping: dot
(‘digital’) or counter
(pulse). The top
images are the grainy,
coarse resolution dot
maps, whereas the
bottom images are the
higher resolution
counter maps.The later
is more timely to
acquire, but is worth
the wait. Note the
WDS defocusing.
EDS
X-ray map Bragg defocussing
Low mag (63x) WDS
maps on metals:
Sp1&4=Si Ka (TAP),
Sp3&5= Fe Ka (LIF),
Sp2=Fe La (PC1); also
EDS below
Enlarged
representation of
plan view of each
spectrometer crystal
Bird’s
Eye
View of
SX51
Note large
solid angle of
EDS above
Large
Area PC1
Area of each crystal
on Rowland Circle
Mosaic Images
There are occasions where the feature you wish
to image is larger than the field of view
acquirable by the rastered beam. A complete thin
section (24x48 mm) can have a mosaic BSE
image acquired in < 1 hour (though an X-ray map
could take a week, so only smaller areas are
typically X-ray mapped.)
From Emily Johnson, UofO
This is achieved by tiling or mosaicing smaller
images together. The software calculates how
many smaller images are needed based upon the
field of view at the magnification used, drives to
the center of each rectangle, and then seemlessly
stitches the images into one whole.
The false colored BSE image of a cm-sized zoned
garnet to the right was made by many (>100) 63x
scans (each scan 1.9 mm max width).
From research of Cory Clechenko and John Valley.
X-ray maps …. time and money
Reed, 1996, Fig 6.1, p. 102
3 X-ray maps combined; each element set to a
color, and then all merged together in Photoshop.
The maps took ~8 hours to collect.
X-ray maps can provide useful information as well as attractive ‘eye candy’. However, due to
the low count rate of detected X-rays, dwell times generally need to be hundreds of milliseconds. A 512x512 X-ray map at 100 msecs takes ~8 hours to acquire. Large area maps that
combine beam and stage movement require additional ‘overhead’ (~1-10%) for stage activity.
The recent improvements to our EDS system give us more leeway, as the larger solid angle of
EDS and improved digital processing throughput lets us use 1-10 msec dwell times, as well as
allowing low mag images (no need to worry about Rowland circle defocusing).
X-ray maps … Fully quantitative
The X-ray maps usually acquired are
quantitative, although not to the
maximum extent possible, i.e., the
background is not subtracted, nor is
the matrix correction applied. These
operations can be applied, to make
the X-ray map fully quantitative, as
the adjacent 5 maps are – to save
time in this case, backgrounds were
not acquired, rather the MAN
background technique was applied,
and peaks were counted for 10 secs,
within the Probe for EPMA software,
and the results were then graphed
with Surfer.
MicroImage digital scan
BSE images: 2 ways
Matrox Intellicam framegrabber
There are two different ways to save video (BSE, SE, CL) image files: (right) the
MicroImage software takes control of the beam and scans the image, writing all the
pixels to a file; (left) the native Cameca scan on the right Sony monitor is stored by
the Matrox framegrabber. Both images here have 442x103 pixels, but the Matrox is
much quicker (10 seconds, vs >4 minutes for the MicroImage), though the frame
grab is limited to small regions that can be encompassed at 63x (~1.9 mm wide).
The Matrox image is 768 x 576, whereas the MicroImage can be any dimension
and can also be combined with stage movement to give large mosaic images.
Image Acquisition
What is Image depth?
– 8 bit (SE,BSE,CL) 256 intensity (‘gray’) levels (2^8)
–16 bit means 65536 intensity (‘gray’) levels
• Image size
– mm in x and y (rectangular vs square; depends on machine/software)
– pixels in x and y
• Image resolution-- is it sufficient for the need? mm/pixel + total pixels + final printed
size ==> will determine whether or not it is pixelated
• Time for acquisition: SE,BSE,CL is rapid; X-rays require much longer time
• EDS spectra: sometimes a picture of two contrasting spectra is useful.
• Adjust conditions (brightness, contrast) for optimal image quality BEFORE you
acquire. Be sure not to oversaturate the brightest phases.
• Record conditions (keV, nA, A to D conversions or pixel dwell time, mag) in your lab
notebook (not all software records these parameters like Probe for EPMA)
Adjust gain and brightness Before BSE Acquistion
Using MicroImage
First try: contrast could be better.
Need to tweak gain…
We want to do some rapid scans
and watch the histogram improve.
Set to small size image and to
continuous image refreshing …
While beam is scanning,
adjust contrast (“gain”) as
well as brightness (“offset”) if
necessary to achieve desired
contrast and brightness. Then
set to final image size (512 or
anything) and collect 1 image.
SX100 Optical Microscope Images
The Cameca Cassegrainian objective lens optics are excellent,
as seen in these images (left: reflected; right: transmitted
light) captured with the Matrox framegrabber. There are
occasional instances where there is value in preserving the
reflected light image (e.g., locations of beam – preserved as
carbon contamination spots; cathodoluminescence).
(scale = 400x, ~300 microns across)
Image Storage/Modification
• Software should save file automatically (not always the case); always modify
copies, not originals
• Use clear, descriptive names for your images
• Original format sometimes is not a choice by user (i.e.,proprietary format may
be default, or quasi-generic with a header taking up the first ~1000 bytes)
• If format choice is possible, TIFF is a good choice for storage; keeps maximum
amount of information (do not use compression for portability)
• You particularly want to keep the original 16 bit data of the X-ray image, to be
able to extract actual data. However, to open images in some software you need
to rescale (“normalize”) to 8 bits.
• It is acceptable to reformat as smaller jpeg format for use in presentations (e.g.,
powerpoint, illustrator) and publications
Some Image Formats
• TIFF: currently most universal, well suited for
large images. Lossless* compression (image does
not degrade with repeated opening/closing).
Photoshop gives option of LZW compression, best
not used. (Tagged Information File Format)
• JPEG: Name refers to a compression method
that is Lossy*: there is some loss of exact pixel
values; square subregions are processed with
‘cosine transform’ operation; compression of 10:1
to 100:1 is possible (Joint Photography Experts
Group)
• Photoshop (psd): layered image; must flatten if
to be used elsewhere.
• Adobe Acrobat (pdf): non-Lossy compression
Graphic Converter (Mac) is a
‘Swiss Army tool’ program that
can open about any format you
can think of, and save to
anything else. (Share/cheapware)
Lossy compression throws away some data to better compress the image size; different schemes
focus on different features, i.e. JPEG is based on fact that human eye is more sensitive to changes
in brightness than in color, and more sensitive to gradations of color than to rapid variations within
that gradation. JPEG keeps most brightness info and drops some color info.
Image Defects
• Correct conditions beforehand! It is best not to modify your images.
• Two possible defects in BSE images:
– horizontal lines in BSE images comes from 50 cycle AC of lights, esp at
high contrast. Best to turn off the light
– uneven shading in large area mosaic images (bright upper left corner) due
to BSE detector picking up light from stage LEDs. It may be possible to
apply a correction in Photoshop. Alternatively put a dummy thin section
there and image thin sections in other positions in holder.
• SE images have brighter right side due to detector being there. As far
as I know, there is nothing we can do about it.
•Sometimes artifacts occur. If small, they do not detract: just include
make a note. If large, best to acquire another image.
Image Enhancement - by Machine
• A major negative feature of images
can be ‘noise’, i.e., the features are
not as sharp as they could/should be.
The prime reason is the scan rate is
very fast and the time paid to each
pixel is ~microseconds. The top
image is at the normal “mode TV”
rate.
• This can be addressed by acquiring
multiple images and averaging
them, to reduce the random noise.
Or better to utilize a scanning mode
that goes slower, acquires longer
counts on each pixel, averaging each
pixel on the fly. The bottom image
is at the “Nice image” (sx>mode
user 1 1 line) rate, taking 10
seconds.
Image Enhancement Done Later
• Histogram normalization: crunching from 16 to 8 bit. This usually is a
first step for visual presentation purposes, as most software packages
only operate on 8 bit images. However, this does not apply for
measuring absolute values of pixel intensity, such as X-ray counts.
• Brightness/contrast (and importantly, gamma): adjusting histogram
“levels”
• Histogram equalization: divide intensities into equal/weighted number
of categories
• Kernels/Rank operators: modify each pixel by some operation upon it
and nearest neighbors
• Image math: background subtraction; ratio 2 elements
• Processing in frequency space (Fourier transform): removing periodic
noise
• Applying alternate lookup tables (LUTs) for improved presentation
Intensities, Histograms, LUTs
LUT
All images we are concerned with (e.g., BSE,
CL, X-ray) contain one channel of information,
where each constituent pixel has a value from 0 to
255 (28) or 65535 (216). These can be ordered in a
histogram of intensities, with the spread defining
the contrast, and the absolute values defining how
bright or dark the image is. These INPUT
intensities are mapped onto an OUTPUT grayscale
or color table known as a Look Up Table (LUT).
The transfer function is known as gamma. A
gamma of 1.00 indicates a linear relationship
between pixel intensities and grayscales. A gamma
>1 is a non-linear function where the darker pixels
are made preferentially brighter, whereas gamma
<1 has the very bright pixels preferentially
darkened somewhat.
Adjusting only “brightness” and “contrast”
controls (highlighted in many image packages)
generally give poorer results compared to tweaking
the gamma as part of histogram adjustment.
Photoshop
Brightness and Contrast: or How I
Adjust
Learned to Love the Histogram Levels
The original histogram is too bunched
up – poor contrast. Notice the top
(input) left and right sliders are not
close to the min/max brightness.
g
So we move the top (input) left and
right sliders in to the min/max
brightness levels.And we move the
bottom (output) sliders to 10 and 254.
A last (important) step is to adjust the
gamma, the top middle slider. To left
(higher) increases brightness of mid
grays (normally the best option).
Gamma Processing
Goldstein et al, 1992, Fig. 4.53, p;. 238
The traditional imaging medium,
photographic paper, has a non-linear
response to light exposure through the
overlying negative. Skilled darkroom
technique used this to bring out subtle
features in the shadows, or enhance bright
features that tend to wash out.
For digital images, such nonlinear
processing, gamma processing, provides
selective contrast enhancement at
Signal out  K  Signaling
either the black or white end of the gray scale, while preventing saturation or
clipping of the resulting image. The signal transfer function is defined as
where g is an integer (1, 2, 3, 4) or a fraction (1/2, 1/3, 1/4) and K is a linear
amplification constant. For g=2, a small range of input signals at the dark end of
the gray scale are distributed over a larger range of output gray levels, enhancing
the contrast here; signals at the white end are compressed into fewer gray levels.
For g =1/2, expansion occurs at the bright end, enhancing bright features.
Histogram Levels & Equalization
One alternative/complementary procedure
to manual adjust of brightness/contrast is
equalization, which can be applied to the
raw image. It stretches out the histogram,
with the distinction that it separates the
intensities into weighted bins, so that if
there are a lot of pixels piled in a few bins,
these bins (intensities) will have a larger
number of new intensities mapped onto
them – i.e., there will be “spaces” between
them on the histogram, meaning those
intensities will be stretched out. At the same
time, bins with not many pixels in them may
be squeezed together, as there is less total
information relative to the high populated
pixels.
Russ, 1999, Fig. 4.11, p. 238.
Kernels/Rank Operators
Noisy images sometimes occur for a variety of reasons, some avoidable,
some not. Noise refers to some randomness added to pixel intensity
values, with noise worse where count rates are low. The simplest
procedure to reduce noise is to take the average of the pixel and its
surrounding neighbors, and put this new average value in as the new
pixel intensity. You can create a matrix with values for the coefficient by
which you weigh (multiply) each pixel and adjoining neighbors. For
example, one such matrix could be
1
1
1
and
1
2
1
1
1
1
another 2
4
2
1
1
1
1
2
1
These are called kernels, or rank operators.
Say there was a ‘noisy’ pixel with a value of 100, when all the adjoining
values were 10. The first kernel would return a new value of 20, and the
‘noise’ would be drastically reduced.
Neighborhood averaging
Results of applying one
kernel:
a) A noisy original image,
b) each 4x4 block of pixels
is averaged ([less noise,
but too coarse),
c) each pixel replaced by
average of 3x3 neighborhood ([ pretty nice),
d) each pixel replaced by
average of 11x11
neighborhood ([ less
noise, but too big, causing
blurring)
Russ, 1999, The Image Processing Handbook (3rd edition), Fig 3.3, p. 166
Image Math
The values of each pixel can be
operated on (e.g. multiplied, divided,
added or subtracted relative to some
constant), or different elements of the
same image can be operated on. The
most common operations are division
and subtraction. Two elements that vary
together (e.g. Ca and Na in feldspar) can
be divided to yield an optimized
zonation map. Subtraction is useful for
removing the continuum contribution,
Goldstein et al, 1992, Fig 10.6, p. 535
particularly for minor or trace elements.
Above is an example of false compositional contrast, an artifact of the background
being a function of Z (MAN). Specimen is Al-Cu eutectic; X-ray maps are (a) Al,
(b) Cu, (c) Sc. The contrast in (c) suggests Sc is present in the Cu-rich phase.
However, there is no Sc, only the background in the Cu-rich phase is elevated
relative to the background in the Al-rich phase. If image math is used – subtracting
an additional X-ray map acquired at an off-peak (background) Sc position – a true
map of Sc is seen in (d), where it is clear there is no Sc present.
Another ‘mining’ of Xray images utilizes
both the elemental
information as well as
the spatial (X,Y)
coordinates.
“Micro-Image
includes a unique
histogram-histogram
plotting feature for
unambiguous
identification of
numerous phases. In
this screen shot, the
lower right image
displays a histogramhistogram plot which
shows the presence of
at least 6 phases
including a solid
solution
2 Dimensional Histograms
component. The upper right image display a "traceback" of
one selected phase cluster which provides black and white
mask of spatial information.”
(From the Advanced Microbeam)
Processing in Frequency Space
Examples from Russ, Image ProcessingTool Kit Tutorial, Part 4, Fig 4.C.1, page 8.
If there periodic noise in an image (e.g.,
the 2 frequencies on top of the clown
image), the image can be processing by
a Fast Fourier Transform (FFT) of it, as
is done in the small subregion in the left
frame. The 2 frequencies of noise show
up as 2 pairs of dots (the clown features
are the NS, EW lines and center dot). If
4 small solid circles are placed upon the
4 dots and then the resulted inverted, a
mask is made (center), which is then
subtracted from the left FFT image.
Then an inverse FFT operation is done
on this image, and the result is the right
image, where the noise is removed.
These operations must be done on
square images, using NIH Image or
Russ’s Image Toolkit with Photoshop.
Look Up Tables
The mapping of intensites (e.g., BSE voltages or X-ray counts) to
a displayed image uses a Look Up Table, the most common one
being a gray scale. The default with MicroImage is the thermal
LUT. There are many others, and you can make up your own. It is
a good idea to display the LUT as a bar next to the image if they
might be some confusion as to what color means what intensity.
Gray scale
Some LUTs
from NIH
Image
Fire 1
Fire 2
Rainbow
Ice
Processing binary images
When we acquire images, we are in essence acquiring information about
features – defined as compositions, or sizes or shapes, of phases or boundaries
or whatever. Our eyes + brains are sorting out features constantly, such as in the
process of sorting out the black lines and shapes against the white background
here, translating into words and then into meanings.
We can apply similar binary operations to our images – focusing on one
characteristic and ignoring the rest for the moment. This is known as
thresholding, where we set upper and lower thresholds of intensity (e.g., BSE)
and then define as a feature (e.g., one phase) the intensities that fall in between.
Software can then be applied to such a binary image to do many things, e.g.,
count the number of pixels (thus, determine phase area).
Boolean (logical) operations can be done on sets or images, taking two element
maps and create a third one that shows the regions where features containing
both elements are present, or only one without the other. Morphological
operations can be done to modify individual pixels within an image–apply
erosion and dilation operators to separate touching phases and then count total
number of separate phases or measure the dimensions or orientation of each.
Thresholding
NIH Image provides an easy way to threshold
Cr-spinel
57208/442225=12.9%,
images, shown here. You double click the little
Mg-rich clay 215634/442225= 48.8%,
up/down icon (6th from top, right column)
Diopside
153904/442225=34.8%,
Cracks
14947/442225=3.4%
which gives you a red sliding palette that you
Total (without fudging!)
= 99.9%
use to color in the phase you are selecting. You
then click Measure under the Analyze menu
and the total number of pixels is shown in the
Presently, you should be able to get a
Info Box. If you do this for all the phases
total of 100 ±5% easily.
Making an Image
into a Binary
Besides being able to determine area
percentages, you use the thresholded
region to make a binary image of that one
feature/phase. In NIH Image it is simple:
Process > Binary > Make Binary. The
result of that operation is shown in the
center image. Note that there are some
“outliers”, mainly in cracks. You need to
make some reasoned judgements about
whether or not to include them. Here, I
decided not to include them, so I then did 2
consecutive “erode” operations (under
Binary menu), and then 2 consecutive
“dilate” operations, to yield the final image
on the right. Of course there could well be
cases where you would not do the erodes.
Boolean* Operations
Binary images consist of groups of
pixels selected on the basis of some
common property. Logical or Boolean
operations can be applied, pixel by
pixel, to sets of images. The logical
operations typically are AND, OR,
XOR (exclusive or), NOT. The logical
operator looks at each pixel to see if it
is “on” or “off”. AND: requires both
pixels be ON to be ON in the result.
OR: if either pixel is ON, it will be ON
in the result. XOR: turns a pixel ON in
the result only if it is ON in only one,
not both, of the images. All 3 require 2
images. The NOT operator only
requires one, and it reverses the
meaning of each pixel.
* From the symbolic logic developed by George Boole, British
mathematician, 1815-1864
Original X-ray maps (top): c) Si, d) Fe These
have been smoothed and thresholded to make
binary images. The thresholded Fe image is
shown below left (a), with Fe black. The Fe
and Si images have been combined as Fe AND
NOT Si, to yield the right (b) image of the Feoxide phase, excluding the Fe-silicate phase.
Russ, The Image Processing Handbook, 1999, Figs 7.5, 7.6, p. 436.
Color Superposition of Elemental Maps
Si=Green, Fe=Red, Ti=Blue
Si=Red, Ca=Green, K=Blue
While not strictly a Boolean operation
(not binary images), by defining each
elemental map with hues of either R, G
or B, and then combining (flattening)
the image in Photoshop, phase
information can be extracted.
Si=Red, Fe=Green, Al=Blue
Images from research of Josh Kearns
and Jill Banfield: sand from Tanana
River, central Alaska
Erosion/Dilation
Sometimes you want to
measure features but the
binary image isn’t
unambiguous, as shown in
the example to the right.
Here, you are attempting to
measure the area of the
middle gray phase (a), but
when you threshold it, there
are outlines of the bright
phase (b). The outline is only
1 pixel wide, so you can
apply an erode operation,
which will remove the
outlines that you want to get
rid of, but also it will remove
the outer layer of pixels from
all of the features you are
interested in (c). No problem.
Just apply the dilate operation, and where there are
any existing pixels, there will be added a layer of
pixels (d), and now you can do your measurement.
Russ, The Image Processing Handb ook, 1999, Fig. 7.36, p. 462
Image measurements (particle size/shape)
NIH Image 1.63
ImageJ 1.28
Features in images lend themselves to measurement without too
much difficulty
Related Topics:
Diffraction —
X-rays and Electrons
Information from Diffraction:
There are several other techniques that utilize
concepts studied in this class, that may be of
use in geologic or material science research:
Diffraction — using either electron or x-ray
sources—for determining crystallographic
information
This can be either macro- or micro-analytical
(vis a vis the volumes being studied)
Diffraction—Defined*
Diffraction is the spreading of waves around obstacles. It
takes place with sound; with electromagnetic radiation, such as
light, X-rays, and gamma rays; and with such fast moving
particles such as atoms, neutrons, and electrons, which show
wavelike properties.
It is the result of interference
(i.e., when waves are
superimposed, they may
reinforce or cancel each other
out) and is most pronounced
when the wavelength of the
radiation is comparable to the
linear dimensions of the
obstacle.
* Encyclopedia Britannica, 1974
Coherent Scattering
When x-rays interact with matter, the dominant effect is
scattering. Considering x-rays as waves we deal with coherent
scattering (rather than as particles, where we deal with
incoherent scattering).
With coherent scattering, photons scatter with no loss of
energy, and give rise to scattered radiation of the same
wavelength.
Classical physical theory says that when electromagnetic
radiation (waves) hit electrons, the electron begins to vibrate
and become the source of a wave whose phase is determined by
that of the incident wave. All the electrons in the material that
the wave meets then form a group of coherent sources whose
radiation can interfere constructively or destructively.
This discussion (above) is taken mainly from Andre Guinier’s X-ray Cryallographic
Technology, a 1952 translation of his 1945 classic. Some of the following material is taken
from Jim Connolly’s highly recommended UNM CXRD Class Notes.
Constructive Interference
The distance between atoms in solids are of the same order
size as the x-ray wavelength, and therefore interference
phenomena are observed:
Instead of feeble energy being distributed throughout space,
it is concentrated in certain directions. These concentrations are
diffraction patterns whose particular geometries are functions of
the positions of the atoms in the material (the crystallography of
the solid) and the wavelength of the x-rays.
There is another kind of scattering, incoherent (Compton) which is easiest
understood in terms of the particle nature of photons: the photon deviates
from path and electron takes from it part of its energy. The scattered photon
has lost energy (so has a higher wavelength), and there is no relationship
between the phases of the 2 waves. There is no interference and of little
significance here (though it is for XRF) and we will not consider it further.
Geometry of Diffraction”
“Point Source”
The electrons within an atom
will scatter x-rays, and because
the electrons are “everywhere”
within the atom, a secondary
point source of scattered
radiation appears to originate
from the center of the atom (i.e.,
the nucleus).
Geometry of Diffraction:
“Row source”
Consider a one-dimensional
row of equally spaced atoms.
Each atom in the path of the xray beam (wave) can be
considered to be the center of
radiating, spherical wave shells
of x-rays.
Most scattered x-rays destructively interfere, i.e. cancel out. In
certain directions, however, “in phase” scattered x-rays will add
together to form a new wave. Since wavelengths of l, 2 l and 3 l
will all add to produce a different wavefront, these are called first-,
second- and third-order wavefronts.
Diffraction Methods
There are several standard experimental techniques used in Xray diffraction studies:
•
Laue method: a single crystal is held stationary in a beam
of polychromatic x-ray radiation. The crystal diffracts the
discrete values of l for which planes exist of spacing d and
incidence angle q;
•
Rotating-crystal method: a single crystal is rotated about a
fixed axis in a beam of monchromatic x-rays. The variation
in q brings different atomic planes into position for
reflection;
•
Powder (Debye-Scherrer-Hull) method: a finely powdered
sample is placed in a holder in a monochromatic x-ray
beam, with the angle q gradually changing due
synchronous movement of holder and detector. Assuming
random orientation of the tiny crystallites, there will be
diffraction off of different atomic planes at specific angles.
X-ray Diffraction Lab
Contact: Lev Zakarhov (lev@uoregon.edu)
• Single crystal and powder x-ray diffractometers
Also: Surface Analytical Facility:
Contact: Steve Golledge (golledge@uoregon.edu)
• Kratos Hsi monochromatized X-ray Photoelectron Spectrometer (XPS)
• ION Time-of-Flight Secondary Ion Mass Spectrometry (Tof-SIMS)
•
(with polyatomic Bi source and depth profiling capability)
• Nanoscope IIIa Atomic Force Microscopy (AFM)
• Woollam M44 spectroscopic ellipsometer
• Phi Model 670 Scanning Auger Microscope
XRD Powder Patterns
Set up the machine to scan a range of q (here, 4-70°); typical time
is ~60 minutes; reconnaissance scans can be much quicker. Then
need to process data (model the background, subtract it) and
proceed to software identification -->
XRD Powder Patterns
-> Identification of natural or synthetic crystalline
materials using software (here, MDI’s “Jade” program)
Other Powder XRD
Applications
• Crystallographic structural analysis and unit-cell calculations
• Quantitative determination of amounts of different phases (in
multi-phase mixture) by peak-ratio calculations
• Quantitative determination of phases by whole-pattern
(Rietveld) refinement
• Determination of crystallite size from peak broadening
• Determination of crystallite shape from peak symmetry
• Study of thermal expansion by using in-situ heating stage.
EBSD
Electron backscatter diffraction (EBSD) is a technique for determining
crystallographic information of submicron regions of flat polished samples.
It has made possible studies of microtextures, phase identification (of
polymorphs), grain boundary distribution, and deformation microstructures.
EBSD is also known by the names backscatter Kikuchi diffraction BKD, or
electron backscatter pattern EBSP. The phenomenon has been known since
1928 by Kikuchi, who noted ‘remarkable lines’ resulting from electron
diffraction thru a thin mica crystal. Two research groups (in UK) started
working on EBSD ~1973, and it has only been commercially available
since 1994.
In many cases it replaces more time-consuming/difficult TEM or XRD,or
possibly electron channeling studies, with the benefit of SEM’s point by
point high spatial resolution (<1 mm) together with its ability to scan large
areas (~cm). It is relatively inexpensive ($50-100K), in being an add-on
attachment to a previously existing SEM.
EBSD
Kikuchi recognized the importance of a divergent electron
beam being diffracted -- how the spreading of the incident
beam (by inelastic scattering in upper surface of sample)
Orientation mapping (OIM, orientation imaging
microscopy)
Phase identification by step by step deduction of pattern point
group symmetry, though some problems; other technique is to
determine approx value of unit cell volume from measured
lattice spacing and interplanar angles, together with EDS,
searching a database for possible matches, then match angles
EBSD
The sample is tilted steeply (70°, so beam is
20° to sample) which enhances the number of
BSEs able to undergo diffraction and escape
the surface. The HV electrons are scattered by
the electrons of the atoms in the top unit cells
of the material, scattering from electrons in
crystallographic planes producing intersecting
bands imaged by film or a phosphor screen
immediately adjacent.
The pattern and bands provide information
about the crystal structure:
• Symmetry of crystal lattice
• Width and intensity of bands are a measure
of the plane spacing (and unit volume)
• Angles between bands are related to the
angles between planes in the lattice.
EBSD Specimen Preparation
Specimen prep important:
•Surface must have damaged layer removed, e.g.
with colloidal silica (which is also chemical etching
action)
•Carbon coat must be very very thin (~10Å)
From
Microscopy
Today,
Jan/Feb 1993
Some References
Introduction to X-Ray Powder Diffraction, by Jim Connolly (notes for U NM
EPS400-002, epswww.unm.edu/xrd)
X-Ray Crystallographic Technology by Andre Guinier (English Translation, 1952)
Modern Powder Diffraction by D. L. Bish and J. E. Post (eds), Mineralogical
Society of America Reviews in Mineralogy, Vol 20, 1989
Electron Backscatter Diffraction in Materials Science, Edited by Adam J. Schwartz,
Mukul Kumar and Brent L. Adams, Kluwer/Plenum, 2000, ISBN 0-306-46487-X
(25 articles)
An Atlas of Electron Backscatter Diffraction Patterns by D. J. Dingley, K. BabaKishi, and V. Randle, 1994, Institute of Physics Publishing.