- Email: [email protected]
The mapping of unresolved spatial structure in STIM images
378
Nuclear Instruments and Methods in Physics Research B54 (1991) 378-382 North-Holland
The mapping of unresolved spatial structure in STIM images G. Bench a, H.W. Lefevre b and G.J.F. Legge a a Micro Analytical Research Centre, School of Physics, University of Melbourne,
ParkviNe, Victoria, 3052, Australia
b Physics Department, University of Oregon, Eugene, OR 97403, USA
With scanning transmission ion microscopy (STIM), images are formed by taking an “average” of the energies of a number of ions within a pixel. Moments can be calculated by summing various powers of energy difference from this average. This paper will explore the use of moments in STIM imaging. Moments from both median and mean averaging have been calculated and compared to theoretical calculations for a beam scanned across an edge. The use of moments to emphasize regions of unresolved structure and to display areas of complexity within an object has been examined with a 0.220 pm latex sphere as an example. In the presence of noise from slit scattered ions and incomplete charge collection within the surface barrier detector, the optimal moment has been found to be the second moment of ions whose energy is greater than the “average” value. Examples of moments emphasizing regions of unresolved structure in animal tissue are presented.
1. Introduction Several STIM techniques [l-5] have been reported whereby images are formed from measured energy losses of individual ions at each incident beam location. The energy loss of each ion essentially gives a measurement of the area1 electron density at each picture element or pixel. In principle, images can be obtained from only one ion per pixel; however, for high-definition images several particles are required. This can result in a spectrum of trans~tt~ particles associated with each pixel. This spectrum can contain much detail due to unresolved spatial structure and other forms of noise. In forming an image, a value of energy loss is derived from the transmitted ions accumulated at each pixel. Two of the more common strategies which are used to choose a value of energy loss when several particles of different energies are detected at each pixel are mean energy and median filtering [l]. With mean energy averaging the measured values of energy loss at each pixel are averaged. As outlying events can have a large effect on the value of the mean a window can be set to exclude extraneous events reducing noise. With median filtering, the energy losses in each pixel are ordered into increasing energy loss and the central value is chosen. With both these image-forming techniques, only one value is derived even though most of the transmitted ions contain useful information. Spectral complexities in each pixel that could indicate spatially unresolved electron density variations are lost in the final image. Overley et at. [t] suggested a possible way to portray spectral complexity while still collecting around 10 ions per pixel. They suggested that anomalous values of 0168-583X/91/$03.50
energy loss in each pixel could justifiably be discarded if they were too far from the mean/median. The remaining values could be used to construct a primary image. Moments of the remaining values could be calculated by summing various powers of energy difference from the mean/median. Images constructed from these moments could then indicate regions of spectral complexity in the object. This paper will explore the use of moments in STIM imaging using the Melbourne microprobe to make measurements on a copper edge, a 0.220 pm latex sphere on nylon foil and a self-supporting mouse villus tip.
2. Definition of moments We define to be
Moment(x,
the moment
y) =mP(x,
of a pixel at position
y) = i=t
n
(x, y)
> (1)
where MP is the value of the moment, n is the number of transmitted ions in the pixel, E,, is the derived value of the mean/median energy loss in the pixel, E, is the energy loss of each individual ion and p is the integer valued order of the moment. Thus p = 1 signifies the first moment, p = 2 signifies the second moment, etc. From eq. (1) it is obvious that for mean energy averaging m’(x,
y) = 0 v x, y
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
(2)
G. Bench et al. / Unresolved spatial structure
whilst for median filtering this is not necessarily case. It is also apparent that
the
mJ’(x,
(3)
y) 2 0 V x, y and even p
for both median filtering and mean energy averaging, i.e. even moments only contain information on the magnitude of the spectral complexity in a pixel. As moments emphasize outlying values of energy loss, the sign of odd moments can provide details as to whether the energy loss of small unresolved features is greater or less than the mean/median value. Further, if the sign of successive odd moments changes for a particular pixel this can give information as to the magnitude of the deviation in energy loss of small features from the mean/median value. Thus odd moments can provide structural information that may not be obtained from a mean, median or even moment image. In this paper we will concentrate on the lower-order moments. Higher-order moments, although they can show complementary information and regions of spectral complexity in greater contrast, are not significantly different in concept from the lower moments. In addition, in the presence of even a small amount of noise, image clarity and definition can be poor due to the greater effect outlying events have on the value of higher-order moments. To determine whether the majority of noise in an image comes from ions whose energy loss is greater or less than the mean/median value the second moment was further refined. The upper second moment at (x, y ) is defined as
n+
c (E: - Ed2 M2+(X,
y)
=
j=l
n ’
(4)
where m2+ is the value of the upper second moment, E;’ and n+ refer to the energy loss and number of ions whose energy loss is greater than the mean/median energy loss. The lower second moment of a pixel is
ii
m2-(X, Y)=
-Ed2
(K
‘=l
n
(5)
where me2 is the value of the lower second moment, E; and n- refer to the energy loss and number of ions whose energy loss is less than the mean/median energy loss.
3. Moments across an edge As a simple contrived example to illustrate moments a line scan across a copper edge was performed with a 2 MeV focused alpha-particle beam. The copper edge had
379
a varying thickness to the transmitted beam of 1100 + 600 keV. Transmitted particles were collected in a silicon surface barrier charged particle detector of energy resolution 30 keV for 2 MeV alpha-particles. This detector subtended a half angle of 24 mrad and was placed at O” to the target. The scan was continued until each of the 121 pixels in the 3.17 urn scan had at least 14 events. As the edge was not uniformly thick and to simplify the analysis of the data, events whose energies fell within a window of half-width equal to twice the FWHM of the full energy peak and centred at 2 MeV were assigned the energy loss value 0. Events whose energies were less than events in this window were assigned the energy loss value 1. No events fell outside these two domains. Any ion passing through the edge should have an energy loss of 1, while full energy events should have no energy loss. Noise from sources such as slit scattering may still exist, but noise from energy straggling and detector resolution will almost be eliminated. We will further assume that the edge is ideal in that it is perfectly straight. Fig. la shows the mean and median values of energy loss as the beam is scanned over the edge. The median filter, as Overley et al. noted, sharply defines the location of the edge [l] to within a pixel and effectively eliminates noise. The mean energy image is noisier as it is influenced more by outlying events. The smooth curve through the mean energy points is a calculated fit for an ideal edge using a Gaussian profile for the beam spot. Assuming the spot to be Gaussian, a FWHM of 0.31 pm is inferred from the fit. Fig. lb shows m2, m2+, and m2-, for mean energy averaging. Fig. lc shows m’, m2, m2+, rnzP and m3 for median filtering across the edge. The curves through the data points correspond to the theoretical value of the particular moment assuming the beam profile is Gaussian. As the pixel size is 0.0262 urn, compared with the beam FWHM of 0.31 urn, several energy loss values deviant from the mean/median value are found for pixels in the vicinity of the edge. These outlying values give rise to the moments across the edge. For the median filtered moments m1 and m3 will be identical in this case. It is also evident that, like the median, these moments can localize the position of the edge to within a pixel; however they are noisier than the median filter as they do not discard outlying events. Conversely, the mean energy moments do not localize the position of the edge as sharply as the median moments. Only even powered (with the exception of m2+ and m2-) moments can have a maxima at the location of the edge. Also, in this example, the magnitudes of the maxima are not as great as for the corresponding median moments. This example shows that moments of even simple objects can be quite complex and the type of moment X. STIM
380
G. Bench et al. / Unresolved spatial structure
used can significantly alter the image produced. The user has to be aware of the properties of different moments before a proper interpretation of the image can be made.
c 0.80
’
1
1 .oo
’
a
z 9
0.60 & f5 5 0.40
1 .o
3.0
2.0 Position
Fig. 2. Comparison of the median energy loss image of a 0.220 pm diameter latex sphere on a thin nylon foil, in (a), with m* in (b), m ‘+ in (c) and m2- In (d). The vertical scales in all four plots vary but each plot consists of 50 contours evenly spaced. Tbe scan size is 0.96 X 0.99 pm.
(Fm)
4. Moments of a latex sphere
0.25
As a second example of moments a study of a 0.220 pm diameter latex sphere on a thin nylon foil is presented. The beam species and detector geometry are the same as for the previous example. The beam spot size was calculated to be 0.11 + 0.02 pm [5]. Fig. 2a shows a contour map of the median filter of all the ions in the dataset. The z range displayed varies from an energy loss of 33 to 67 keV. The position of the sphere is sharply defined and it has a FWHM of 0.16 k 0.03 pm.
0 1.60
1.80 Position
I
-0.50-
I
I
,
I
1.60
2.00 (pm)
I
2.00 1.80 Position (pm)
2.20
I
I
, -
2.20
Fig. 1. (a) Energy loss vs beam location for a line scan across a copper edge. Mean energy loss is plotted as the square data points whereas the median is plotted as triangles. The median has been displaced upwards 0.1 energy loss units for clarity. (b) Average energy loss moments, from the mean energy loss data in (a), m2 (solid squares), m2+ (solid triangles) and m*(open circles). The solid lines represent the theoretical curves for each moment assuming the beam profile is Gaussian. (c) Median moments, from the median data in (a), m’ (open inverted triangles), m2 (solid squares), m2+ (solid triangles), rn2- (open circles) and m3. For this dataset m’ and m3 are identical and so only m 1 is drawn. m2 has been displaced upwards 0.1 units, m ‘+ has been displaced upwards 0.2 units and m *- has been displaced upwards 0.3 units for clarity. The solid lines once again represent the theoretical curves for each moment assuming the beam profile is Gaussian.
G. Bench et al. / Unresolved spatial structure
Moment images m2, m2’, and m2were constructed using this median image from ions whose energies were within the energy window 1873 to 2000 keV. Ions outside this energy window made up less than 2% of the total number of collected events. Maps of the distribution of these ions did not indicate any spatial structure within statistics and so they were discarded. Fig. 2b shows the second moment, m2, for which the z range varies from 40 to 524 keV2. The location of the latex sphere can be identified; however, it is not as sharply defined as in the median image as outlying events are included in the calculation of the moment. Noise spikes caused by highly deviant values of energy loss in some pixels are evident. Fig. 2c shows the upper second moment, rnzl-. for which the z range varies from 29 to 362 keV’. rnzt forms a craterlike structure in the vicinity of the sphere. Noise is once again evident in the image and in the majority of cases it occurs in the same locations as for m2.
Fig. 2d shows the lower second moment, rn’for which the z range varies from 9 to 292 keV2. Noise in this image is substantially reduced in comparison with the other moment images. This moment also produces an image most similar to the median image. The position of the latex sphere is even more sharply defined than in fig. 2a, the latex sphere has a FWHM of 0.14 i 0.03 urn. displays the latex sphere with much greater m ‘contrast than the median image. The peak to average background ratio for the latex sphere is a factor of 9.5
381
greater for the m2- image. Even if we take the square root of the rnzp values to convert the units to the same dimensions used in the median image the peak to average background ratio is a factor of 2.2 greater for the m2image. The contrast is greater as the sphere’s radius is of similar size to the beam diameter and as a result the sphere’s shape is unresolved, whereas area1 density variations in the nylon foil are small in comparison. Analogous results were obtained from the use of mean energy averaging moments taken of the latex sphere with m2 and rn2+ noisier than m2-. These moments of the latex sphere indicate that the majority of noise in moment images comes from ions whose energy loss is greater than the mean/median value in a pixel. Sources of this noise are likely to be slit scattered ions, ions scattered off residual gas molecules in the vacuum and pulse height defects in the detection of particles. As m2- is the only moment that excludes these sources of noise it is the preferable lower-order moment to use. Similar refinements to higher-order moments can be made but these will give greater emphasis to the more deviant values of energy loss in a pixel.
5. Applications of moments When a microprobe is used for biological analysis, much emphasis is placed on the identification of features associated with elemental localizations within a
Fig. 3. (a) Median filtered STIM image of an unstained freeze-dried cryosection (4 pm thick) of mouse ileum showing the tip of one villus with other villi on either side. The image consists of 32 grey scales and shows epithelial cells around the edge of the tip, a goblet cell, lamina propria, microvilli brush border and other features. (b) The same dataset as in (a), but this time the image shows structure identified with the lower second moment, m2-. The contrast of such features as the brush border is much greater. X. STIM
382
G. Bench et al. / Unresolved spatial structure
sample. STIM offers an imaging technique based on area1 density that can be used to help identify features that may be hard to image using electron or optical techniques, particularly if the sample cannot be stained. Fig. 3a is a greyscale plot formed from the median energy loss of all the ions collected in a 2 MeV alphaparticle scan of an unstained freeze-dried cryosection of ileum tissue from a mottled mouse. The image is of dimensions 68 X 68 urn and was obtained with a spatial resolution of 100 nm although the pixel size shown here is 0.25 pm. Considerable structure can be seen in the image, and in many places the edges of the villi show a faint indication of the brush border which is more dense than neighbouring tissue. The brush border consists of densely packed microvilli of approximate diameter 0.1 pm and length 2 urn. From this knowledge one would expect that a spectrum of particles associated with a pixel on the brush border would coniain much detail due to unresolved structure resulting in a wide range of energy losses. Such data should show large contrast when plotted as a moment. Fig. 3b shows the lower second moment, m2-, of the median image. The moment was calculated using ions whose energies are between 1500 and 2030 keV. This window was selected using a similar criterion as for the window used to form the moments of the latex sphere. This figure shows the brush border and other features in much greater contrast than in the median image. The applications of STIM and moments are not limited to biological specimens, but this area may see most use because the thin specimens are transparent to the beam and frequently contain structure extending to
near the molecular level. Moments, as they can clearly demarcate features of spectral complexity, are a useful tool for the identification of features within a sample.
6. Conclusion When a mean/median STIM image is formed from a sample only one value is derived at each pixel, although the majority of ions collected in a pixel contain useful information. Moments provide a simple but effective means of displaying this spectral complexity in a pixel and can indicate regions of unresolved electron density variations in a sample. In so doing they provide an informative complement to a mean/median image.
Acknowledgements The authors in preparation ileum tissue.
wish to thank Dr B.J. Kirby for his help and identification of features in the
References PI J.C. Overley, R.M.S. Schofield, J.D. MacDonald and H.W.
Lefevre, Nucl. Instr. and Meth. B30 (1988) 337.
PI J.C. Overley, R.C. Connolly, G.E. Sieger, J.D. MacDonald and H.W. Lefevre, Nucl. Instr. and Meth. 218 (1983) 43. [31 B.E. Fischer, Nucl. Instr. and Meth. BlO/ll (1985) 693. [41 R.M. Sealock, D.N. Jamieson and G.J.F. Legge, Nucl.
Instr. and Meth. B29 (1987) 557. [51 G. Bench and G.J.F. Legge, Nucl. Instr. and Meth. B40/41
(1989) 655.
Nuclear Instruments and Methods in Physics Research B54 (1991) 378-382 North-Holland
The mapping of unresolved spatial structure in STIM images G. Bench a, H.W. Lefevre b and G.J.F. Legge a a Micro Analytical Research Centre, School of Physics, University of Melbourne,
ParkviNe, Victoria, 3052, Australia
b Physics Department, University of Oregon, Eugene, OR 97403, USA
With scanning transmission ion microscopy (STIM), images are formed by taking an “average” of the energies of a number of ions within a pixel. Moments can be calculated by summing various powers of energy difference from this average. This paper will explore the use of moments in STIM imaging. Moments from both median and mean averaging have been calculated and compared to theoretical calculations for a beam scanned across an edge. The use of moments to emphasize regions of unresolved structure and to display areas of complexity within an object has been examined with a 0.220 pm latex sphere as an example. In the presence of noise from slit scattered ions and incomplete charge collection within the surface barrier detector, the optimal moment has been found to be the second moment of ions whose energy is greater than the “average” value. Examples of moments emphasizing regions of unresolved structure in animal tissue are presented.
1. Introduction Several STIM techniques [l-5] have been reported whereby images are formed from measured energy losses of individual ions at each incident beam location. The energy loss of each ion essentially gives a measurement of the area1 electron density at each picture element or pixel. In principle, images can be obtained from only one ion per pixel; however, for high-definition images several particles are required. This can result in a spectrum of trans~tt~ particles associated with each pixel. This spectrum can contain much detail due to unresolved spatial structure and other forms of noise. In forming an image, a value of energy loss is derived from the transmitted ions accumulated at each pixel. Two of the more common strategies which are used to choose a value of energy loss when several particles of different energies are detected at each pixel are mean energy and median filtering [l]. With mean energy averaging the measured values of energy loss at each pixel are averaged. As outlying events can have a large effect on the value of the mean a window can be set to exclude extraneous events reducing noise. With median filtering, the energy losses in each pixel are ordered into increasing energy loss and the central value is chosen. With both these image-forming techniques, only one value is derived even though most of the transmitted ions contain useful information. Spectral complexities in each pixel that could indicate spatially unresolved electron density variations are lost in the final image. Overley et at. [t] suggested a possible way to portray spectral complexity while still collecting around 10 ions per pixel. They suggested that anomalous values of 0168-583X/91/$03.50
energy loss in each pixel could justifiably be discarded if they were too far from the mean/median. The remaining values could be used to construct a primary image. Moments of the remaining values could be calculated by summing various powers of energy difference from the mean/median. Images constructed from these moments could then indicate regions of spectral complexity in the object. This paper will explore the use of moments in STIM imaging using the Melbourne microprobe to make measurements on a copper edge, a 0.220 pm latex sphere on nylon foil and a self-supporting mouse villus tip.
2. Definition of moments We define to be
Moment(x,
the moment
y) =mP(x,
of a pixel at position
y) = i=t
n
(x, y)
> (1)
where MP is the value of the moment, n is the number of transmitted ions in the pixel, E,, is the derived value of the mean/median energy loss in the pixel, E, is the energy loss of each individual ion and p is the integer valued order of the moment. Thus p = 1 signifies the first moment, p = 2 signifies the second moment, etc. From eq. (1) it is obvious that for mean energy averaging m’(x,
y) = 0 v x, y
0 1991 - Elsevier Science Publishers B.V. (North-Holland)
(2)
G. Bench et al. / Unresolved spatial structure
whilst for median filtering this is not necessarily case. It is also apparent that
the
mJ’(x,
(3)
y) 2 0 V x, y and even p
for both median filtering and mean energy averaging, i.e. even moments only contain information on the magnitude of the spectral complexity in a pixel. As moments emphasize outlying values of energy loss, the sign of odd moments can provide details as to whether the energy loss of small unresolved features is greater or less than the mean/median value. Further, if the sign of successive odd moments changes for a particular pixel this can give information as to the magnitude of the deviation in energy loss of small features from the mean/median value. Thus odd moments can provide structural information that may not be obtained from a mean, median or even moment image. In this paper we will concentrate on the lower-order moments. Higher-order moments, although they can show complementary information and regions of spectral complexity in greater contrast, are not significantly different in concept from the lower moments. In addition, in the presence of even a small amount of noise, image clarity and definition can be poor due to the greater effect outlying events have on the value of higher-order moments. To determine whether the majority of noise in an image comes from ions whose energy loss is greater or less than the mean/median value the second moment was further refined. The upper second moment at (x, y ) is defined as
n+
c (E: - Ed2 M2+(X,
y)
=
j=l
n ’
(4)
where m2+ is the value of the upper second moment, E;’ and n+ refer to the energy loss and number of ions whose energy loss is greater than the mean/median energy loss. The lower second moment of a pixel is
ii
m2-(X, Y)=
-Ed2
(K
‘=l
n
(5)
where me2 is the value of the lower second moment, E; and n- refer to the energy loss and number of ions whose energy loss is less than the mean/median energy loss.
3. Moments across an edge As a simple contrived example to illustrate moments a line scan across a copper edge was performed with a 2 MeV focused alpha-particle beam. The copper edge had
379
a varying thickness to the transmitted beam of 1100 + 600 keV. Transmitted particles were collected in a silicon surface barrier charged particle detector of energy resolution 30 keV for 2 MeV alpha-particles. This detector subtended a half angle of 24 mrad and was placed at O” to the target. The scan was continued until each of the 121 pixels in the 3.17 urn scan had at least 14 events. As the edge was not uniformly thick and to simplify the analysis of the data, events whose energies fell within a window of half-width equal to twice the FWHM of the full energy peak and centred at 2 MeV were assigned the energy loss value 0. Events whose energies were less than events in this window were assigned the energy loss value 1. No events fell outside these two domains. Any ion passing through the edge should have an energy loss of 1, while full energy events should have no energy loss. Noise from sources such as slit scattering may still exist, but noise from energy straggling and detector resolution will almost be eliminated. We will further assume that the edge is ideal in that it is perfectly straight. Fig. la shows the mean and median values of energy loss as the beam is scanned over the edge. The median filter, as Overley et al. noted, sharply defines the location of the edge [l] to within a pixel and effectively eliminates noise. The mean energy image is noisier as it is influenced more by outlying events. The smooth curve through the mean energy points is a calculated fit for an ideal edge using a Gaussian profile for the beam spot. Assuming the spot to be Gaussian, a FWHM of 0.31 pm is inferred from the fit. Fig. lb shows m2, m2+, and m2-, for mean energy averaging. Fig. lc shows m’, m2, m2+, rnzP and m3 for median filtering across the edge. The curves through the data points correspond to the theoretical value of the particular moment assuming the beam profile is Gaussian. As the pixel size is 0.0262 urn, compared with the beam FWHM of 0.31 urn, several energy loss values deviant from the mean/median value are found for pixels in the vicinity of the edge. These outlying values give rise to the moments across the edge. For the median filtered moments m1 and m3 will be identical in this case. It is also evident that, like the median, these moments can localize the position of the edge to within a pixel; however they are noisier than the median filter as they do not discard outlying events. Conversely, the mean energy moments do not localize the position of the edge as sharply as the median moments. Only even powered (with the exception of m2+ and m2-) moments can have a maxima at the location of the edge. Also, in this example, the magnitudes of the maxima are not as great as for the corresponding median moments. This example shows that moments of even simple objects can be quite complex and the type of moment X. STIM
380
G. Bench et al. / Unresolved spatial structure
used can significantly alter the image produced. The user has to be aware of the properties of different moments before a proper interpretation of the image can be made.
c 0.80
’
1
1 .oo
’
a
z 9
0.60 & f5 5 0.40
1 .o
3.0
2.0 Position
Fig. 2. Comparison of the median energy loss image of a 0.220 pm diameter latex sphere on a thin nylon foil, in (a), with m* in (b), m ‘+ in (c) and m2- In (d). The vertical scales in all four plots vary but each plot consists of 50 contours evenly spaced. Tbe scan size is 0.96 X 0.99 pm.
(Fm)
4. Moments of a latex sphere
0.25
As a second example of moments a study of a 0.220 pm diameter latex sphere on a thin nylon foil is presented. The beam species and detector geometry are the same as for the previous example. The beam spot size was calculated to be 0.11 + 0.02 pm [5]. Fig. 2a shows a contour map of the median filter of all the ions in the dataset. The z range displayed varies from an energy loss of 33 to 67 keV. The position of the sphere is sharply defined and it has a FWHM of 0.16 k 0.03 pm.
0 1.60
1.80 Position
I
-0.50-
I
I
,
I
1.60
2.00 (pm)
I
2.00 1.80 Position (pm)
2.20
I
I
, -
2.20
Fig. 1. (a) Energy loss vs beam location for a line scan across a copper edge. Mean energy loss is plotted as the square data points whereas the median is plotted as triangles. The median has been displaced upwards 0.1 energy loss units for clarity. (b) Average energy loss moments, from the mean energy loss data in (a), m2 (solid squares), m2+ (solid triangles) and m*(open circles). The solid lines represent the theoretical curves for each moment assuming the beam profile is Gaussian. (c) Median moments, from the median data in (a), m’ (open inverted triangles), m2 (solid squares), m2+ (solid triangles), rn2- (open circles) and m3. For this dataset m’ and m3 are identical and so only m 1 is drawn. m2 has been displaced upwards 0.1 units, m ‘+ has been displaced upwards 0.2 units and m *- has been displaced upwards 0.3 units for clarity. The solid lines once again represent the theoretical curves for each moment assuming the beam profile is Gaussian.
G. Bench et al. / Unresolved spatial structure
Moment images m2, m2’, and m2were constructed using this median image from ions whose energies were within the energy window 1873 to 2000 keV. Ions outside this energy window made up less than 2% of the total number of collected events. Maps of the distribution of these ions did not indicate any spatial structure within statistics and so they were discarded. Fig. 2b shows the second moment, m2, for which the z range varies from 40 to 524 keV2. The location of the latex sphere can be identified; however, it is not as sharply defined as in the median image as outlying events are included in the calculation of the moment. Noise spikes caused by highly deviant values of energy loss in some pixels are evident. Fig. 2c shows the upper second moment, rnzl-. for which the z range varies from 29 to 362 keV’. rnzt forms a craterlike structure in the vicinity of the sphere. Noise is once again evident in the image and in the majority of cases it occurs in the same locations as for m2.
Fig. 2d shows the lower second moment, rn’for which the z range varies from 9 to 292 keV2. Noise in this image is substantially reduced in comparison with the other moment images. This moment also produces an image most similar to the median image. The position of the latex sphere is even more sharply defined than in fig. 2a, the latex sphere has a FWHM of 0.14 i 0.03 urn. displays the latex sphere with much greater m ‘contrast than the median image. The peak to average background ratio for the latex sphere is a factor of 9.5
381
greater for the m2- image. Even if we take the square root of the rnzp values to convert the units to the same dimensions used in the median image the peak to average background ratio is a factor of 2.2 greater for the m2image. The contrast is greater as the sphere’s radius is of similar size to the beam diameter and as a result the sphere’s shape is unresolved, whereas area1 density variations in the nylon foil are small in comparison. Analogous results were obtained from the use of mean energy averaging moments taken of the latex sphere with m2 and rn2+ noisier than m2-. These moments of the latex sphere indicate that the majority of noise in moment images comes from ions whose energy loss is greater than the mean/median value in a pixel. Sources of this noise are likely to be slit scattered ions, ions scattered off residual gas molecules in the vacuum and pulse height defects in the detection of particles. As m2- is the only moment that excludes these sources of noise it is the preferable lower-order moment to use. Similar refinements to higher-order moments can be made but these will give greater emphasis to the more deviant values of energy loss in a pixel.
5. Applications of moments When a microprobe is used for biological analysis, much emphasis is placed on the identification of features associated with elemental localizations within a
Fig. 3. (a) Median filtered STIM image of an unstained freeze-dried cryosection (4 pm thick) of mouse ileum showing the tip of one villus with other villi on either side. The image consists of 32 grey scales and shows epithelial cells around the edge of the tip, a goblet cell, lamina propria, microvilli brush border and other features. (b) The same dataset as in (a), but this time the image shows structure identified with the lower second moment, m2-. The contrast of such features as the brush border is much greater. X. STIM
382
G. Bench et al. / Unresolved spatial structure
sample. STIM offers an imaging technique based on area1 density that can be used to help identify features that may be hard to image using electron or optical techniques, particularly if the sample cannot be stained. Fig. 3a is a greyscale plot formed from the median energy loss of all the ions collected in a 2 MeV alphaparticle scan of an unstained freeze-dried cryosection of ileum tissue from a mottled mouse. The image is of dimensions 68 X 68 urn and was obtained with a spatial resolution of 100 nm although the pixel size shown here is 0.25 pm. Considerable structure can be seen in the image, and in many places the edges of the villi show a faint indication of the brush border which is more dense than neighbouring tissue. The brush border consists of densely packed microvilli of approximate diameter 0.1 pm and length 2 urn. From this knowledge one would expect that a spectrum of particles associated with a pixel on the brush border would coniain much detail due to unresolved structure resulting in a wide range of energy losses. Such data should show large contrast when plotted as a moment. Fig. 3b shows the lower second moment, m2-, of the median image. The moment was calculated using ions whose energies are between 1500 and 2030 keV. This window was selected using a similar criterion as for the window used to form the moments of the latex sphere. This figure shows the brush border and other features in much greater contrast than in the median image. The applications of STIM and moments are not limited to biological specimens, but this area may see most use because the thin specimens are transparent to the beam and frequently contain structure extending to
near the molecular level. Moments, as they can clearly demarcate features of spectral complexity, are a useful tool for the identification of features within a sample.
6. Conclusion When a mean/median STIM image is formed from a sample only one value is derived at each pixel, although the majority of ions collected in a pixel contain useful information. Moments provide a simple but effective means of displaying this spectral complexity in a pixel and can indicate regions of unresolved electron density variations in a sample. In so doing they provide an informative complement to a mean/median image.
Acknowledgements The authors in preparation ileum tissue.
wish to thank Dr B.J. Kirby for his help and identification of features in the
References PI J.C. Overley, R.M.S. Schofield, J.D. MacDonald and H.W.
Lefevre, Nucl. Instr. and Meth. B30 (1988) 337.
PI J.C. Overley, R.C. Connolly, G.E. Sieger, J.D. MacDonald and H.W. Lefevre, Nucl. Instr. and Meth. 218 (1983) 43. [31 B.E. Fischer, Nucl. Instr. and Meth. BlO/ll (1985) 693. [41 R.M. Sealock, D.N. Jamieson and G.J.F. Legge, Nucl.
Instr. and Meth. B29 (1987) 557. [51 G. Bench and G.J.F. Legge, Nucl. Instr. and Meth. B40/41
(1989) 655.