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K-Ratio Images

K-Ratio images are micrographs (x-ray maps), usually taken with an electron microprobe, that have been processed so that the value of each pixel (now a floating point number between 0.0 and 1.0) is more proportional to chemical concentration than is the corresponding raw x-ray intensity.

"In his doctoral thesis, Castaing developed the physical theory enabling the analysis to convert measured x-ray intensities to chemical composition*.  Castaing proposed a method of analysis based on comparisons of intensity, i.e., the comparison of the intensity Ii of a characteristic line of a given element emitted by a specimen under one set of conditions of electron bombardmene and the intensity I(i) of the same characteristic radiation when emitted by a standard containing the same element under the same electron bombardment conditions.  The ration of the two readings (the so-called k ratio) is proportional to the mass concentration of a given element in the region analyzed." (Goldstein et. al., 1992).  Current quantitation methods add corrections to the k-ratio values for atomic number, matrix effects, self absorbtion, etc.

*Castang. R.  (1951),  Ph.D. thesis, University of Paris.

K-Ration Notes

Raw x-ray maps + text file with experimental parameters = K-Ratio images (maps).

The log-3-band color scale is designed to display K-Ratio images..

K-Ratio Functions are in the FINI button of the Periodic Table Tool, bottom row.


Sample FINI files: 

txt1 | txt2 | xls1 | xls2 

Sample 1 is from lx-Images\Kratio-example, and displays K-ratio images from a set of elemental and background images. 

Sample 2 is from more-lx-images\RaneyNickelCube and displays K-ratio images from a data cube. 

The files are in two formats -- txt which both Lispix and Excel* read, and xls which Excel reads.  The xls files have comments explaining the various parameters.


Text description | Paper on Log-3-band color scale


The at the bottom of the above figure, is the EXCEL representation of a FINI file.

FINI stands for Frame Initialization File. Frame is a NIST electron probe quantitation program incorporated into DTSA. Lispix uses the Fini file to load the maps and do the k-ratio calculations.

This sample file, along with the images, can be downloaded from here. The red triangles indicate comments in the Excel file, explaning the parameters. The comments do not appear in the text file.

Lispix reads the Fini file as text tab delimited. Here is what it looks like. I find it easier to input the data in Excel, then export the file from Excel as text, tab-delimited.  This is what the file looks like as text:

EDS Map Data Chart for macLispix K Ratio map calculations

Parameter Value
Beam keV 20
Beam nA 0.5
TOA deg 40
Dwell sec 0.5
Oxygen no

Background Windows
File Name Elm Maps Low ev High ev
ra2bkg1 AlK 1000 1200
ra2bkg2 AlK 2000 2200
ra2bkg3 FeK 6000 6200
ra2bkg4 FeK NiK 7000 7200
ra2bkg5 NiK 8000 8200

Element Windows Standard Data
File name Elem&line Low ev High ev Counts Cur nA Time sec Valence
Ra2Al-k AlK 1420 1550 2060360 0.5 1000 3
Ra2Fe-k FeK 6310 6500 627467 0.5 1000 2
Ra2Ni-k NiK 7380 7580 468694 0.5 1000 2

Partial FINI file

The PPP tool can write a FINI file that is partially filled in. ‘x’ denotes missing data for the full k-ratio calculation. The K-ratio Tool, as of 11/17/2003, will use the data as-is (without standards data) to make background subtracted maps. These amount to the numerator of the k-ratio maps.

EDS Map Data Chart for Lispix K-Ratio map calculations

Parameter Value
Beam keV x
Beam nA x
TOA deg x
Dwell sec x
Tot % cut x
DetPkW eV x
Oxygen x

Background Windows
File name Elm Maps Low ev High ev
bkg01 AuL 10010.0 10190.0
bkg02 CuK AuL 9220.0 9420.0
bkg03 TiK 4720.0 4880.0
bkg04 TiK 4270.0 4420.0
bkg05 NiK CuK 7700.0 7860.0
bkg06 NiK 7110.0 7270.0

Element Windows Standard Data
Elem Elem&line low Ev high Ev Counts Cur nA Time sec Valence
Ti TiK 4444.5 4571.5 x x x x
Ni NiK 7394.3 7547.7 x x x x
Cu CuK 7960.0 8118.0 x x x x
Au AuL 9626.6 9797.4 x x x x