EELS elemental mapping with unconventional methods II. Applications to biological specimens

A new quantification procedure for elemental mapping by X-ray (absorption) microscopy

“…The use of unconventional methods related to multivariate statistics and entropy concepts (i.e. factor analysis of correspondence or principal component analysis) should be inspected because they run without any a priori hypothesis for the background and the noise [24,25]. (21) is only valid when the total surface atomic density, NI t, is postulated to be the same for the two investigated regions, (A) and (A+M).…”

“…2.3), the influence of the factor 30394i/i is that the sensitivity of X-ray microscopy as well as that of X-ray tomography [17][18][19][20][21][22][23][24][25][26]27] is optimum when the function ex/2x is minimum (x = J-Lt/2) and this minimum is close to the unity when 03BCt ~ 2. For an order of magnitude, 3(Az/z)MDC is of around 10-2 when no (per pixel) is of around 105 photons with the optimum choice of E : Eopt.…”

“…9) or from the use of more or less refined theoretical calculations like that widely explored for the background modeling in electron probe microanalysis, see for instance reference [3], chapter 8, p.393. The knowledge of r(E) and g(E) allows us to calculate (analytically or numerically) the integral appearing in expression (24) in order to deduce the quantity r (Ej) 19 from the measured intensity 19 (R) and this quantity can also be put into the first term in the right hand side of expression (25).…”

“…If the number of elements composing the specimen is n, n different pairs of measurements similar to 19 (R) and Ij (R) have to be performed in order to obtain n expressions similar to (24) and (25). The first term on the right hand side of each expression represents the monochromatic contribution while the second, the integral, represents the continuous correction but both terms are functions of the required concentrations CA, CB, ...CN, and of N°t.…”

“…This step is exactly that which has been described in sub-section 2.2 for the concentration determination in the monochromatic situation. It is then possible to insert these approximate values into expression (26) in order to evaluate the continuous correction (to the first order) by calculating the integral in the right hand side of expression (25).…”