edfas.org 7 ELECTRONIC DEV ICE FA I LURE ANALYSIS | VOLUME 24 NO . 4 objective lens is still sensitive enough todetect the photon emission. However, for the calibration process, it is necessary to find an appropriate pinhole that limits the spatial extend of the reference light source emission. Having noted the XY coordinates of the photon emission origin, the prism can be moved into the optical path to spectrally distribute the PE. By inserting narrow band pass filters into the filter slide, XY coordinates for the band pass filter wavelength used can be extracted by noting the maximumof themeasuredemission. TheseXY coordinates are noted in relative distance to the previously defined origin of the photon emission, resulting in an extractable shift for each band pass filtermeasured. Figure 4 shows an example dispersion characteristic in terms of pixel shift in the X-direction. Adata interpolation function is required to extract thewavelength for every pixel within the sensitivity range of the detector. Mechanical spatial displacements in the X-direction are addressedby characterizing the dispersion properties of the system. Observing a non-constant displacement in the Y-direction is most likely caused by a prism that is not correctly inserted into the system. In this case, it is recommended to reinstall the prism with a correct alignment. Observing a constant displacement in Y-direction can be easily compensated by the data extraction algorithm, this will be shown later. EXTRACTING Draw (λ) Even though the angular error of the prism is minimized during prism adjustment, it is recommended to not extract only one X-line array for the raw spectral data. Extracting the median of the predetermined center line as well as a symmetrical number of lines above and below the center line compensates for mechanical tolerances that may occur during the movement of the prism, remaining angular errors and photon emissions with a spatial extend. For example, one line below and one line above the center line. Especiallywithhighermagnification lenses, the spatial extent of the photon emission increases in a way that the assumptionof apoint-shapedemission source ismoreand more violated. This problemcan be partially addressed by choosing a pinholewith a smaller diameter or by reducing the spectral intensity by limiting the supply voltage of the reference light source. Overall, magnifications of 50x or even 100x have been found to show a significant spatial expansion of the photon emissions spot. As spatial expansion of the photon emission source results in a widening of spectral data in Y-direction as well as a superposition of spectral information in X-direction, this initial situation should be avoided if possible. However, a spatial extent in Y-direction must be taken into account by calculating the median for Draw(λ) from an increased number of X-lines, for example five. MEASURING Csys(λ) Having the dispersion characteristics, the spatial displacement, as well as the raw data of the spectral distribution of the reference light source available are the basics for determining the wavelength dependent system transformation factor Csys(λ). Therefore, the reference light source is measured in the SPEM system under the same electrical conditions as measured during the characterization of the reference light source. First, the emission is measured without the prism in order to determine the origin coordinates. Next, the prism is moved into the optical path tomeasure the corresponding spectra. The raw spectral data, which are then measured by the SPEM system, represent a transformed version of the reference spectrum. Components that contribute to the data transformation are the lens objective (Cobj), the tube lens (Ctube), and the prism (Cprism). In the presence of a reference spectrum, the transformations of the various components can be combined to form the system transformation factor, Csys. The system transformation factor Csys can be calculated by dividing the reference data (Dref) by the measured raw data (Draw): Draw(λ) · Csys(λ) = Dref(λ) Eq 1 Due to the nonlinearity of the dispersion characteristics, thewavelength resolutionper pixel ranges from3.5 to 15 nm. Now the previous work of extracting a fitting function for the spectral distribution of the reference light source as well as the functional description of the dispersion characteristics pay off. An accurate wavelength can be calculated for each pixel within the spectral line array. Afterward, the intensity of the reference light source can be calculated for these specific wavelengths associated to the pixels. This proceduremust be performed for every Fig. 4 Exemplarydispersioncharacteristicof aSPEMsystem.
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