Subsections

• 4.6.1 PHT-S instrumental line profile
• 4.6.2 PHT-S wavelength calibration

4.6 Spectral Performance

4.6.1 PHT-S instrumental line profile

The PHT-S instrumental line profiles have been measured in laboratory. The profiles exhibit a Gaussian shape to good approximation. For the PHT-SS pixels the FWHM is $42{\pm}4$ nm, for SL $97{\pm}6$ nm. The physical distance between adjacent pixels is 350 ${\mu}$m which corresponds to 38.3 nm and 91.8 nm in wavelength for SS and SL respectively, assuming a linear scale. The physical size of a pixel in dispersion direction is 310 ${\mu}$m which corresponds to a width in wavelength of 33.9 and 81.3 nm for SS and SL. In Table 4.5 we have summarized the laboratory data. Also listed are the fraction of the incident power measured by the detector pixel in the case the line is centred on a pixel and in case the line falls exactly in between two pixels of the PHT-S arrays. For these values it is assumed that the detectors have an ideal flat-topped responsivity profile in dispersion direction. Since this is not the case (see Section 4.5.1.3) the ratio between the centre and adjacent pixel in case the line is centred on the pixel is somewhat higher. For the values in Table 4.5 an accurate approximation for the wavelength scale is used. For the exact scale see Section 4.6.2. Under the given assumptions, a 10% variation in the FWHM changes the fraction in the centre pixel by less than 7%.

Table 4.5: Instrumental line profile parameters.

parameter	SS	SL	unit	description
${\Delta}$x	350	350	${\mu}$m	physical distance between pixels
${\Delta}{\lambda}$	38.3	91.8	nm	wavelength difference corresponding to pixel distance
${\Delta}$l	310	310	${\mu}$m	physical pixel size in Z-direction
${\Delta}{\lambda}_{pix}$	33.9	81.3	nm	pixel width in wavelength
FWHM	42	97	nm	mean full width at half power of profile
${\sigma}_{FWHM}$	4	6	nm	uncertainty in FWHM
$P_C/P_{total}$	0.73	0.74	-	power fraction measured on pixel if line is centred
$P^1_C/P_{total}$	0.09	0.08	-	power fraction measured on adjacent pixel
				if line is centred
$P_M/P_{total}$	0.43	0.43	-	power fraction on pixel if line is centred
				between two pixels

4.6.2 PHT-S wavelength calibration

The PHT-S wavelength scale, i.e. the relation between pixel number and wavelength, is approximately linear. In orbit calibration confirms the presence of a small second order term. The wavelength scale has been calibrated to an accuracy of less than 1/10 of a pixel (see also Table 4.5) from the analysis of several targets with well defined emission lines. A polynomial fit to the wavelength scale for PHT-SS and PHT-SL gives:

$$\lambda(pix) = a_1 + a_2 * (pix-1) - a_3 * (pix-1)^2 ~~~~~~[{\rm {\mu}m}]$$ (4.7)

where $pix$ is the integer pixel number in the SS or SL array, counting from 1 to 64 for both SS and SL. The coefficients $a_1, a_2$, and $a_3$ are presented in Table 4.6.

Table 4.6: Coefficients for the conversion of PHT-S pixel to wavelength.

Coefficient	SS	SL
$a_1$	2.4687	5.8396
$a_2$	$4.0765~10^{-2}$	$9.4263~10^{-2}$
$a_3$	$4.1563~10^{-5}$	$3.9702~10^{-5}$