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REFINEMENTS TO THE LEIT CALIBRATIONS

This article describes recent refinements to the low energy imaging telescope, LEIT, calibrations. These represent small changes and in general are only relevant to grating observations. They are based on the final reduction and evaluation of the ground calibration measurements of both LE telescopes as well as the results of in-flight calibrations using grating observations. A final version of the Current Calibration File (CCF) will be released in the near future that will include new values for the filter characteristics and the 1000 l/mm grating (LE1) Line-Spread Function (LSF). This new CCF will also include the update to the LE misalignment described in Express No 17, p3.

A re-analysis of the ground calibration filter measurements has shown slightly different values for the mass-absorption coefficients of the materials used in the polypropylene and aluminium-parylene (Al/P) filters. The polypropylene revised numbers mainly concern small changes in depth of the absorption edges. For the Al/P filter the changes are again small and result from the fact that the mass- absorption coefficient of aluminium shows an oscillatory behaviour shortward of the L-edge at 170Å. This small effect is known to be present from continuum synchrotron radiation measurements (Haensel et al. 1970, Phys. Stat. Sol. A. 2, 85), and is due to quantum effects within the filter. Although the groundbased measurements were of insufficient resolution, the oscillatory behaviour can be well parameterized by in-flight 500 l/mm grating observations of HZ43 and Sirius-B. Figure 1 shows curves of the mass-absorption coefficient, as measured during ground calibrations (solid line) and the modification derived from the grating measurements (thin line) in the wavelength range 60 to 170Å. The spacing of the energy grid in the CCF (record A1) in the range 60 to 170Å is too wide to give a proper description of the oscillatory behaviour and we provide at the end of this report a routine (FUNCTION EXO_ALUM) which calculates the mass-absorption coefficient (in units of cm2g-1) at any particular energy EN (in keV). The effects of this change are minor and inclusion of the new coefficients is only warranted in the reduction of grating observations, and perhaps filter observations of sources with strong line-emission (or a drastic change in flux) within the 60-170Å band.

The on-axis filter thickness (gcm-2) for all filters, as derived from the final ground calibration analysis, are given in Table 1. The off-axis values for the filter thickness deviate at most 3 % from this value, with the exception of the Boron filter. In general these revised figures are at most only a few percent different from those given originally and are only relevant to grating spectra.

Line profiles for the 1000 l/mm grating on LE1 were derived from ground based (Longbeam test) measurements at 8 energies. Cores of lines at short wavelengths (lambda less equal 25 Å) are similar to a Gaussian profile. However, the wings deviate from this curve and are asymmetric. The line-profile at longer wavelengths (lambda greater equal 25 Å) deviates strongly from a simple profile. There is always an extended wing at the long-wavelength side of the line-center. Therefore only the measured 1000 l/mm line-profiles at 8 different energies are given in the E3 record in the CCF. The values of FWHM and HEW, which are ambiguously defined, are not provided in E2 (all data are set to -1), to prevent confusion.

H. van der Woerd
J. Osborne


Figure 1.

Mass Absorption coefficent versus wavelength (30 to 200 Å) for Aluminium, as derived from the 500 l/mm soft X-ray spectra of HZ43 and Sirius-B (thin line), and as derived from ground calibration (heavy line). The dots represent laboratory measurements by Haensel et al. (1970).

fig1 description above


Table 1

The on-axis filter thickness rho d (*10-5 gcm-2) for both telescopes.

LE1 LE2
Filter rho d +/- rho d +/-
PPL4.95 0.07 5.07 0.03
4LX 4.87 0.03 4.60 0.05
3LX 3.37 0.03 2.84 0.03
AL 2.73 0.03 2.51 0.03
PA-N 1.50 0.05 1.45 0.05
BOR 10.40 0.05 10.00 0.02

C     
C**********************************************************
C     THIS FUNCTION CALCULATES THE MASS-ABSORPTION COEFFICIENTS 
C     FOR ALUMINUM (cm2/gm) at the energy EN (keV). 
C     THE COEFFICIENTS FOR THE WAVELENGTH INTERVAL 60-170 A 
C     ARE DETERMINED BY SPLINE CURVES.
C     
C     DATA ARE BASED ON MEASUREMENTS OF EXOSAT FILTERS AT THE 
C     SPACE RESEARCH LABORATORY IN UTRECHT.
C     
C     
C     AUTHOR : F. PAERELS, SPACE RESEARCH LABORATORY UTRECHT
C     
C***********************************************************
C     
      
      REAL	MA_SPLINE
      DIMENSION	W(20),AMURHO(20)
      DIMENSION	CC(4 ,20)
      
      DATA W/                   ! Angstrom; wavelength grid
     &     5.9000E+01, 6.0480E+01, 6.2250E+01, 6.8500E+01,
     &     7.1260E+01, 7.3800E+01, 8.8560E+01, 9.1840E+01,
     &     9.5370E+01, 9.9190E+01, 1.0500E+02, 1.1310E+02,
     &     1.2750E+02, 1.3000E+02, 1.4500E+02, 1.5500E+02,
     &     1.5600E+02, 1.6980E+02, 1.7000E+02, 2.0000E+02/

      DATA AMURHO/              ! cm2/gr; values for these gridpoints
     &     5.0999E+04, 5.6657E+04, 6.5144E+04, 6.7514E+04,
     &     7.0802E+04, 7.7989E+04, 7.7225E+04, 8.5253E+04,
     &     9.1370E+04, 1.0628E+05, 1.3381E+05, 1.1622E+05,
     &     1.1660E+05, 1.3457E+05, 9.1752E+04, 6.5832B+04,
     &     5.5434E+04, 7.4166E+04, 7.4166E+04, 7.4166E+04/
C     ! spline coefficients for these gridpoints
      DATA (CC(i,l),i=1,4)/ 3.4974E+2, 8.4669E+1, 3.3693E+4, 3.8096E+4/ 
      DATA (CC(i,2),i=1,4)/ 7.0796E+1,-1.9428E+2, 3.1788E+4, 3.7413E+4/ 
      DATA (CC(i,3),i=1,4)/-5.5019E+1, 2.2482E+1, 1.2572E+4, 9.9241E+3/ 
      DATA (CC(i,4),i=1,4)/ 5.0911E+1, 5.6332E+1, 2.4074E+4, 2.5224E+4/ 
      DATA (CC(i,5),i=1,4)/ 6.1211E+1,-6.1606E+1, 2.7480E+4, 3.1102E+4/ 
      DATA (CC(i,6),i=1,4)/-1.0602E+1, 9.8130E+0, 7.5934E+3, 3.0942E+3/ 
      DATA (CC(i,7),i=1,4)/ 4.4159E+1,-3.8740E+1, 2.3069Z+4, 2.6409E+4/ 
      DATA (CC(i,8),i=1,4)/-3.5996E+1, 4.3394E+1, 2.4600E+4, 2.5343E+4/ 
      DATA (CC(i,9),i=1,4)/ 4.0100E+l, 2.5150E+l, 2.3334E+4, 2.7455E+4/ 
      DATA(CC(i,10),i=1,4)/ 1.6536E+1,-4.7428E+1, 1.7734E+4, 2.4631E+4/ 
      DATA(CC(i,ll),i=1,4)/-3.4019E+1, 3.0335E+0, 1.8751E+4, 1.4149E+4/ 
      DATA(CC(i,12),i=1,4)/ 1.7064E+0, 1.6030E+1, 7.7170E+3, 4.7734E+3/ 
      DATA(CC(i,13),i=1,4)/ 9.2331E+1,-1.5922E+2, 4.6064E+4, 5.4823E+4/ 
      DATA(CC(i,14),i=1,4)/-2.6536E+1, 1.4723E+1, 1.4942E+4, 2.8042E+3/ 
      DATA(CC(i,15),i=1,4)/ 2.2084E+1,-4.8090E+1, 6.9668E+3, 1.1392E+4/ 
      DATA(CC(i,16),i=1,4)/-4.8090E+2, 5.6471E+2, 6.6313E+4, 5.4869E+4/ 
      DATA(CC(i,17),i=l,4)/ 4.0921E+1,-2.3517E+1,-3 7761E+3, 9.8529E+3/ 
      DATA(CC(1,18),i=l,4)/-1.6227E+3,-1.5906E+3, 3.7090E+5, 3.7090E+5/ 
      DATA(CC(i,l9),i=1,4)/-1.0604B+1, 2.1422E+1, 1.2016E+4,-1.6807E+4/ 
      DATA(CC(i,20),i=1,4)/ 0.0000E-l, 0.0000E-1, 0.0000E-1, 0.0000E-1/ 
      
C     
      M = 20                            ! NR OF SPLINE CURVES
      ALNE = ALOG(EN)
      IF(EN.GT.0.0728) GOTO 10

C     
C**   COEFFICIENTS FOR ENERGIES LE 0.0728 KEV
C     
      
      RLN = 4.73 - 1.58*ALNE - 0.046*ALNE*ALNE
      
      
C     
C**   COEFFICIENTS FOR ENERGIES GT 0.0728 KEV AND LE 0.210 KEV
      
      
 10   IF(EN.GT.0.210)GOTO 20
      WW = 12.3985 / EN         ! Angstrom
      RLN = ALOG(MA_SPLINE(W,AMURHO,M,CC,WW))
      GOTO 100
      
C     
C     
C**   COEFFICIENTS FOR ENERGIES GT O.210 KEV AND LE O.54 KEV
      
 20   IF(EN.GT.0.54)GOTO 30
      RLN = 6.814 - 3.463*ALNE - O.567*ALNE*ALNE
      GOTO 100
      
C     
C**   COEFFICIENTS FOR ENERGIES GT 0.54 KEV AND LE 1.56 KEV
C     
 30   IF(EN.GT.1.56)GOTO 40
      RLN = 7.105 - 2.756*ALNE - O.173*ALNE*ALNE
      GOTO 100
C     
C**   COEFFICIENTS FOR ENERGIES GT 1.56 KEV AND LE 10 KEV
C     
 40   RLN = 9.539 - 2.501*ALNE - 0.095*ALNE*ALNE
      GOTO 100
C     
C**   TAKE EXPONENT OF INTERPOLATED VALUE
      
      
 100  EXO_ALUM = EXP(RLN)
      RETURN
      END

C
C*********************************************************
C
        
      REAL FUNCTION MA_SPLINE(X,Y,M,C,XINT)
      
      DIMENSION X(*), Y(*), C(4,*)
      IF (XINT-X(1)) 70, 10, 20
 10   MA_SPLINE= Y(1)
      RETURN
 20   K=1
 30   IF (XINT-X(K+1)) 60, 40, 50
 40   MA_SPLINE= Y(K+1)
      RETURN
 50   K= K+1
      IF (M-K) 70, 70, 30
 60   YINT= (X(K+l)-XINT)*(C(1,K)*(X(K+1)-XINT)**2+C(3,K))
      MA_SPLINE= YINT + (XINT-X(K))*(C(2,K)*(XINT-X(K))**2+C(4,K))
      RETURN
 70   WRITE (*,*),' OUT OF RANGE '
      RETURN
      END
C
C****************************************************************


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