Expected Effect of 0.3 degree Insertion Offset
on 6/15/2000 HETG Data Sets: Obsids 49898, 374.
These observations were taken with the HETG not fully inserted:
estimated at 0.3 degrees from full insertion. This results in i) a
different effective Rowland Spacing and ii) increased effective
grating dp/p values.
- - -
Rowland Spacing
Assuming the HETG yoke hinge is 600 mm from the center of the HETG,
the 0.3 degree offset results in a center offset
of ~ 600.0 * 0.3 / 57.3 = 3.14 mm
The grating center is CLOSER to the focal plane and so the expected
Rowland Spacing is X_RS = 8632.65 - 3.14 = 8629.51 mm
- - -
Increased "dp/p" values
Additional blur is introduced through the tilt of the HETG which
causes a variation in Rowland Spacing across the grating effectively
looking like a variation of grating period.
The additional rms blur in the dispersion direction, dy_rms, is
proportional to the offset angle, theta_off, and given by:
dy_rms / Yo = 0.7 * 330.0[470.0] * (theta_off/57.3) / X_RS
where the Yo is the distance of the diffracted image from
zeroth-order, 0.7 converts the non-Gaussian distribution to rms
equivalent, 330.0[470.0] is the effective radius of the HEG[MEG] set
of gratings, theta_off is the offset angle in degrees, 57.3 is degrees
per radian, and X_RS is the HETG Rowland Spacing.
For theta_off = 0.3 degree, we get:
dy_rms / Yo = 140. ppm RMS for HEG
dy_rms / Yo = 200. ppm RMS for MEG
For use, these values can be RSSed with the nominal dp/p values (e.g.,
which appear in the MARX parameter file.)
They can also be converted to dE/E ( = d_lambda/lambda) values by
the factor 2.35 [because the "dE" is in FWHM, not rms] and used to
estimate changes in a measured line's FWHM, e.g.:
Capella at 19A as observed with MEG has FWHM of E/dE = 840
(POG Rev.2, p.173); thus nominal dE/E = 1/840 ~ 1190.E-6
The additional blur from above adds 2.35 * 200.E-6 [FWHM]
which is 470.E-6. RSSing these gives combined dE/E =
SQRT(1190.^2+470.^2) x 1.E-6 = 1280.E-6, or E/dE ~ 780;
that is 93 % of the nominal resolving power.
- - -
- Dan Dewey, 6/19/2000