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.

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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.

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 - Dan Dewey, 6/19/2000