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