TMA Objective Grating Assembly (TOGA)

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The TOGA is being brought to you by the people who will bring you the HETG and the LETG.

Last modified: 8/22/96 3 pm

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Table of Contents

  • Scientific design
  • Expected performance
  • TMA notes
  • Engineering details
  • TOGA people
  • Scientific Design

    To support the ground calibration rehearsal at MSFC's X-Ray Calibration Facility, XRCF, a small grating assembly is being fabricated for use with the TMA mirror. The TOGA includes all types of AXAF gratings: a TOP quadrant populated with 8 MEGs, a BOTTOM quadrant with 8 HEGs, and SOUTH and NORTH quadrants each with 5 LEG modules. The dispersion axes of the gratings are as for the LETG and HETG with the LEG dispersion along the Y axis and the MEG and HEG axes located +/- 5 degrees from the Y axis. Through the use of the TMA shutters all or subsets of these gratings can be illuminated.

    The TOGA is designed to place grating centers on the Rowland circle to intercept the converging beam exiting the TMA. Because of the three different roll angles of the dispersion axis there are three different Rowland circles all with the same diameter. The general layout and design parameters are given in the figure below.

    diagram of TMA rays and TOGA facet

    The on-axis Rowland circle location is designed to be 150 mm behind the TMA shutter blade plane. Using values from Podgorski this yields a Rowland circle diameter of 6469.55 - (947 + 150) = 5372.55 mm. This and other design values are summarized here:

      X_rc (Rowland diameter) = 6469.55 - (947+150) = 5372.55 mm
      hyperbola_front =   6469.55 - 441.37          = 6028.18 mm
      hyperbola_back =    6469.55 - 801.82          = 5667.73 mm
      R_front = 209.07069 mm
      R_back  = 199.87773 mm 

    Installed at XRCF, measurements by Mark Ordway, 7/23/96, yield an as-built grating on-axis location 1103 mm from the wide end of the TMA parabola, thus:

           X_rc (Rowland diameter) = 6469.55 - (1103) = 5366.55 mm

    The width of the TMA beam as it goes through the gratings is about 3.1 mm.

    Expected Performance

    As with any spectrometer the key performance parameters are the spectral resolving power (E/dE) and the effective area (cm^2). Both of these depend a great deal on the TMA and grating performance. Secondarily, the variation in the grating-line orientation produces a cross-disperion blur which effectively increases the spectrometer background by requiring a large acceptance region at the detector.

    TOGA Gratings

    The MEG/HEG TOGA gratings are flight quality but at the low end of efficiency or period performance. The LEG gratings are from EQM samples.

    The gratings were inspected 7/22/96 just before installation and except for MA1006 all appeared completely intact. MA1006 has a small vee-shaped puncture in its "upper-right" (LR convention) corner. A grating that was more severely punctured at MIT, MA1002, showed that the region away from the puncture was within 100 ppm of the previous period and period variations were limited to the puncture region, lower right in LR plot. Based on this result, I think it unlikely that we will see the effect of the MA1006 puncture with TMA-TOGA data.

    Resolving power

    The resolving power for the TMA/TOGA is determined largely by the TMA PSF through the equation:

           E     Y      1        m lambda                    m
          --- = --- =  ---  X_rc --------   ~  1100  ----------------
           dE    dY     dY          p                 dY_30 E_keV p_2kA

    where Y is the dispersion coordinate, X_RC is the Rowland diameter, m the diffraction order, the grating periods are ~10,000 A, 4,000 A, or 2,000 A for the LEG, MEG and HEG respectively (and thus p_2kA is 5, 2, or 1), and the TMA 1D blur, dy_30, is in units of 30 microns FWHM. A plot of the expected grating resolving power is given. The high spectral resolution of the gratings can be better communicated by comparing the view of the EIPS source spectrum at grating, SSD, and SMD resolutions (this comparison does not include mirror, grating, or detector efficiencies.)

    The period variation of the gratings is adequately small (100 ppm rms) to allow resolving powers in excess of 1,000; the period histogram plots below show the grating-only line spread function derived for the specific TOGA gratings and compares this distribution to an E/dE = 1000 gaussian.

    Cross-dispersion Blur

    Generally, the cross-dispersion width of the diffracted beam depends on i) the mirror blur, ii) the astigmatism inherent in the Rowland Torus design, and iii) the variations in the alignment of the grating lines within and between facets.

    Because the different grating types on TOGA are not complete rings, the astigmatism terms are modified from the nominal theory. For the LEGs, the astigmatism blur is reduced by a factor of ~0.60 compared to the full-ring model. For the MEGs and HEGs the astigmatism will show up primarilly as a slight quadratic cross-dispersion deviation or offset from the nominal dispersion axis.

    For the MEGs and HEGs the main cross-dispersion blurs are the TMA blur and the facet-to-facet roll alignment, which is more important at larger dispersions. The expected cross-dispersion profiles are formed by summing the TMA blur from each grating offset by the grating's roll angle times the dispersion distance.

    Effective area

    The effective area for the TMA/TOGA combination depends on the TMA effective area and the grating efficiency. The TMA support ribs also complicates the calculation of the precise grating effective areas. Expected grating effective areas for the gratings in first and zero order are shown in plots below. Because there are gaps between the gratings the zero-order efficiency is the sum of the grating efficiency and the "direct-through" efficiency. The zero-order plots below show the grating-only zero-order area as a solid line and the direct-through area as a dotted line.

    Tables of the TMA effective area and the grating efficiencies (including all vignetting) are available below.

    The grating efficiencies used are based on rectangular grating models that are a good approximation to the expected performance. These grating parameters are summarized here:

        Parameter       LEG         MEG          HEG     units
         --------       ---         ---          ---     -----
           Period      9912.36     4000.72      2002.36    A
        Thickness      4758.       4106.        4844.      A
       Line-width      5154.       2119.        1219.      A
        Polyimide       N/A        0.58         0.95       um
      Platingbase       N/A        1.01         1.01       200A Au + 50A Cr
     Other factor      0.806        N/A         0.783      
       Vignetting      0.397       0.184        0.166
    Clear fract'n      0.050       0.031        0.054

    The "other factor" corrects for the LEG support structure and for the HEG it is an approximation to the effect of the non-rectangular bar shapes. The "vignetting" factors for the gratings are the fraction of the TMA beam that active grating area intercepts, ideally they would be 0.5, 0.25, 0.25. The "clear fractions" are the fractions of the TMA beam that pass through spaces between gratings.

    The vignetting and clear fraction are estimated by treating the X-ray illumination as one dimensional (circumferencial). The TMA beam radius at TOGA is ~ 187.7 mm for a total circumference of 1179 mm. Approximately 90% of this circumference is "active" or 1061 mm (i.e., each support rib removes ~7.37 mm). The 30 15.5 mm diameter LEGs will nominally intercept (30*15.5 - 6*7.37)/1061 = 39.7% of the TMA beam. For MEGs the fraction is (8*1.035*25.4 - 2*7.37)/1061 or 18.4%. Likewise, the HEGs (0.94" ID) intercept roughly 16.6%. The amount of clear circumference for the LEGs is 8 times 6.6 mm gaps for ~0.050. For the MEGs the clear ratio is ~(2*7.6+2*3.8+4*2.5)/1061. = 0.031; and for HEGs ~(2*11.4+(11.4-7.4)+2*5.+4*5.)/1061. = 0.054. These values are based on crude measurements from a drawing.

    Decentering of the TOGA w.r.t. the TMA can also produce additional vignetting. Because of the oversized nature of the HETG gratings compared to the 3 mm beam width additional HETG grating vignetting is unlikely. For a 3 mm wide illumination of a circular LEG facet I estimate the following vignetting vs offset from facet-center:

           LEG facet vignetting vs beam offset
          Offset (mm)     Relative non-vignetted fraction (%)
             0.0             99.5
             1.5             97.6
             3.0             91.6
             4.5             80
             6.0             61

    Given the alignment tolerances it is likely that more than 90% of the predicted performance will be obtained.

    Ray-trace Example

    The TMA-TOGA-Detector can be crudely simulated using the CSIM software [now MARX - Ed] from the MIT ASC ( The simulator allows input of a text source spectrum. The CSIM currently has no TMA-TOGA model however, the results from a HRMA shell 6 combined with each of the three TOGA gratings and scaled by the Rowland diameter ratio (5366.55/8634.) provides a good approximation to the TOGA-TMA combination. An ACIS-S detector module was used as well.

    TMA Notes

    The TMA has an infinite-source focal length of 6005.512 mm. Bill Podgorski has predicted the XRCF finite-source focus at 532 m to be 6469.55 mm from the TMA entrance or 6068.61 mm from the TMA midplane. Other useful TMA geometric parameters are give in Bill's e-mail note. The radii of the hyperbola are from Leon's detailed TMA summary:

      front radius = 209.07069   back radius = 199.87773

    Leon says effective area can be accurately calculated from a modeled gold coating of 0.9 times nominal bulk density and a support structure area factor of 0.9. Measured effective areas at some energies he reported as:

       Energy  Area
         keV   cm^2
        1.49   27.0
        2.98   16.3
        4.96   17.5
        6.40   15.7
        8.04    8.9

    These values and their errors are over plotted on a simple model of a double Gold reflection at ~ 30 arc minutes (8.73 mrad) graze angle and using gold optical constants at 0.85 of their bulk value, TMA effective area.

    TMA encircled energy performance could be as good as 68% in 40 um diameter. Ron Eng and crew of MSFC performed the TMA off-loading to create a sharp image.

    Measurements on 8/18/96 at XRCF indicate ~23-26 microns FWHM was achieved!

    The TMA has support structure ribs every 22.5 degrees each with a width of order 0.3(?) inches.

    Engineering Details

    The TOGA is made up of the TOGA Objective Grating Support Structure, TOGSS ("TMA-05"), which attaches to the SAO Grating Support Structure, GSS. The gratings themselves are mounted to intermediate support structures (MISs and SISs) which are then mounted to the TOGSS.

    The mechanical envelope of the TOGA is 150 mm behind the TMA Shutter Blades. Other axial locations of interest are:

       wide end of TMA P      0.00 mm
       shutter blade plane  947.00 mm
       grating on-axis RC  1097.00 mm  (947 + 150)
       GSS - TOGGS plane   1109.70 mm  (947 + 150 + 12.7)
       focus at XRCF       6469.55 mm

    The GSS-TOGSS interface/hinge is on the south side when in XRCF. The GSS has three 1/4-20 tapped holes, the TOGSS has three coresponding 0.281" clearence holes.

    Two MIT intermediate support structures, MISs, and two SRON intermediate support structures, SISs, are provided. The MISs and SISs mount on the TMA side of the TOGSS. Two pins (Nordex EPS-A5-10, 0.1251"+0,-0.0002) on the TOGSS engage a hole (0.127") and a slot on the 'ISs. The pins have clearance of order 0.002 inch and a separation ~8.7". Thus, the 'ISs can be installed with +/- 0.8 arc minute repeatability. Two 10-32 screws torqued to "just snug" hold each 'IS to the TOGSS. The MISs can only be installed on the top or bottom quadrants, the SISs on the south and north.

    There are two independent MIS's: one with eight HEGs ("TMA-03") and one with eight MEGs ("TMA-04").

    There are two independent and identical SISs each with 5 LEG modules (30 LEG facets total on TOGA.) The SIS drawings are marked with "TMA-01" and "TMA-02". The SIS have been scribed with the identifiers "1A" and "1B"; "1A" is mounted in the South quadrant and 1B in the North. For reference, the grating plane is 0.5 mm above the module mounting surface. Modules mount with two screws 33 mm apart and 13.5 mm from the central facet center.

    The MST Grating Support Structure is capable of inserting and retracting the TOGA into/outof the TMA exit beam. This is accomplished with one stepper motor driver "door" type mechanism which swings the gratings in and out of the field of view about the vertical axis. Limit switches signal the position. The stepper motor is directly connected to the TOGA and inserts the TOGA in ~20 seconds. The basic resolution of the motor is 1.8 degrees (200 steps/rotation) and it is micro-stepped (without encoder.) The motor when static looks like a torsional spring, when combined with the high TOGA moment of inertia and low friction in the bearings, the motor-TOGA system can pendulate at a frequency in the 1 Hz range. This motion is less than 20 mm peak-to-peak and dies out in ~ 30 seconds. It will be a challenge to see this with an HSI data set!

    The gratings have maximum bake temperature of 40C and are '1238 tested at 26C.

    Alignment Tolerances and Methods

    Alignment tolerances ("three-sigma") between the TOGA alignment target and TMA alignment target were set (10/5/95 meeting at SAO) and are listed below.

       X (focus direction) : +/- 5 mm     theta_X (about FOA) : +/- 2 deg.
       Y (decenter) : +/- 1 mm            theta_Y (normality) : +/- 1 deg.
       Z (decenter) : +/- 1 mm            theta_Z (normality) : +/- 1 deg.
       Insertion repeatability (dtheta_X) = 0.1 degree.

    It is expected that these tolerances will be easily met. Cross hairs ("TMA-07") are available for decenter alignment and tip-tilt (via reflection). The cross hair disk, Edmund C39443, diameter 0.530", is mechanically constrained ("TMA-06") to a centering of +/- 0.020 inch (+/- 0.5 mm). Mechanical measurement can be used for X and theta_X (e.g., location of screw holes along horizontal line, TBD). The tilt (theta_Z) will have to be calibrated as so-many steps off the inserted-position limit switch to an accuracy of 0.1 degree or better.

    TOGA People

    Dan Dewey, MIT/HETG, 617 253-7244, fax 617 253-0861,  home 617 868-8140
    Ed Warren, MIT/HETG, 617 253-1366, fax 617 253-0861,
    Chris Pak, MIT/HETG, 617 253-9342
    Mike McGuirk, MIT/HETG, 617 253-3722
    Dick Elder, MIT/HETG, 617 258-7481
    Bert Brinkman, SRON/LETG, fax 011-3130-540860
    Bill Podgorski, SAO, 617 495 7363, fax 617 495-7098
    Jack Hughes, SAO, 495-7142
    Tim Norton, SAO, 617 495-7188 x304
    Tim Norton text beeper:
    SAO at XRCF control room: 205 961-4458, FAX: 205 961-4424
    Ed Kellogg, 205 544-8226
    Mark Ordway, SAO, trailer  at MSFC: 205 544-4515, 6060
                      XRCF clean room: 205 961-4453
    Jack Barberis, SAO Design, 617 495-7353, x176
    Dan Schwartz, SAO,  fax 617 495-7098
    Ed McLaughlin, SAO, 617 495-7362 x139
    Frank Cucuzzo, SAO, 617 495-7338
    Phil KcKinnon, SAO, 205 544-0579
    Charlie Jones, SAO, (205 544-0646 ?)
    Danny Johnston, MSFC, 205 544-6558
    Jay Carpenter, MSFC XRCF contam. control, 205 544-1313
    Ed Semms, MSFC bakeout facilities, 205 544-1751
    John Keidel, MSFC, 205 544-8626
    Ron Eng, MSFC, TMA alignment
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