Introduction

The following summarizes requirements on HRMA and HRMA/SI calibration. The following lists of calibration measurements assume that the HRMA meets the CTT requirement that the XRCF test environment shall have not more than a 10% effect on the encircled energy in 1 arcsec raw data, and that it can be calibrated to 1%. This implies that the offloading scheme has been implemented in the HRMA.

It should be remembered that there are additional calibrations needed for

aspect system
Tracking
gyros
other parts of the PCAS
spacecraft timing, and checks on timing accuracy for all SIs after integration in the spacecraft
ficucial lights & periscope
~~HRMA actuators~~
alignments
optical metrology data: lengths and diameters with errors on mirror elements, optical interferometer data on surface figure
throughput and imaging stability test: an end-to-end test that can be used after the XRCF to verify that the x-ray throughput and imaging quality have not been degraded.

The tables on the following pages give a summary of the integration times for HRMA and HRMA/SI calibration. We are in the process of adding the overhead times to give the total time needed.

Table 1 gives an overall summary of the requirements, compared with those for the VETA-I test, and shows why each new piece of required calibration instrumentation is needed. The significant new measurement requirements are shown in bold face type in the Accuracy Requirement column. The new instrumentats required are shown in the Additional Instrument Required:Type column. We have tried to distinguish the original new requirements and instruments from additional requirements and instruments that would also have been operative, by showing the additional ones in italics. In addition to the specific instruments there is a need for the Master Controller to operate the system efficiently, performing such functions as issuing test directives, collecting and archiving data, providing an accessible database and providing an analysis environment.

See Table 1: Calibration Instrument Requirements Summary

Table 2 shows the estimated data acquisition time for all the calibration measurements.

See Table 2: Total data acquisition time for all configurations

We use the XRCF facility coordinate system, which has the same general orientation and sense as the spacecraft coordinate system. The following illustrates it:

This quantity referred to later in the tables, PRF/Encircled Energy/Effective Area , is more rigorously defined as , the differential effective area per unit solid angle in the back hemisphere as function of

: incident angles of x-rays hitting HRMA

: emerging angles from HRMA to focal plane

: polarization

E : energy

: x-ray intensity

: position of detector along telescope axis (i.e. focus)

Also a function of filter inserted, aging effects, radiation damage, magnetic fields, microphonics, calibration source leakage, etc.

For the gratings, this quantity as a function of position along the dispersed spectrum, together with the limit on spectral resolution imposed by the pixel size of the readout device, be it the HRC, the ACIS or the internal detector of the BCS, tells how well energy resolution can be measured. For example, with the LETG, the first order spectrum covers about 10mm on the HRC, going from 0 to 140A wavelength.

Therefore, The dispersion is 1.4 A/mm, or 0.0175 A per 12.5 m tube diameter along the dispersion direction. The expected resolution at 70 A is 0.047 A, so there are 2.67 independent measurements within the spectral PRF. As the spatial sampling frequency is 2 or 3 times greater than the resolution, we can measure the width of the resolution to about TBD.

We need a model to be able to interpolate between measured data points. We will use a relatively sparse matrix of data points, and use the model to calculate the properties of AXAF for values of the parameters .

Algorithms for Calculating Data Acquisition Time¹

Assumptions:

Off-axis rotation of the HRMA plus SIM = 10 min = 600 sec
Source energy change = 900 sec = 15 min. This includes setting up detector gains and high voltages.
Motor motion (see footnote² ): t_m = (4.5 sec + 1.6 sec mm^-1)
Time to come to thermal equilibrium = 1 day (=86,400 sec) for measurements vs. T.
We assume this overhead is incurred only for the encircled energy measurements, because a later shuffling of the schedule will permit us to do all measurements at each T, only requiring change of T once. This will require that the SIM and HXDS/XDA be mounted together and we can switch between them without breaking vacuum.
Times to acquire data for HRC and ACIS and to move the SIM are the same as for comparable HXDS equipment. This one should be checked.

Algorithms:

Motor motion
- t_m (d) = 4.5 + 1.6d sec
  (d in mm)
Centering the aperture on the beam; necessary each time we change apertures, off-axis angles, temperatures and energies
- beamcen(t_i) = 127+6t_i sec, or if a move is done as well,
- beamcen(d, t_i) = t_m(d)+127+6t_i sec
  where t_i is integration time
Alignment
- hsialign(t_i) = 268 + 4t_i sec
- mcaalign(n_z, n_y, t_i ) = 235 + 14 n_z + n_z n_y x (97 + 2 t_i ) sec
  where n_z = number of z positions and n_y = number of y positions
Simple proportional counter data acquisition with nomove
- mcadata(t_i) = t_i + 15 sec
Simple proportional counter data acquisition with a move of d
- mcadata(d, t_i) = t_m (d) + t_i + 15 = 19.5 + 1.6d + t_i sec, or
- mcadata(d, t_i
  1:n₁,t_i
  2:n₂ ...t_ij:n_j) = m x t_m (d) + n_j x mcadata(d,t_ij)
2D scans: mcascan(n_z, n_y, t_i ) = 215 + 14 n_z + n_z n_y x (22 + t_i ) sec
1D Scans: beamceny(n_y, t_i ) = 64 + 3.5 n_y t_i
beamcenz(n_z, t_i ) = 64 + 3.5 n_z t_i
Encircled energy or effective area exposure
- EE(t_i, t_i
  1:n₁, t_{i 2}:n₂, ... t_im:n_m) = x beamcen(t_i) + mcadata(200, t_{i 1}:n₁,t_{i 2}:n₂ ...t_ij:n_j ), where t_ij is the integration time for the j-th pinhole
  = (6t_i + 342) +
HSI Exposure
- hsiimage(t_i , d) = (5.5 +t_i + 1.6 x d) , sec
  d in mm
Compounding of proc(t_i , param.) at various off-axis angles( n ), temperatures( n ) and energies( n ): in general,
- Proc(t_i, param., n, n, n) = {[proc(t_i , param.)x n + 600 x (n - 1)] x n + 900 x (n - 1)} x n + 86,400 x (n - 1), sec
so for specific cases
- EE(t_i, t_i
  1:n₁,t_{i 2}:n₂ ...t_im:n_m n, n, n) = {[ ( (6t _i + 342) + )x n + 600 x (n - 1)] x n + 900 x (n - 1)} x n + 86,400 x (n - 1), sec
- hsiimage(t_i, d, n, n, n) = {[(5.5 +t_i + 1.6 x d)x n + 600 x (n - 1)] x n + 900 x (n - 1)} x n + 86,400 x (n - 1), sec
- beamceny(n_y, t_i, n, n, n) = {[beamceny(t_i, n_y)x n + 600 x (n - 1)] x n + 900 x (n - 1)} x n + 86,400 x (n - 1), sec

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See Table 3: Initial Measurements: Alignment and Focus

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See Table 4: HRMA PRF/Encircled Energy/Effective Area

See Table 5: HRMA/LETG/HXDS

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See Table 6: HRMA/HETG/HXDS

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See Table 7: HRMA/HRC-I

See Table 8: HRMA/ACIS

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See Table 9: HRMA/LETG/HRC

See Table 10: HRMA/LETG/ ACIS

See Table 11: HRMA/HETG/ACIS

See Table 12: HRMA Off-line measurements

See Table 13: SI Off-line measurements

See Table 14: Facility Characterizations

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See Table 15: Calibration Targets, Filters, Engergies and Detectors.

The following, Table 16 , gives the required PRF measurement accuracy to allow detection of the weakest possible sources near a strong point source, as a function of the strength of the strong source and the angular separation between the two sources.

See Table 16: Required PRF Accuracy for Four Strong Source Strengths

In the analysis going into the derivation of this table, many assumptions were made. Some of them are

The duration of an observation is 10⁵ sec
The PRF measured at HRMA calibration is identical to the VETA-I result obtained with the HSI at Zr-L
There are 3 sources of error: counting statistics in the on-orbit observation, a 1% error in EE at 1 arcsec radius in correcting for XRCF effects in measuring the PRF, and the accuracy of measuring the PRF at the XRCF. The latter is that quoted in Table 12
The PRF fits a power law vs. radius for the purpose of accounting for the 1% EE error
The smallest number of counts that constitutes a detected source on-orbit is 50 counts

The counting rate from the Crab is 1000 s^-1.

The following figure shows the intrinsic energy resolution of the K lines from solid electron impact targets as a function of the energy. This illustrates the problem that at energies below 1 keV, there are no solid target lines narrow enough to calibrate the energy resolution of the AXAF gratings.

1. See "Notes on HRMA Timeline", R. Brissenden, SAO, 6/3/92. All XDACS times were reduced by 1/2 to model the speedup of the HXDS over the VXDS.

2. J. Roll, SAO, private communication, 7/2/92.

Introduction

Coordinate Systems

Definition of Telescope Properties Measured