HRC-I On-Orbit Shutter Focus Simulations

• Introduction
• Simulations
• Results
• Conclusions
• Index of Results
• Original Simulations

Introduction

This page summarizes the simulations of the HRC-I on-orbit shutter focus algorithm. The simulations represent measurements HI-2.[6,7] and HI-4.2. Using spectra for LMC X-1 and HR1099 and exposure times from the OAC timeline, the simulations explore the effects on the determination of focus and inter-optic tilts of

• the placement of the SIM along the optical axis;
• uncertainty in the position of the shutters relative to the image;
• uncertainty in the angular positions of the shutters,
• uncertainty in the source's position relative to the optical axis

The shutter focus algorithm is derived from the alignment formulae described in L. Van Speybroeck's 01/03/1990 memo X-ray Alignment Formulae and implemented in the script qsf.

The alignment algorithm uses the HRC shutters as quadrant shutters. Centroids are calculated for each quadrant and combined as described in X-ray Alignment Formulae to determine the defocus and tilts between the optics.

Simulations

Rays were generated using trace-nest1 with the orbit_XRCF+tilts_01 configuration database. Initially, 100 independent simulations were run for both sources, with the detector centered on the image in the focal plane, the shutters in their ideal positions, and ideal source position (on-axis) for the following defocus values: ± 1, ± 0.5, ± 0.25, ± 0.1, ± 0.05, and 0 mm.

Three additional studies were run with LMC X-1 as the source, with the following scenarios:

• The image was not placed at the nominal position relative to the shutters.
  The shutters were positioned nominally and the image was positioned at the interstices of a 5 x 5 grid with 10 micrometer spacing, centered at the nominal image position.
• The shutter blades had incorrect angular positions.
  The shutters were positioned at ± 0.25, ± 0.125, ± 0.0625, and 0 degrees relative to their nominal positions. These correspond to ± 4, ± 2, ± 1, and 0 encoder steps, respectively. The focus calculations were done assuming the nominal angular positions.
• The source was not placed on axis.
  The source was placed in each of 24 different positions relative to the optical axis. Source positions were defined in polar coordinates, with theta equal to 0, 5, and 10 arcseconds and phi equal to 45, 90, 135, 180, 225, 270, 315 degrees.

Results

• Focus error vs. Defocus
  These show the error in the focal position derived by the quadrant shutter algorithm as a function of the SIM X offset from nominal focus. Positive numbers indicate that the determined focus was too close to the HRMA. A focus error of 0 indicates a spot-on prediction. Results from all 100 simulations are shown.
• 95 Percentile Focus error vs. Defocus
  These present the 95% confidence levels as a function of the SIM X offset from nominal focus; 95% of the simulations derived a focal error less than or equal to that plotted. Smaller is better.
• Y Tilts vs. Defocus, Y Tilts vs. Defocus
  Plots of Y and Z inter-optic tilts. What's important here is the stability of the determination, rather than its actual value.

• Ideal Setup
• Displacement of image relative to shutters
• Error in Shutter Angular Positions
• Off-Axis Source Placement

Conclusions

While the magnitude of the various offsets we have chosen are fairly significant, their effects on the focus error are small. The 95th percentile focus errors vary by no more than 0.009 mm for any given position along the optical axis.

One interesting trend to note is that the magnitude of the focus error is not symmetric about the focal point. Instead, it reaches its minimum 0.25 mm towards the HRMA. This implies that to attain best focus, we would like to place the detector one the +X side of the focal point, towards the HRMA.

Index of Results

Below are links to navigation maps and tables for the detailed plots for each configuration. One can use either the maps or the tables. To use the maps, simply click on the colored points in the map; each point represents an offset from the ideal detector, shutter, and source placement. To use the tables, click on the checkmarks. Clicking on the images of the plots will bring up PostScript figures for your amusement.

• Ideal Setup
• Displacement of image relative to shutters
• Error in Shutter Angular Positions
• Off-Axis Source Placement

Ideal Setup

• LMC X-1
• HR1099

Displacement of image relative to shutters

Theta Phi Y Z +Y -Y GIF 0 0 -0.02 0.02 0.0000 0.0000 0 0 -0.02 0.01 0.0000 0.0000 0 0 -0.02 -0.00 0.0000 0.0000 0 0 -0.02 -0.01 0.0000 0.0000 0 0 -0.02 -0.02 0.0000 0.0000 0 0 -0.01 0.02 0.0000 0.0000 0 0 -0.01 0.01 0.0000 0.0000 0 0 -0.01 -0.00 0.0000 0.0000 0 0 -0.01 -0.01 0.0000 0.0000 0 0 -0.01 -0.02 0.0000 0.0000 0 0 0.00 0.02 0.0000 0.0000 0 0 0.00 0.01 0.0000 0.0000 0 0 0.00 -0.00 0.0000 0.0000 0 0 0.00 -0.01 0.0000 0.0000 0 0 0.00 -0.02 0.0000 0.0000 0 0 0.01 0.02 0.0000 0.0000 0 0 0.01 0.01 0.0000 0.0000 0 0 0.01 -0.00 0.0000 0.0000 0 0 0.01 -0.01 0.0000 0.0000 0 0 0.01 -0.02 0.0000 0.0000 0 0 0.02 0.02 0.0000 0.0000 0 0 0.02 0.01 0.0000 0.0000 0 0 0.02 -0.00 0.0000 0.0000 0 0 0.02 -0.01 0.0000 0.0000 0 0 0.02 -0.02 0.0000 0.0000

Error in Shutter Angular Positions

Theta Phi Y Z +Y -Y GIF 0 0 0.00 -0.00 -0.2500 0.0000 0 0 0.00 -0.00 -0.1250 0.0000 0 0 0.00 -0.00 -0.0625 0.0000 0 0 0.00 -0.00 0.0000 -0.2500 0 0 0.00 -0.00 0.0000 -0.1250 0 0 0.00 -0.00 0.0000 -0.0625 0 0 0.00 -0.00 0.0000 0.0000 0 0 0.00 -0.00 0.0000 0.0625 0 0 0.00 -0.00 0.0000 0.1250 0 0 0.00 -0.00 0.0000 0.2500 0 0 0.00 -0.00 0.0625 0.0000 0 0 0.00 -0.00 0.1250 0.0000 0 0 0.00 -0.00 0.2500 0.0000

Off-Axis Source Placement

Theta Phi Y Z +Y -Y GIF 0 0 0.00 -0.00 0.0000 0.0000 5 0 0.00 -0.00 0.0000 0.0000 5 45 0.00 -0.00 0.0000 0.0000 5 90 0.00 -0.00 0.0000 0.0000 5 135 0.00 -0.00 0.0000 0.0000 5 180 0.00 -0.00 0.0000 0.0000 5 225 0.00 -0.00 0.0000 0.0000 5 270 0.00 -0.00 0.0000 0.0000 5 315 0.00 -0.00 0.0000 0.0000 10 0 0.00 -0.00 0.0000 0.0000 10 45 0.00 -0.00 0.0000 0.0000 10 90 0.00 -0.00 0.0000 0.0000 10 135 0.00 -0.00 0.0000 0.0000 10 180 0.00 -0.00 0.0000 0.0000 10 225 0.00 -0.00 0.0000 0.0000 10 270 0.00 -0.00 0.0000 0.0000 10 315 0.00 -0.00 0.0000 0.0000 15 0 0.00 -0.00 0.0000 0.0000 15 45 0.00 -0.00 0.0000 0.0000 15 90 0.00 -0.00 0.0000 0.0000 15 135 0.00 -0.00 0.0000 0.0000 15 180 0.00 -0.00 0.0000 0.0000 15 225 0.00 -0.00 0.0000 0.0000 15 270 0.00 -0.00 0.0000 0.0000 15 315 0.00 -0.00 0.0000 0.0000

Original Simulations

A link to the original simulations is provided here. It is here simply for completeness. The new simulations referenced on this page supercede the results presented with the older simulations. The simulations on this page are more realistic and explore a wider range of effects on the focus determination. If you do compare between the old and new simulations please note that we have changed coordinate systems between the two. This older simulations were done using the OSAC coordinate system and the newer simulations on this page were done using the HRMA coordinate system. This is evident is the plots of focus error vs. distance from focus where the slope of the plot is reversed due to the change in sign of the optical axis in the two systems.