HRC-S u,v to LSI Coordinate Mapping

Introduction

The HRC-S crossed-grid charge detector (CGCD) provides a 2-dimensional readout of event positions. However, the HRC-S MCPs and CGCD do not form a single plane; the two outer MCP segments are tilted so that the three segments approximate the circumference of the OTG Rowland circle. X-rays will interact with the MCPs at some location in 3-dimensions for which we receive only two numbers. In addition, discontinuities in the linear mapping of the location of an event on the MCP surfaces and the v-axis coordinate observed, caused by the tilts in the segments, must be accounted for. Some mapping between HRC-S u,v coordinates and x,y,z coordinates in the reference frame of the detector are needed. The CXCDS uses a Local Science Instrument (LSI) coordinate system to describe the 3-dimensional geometry of the detector (see Jonathan McDowell's Coordinates Memo for a description).

HRC-S V-axis MCP Segment Locations

Mapping of the locations of the ends of MCP segments and other fiducial points along the v-axis can be determined from flat-field illuminations done in the HRC lab. The following table lists these v-axis locations as well as the linear distance (6.4294 microns/pixel) along the MCP surfaces of the locations, taking into account the discontinuities between the MCP segments. Between the +Y and center segment a 0.1022 mm (15.9 pixels) discontinuity was removed; while between the -Y and center segment a discontinuity of 0.0874 mm (13.6 pixels) was removed. Also included in the table are descriptions and some general comments about the locations. The projection histograms of the flat-fields tend to have peaks at the ends of the MCP segments as if the region were brighter than over most of the segment. In some cases this may be caused by mis-located events. Note in particular that there are problems in determining the locations of the events at the inner end of the +Y segment (v > 16384) due to the lack of information from "left-most" of the three taps.

MCP Segment HRC v-coordinate Linearized Y (mm) Notes

+Y ~1190 154.255 Apparent physical end of +Y MCP segment
Exact location difficult to asses due to uncertainty in degapping

~1616 151.516 Edge of CsI photocathode
Exact location difficult to asses due to uncertainty in degapping

1664 151.207 Outer edge of first full 1/2 tap of CsI coated region

16384 56.567 Inner edge of last full 1/2 tap on the +Y segment

~16435 56.239 Edge of region with counts from the +Y segment
Events from v=16384 to here have incorrectly assign positions due to the lack of a "right-hand" tap amplifier

Center ~16960 52.965 Apparent physical edge of central segment

17024 52.554 Outer edge of first full 1/2 tap on the central segment
Still the brightened region at the end of the segment

~17060 52.322 Just off the bright end-region

24576 4.000 Detector readout center

25198 0.000 Nominal optic axis location (4 mm from detector center)

32128 -44.556 Outer edge of last full 1/2 tap on the central segment

~32165 -44.794 Start of brightened region at end of detector segment

~32250 -45.340 Apparent physical edge of central segment

-Y ~32930 -49.625 Apparent physical edge of -Y segment
Many events have zero signal on the "left-hand" tap

32960 -49.818 Just off the bright end-region

33024 -50.229 Inner egde of first full 1/2 tap on the -Y segment

47616 -144.047 Outer edge of last full 1/2 tap on -Y segment

~47632 -144.150 Edge of CsI photocathode coating
Exact location difficult to asses due to uncertainty in degapping

~48112 -147.236 Apparent physical edge of -Y segment

MCP Segment	HRC v-coordinate	Linearized Y (mm)	Notes
+Y	~1190	154.255	Apparent physical end of +Y MCP segment Exact location difficult to asses due to uncertainty in degapping
~1616	151.516	Edge of CsI photocathode Exact location difficult to asses due to uncertainty in degapping
1664	151.207	Outer edge of first full 1/2 tap of CsI coated region
16384	56.567	Inner edge of last full 1/2 tap on the +Y segment
~16435	56.239	Edge of region with counts from the +Y segment Events from v=16384 to here have incorrectly assign positions due to the lack of a "right-hand" tap amplifier
Center	~16960	52.965	Apparent physical edge of central segment
17024	52.554	Outer edge of first full 1/2 tap on the central segment Still the brightened region at the end of the segment
~17060	52.322	Just off the bright end-region
24576	4.000	Detector readout center
25198	0.000	Nominal optic axis location (4 mm from detector center)
32128	-44.556	Outer edge of last full 1/2 tap on the central segment
~32165	-44.794	Start of brightened region at end of detector segment
~32250	-45.340	Apparent physical edge of central segment
-Y	~32930	-49.625	Apparent physical edge of -Y segment Many events have zero signal on the "left-hand" tap
32960	-49.818	Just off the bright end-region
33024	-50.229	Inner egde of first full 1/2 tap on the -Y segment
47616	-144.047	Outer edge of last full 1/2 tap on -Y segment
~47632	-144.150	Edge of CsI photocathode coating Exact location difficult to asses due to uncertainty in degapping
~48112	-147.236	Apparent physical edge of -Y segment

Adding Another Dimension

If we assume that the tilts of the +Y and -Y segments are due to rotations only about the Z-axis and that the planes of the tops of the MCPs intersect as designed (i.e. the +Y and center planes intersect at 55.905 mm and the -Y and center planes intersect at -47.904 mm), then the X and Y locations, relative to the optic axis, of the points listed above can be determined.

For Linearized Y (y) greater than 55.905 mm
- X = sin(1.43)×(y - 55.905)
- Y = 55.905 + cos(1.43)×(y - 55.905)
For Linearized Y (y) less than -47.904 mm
- X = sin(1.22)×(-47.904 - y)
- Y = -47.904 - cos(1.22)×(-47.904-y)

MCP Segment HRC v-coordinate Y (mm) X (mm)

+Y ~1190 154.224 2.454

~1616 151.486 2.386

1664 151.177 2.378

16384 56.567 0.017

~16435 56.239 0.008

Center ~16960 52.965 0.0

17024 52.554 0.0

~17060 52.322 0.0

24576 4.000 0.0

25198 0.000 0.0

32128 -44.556 0.0

~32165 -44.794 0.0

~32250 -45.340 0.0

-Y ~32930 -49.625 0.037

32960 -49.818 0.041

33024 -50.229 0.050

47616 -144.025 2.047

~47632 -144.128 2.049

~48112 -147.213 2.115

MCP Segment	HRC v-coordinate	Y (mm)	X (mm)
+Y	~1190	154.224	2.454
~1616	151.486	2.386
1664	151.177	2.378
16384	56.567	0.017
~16435	56.239	0.008
Center	~16960	52.965	0.0
17024	52.554	0.0
~17060	52.322	0.0
24576	4.000	0.0
25198	0.000	0.0
32128	-44.556	0.0
~32165	-44.794	0.0
~32250	-45.340	0.0
-Y	~32930	-49.625	0.037
32960	-49.818	0.041
33024	-50.229	0.050
47616	-144.025	2.047
~47632	-144.128	2.049
~48112	-147.213	2.115

Adding the Last Dimension

The u-axis of the HRC-S is aligned with the spacecraft Z-axis. Because of the need to shield the High-Energy Suppression Filter during the flat-field illuminations, to prevent reflections from compromising the measurements, the low u-axis edge of the HRC-S is not readily determined from the data. The lower edge of the active area is roughly at a u of ~560; the upper edge is at ~3536. However, since the SIM motion allows us to place the aim-point of the HRMA at any u-coordinate we are free to choose the detector readout center of u = 2048 as the Z = 0.0 mm line. Using this assignment and the pixel scale (6.4294 microns/pixel), the Z-locations of the edges are at -9.567 mm (for u = 560) and 9.567 mm (for u = 3536). The nominal optic axis location, (Y,Z) = (0.0,0.0) is at u,v = (2048, 25198).

The table below gives the (u, v) and LSI (X, Y, Z) coordinates of the corners of the "active" area of each of the MCP segments, where the active areas are the regions coated by CsI but are outside the "bright" regions near the ends of the segments or where the the events locations may be piled up due to mis-location.

Segment u v LSI X (mm) LSI Y (mm) LSI Z (mm)

+Y 560 1616 2.386 151.486 -9.567

3536 1616 2.386 151.486 9.567

560 16384 0.017 56.567 -9.567

3536 16384 0.017 56.567 9.567

Center 560 17060 0.000 52.322 -9.567

3536 17060 0.000 52.322 9.567

560 32165 0.000 -44.794 -9.567

3536 32165 0.000 -44.794 9.567

-Y 560 32960 0.041 -49.818 -9.567

3536 32960 0.041 -49.818 9.567

560 47632 2.049 -144.128 -9.567

3536 47632 2.049 -144.128 9.567

Segment	u	v	LSI X (mm)	LSI Y (mm)	LSI Z (mm)
+Y	560	1616	2.386	151.486	-9.567
3536	1616	2.386	151.486	9.567
560	16384	0.017	56.567	-9.567
3536	16384	0.017	56.567	9.567
Center	560	17060	0.000	52.322	-9.567
3536	17060	0.000	52.322	9.567
560	32165	0.000	-44.794	-9.567
3536	32165	0.000	-44.794	9.567
-Y	560	32960	0.041	-49.818	-9.567
3536	32960	0.041	-49.818	9.567
560	47632	2.049	-144.128	-9.567
3536	47632	2.049	-144.128	9.567

Dr. Michael Juda
Harvard-Smithsonian Center for Astrophysics
60 Garden Street, Mail Stop 70
Cambridge, MA 02138, USA
Ph.: (617) 495-7062
Fax: (617) 495-7356
E-mail: mjuda@cfa.harvard.edu