two-dimensional metrology with flatbed scanners at room
TRANSCRIPT
Informes Técnicos Ciemat 945diciembre, 2000
Two-Dimensional Metrology withFlatbed Scanners at Room andLiquid Nitrogen Temperatures
A. Grau CarlesA.GrauMalonda
Instituto Estudios de la Energía
Toda correspondenica en relación con este trabajo debe dirigirse al Servicio de
Información y Documentación, Centro de Investigaciones Energéticas, Medioambientales y
Tecnológicas, Ciudad Universitaria, 28040-MADRID, ESPAÑA.
Las solicitudes de ejemplares deben dirigirse a este mismo Servicio.
Los descriptores se han seleccionado del Thesauro del DOE para describir las materias
que contiene este informe con vistas a su recuperación. La catalogación se ha hecho
utilizando el documento DOE/TIC-4602 (Rev. 1) Descriptive Cataloguing On-Line, y la
clasificación de acuerdo con el documento DOE/TIC.4584-R7 Subject Categories and Scope
publicados por el Office of Scientific and Technical Information del Departamento de Energía
de los Estdos Unidos.
Se autoriza la reproducción de los resúmenes analíticos que aparecen en esta
publicación.
Depósito Legal: M -14226-1995ISSN: 1135-9420ÑIPO: 238-00-002-0
Editorial CIEMAT
CLASIFICACIÓN DOE Y DESCRIPTORES
S46MEASURING INSTRUMENTS; MEASURING METHODS; IMAGE SCANNERS;
CALIBRATION; NITROGEN; CERN
Two-Dimensional Metrology with Flatbed Scanners at Roomand Liquid Nitrogen Temperatures
Grau Carles, A.; Grau Malonda, A.
81 pp. 24 fig. 8 refs.
Abstract:
We study the capability of the commerçai flatbed scanner as a measuring instrument of two-coordinatesamples both at room and liquid nitrogen temperatures. We describe a simple procedure to calibrate thescanner, and the most adequate standard configuration to carry out the measurements. To ilústrate theprocedure, we measure the relative positions of the conductors in a cross^ection of a superconductingmagnet of CERN.
Metrología Bidimensional con Escáneres Planos a Temperatura Ambientey a la del Nitrógeno Líquido
Grau Carles, A.; Grau Malonda, A.
81 pp. 24 fig. 8 refs.
Resumen:
Se estudian las posibilidades del escáner plano comercial como instrumento de medida en muestrasbidimensionales tanto a temperatura ambiente como a la temperatura del nitrógeno líquido. Se describeun procedimiento simple de calibración del escáner, así como el patrón más adecuado para realizar lasmedidas. A modo de ejemplo, se han medido las posiciones relativas de los conductores en una seccióntransversal de un imán superconductor del CERN.
CONTENTS
1. Introduction 1
2. Metrology with flatbed scanners 2
2.1. General characteristics of flatbed scanners 2
2.2. Definition of point 5
2.3. Standard 6
2.4. Optical Interfaces 7
2.5. Calibration of the scanner 8
2.6. Precision of the device 8
3. Measurements at liquid nitrogen temperature 11
3.1. Experimental setup 11
3.2. The thermal isolation of the scanner 13
3.3. Test of the device 14
4. Measurement of mechanical deformations in the magnet cross section
16
4.1. Adjustment of the scanning parameters 17
4.2. Histogram of scanned images 20
4.3. The program MAGNET.LSP 23
4.3.1. Calibration of the scanner 23
4.3.2. Image scaling. Measurement of the vertex coordinates 26
4.3.3. Measurement of other interesting geometrical
quantities 31
4.3.4. Intersection of nominal positions onto the image 33
4.4. The program MAG^ET.FOR 34
4.4.1. Six block dipole configurations 35
5. Measurement of thermal deformations 36
6. References 37
APPENDIX A: Input files in the program MAGNET.FOR 1
APPENDIX B: The output data file SAL 7
Two-Dimensional Metrology with Flatbed Scanners at Room andLiquid Nitrogen Temperatures
A. Grau Caries, A. Grau Malonda
1. Introduction
The application of commercial flatbed scanners for two-dimensional (2D)
measurements is apparently an unexplored field [1,2]. The main reason for this
surprising fact seems to be that, only in the few last years, flatbed scanners have reached
acceptable optical qualities and resolutions. The improvement of the scanner
capabilities has been accompanied by a parallel improvement in speed and memory of
today Personal Computers (PC). Scanning and tonal correction of high-resolution
images requires a last generation PC. For example, a colored (32-bit) image of 200x 200
mm2, and resolution of 600 samples per inch (spi) needs 87 Mbytes. From a
metrological point of view, a resolution of 600 samples per inch is equivalent to a
precision of 0.042 mm. Therefore, accurate measurements may require one to make use
of a large amount of computer memory.
However, the application of the scanner for two-coordinate measurements offers
several advantages. First, the fact of obtaining a bitmapped image reveals to be the most
adequate method to analyze an object with great detail. We should notice that large
memory is needed because images contain very much information. Second, the
correction of perspectives is not required like in photogrammetry. Third, the software
required to correct images is complete and easily available (Photoshop, CorelPhoto-
Paint, PhotoPlus, etc.) '
The aim of this report is to compile our knowledge about 2D metrology with
scanners, both at room and liquid nitrogen temperatures, and illustrate the procedures
applied to measure mechanical and thermal deformations in composite fiat samples. In
particular, we will measure the coordinates of the keystone vertex points on a
superconducting magnet cross-section of the Large Hadron Collider (LHC) of CERN
[3,4]. This report is divided into three parts. The first part describes the optical and
mechanical characteristics required to carry out measurements with a flatbed scanner,
and the procedure applied to calibrate it. The second part gives details of the device
built to measure thermal contraction and deformations in a flat sample when it is cooled
at liquid nitrogen temperature. The third part is a complete description of the procedure
and the computer codes developed to measure points, angles and lengths into the
scanned image.
2. Metrology with flatbed scanners
Commercial scanners are not usually applied for dimensional measurements.
Therefore, the scanner possibilities as a metrological instrument must be conveniently
analyzed. Clearly, absolute measurements are not possible, only relative measurements
with the aid of a standard can be carried out. The best characteristics of the standard are
not clear. Flatbed scanners are not microscopes, and standards usually applied in
microscopy are not the best for scanner applications.
For measurements at liquid nitrogen temperature, the sample must be protected
from cool, and scanned at certain height from the scanner window. Since conventional
scanners are not ready for distant scans, the best characteristics of the optical interface
must be studied.
2.1. General characteristics of flatbed scarifiers
The components of flatbed scanners are basically three: a linear array of sensors, an
optical interface and one stepper motor. Sensors are commonly thousands of CCD
(Charged-Coupled Devices). Each sensor takes in a single sample of data. E.g., a
scanner of optical resolution 300 spi contains 300 CCD on the linear array. The working
scheme of a CCD is very similar to a photomultiplier tube (PMT), i.e., CCD sensors
transform light into an electrical signal of amplitude that depends on light intensity.
However, reading a color or a tone requires some conversion. The analog-to-digital
(A/D) converter turns the signal created by the sensor into a number.
Depending on CCD characteristics, bit depth, dynamic range and tonal sensibility
of the scanner are different. Bit depth is a measure of how many colors or tones the
scanner can potentially capture. A 1-bit per sample scanner can only capture 2 colors,
while a 24-bit scanner can measure any of the 224=16,777,216 different colors. Dynamic
range describes how far are the limits of color and tonal differentiation from light to
dark. Dynamic range represents what is called in photography density. Density of a film
is obtained by subtracting the minimum and maximum tonal rates the film can capture.
Tonal sensibility refers to the ability of the scanner to differentiate similar tonal values.
The efficiency to capture light is not the same for a scanner and a human eye or a
camera film. The response of the scanner is linear while the response of a human eye or
a film is logarithmic. For such a reason, bit depth of the scanner must be very large to
capture sufficient information in densest areas, where the logarithmic curve of a film is
much more effective than the linear curve of a scanner. The interface distance between
the scanned object and the array of sensors requires the use of convergent lenses, and
optionally mirrors. Figure 1 illustrates the optical interface differences between
SIMPLEX (Compeye) and EPSON GT-12000 scanners.
vL) Lamp
i MirrorsCCD
A I
LJ y Lens'
Lamp/Mirror Unit
i r* n nu I V ICCD Lens Unit
Sensors
(a)
Scanner Window/
Mirror Unit
(b)
Fig. 1. Optical interfaces for two different flatbed scanners: (a) SIMPLEX(Compeye), and (b) EPSON GT-12000
The motors of many flatbed scanners move in increments, which are exactly the
same as the scanner resolution. These scanners are said to have the same vertical and
horizontal resolutions. However, for the majority of scanners the motor step increments
are smaller than resolution. For instance, a 300 x 600 spi scanner has 300 CCD per inch,
but the motor moves in 1/600-inch increments. The interpolated resolution, which is
always considerably higher than optical resolution, refers to the scanner software
capability to interpolate data during the scanning process.
The usual maximum optical resolution for commercially available scanners is 2,000
spi. However, some new scanners (Agfa DuoScan T2500, Agfa XY-15) offer optical
resolutions up to 5,000 spi. Since lenses and mirrors are essential components of the
scanner, the selection of equipment from a company with long experience in optical
components is a guaranty for good quality in the scanned images. However, better
optics only increases the precision of the device twice or three times. We should remark
that commercially available scanners are, for the moment, not designed for working like
a microscope, and zooms larger than x 20 are always defocused. Therefore, a precision
better than 0.01 mm is not accessible even for the best commercial scanners.
Figure 2 compares enlarged images of a magnet cross section for two different
optical quality scanners. Although the image quality is much better for (b) than for (a),
the measurement of vertex coordinates by extrapolation is quite similar in both cases.
(a) (b)
Fig. 2. Enlarged images with identical resolutions (1,200 dpi) obtained for two differentoptical quality scanners: (a) ScanEasy 9630, and (b) Agfa DuoScan T1200.
2.2. Definition of point
Geometry defines a point as the intersection of two lines. However, lines are ID
objects, and therefore mathematical idealizations. Scanners, similarly to human eye,
detect the separation line between two complementary colors much better than a thin
line on one single color. Figure 3 illustrates, for different geometrical configurations,
the adopted definition of point, i.e., the vertex generated by the intersection of two
straight boundaries of complementary colors.
Fig. 3. Definition of a point as the intersection oftwo straight boundaries
When no points are identified on the sample, they must be plotted on the sample
surface (e.g., with a 0.5 mm flat pen). In such a case, points are defined by one of the
four corners generated by two crossing thick lines (Figure 4). The points defined by
two crossing thick lines are the best method to determine the contraction percentage
between room and liquid nitrogen temperatures in homogeneous plates.
Fig. 4. Scanners better detect the 4corners generated by the intersection oftwo thick lines
23.Standard
A standard must fulfill two conditions to be suitable for scanner measurements.
First, points must be defined as described above. Thin lines are therefore not suitable
(specialists in reprography know well that line-art scanning requires always much
higher resolutions than conventional scanning). Second, the position of the points into
the standard should be easily verified by other methods.
The standard in Fig. 1 was plot on a rigid transparent material (e.g., glass or quartz)
to conserve flatness. The points of interest were measured with a microscope [5]. The
standard consisted of a mesh of 4 mm side black squares. The squares were labeled
with two numbers (denoting the file and the column) to facilitate the identification of
each square inside the mesh. The separation distance between the squares was 14 mm.
In addition, squares of 2 mm were inserted into the mesh to study the behavior of
smaller structures.
Fig. 5. Geometry of the standard
The left-up vertexes of all squares can be selected as points for the standard. The
size of the standard must be similar to the sample we want to measure.
2.4. Optical interfaces
The protection of the CCD sensors from cool requires several millimeters of
isolator over the scanner window. Unfortunately, focussing mechanisms along
directions perpendicular to the scanner surface (Z-axis) are not available for
commercial flatbed scanners. The separation distance between the sample and the lens
is always conserved for normal scanning. The problem of defocusing can be partially
avoided for some scanners of special optical interfaces. However, for the majority of
scanners, images are completely defocused if the sample is placed only a few
millimeters over the scanner window. Therefore, the selection of an adequate scanner
for our porpoises depends largely on the optical interface.
Figure 6 simulates the scanner defocusing effect when the sample is placed at
increasing distances form the convergent lens. Defocusing occurs because CCD sensors
do not fall exactly on the image. However, we should notice that the position of the
image does not change appreciably when objects are far away from the lens, and CCD
sensors are near the focus.
Fig. 6. Images resulting from increasing lens-object distances
We conclude that good scanners for cold measurements must have large optical
lengths between the sample and the lens. As a rule of thumb, the presence of mirrors
helps to increase appreciably the optical length, and is a good reference point to
consider a scanner among the best candidates for cold measurements.
2.5. Calibration of the scanner
The coordinates of all points (as they were defined in 2.2) must be referred to a
two-coordinate reference frame. The vertical direction, or 7-axis, is defined along the
direction of movement of the motor, while the horizontal direction, or X-axis, is defined
perpendicular to it. Both the X- and the 7-axis can be translated everywhere inside the
scanning surface.
When the step increments of the motor are perfectly synchronized with the
scanning resolution, X- and 7-scales are identical. However, if the stepper motor moves
uniformly, but it is not well synchronized, or the sample is scanned several millimeters
over the scanner window (i.e., Z is different from zero), the horizontal and vertical
scales are no longer identical. Fortunately, the ratio between the horizontal and vertical
scales is generally conserved during the scanning process, and can be easily corrected.
Making use of a two-coordinate standard (e.g., the one shown in Figure 1), we can
determine the scale factors fx and fy, and afterwards the scale ratio d = fxlfy of
one scanned image. Therefore, any point P of coordinates (xn,yn) in the image must
be transformed into \fxxn,fyynj. Figure 6 illustrates that the more we increase the
separation distance between the object and the scanner window (i.e., Z), the more we
reduce the size of the image along the X-axis direction. The linear behavior of the curve
is in agreement with the expected geometrical optics of a convergent lens.
The separation distance between the sample and the scanner window does not
modify the scale of the 7-axis. The reason is obviously that 7-scale depends only on the
step increments of the motor, but not on the optical interface.
2.6.Precision of the device
Apparently, the device can measure lengths with a resolution, which is in
agreement with the optical resolution of the scanner. For instance, a scanner of optical
resolution 1,200 spi should be able to measure lengths with a precision of 21.2 (am.
However, this resolution refers to the scanner capability to reproduce one spot of small
size into the scanned image.
The adopted definition of point in Section 2.2 involves one more elaborated
concept. The intersection of two straight boundaries is obtained by fitting hundreds of
sample points of the same characteristics (e.g., same level in the gray scale). Therefore,
the uncertainty in position of one point refers to the intersection of two lines fitted by
least square fitting.
Let (xp,yp) be the coordinates of the point P that results from the intersection of
the two fitted boundaries yp = äxp +b' and yp = a" Xp + b". The uncertainty in yp
must consider the standard deviation of both fitted lines. Thus,
(1)
1.005
0.995 i0.99 -,
0 0.985 -j
1 0.98 -i
I 0.975 i« 0.97 -j
0.965 i
0.96
0.955
0.95 -I0
Y-axis
• X-axis
4 6 ¡
Distance (mm)10
—1
12
Fig. 7. Variation of the horizontal and vertical scales forincreasing distances between sample and the scannerwindow (Z distance)
By applying the same notation for both lines, we have for the standard deviation:
(2)
where
\2Syt-yp?= 0.6745-\M , (3)
n-2
(4)
being n the number of samples with the same tonal level, and (x,-,^) their respective
coordinates.
The standard deviation obtained from the intersection of two straight boundaries is
always less than the scanner resolution. To illustrate this fact, we measured the length
between two points along the horizontal and vertical directions of the standard in Fig. 5.
The scanner optical resolution was 800 spi. Table 1 gives the results obtained by
intersecting boundaries for 8 different assays.
Table 1. Measurement of 8 lengths along the horizontal and vertical directions by themethod of intersecting straight boundaries
Assay
12345678
Horizontal(mm)
36.01536.00836.01535.99136.00035.99735.981
, 35.98135.99±0.01
Vertical(mm)
36.02336.04236.03135.98236.03735.98236.03136.046
36.02±0.02
We should notice that the uncertainty along the vertical direction is nearly twice
larger than along the horizontal direction. The Lamp/Mirror and the Lens units of the
10
scanner EPSON GT-12,000 carry out different length step increments to get focussed
images on the CCD sensors unit, which remains still. Obviously, the simultaneous
calibration of two stepper motors is more inaccurate than the calibration of one single
motor. The comparison of standard deviation along the horizontal direction in Table 1
with the optical resolution of the scanner (800 spi) reveals that the method of
intersecting boundaries is three times more accurate than any other method based on
microscopic marcs. The optical resolution suggests that a dark spot of a size smaller
than (800/25.4)-4 = 0.032 mm is not detected.
3. Measurements at liquid nitrogen temperature
Technical specifications of many scanners consider environmental temperatures
between 10 and 30°C for correct working. Therefore, optical and electronic components
must never work at temperatures below 0°C. Thermal isolation requires a minimum
separation distance of 7 mm between the cold sample and the scanner window. This
modifies by about 3% the horizontal scale (Figure 7).
3.1. Experimental setup
Figure 8 shows the scheme of the first prototype built at CIEMAT to measure
thermal contraction at liquid nitrogen temperature. The device consisted of a
transparent quartz tray able to resist the direct addition of liquid nitrogen. The tray was
set directly on a conventional glass window, which held a quartz tray 2 mm away from
the scanner window. The scanner was brought close to the outer chassis window by a
height-adjustable shelf. The puter chassis glass window and a 2 mm air chamber
protected the scanner electronics and CCD sensors from the rapid drop of temperature.
The scanner (an A3 Simplex Compeye of optical resolution 300x600 spi) was
sufficiently light (3 kg) to permit the correct adjustment in height of the shelf with sub-
millimeter screws.
11
Quartz tray
Outer chassis
Scanner"JZZ
Height-adjustableshelf for the scanner
Outer chassiswindow
Fig. 8. Experimental setup for light scanners
The larger weight (20 kg) and size (650x458 mm) of the A3 scanner EPSON GT-
12000 makes necessary to carry out several modifications in the primitive prototype.
First, the very different size of the outer chassis glass and the quartz tray caused
bending, and the subsequent fracture, of the glass when the tray was cooled at 77 K.
Second, the heavy of the scanner made difficult to use a height-adjustable shelf for the
scanner. To adapt the outer chassis glass to the dimensions of the tray, the glass
window was cut to be only a few centimeters larger than the tray, and framed with
glass-fibre. A step of 2 mm depth carved in the glass-fibre plate permitted one to hold
the glass window. Instead of a height-adjustable shelf for the scanner, the primitive
design was modified to adjust the tray in height. The scanner cannot move in this
second design. Figure 9 shows the modifications.
Quartz tray
Outer chassis
Scanner
Height-adjustableshelf for the tray Outer chassis
window
Fig. 9. Experimental setup for the scanner EPSON GT-12,000
12
3.2. The thermal isolation of the scanner
All components between the sample and the detection system (i.e., quartz tray,
glass windows and air chamber) contribute to isolate of the scanner from cool. Heat is
transmitted from inside the scanner to the tray by conduction, radiation and convection.
Immediately after the addition of liquid nitrogen into the tray, the conduction of
heat between the scanner (Tx =300 K) and the tray {T2 = ll K) induces a time varying
temperature gradient. This gradient follows the Fourier's equation
d2T _ 1 dT
dz2~ adt {)
where the Z-axis is defined perpendicular to the scanning surface, t is the time after the
addition of liquid nitrogen, and a is the thermal diffusivity of the medium in which heat
is transported.
The very low thermal diffusivity of quartz is one of the reasons that motivated
the selection of this material for building the tray. Quartz delays the stationary situation,
and avoids the glass window that holds the tray to break. Other two reasons are the
quartz capability to resist the direct addition of liquid nitrogen and the possibility of
joining walls to a transparent bottom with fussed quartz.
The amount of energy involved in the cooling process requires to carry out
measurements immediately after the sample is cooled at 77 K, long before the thermal
equilibrium has been reached for all components of the device. Figure 10 shows the
distribution of isolators proposed to delay as much as possible the stationary state. Since
the coefficient of thermal conduction of air is more than three orders of magnitude
smaller than that of quartz or glass, an air chamber of 2 mm thick has been included to
reduce the transport of heat by conduction between the scanner and the sample.
The convection of air inside the scanner causes temperature changes in CCD
sensors. However, this process is very slow for the scanner EPSON GT-12000, in which
CCD sensors are far away from the scanner window, and cold measurements can be
carried out before images lose the scaling reference because of the temperature change.
13
QuartzGlassAirGlass
Sample
«3
• • • k A
Heat Flux
Scanner
Fig. 10. Distribution of the isolator layers between the scanner and thesample
The scanner behaves like a radiating blackbody at 7=300 K. According the
Stefan-Boltzmann's law, in absence of the scanner window, the power radiated by the
scanner is approximately 30 W. The scanner glass window significantly avoids radiation
to escape, because glass transmitivity is nearly zero for infrared radiation of wavelength
longer than 3 mm
Table 2 lists the isolating components of the device, and their functions.
Table 2. Function of the different material layers for the thermal isolation of the scanner
Material
Quartz
Holding Glass
Scanner Window
Air Chamber
Thick
3 mm
3mm
3 mm
2 mm
Function
Allows one the direct addition of the liquid nitrogen without breaking. The
thermal diffusivity of quartz is very low. Walls can be joined with fussed
quartz.
Glass window with similar size to the tray. The window is framed with
glass-fibre completing the whole size of the scanner window
Avoids infrared radiation to escape from the scanner.
Reduces the heat flux between the scanner and the tray.
14
3.3. Test of the device
The scale conservation must be verified after cooling the sample. One simple way
to test the device is to measure the contraction percentage of an aluminum plate. To fix
the reference points, we draw several horizontal and vertical thick crossing lines on the
flat surface of the sample. Figure 9 shows the scanned images of the plate before (a)
and after (b) the addition of liquid nitrogen into the tray. The percentage of thermal
contraction is obtained by comparing lengths of the vertical lines. Table 1 lists the
results. Table 1 gives an averaged value for thermal contraction percentage
— x 100 = 0.38±0.03(lo-), (6)
in excellent agreement with the values reported in the literature [6].
Table 3. Measured thermal contraction for aluminum
Line
1234567891011121314
Length(mm)
(at 22 C)215.968215.997215.096216.150216.255216.169216.294216.170216.173216.283216.3342Í6.318216.285216.311
Length(mm)
(at 77 K)215.113215.263215.279215.280215.290215.380215.398215.302215.457215.469215.474215.573215.455215.543
PercentageContraction
(%)0.3960.3390.3780.4020.4460.3650.4140.4030.3310.4220.3980.3460.3850.355
15
ï t
t íC i
t ¡t ï 1444
t. +**•
r
i * M
i i £ - Í* \\
- '% '
t t
1 ' ^
i c
V t s ^ ^ ^
* < -
* V4-
f
>\
y' j
+ ^
; • í
^* If+ i f- ~
+ ^ ^ í
(a) (b)
Fig. 11. Scanned images of the aluminum plate at room (a) and liquid nitrogen(b) temperatures
4. Measurement of mechanical deformations in the magnet cross section
The method adopted to measure points of interest in a magnet cross section
includes the following five steps: scan the sample and standard (1), apply tonal
correction to the two images (2), calibrate the scanner (3), measure coordinates (4) and
compare the measured coordinates with their nominal positions (5). Prior to scan, the
scanner software requires to adjust certain parameters such as the scanning mode,
frame, resolution, and tones. Since all information is contained into the first scanned
image, these parameters must be defined conveniently. We should notice that any later
16
tonal correction never increases the amount of information of the original scanned
image, it always reduces it.
The program Adobe Photoshop [6] can be applied to modify and simplify the
standard and sample scanned images. Tonal correction is applied to enhance contrast of
edges, while by cutting down bit-depth, much unnecessary information is erased. By
comparing horizontal and vertical dimensions of the standard and the scanned image
the scanner is calibrated. We apply the program AutoCAD [7] for dimensional
measurements. However, the determination of the keystone vertex coordinates in
magnet cross sections is time consuming. Since one side of the LHC dipole cross-
section contains 160 keystones, and 640 vertexes, the development of a routine to
measure the vertexes is highly advisable in order to save time. The AutoLISP program
VERTEX permits us to save up to75% of the time.
The comparative statistics between the measured keystone coordinates and the
nominal positions obtained from ROX3E [8] is finally performed by running the
FORTRAN program VERTEX.
4.1. Adjustment of the scanning parameters
The good adjustment of the scanning parameters is very convenient if we do not
want to lose essential information during the scanning process. Below we list the
parameters, giving a brief description of how to adjust them
Scanning mode parameter. The scanner software allows one to choose among several
scanning modes, e.g., line-art, grayscale or color. Obviously, the selection of the color
option will provide unnecessary information if the scanned sample is black and white.
As a general rule, 8-bit depth of grayscale is sufficient for dimensional measurements.
Resolution. The smallest superconducting cables in the outer layer of the dipole have
diameters of about 1 mm. A resolution of 800 spi provides sufficiently detailed
representations of 33 x 33 samples for each cable cross-section.
17
1
¡
viV J
'* 1
(a)
(b)
(c)Fig. 12. Details of the scanned dipole at different resolutions, (a) 100 spi,(b) 300 spi and (c) 800 spi
18
Size of the image. Standardizations with the scanner require one to compare two
images of identical resolutions (spi) and sizes (weight and height). Every time the
scanning frame is defined, it must remain unaltered for all samples.
Tonal correction. The scanner software permits one to modify the response of CCD
sensors to light tones. Suppose the scanner is able to capture 256 levels of gray (8-bits).
Since the response of the scanner is linear (Figure 11), two consecutive dark tones are
poorly separated. The scanner software permits one to modify bright (by translating
entirely the line in Figure 11 along F-direction), contrast (by changing the line slope)
and gamma parameter (by transforming linear scale into logarithmic to discern better
two consecutive tones).
CCDsensibility
Graylevel scale(from dark to light tones)
Fig. 13. CCD sensibility to grayscales
The steps adopted to scan the standard and the dipole cross-section were the following:
1.- Center the dipole cross-section on the scanner window.
2.- Open the application Adobe Photoshop.
3.- Select Import of the File menu, and choose the TWAIN option to have access to the
scanner software window.
4.- Select the grayscale scanning mode.
5.- Change resolution to 800 spi.
6.- Use a preview scanning to adjust bright, contrast and gamma options.
7.- Frame the object to be scanned.
19
8.- Save the scanned image using TIFF (Tagged Image File Format).
9.- Use marks to center the standard into the frame applied for the magnet cross-
section.
10.- Set the standard on the scanner and scan again. Save the standard as a TEFF image.
4.2. Histogram of scanned images
Image correction or filters never increase the available information. However,
images can be modified to erase unnecessary information or sharp details. A convenient
way to modify images is to study their histogram. Figure 12 shows the histograms for
the scanned dipole cross section and the standard.
(a)
(b)
Fig. 14. Histograms for the dipole cross-section (a) and tlie standard (b)
20
By increasing bright in 10 units, we shift the histogram slightly to the right. Also
histogram is too narrow to appreciate details. We can spread tones, and make the
histogram wider by increasing contrast 80 units. The resulting histograms are shown in
Figure 13.
(a)
(b)
Fig. 15. Histograms for the dipole cross-section (a) and the standard (b), after modifying brightand contrast
21
A high-resolution 800 spi TIFF image is of nearly 30 Mbytes. One possible way to
reduce the file size is to use 1-bit depth grayscale instead of the common 8-bit. This
reduces the file information by a factor 8, and must be applied carefully.
The sharp location of the keystone and square sides in the magnet cross section
and standard is essential. However, edges can be accurately defined in a transition from
black to white. To locate edges sharply, a grayscale of 256 tones is clearly excessive.
The conversion of the grayscale into two unique tones is possible by applying a
threshold number. Gray tones above and below the threshold number are transformed
into black and white, respectively.
The histogram of the standard shows a minimum near 200 in the grayscale. We
may conserve the position of edges, and additionally transform the image into black
and white, by using this minimum as a threshold. Similarly, to locate the keystone
edges into the dipole cross-section image, the inflection point at 200 can be used as a
threshold. Figure 14 shows details of the standard and dipole images after the
application of the threshold function
Fig. 16. Standard and dipole transformed images after the application of the threshold function
22
4.3. The program MAGNET.LSP
4.3.1. Calibration of the scanner (Standard)
Before carrying out any measurements in the scanned image, the scaling factor
(or real size) of the image must be determined. Since both the standard and the magnet
cross-section are scanned with identical resolutions, the horizontal and vertical scale
factors,/t and fy, must be the same for both images. Figure 17 depicts the standard
vertical and horizontal lengths applied for the determination of the scale factors.
fec fe >
, QQi I D< h'
h,
• MB Ë3 Bfe
e ID a ' H ah n
a HI a l a
B S s S a
i
I s b B l a
!i
1 1 Mm @B
Sa i o S H
!
Ï D IS a l a
üa Ma 1 1
Fig. 17. Standard lengths along the horizontal and vertical scanning directions
Below we give the steps followed by the program MAGNET.LSP to obtain the
vertical and horizontal scale factors:
1.- Open the program AutoCAD 14.0 by double clicking on the Autocad icon.
2.- Load the application C:\LISP\MAGNET.LSP by choosing the option LOAD
APPLICATION of the main menu TOOLS.
3 .-Run the program MAGNET
Command: magnet
4.-Type s (standard)
Standard/Vertex/Especial/Insert: s
23
5.-Select the option Image (marc the standard points) or Dimension (save the standard
lengths). When you type i, the scanned image of the standard is displayed on the screen,
and the square vertex points can be determined by two intersecting lines. When you
type d, the lengths between two selected points are saved into the file
C:\LISP\STANDARD.DAT. Let us consider first the option i (the option d will be
described below on point 6)
Image/Dimension: i
Three windows will appear consecutively on the screen:
PREFERENCES: allows one to select screen options for the display. We
recommend a white background and at least two command lines.
ATTACH IMAGE FILE: searches for the image into the hard disc.
ATTACH IMAGE: we recommend attaching the image on point 0,0 and start with the
scale factor 100.
Insertion point <0,0>: (ENTER)
ON/OFF/<Lower left corner><0.000,0.000>: (ENTER)
Upper right corner <420.000,297.000>: 100,100
Zoom twice the desired corners
First corner: (click)
Other corner: (click)
First corner: (click)
Other corner: (click)
Mark the points by plotting two intersecting lines as shown in Fig. 17
Command: line From point (click)
To point: (click)
Command: line From point (click)
To point: (click)
Proceed in the same way with the remaining square vertexes. If you fail with one line,
do not stop the program; continue till the end, and press ESC to stop. Then delete all the
failures at once, and save the file as STANDARD.DWG.
24
Fig. 17. The intersection of two lines defines the standard points
6.-Run the program MAGNET
Command: magnet
Standard/Vertex/Especial/Insert: s
Image/Dimension: d
Before saving the standard lengths, first label them
Type point identifie. : hl (ENTER)
First point: (click)
Second point: (click)
and proceed in the same way with the remaining lengths. All lengths will be saved
automatically into the file C:/LISP/STANDARD.DAT.
To compute the scaling factors, first paste the file STANDARD.DAT in Excel, and
follow the calculations outlined in Tables 4 and 5.
Table 4
LabelHIH2H3H4H5H6H7H8H9
H10Hl lH12
. Computation of the
Stand. Length (mm)17.93035.88453.83717.93635.85253.82417.95835.91053.84917.87235.84653.809
tiorizontal scale factor
Image Length (a.u)11.74723.52935.30811.73623.517
/ 35.28711.73623.51935.29511.73723.49235.253
Scale Ratio0.65520.65570.65580.65430.65590.65560.65350.65490.65540.65670.65540.6551
0.6553 ±8xlO~4
Scale Ratio0.65520.65570.65580.65430.65590.6556
0.65490.6554
0.65540.6551
0.6553 ±5 xl0~4
25
Table 5
LabelVIV2V3V4V5V6V7V8V9VIOVi lV12
. Computation of the vertical scale factor
Stand. Length17.96636.05654.03617.95635.98434.02417.96036.08554.03717.97236.02853.975
(mm) Image Length (a.u)11.97923.91335.88712.00323.91335.88511.98423.90935.80911.90823.89735.822
Scale Ratio0.66670.66320.66410.66850.66450.66420.66730.66250.66260.66260.66330.6636
0.664±2xl0~3
Scale Ratio
0.66320.6641
0.66450.6642
0.66250.66260.66260.66330.6636
0.6634 ±7 xl0~4
4.3.2. Image scaling. Measurement of the vertex coordinates (Vertex)
The AutoLISP program MAGNET optimizes the steps required to measure the
keystone vertex coordinates in scanned images of magnet cross-sections, and allows one
to save more than 75% of the time commonly spent with the use of the AutoCAD
toolbars. The process of saving all vertex coordinates is divided into three parts. First
the image is scaled considering the scale factors determined with the standard. Second
all points of interest are determined following the criteria of two intersecting lines.
Third the intersection points are marked and saved into a file with the numeration order
adopted by the program ROXIE. All vertex coordinates are, however, referred to the
center of the image. Section 5 gives details of how the FORTRAN program MAGNET
computes the orientation and the position of the center of the magnet cross-section, and
transforms the coordinates of all points in order to compare them with their nominal
positions.
The steps to scale the image are the following:
1.- Open the program AutoCAD 14.0 by double clicking on the Autocad icon.
2.- Load the application C:\LISP\MAGNET.LSP by choosing the option LOAD
APPLICATION of the main menu TOOLS.
3.-Run the program MAGNET
Command: magnet
4.-Type v (vertex)
26
Standard/Vertex/Especial/Insert: v
5.-Type i (image)
Image/coordinates: i
6.-Attach the scanned image
Starting new image (Yes/No)?: y
Three windows are displayed
PREFERENCES: allows one to select the display characteristics
ATTACH IMAGE FILE: searches the file into the hard disk
ATTACH IMAGE: attaches the image with the same scale horizontal and vertical scale
factor. E.g.,
Scale factor: 129.1
Insert the image in point (0,0)
Insertion point <0,0>: (ENTER)
The image is defined as a block. Afterwards, it is inserted and scaled along the
horizontal direction. The following windows appear on the screen
BLOCK DEFINITION Block name: dip
Select Objects: (click) (enter)
Deactivate the Retain Objects option
INSERT Block: dip
Activate Specify Parameters on
Screen. E.g.,
Scale: X: 1.00347
Y: 1.0000
Z: 1.0000
The image is inserted at point (0,0)
ON/OFF/<Lower left corner><0.000,0.000>: (ENTER)
and zoomed to fill all the screen
Upper right corner <420.00,297.00>: 100,100
Now we may stop the program with ESC and save the image scaled in millimeters, or
go on and plot all vertex point's.
7.-The center of the image, i.e., the origin of coordinates, is defined by the two
intersecting lines, which connect the midpoints of the framed image.
Command: line From point: mid of (click)
To point: mod of (click)
Command: line From point: mid of (click)
To point: mod of (click)
27
Origin point <0,0,0>: int of (click)
8.-To define all vertexes: First frame one side of the keystone with two zooms. Second,
plot three lines to define the sides of the keystone. Third extend one of the lines to find
the two vertexes (Fig. 18). The keystones can be selected no matter the order. They will
be saved later following the numeration of the program ROXIE.
Two ZOOM:
Command: Press ENTER and frame
twice with 2 corners the keystone (ENTER)
First corner: (click)
Other corner: (click)
First corner: (click)
Other corner: (click)
Three LINES:
Command: line From point: (click)
To point: (click)
Command: line From point: (click)
To point: (click)
Command: line From point: (click)
To point: (click)
EXTEND one line
<Select object to extend>/Project/Edge/Undo (click)
Fig. 18. Determination of the two vertex points at one side of the keystone
28
If you fail in plotting one line, do not stop the program, go on with the remaining lines.
All mistakes will be deleted at the end. Since the number of keystones is relatively high,
stop the program when tired, and save all work into the file MAGNET.DWG. Take a
break. To start, go on in the following way:
1.- Run the program AutoCAD 14.0.
2.-Load the previous work in file MAGNET.DWG.
3.- Load the application C:\LISP\MAGNET.LSP by choosing the option LOAD
APPLICATION of the main menu TOOLS.
4.-Run the program MAGNET
Command: magnet
5.-Type v choosing the option Vertex
Standard/Vertex/Especial/Insert: v
6.-Type / to choosing the option image
Image/coordinates: i
7.-Type n indicating that you do not want to attach a new image
Starting new image (Yes/No)?: n
and follow the steps 7 and 8 as described above.
To mark and save all vertex points into the file C:\LISP\COORD.DAT, one must
follow the steps:
9.- Run the AutoLISP program MAGNET
Command: magnet
10.-Type v choosing the option Vertex.
Standard/Vertex/Especial/Insert: v
11 -Type c choosing the option Coordinates.
Image/coordinates: c
12.-By starting to select points, type y
Starting new image (Yes/No)? y
13.- To save the vertex points following the numeration criteria of the program ROXIE,
first frame the keystones by two successive windows
Press ENTER and frame twice with 2 comers the keystone
First corner: (click)
Other corner: (click)
First corner: (click)
29
Other comer: (click)
And mark the 4 vertex points with the mouse as shown in Fig. 19
Command: Select the intersections with the mouse (4 click)
Fig. 19. The vertex points are marked in the convenient order
Going on with the remaining keystones the numeration given in Fig. 20 is followed. If
you fail, do not stop the program. Remember the keystone number, and repeat it at the
end. By taking a break, stop the program pressing ESC, and save all work into the file
LABEL.DWG. To continue, load the file LABEL, run the program MAGNET.LSP, and
type n when the program asks
Starting new image (Yes/No)? n
Before marking the remaining/vertex points, the number of the last processed keystone
must be typed.
The last keystone was number:
30
Fig. 20. Numeration of vertexes and keystones in agreement with the criteria adoptedby the program ROXEE
4.3.3. Measurement of other interesting geometrical quantities in the magnet cross
section (Especial)
Apart from the keystone vertex points, other points, angles or lengths into the magnet
cross-section may be of interest. To illustrate the possibilities of this option, the
vertexes, sides and internal angles of the piece shown in Fig. 21 will be measured.
l.-The scaled image MAGNET.DWG is loaded.
2.-By applying the Toolbars, plot the line array shown in Fig. 21.
3 .-Run the program MAGNET.LSP
Command: magnet
4.-Choose Especial
Standard/Vertex/Especial/Insert: e
5.-Select the variable to be measured
Point/Length/Angle: p
6.-Type the identification label and select it with the mouse
Type identifie: pi
Select point with the mouse
31
The coordinates of the points are saved into the file C:\LISP\ESP.DAT. To compute
other quantities, select the Length or Angle options by running the program again. Both
lengths and angles require one to mark two points on the screen. The option length
computes the dimension between points, while the option angle computes the angular
equivalent of the slope of the line passing through the points. If P\(xi,yi) and
^2(^2^2) a r e t n e coordinates of the two points marked on the screen, the lengths and
angles are computed from expressions:
(8)
a = tan"1 ^I x2-xi
(9)
Table 6 lists the vertex points, lengths and angles measured for the piece in Fig. 21.
Fig. 21. The reference lines in red are plotted to determine the angulardimensions and lengths of the copper piece between two blocks
Table 6. Measured geometry of the piece shown in Fig. 21
32
1
2
3
4
1
2
3
4
1
2
3
4
Label
PI
P2
P3
P4
Label
Ll
L2
L3
L4
Label
Alphal
Alpha2
Alpha3
Alpha4
X coordinate
(mm)
-39.6325
-41.502
-26.1627
-25.984
Length
(mm)
15.1228
5.3351
15.471
0.5290
Angle
(radians)
0.4452
1.9288
0.1305
5.0569
Y coordinate
(mm)
-18.1468
-13.1499
-11.1361
-11.6341
The computation of the internal angles of the piece is straightforward, because
«int = «/ - a j , where (i,j = l,..,4;i = j
4.3.4. Insertion of nominal positions onto the image
The program ROXIE considers the option of including a DWG plot with the
nominal positions of all conductors among the output files. This file can be inserted
with the adequate orientation onto the scaled image MAGNET.DWG by running the
program MAGNET. LSP (Fig. 22)
33
1.-Load the scaled image of the magnet cross section.
2,-Run the program MAGNET.LSP
Command: magnet
3.-Choose the option Insert
Standard/Vertex/Special/Insert: i
4.-When the Window Insert appears on the screen, first, search for the Drawing file (the
output file from ROXEE); and second, specify the insertion point and the rotation angle.
5.-Save the image.
Fig. 22. Detail of a scanned magnet cross-section in which thenominal positions of conductors have been inserted with theadequate orientation
4.4. The program MAGNET.FOR
The FORTRAN program^ MAGNET computes the position of the geometrical
center and the orientation of the magnet cross section. The coordinates of all points are
transformed into the adequate reference frame, making possible the comparison of the
measured and nominal positions. Also the lengths and cross-sectional areas of all
keystones are averaged.
The program MAGNET.FOR reads data from the three input files: CTL, COORD
and ROXIE (Appendix A). As output files we have SAL and ROXPUT (Appendix B).
34
4.4.1. Six block dipole configurations
Let {u\, v{ ), (uf, vf ), (z/f, vf ), (i/f, vjy ) be the nominal positions given by ROXIE
for all vertexes, and [xj,y'¡ ),{xf,yf lyx1",yf1 lyx'^,y1^) the positions measured with the
program MAGNET.LSP. The subscript / denotes the keystone position into the dipole
0=1,2, ... ,160), and the superscripts /, //, / / / and IV the four vertexes of the keystone.
The scale factor fy transforms the coordinates (xf ,yf ) into \fyxf,yf).
The center of the dipole is derived from equations
xc = (al +a1 +a3 +a4 +a5 +a6)f6, (10a)
(10b)
where
«, ={*" +x<59)/2, (lia)
, (He)
, (lie)
, (lid)
)/2, (He)
, (Hf)
, (Hg)
(no
(Hk)
(HI)
35
To compute the orientation angle of the dipole, a straight line is fitted by linear
regression to the points (xf ^ " K ^ .
The dipole orientation angle a is given by
(12)
where b is the slope of the line. The vertex coordinates are transformed into the new
reference frame by a rotation and a translation:
sinaYxWxc|
cosaJ^J [yj
5. Measurement of thermal deformations
The computer codes applied to measure mechanical deformations can be equally
applied to measure thermal deformations. However, thermal deformations are more
difficult to be measured due to the cooling process. Since the magnet cross-sections are
generally heavy pieces, which require several minutes to be cooled at 77 K, an initial
cooling process is highly recommended.
Basically, the sample must be scanned first at room temperature, and afterwards at
77 K, deriving any thermal deformation by the comparison of the two scanned images.
One simple way of avoiding excessively long cooling times into the quartz tray is to
cool the sample outside the tray. However, the scanning position of the sample at room
temperature is modified for liquid nitrogen measurements, and the comparison of the
two images will require the transformation of the reference frame.
The sample can be cooled into the tray by pacing a cold source on the sample. In
such a way, the sample is cooled by thermal conduction in exactly the same position,
without affecting the surrounding components significantly. The cold source may be,
for instance, a polyethylene bag full of liquid nitrogen.
6. References
36
[1] A. Grau Carles, P. Abramian Barco, J. Martin Andrada and L. García-Tabarés.
Aparato y Método de Metrología Bidimensional para Temperaturas Criogénicas, Spain
Patent P99000693.
[2] A. Grau Carles, L. García-Tabarés and F. Toral Measurement of Mechanical
Deformations and Analysis of the Magnetic Field Quality for the LHC Dipole Cross
Section SD4+2(1J of CERN. CffiMAT Report 868.
[3] The Large Hadron Collider. Conceptual Design (CERN/AC/95-05)
[4] Superconducting in Particle Accelerators (CERN Accelerator School, Geneva,
1989) p.92.
[5] H. E. Kupono, Materials Data Base (New York, Willey, 1992).
[6] Adobe Photoshop 5.0. Adobe Systems. US Patents 4,837,613; 5,546,528.
[7] AutoCAD 14.0. Copyriht © 1997 Autodesk, Inc.
[8] Routine for the Optimization of Magnet x-sections, ROXIE (CERN, Geneva,
1998).
37
Appendix A: Input files in the program MAGNET.FOR
The program MAGNET.FOR reads data from three input data files: CTL, COORD and
ROXIE.
The file CTL.DAT includes the following essential data for the magnet:
• The magnet type (dipole, quadrupole, sextupole, etc.).
• The total number of keystones that conform the magnet.
• The transition numbers from inner to outer layers. The keystone numeration
must agree with ROXEE output data. Figure 17 shows that jumps from inner to
outer layers occur only for the keystone numbers 25, 40, 115 and 160.
• The horizontal symmetry line for the dipole magnet configuration in Figure 17 is
achieved by fitting a line to the upper vertex points of keystones 50, 59, 121 and
126 and the lower vertex points of keystones 26, 41, 116 and 1.
Table Al lists the file CTL.DAT.
Table Al . Listing of the input data file CTL
'CONTROL DATA FILE'
'Magnet =' 'dipole''Number of conductors =' 160'Inner and outer cond.=' 25,40,115,160'Fitting cond. =' 50,59,121,126
The file COORD.DAT in Table A2 contains the magnet vertex coordinates as
they were measured with the program MAGNET.LSP. The coordinates are referred to
the center of the image. <
Table 2. Listing of the input data file COORD
1,46.4 802,0.480907,4 6.5374,-1.07097,61.8967,-1.07398,61.8967,0.4805172,46.4286,2.0554,46.4869,0.62866,61.7624,0.703229, 61.7801,2.37773,46.2 674,3.75037,4 6.393,2.24313,61.6361, 2.62046, 61.6592, 4.10658
1
4,46.103,5.32798,4 6.2335,3.95553,61.5707,4.38111,61.5554,6.037845, 45.7725, 6.93798,4 6.0491,5.53752,61.183,6.26305,61.2542,7.940546, 45.4856, 8.6846,45.6697,7.08024,60.9494,8.16905,60.8163,9.653087,45.2588,10.1606,45.3428,8.79154,60.5659, 9.88486, 60.4575,11.57728,44.7321,11.7819,44.9832,10.3598,60.1607,11.7957,59.9842,13.47189,44.3204,13.3571,44.5 479,11.955,5 9.6734,13.6032,5 9.48 65,15.28 4310,42.7484,16.504,43.4074,15.2297,57.0003,22.1096,56.4084,23.644311,42.0929,18.0156,42.8081,16.74 49,5 6.3002,23.8532,55.5407,25.319212,41.4232,19.47 61,42.1174,18.2068,55.5575,25.4879,5 4.5957,2 6.990213,40.6134,20.9083,41.3541,19.6784,54.5349,27.16,53.73,28.62 6714,39.75 97,22.2417,40.4 626,21.0732,53.629,28.7932,52.7 647,30.229915,38.8333,23.664,39.7272,22.5096,52.6388,30.4155,51.7448,31.809916,37.9775,24.9844,38.7335,23.8511,51.6017,31.9323,50.7315,33.423217,37.0152,2 6.3224,37.7913,25.129,50.508 4,33.5168,49.5 685,34.88418,35.9306,27.5276,3 6.8783,2 6.4724,4 9.28 89,35.0254,4 8.38 03,3 6.48 6219,34.8998,28.7643,35.80 69,27.6655,4 8.1737,3 6.5898,47.15 45,37.906320,33.8072,29.9909,34.7516,2 8.9685,4 6.98 65,37.9765,45.8335,39.259521,32.6342,31.12 08,33.5169,30.0749,45.58 8 6,39.3777,4 4.5957,40.63822,31.4117,32.27,32.45,31.25 41,44.2751,40.7421,43.1783,41.977923,30.1254,33.2878,31.1445,32.2803,42.8663,42.0912,41.7601,43.311124,28.8294,34.3792,29.8424,33.3162,41.5407,43.4016,40.3189,44.486925,27.4977,35.4858,28.5303,34.4459,4 0.0574,4 4.55 03,38.8927,45.714326,30.4586, 0.719091,30.5122,-1.06479,45.8683,-1.05469,45.9238,1.0861127,30.3144,2.70663,30.47,0.924746,45.812,1.27083,45.7988,3.46327
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The file ROXEE.DAT in Table 3 A contains the nominal positions of all vertexes
Table 3A. Listing of the input data file ROXLE
DATE: 8. 1.19 99TIME: 9.58
2d symétrie case
DIPOLE
RADIUS OF THE MULTIPOLE ANALYSIS (MM) 10.0000
NUMBER OF FIELD CALC. AT THE RADIUS 81
INNER RADIUS OF THE IRON YOKE IN MM 98.0000CONTRACTION COEFFICIENT FOR COLD CONDITIONS 0.0OO0E+O0RELATIVE PERMEABILITY OF THE IRON YOKE 4 000.0000
NUMBERS OF BLOCKS FOR WHICH LOAD LINE CALCULATIONSARE CARRIED OUT: 1 2 3 4 5 6
OPTIONS FOR THIS ROXIE CALCULATION:NORMAL PRINT OUT (LPRINT)EXTENDED PRINT OUT (LEXPR)LAYER DEFINITION (LAYER)GRADING OF CURRENT DENSITY (LGRAD)PLOT OF CROSS SECTION (LPLOT)
4
360 DEG CROSS SECTION PLOTCOLORFUL PLOTS
NUMBER OF BLOCKS 24NUi-.BER OF CONDUCTORS 160NUMBER OF FILAMENTS 5280NUMBER OF CUTS IN Z DIRECTION 0NUMBER OF POINTS ON RADIUS 4 0NUMBER OF SURFACE ELEMENTS (3D) 0
ONLY ONE SINGLE CALCULATION WITH OXS
NUMBER OF BLOCK 1NUMBER OF CONDUCTORS 9POSITIONING ANGLE (DEG) 0.1570INCLINATION ANGLE (DEG) 0.0000CURRENT IN EACH CONDUCTOR OF THE 3L0CK (A) 11530.0000INNER RADIUS OF THE BLOCK (MM) 43.9000CABLE HEIGHT (MM).¡INSULATED) 15.4000CABLE INNER WIDTH (MM) . (INSULATED) 1.6176CABLE OUTER WIDTH (MM) . (INSULATED) 1.8624CABLE HEIGHT (MM).(BARE) 15.1000CABLE INNER WIDTH (MM) . (BARE) 1. 3600CABLE OUTER WIDTH (MM).(BARE) 1.6000RADIAL INSULATION THICKNESS (MM) 0.1500AZIMUTHAL INSULATION THICKNESS (MM) 0.1300NUMBER OF STRANDS 36DIAMETER OF STRANDS (MM) 0.8250CU/SC RATIO 1.9000TEMPERATURE AT WHICH JC AND DJC ARE GIVEN (K) 1.9000JC( 9.0 T) (A/MM**2) 1S53.000DJC/DB (A/MM**2 T) 550.030CABLING ANGLE (DEG) 15.000NUMBER OF DISCRETISATION POINTS AZIMUTHAL 2NUMBER OF DISCRETISATION POINTS RADIAL 18CONDUCTOR NAME YELLONOUDIPOLE LHC OUTER LAYER YELLOW 8.96 , 15.1IMAGING AT X AXIS: 1 YES, 0 NO 0SHIFT ANGLE FOR ENTIRE BLOCK 0.0000
COND. NO. 1 Xi BARE; Xli, Pij ¡PHI), Aij (ALPHA) INSULATEDXi = 44.037999 X2 =Yl = 1.610250 Y2 =XII= 43.886980 XI2=YI1= 1.737866 YI2=Rl = 43.921375 R2 =PI 4= 2.268313 A14 =ARC LENGTH (mm):
44.048807 X3 =0.250293 Y3 =
43.899835 XI3=0.120293 YI3=43.900000 R3 =0.910642 P23=
1.8603
59.14 9284 X4 =0.250293 Y4 =
59.300321 XI4=0.120293 YI4=
59.300443 R4 =0.157000 A23=
59.1365691.850243
59.2855211.982627
59.3186640.000000
COND. NO. 2 Xi BARE; Xli, Pij (PHI), Aij (ALPHA) INSULATEXI = 43.980068 X2 =Yl = 3.229491 Y2 =XII= 43.827040 X12=YI1= 3.354691 YI2=Ri = 43.95524 3 R2 =P14= 4.380323 A14=ARC LENGTH (mm):
4 4.0124 88 X3 =1.869878 Y3 =43.865602 XI3=1.737526 YI3=
43.900000 R3 =1.821284 P23=
3.6008
59.111058 X4 =2.109870 Y4 =59.264143 XI4=1.982287 YI4=
59.297286 R4 =2.268313 A23=
59 .0729173 .709415
59.2197463.844150
59.3443840.910642
COND. NO. 3 Xi BARE; Xli, Pij (PHI), Aij (ALPHA) INSULATEDXI = 43.862510 X2 =Yl = 4.846529 Y2 =XI1= 43.707512 XI2=Yll= 4.969281 YI2=RI = 43.989093 R2 =P14= 6.493963 A14=ARC LENGTH (mm) :
43.916535 X3 =3.487602 Y3 =43.771770 XI3=3.352933 YI3=43.900000 R3 =2.731927 P23=
5.3422
59.009383 X4 =3.967526 Y4 =
59.164476 XI4=3.842392 YI4=59.289116 R4 =4.380323 A23=
58.9458255.566264
59.0904955.703315
59.3650941.821284
COND. NO. 4 Xi BARE; Xli, Pij (PHI), Aij (ALPHA) INSULATEDXI = 43.685319 X2 = 43.760934 X3 = 58.844249 X4 = 58.755290Yl = 6.459874 Y2 = 5.101978 Y3 = 5.821712 Y4 = 7.419238XI1= 43.528389 XI2= 43.618328 XI3= 59.001311 XI4= 58.897763
YI1= 6.580147 YI2=Rl = 44.022937 R2 =P14= 8.610171 A14=ARC LENGTH (mm):
4.965025 YI3=43.900000 R3 =3.642569 P23=
7.0853
5.699059 Y14=59.275914 R4 =6.493963 A23=
7.55857159.3807932.731927
COND.XI =Yl =XI1 =YI1 =Rl =P14 =
NO. 5 Xi43.4484648.068032
4 3.2896438.185796
44.05678610.729903
BARE ;X2 =Y2 =XI2=YI2 =R2 =A14 =
Pi] (PHI), Aij (ALPHA) INSULATED
ARC LENGTH (mm) :
43.545651 X3 =6.711509 Y3 =
43.405239 XI3=6.572307 YI3=
43.900000 R3 =4.553211 P23=
8.8306
58.615621 X4 =7.670872 Y4 =58.774613 XI4=7.550731 YI4=59.257647 R4 =8.610171 A23=
58.5012849.266782
58.6415259.408362
59.3914623.642569
COND. NO. 160 Xi BARE; Xli, Pij (PHI), Aij (ALPHA) INSULATEDXI = 9.167 905 X2 =Yl = -26.616462 Y2 =XI1= 9.2288 94 XI2=YI1= -26.435346 YI2=Rl = 28.000000 R2 =P14= 74.803176 A14=ARC LENGTH (mm):
7.529529 X3 =-27.202400 Y3 =7.367515 XI3=
-27.101037 YI3=28.084631 R3 =70.928340 P23=
56.0873
12.463738 X4 =-41.474372 Y4 =12.399755 XI4=-41.656558 Y14=
43 .462889 R4 =70 .755297 A23=
14.403424-40.78067514.568431
-40.88096743.39922469.714170
3ND OF THIS ROXIE CALCULATION
Appendix B: The output data file SAL
After running the program MAGNET.FOR, the resulting output data are printed into the
file SAL.DAT. This file contains the coordinates of the center of the magnet for the
image reference frame {xo,yo), the magnet orientation angle a, vertex shifting, keystone
lengths and areas, and a comparison between measured and nominal values of
parameters r¡, fa and 0¡.
The file SAL.DAT in Table 1 can be used as a test run for the program. The
input files are given in Tables Al, A2 and A3 of Appendix A.
Table Bl. Test run output of the program STAT.FOR
DIPOLE CENTER COORDINATES (mm)X0= 2.608Y0=-1.263
DI POLEALPHA=
VERTEX
ROTATION ANG-.008
COORDINATESCOND. VERTEX123d
567
89
1011121314151617181920212223242526272829303132333435
1T_
1
111_
11111111X1IT_
1T_
1111111]_
11111
LE ÍDEG)
( mm )X-NOM.4 4.03843.98043.8634 3.685
43.44843.15242.79642.379
41.90340.29239.60638.86838.077
37.24536.377
35.46334.4 9833.48532.42431.31630.16128.96127.71426.424
25.08928.13028.01227.75527.35626.81625.34524.47523.50822.41621.203
X-MEASUR.43.87243.8204 3.65 94 3.4 9443.16442.87642.64942.12241.71140.13839.48238.81238.00237.149
36.22235.36634.40333.31932.28831.19530.022¿8.79927.51326.21624.88527.85127.70627.46227.15226.65625.20724.35523.39622.36321.003
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Y-NOM.1. 6103. 2294.3476.4608.0689.670
11.26312.84614.41917.82219.2S220.73522.14923.53924.90726.24527.55028.82030.05431.25032.40933.52634.60335.63736.6261. 9803. 9585.9297.8879.828
12.26214.04015.77017.43319.025
Y-MEASUR.1.7503.3255. 0206.5978.207
9. 95411.4 3013.051
14.62617.77319.28420.74522.177
23.51024.93226.25327.59028.795
30.03231.25832.38833.53734.55535.64636.7521. 9863. 9745. 9247 . 922
9. 85412.11413.93615.70817.44818.966
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100101102103104105106107108109
17.54 816.00914.3849.3977.530
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17.55315.90514.2799.4787.54 9
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0051051050810201502281352252311331891591630160491151241501841832452 9920707914115710605903915912900961506305507 209610110107 414 413812608608211607216906315025913523819923919519718222022428416831902800304 8137099048044055132162
22.23.24.26.27.
T_ _
3.5.6.8.9.
11.13.-1.-3.-4 .-6.-8._ Q
-11.-jo
-14 .-.
— 1
-3.-5 .— 6 .-8.-9.
- 1 1 .- 1 3 .16.18.19.20.22.23.25.26.27.28.30.31.32.33.34.35.
-1 7 .- 1 9 .-20.-22.-23.-24 .-26.-27.-28.-30.-31.-32.-33.-34 .-35.-36.-16.-18.-19.-20.-22.-23.-25.-26.-27.-28.
0573044 465442022508704 881027123159104960716102298474 600686702638464192508704881027123159104960716150955489733747541034207029<i 915832946055059860182229273514953990724555082005425040952660363762661509554 8973374754103420702949
22.23.24 .26.27.
1.3.4 .6 .8.g _
11.13.__ 1
-3.- 5 .-6.-8.— 9
- 1 1 .- 1 3 .-14 .
-.-1.-3.-4 .— 6.-8.-9.
-11 .- 1 3 .16.19 .19.20.22.23.25.26.27 .28.30.31.32.33.34.35.
-17.-19.-20.-22.-23.-2 4.-26.-27.-28.-30.-31.-32.-33.-34.-35.-36.-16.-17.-19.-20.-22.-23.-25.-26.-27 .-28.
0062304 245213292128244179677373199144830947743340326131338334 5602054920381639994 46702718654 92027406164<* 1187329270908136063994 4092175320406541658765314715052592898287519756023222334497505666686373908335851239618022282.573.816
-.051-.074-.022-.023.127
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11011111211311411511611711811912012112212312412512612712812913013113213313413513613713813914014114214314414514614714 8149150151152153154155156157158159160
11_
11T_
11T_
1111111_
1i1111
xx1111111111_
11111i_
111111111
11
32.12630.98929.80528.57627.30225.983
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.2342.1854 .1796.1428.07 5
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-2.198-4.119-6.136-8.01510.55412.40914.13915.85017.528
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' -25.866-26.610
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-.049.195.136.120.087.030
-.103-.023-.126-.028.083.024.025.028.029
-.105-.100.057.099.057.006
VERTEX COORDINATES (mm)
COND.123456789
10111213141516171819
VERTEX2222222222222222222
X-NOM.44.04944.01243.91743.7614 3.54 643.27142.93642.54142.08640.9194 0.25239.53338.76137.94737.09836.20235.25634.26033.217
X-MEASUR.43.9304 3.87 943.78543.6254 3.440¡S3. 06142.7344 2.37 441.93840.79740.19839.50738.74337.85237.11636.12235.18034.26733.195
DIFF.-.119-.134-.132-.136-.105-.210-.202-.167-.148-.122-.055-.026-.017-.096.018
-.080-.07 6.006
-.022
Y-NOH..250
1. 8703.4885.1026.7128.3159.910
11.49613.07116.61518.09519.54 820.97322.37423.7 5425.10326.42027.70228.949
Ï-MEASUR..198
1.8983.5135.2256. 8078.350
10.06111.62913.22416.4 9918.01419.47620.94722.34223.77825.11926.39727.74028.933
DIFF-.052.028.025.123.095.035.151.133.153
-.117-.082-.073-.026-.032.024.016
-.023.038
-.015
20212223242526272829303132333435363738394 0414243444546474 84 95051525354555657585960616263646566676869707172737475767778798081828384858687888990919293
22222222222222229
222222222222222o¿-
2222222222222222222222222?
222222222222222
32.12630.98929.80528.57627.30225.98328.14828.06827.84727.48526.98226.07225.23524.30123.24222.06118.85317.33915.73711.0239.168
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32.13930.90529.83828.53227.23025.91727.90427.86227.65227.30226.94126.02725.17624.25523.14022.07018.94417.30015.65711.1629.292
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10.68112.47514.22115.90217.51120.90622.18223.35225.92426.6161.6103.2294.8476.4 608.0689.670
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30.23631.34 232.52133.54734.58335.713
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10
949596979899
10010110210310410510610"10810911011111211311411511611711811912012112212312412512612712812913013113213313413513613713813914 014114214314 4145146147148149150151152153154155156157158159160
2222222222222222222222222222222222222222222222222222222222222222222
-32-30-29-28-27-2540393838373635343332313028272625
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-23-22-21-26-25-24-23-22252 4232221
-17-16-14-18-17-15171614-9-7
-11-997
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. 161
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. 424
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.54 8
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-32-30-29-28-27-2540393838373635343332313029272625
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z14
-9-7
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. 832
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. 886
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.67 4
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.255
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. 912
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.07 9
.04 0
.062
. 064
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. 112
. 024
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1. 9803. 9585. 9297.8879. 828-.240
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1. 9623. 9695. 9667.8709.796-. 204
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12.19413.959
15.68617.42619.090
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21.99623.271
24.408-20.849-22.110-23.290-21.981-23.341
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VERTEX COORDINATES (mm)COND. VERTEX X-NOM.
1 3 59 .1492 3 59 .1113 3 59 .009
X-MEASUR.59.28959.15459.028
DIFF..140.043. 018
Y-NOM..250
2. 1103. 968
Y-MEASUR..198
1. 9753.892
DIFF-.053-.135-.07 5
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50.58536.66949.579
35.744
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(mm)
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23.90823.758
22. 97323.38223.81623.81423.410
23.93323.73123.595
23.74924.59323.607
23.20123.68923.54123.451
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792258577
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15.20515.27015.18815.26315.20815.32115.37415.32115.41315.42415.33915.41315.30515.31315.27915.27315.18815. 27515.28515.48615.39115.38115.42015.41115.36915.36615.46815.42615.26815.32415.32615.40715.26415.26915.23915.32215.32715.31315.22015.24115.37515.33515.11315.22415.30815.26015.16015.13315.28915.26115.27515.38415.21015.19315.25815.19215.12715.21215.27215.19915.22715.33915.42115.44915.31515.39615.30815.22415.26115.33015.23215.22315.25015.258
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21
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AVERAGED LENGTH= 15.312 mmAVERAGED AREAS= 23.4 64 mm~2
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COND.
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255137012326433541650762877997
122254100206312
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XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSK12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSK12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12
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100 /100 /100 /100 /101101101101102 /102 /102 /
102 /103 /103 /103 /103 /
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31
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122122123123123123124124124124125125125125126126126126127127127127128128128128129129129129130130130130131131131131132132132132133133133133134134134134135135135135136136136136137137137137138138138138139139139139140140140140
32
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14114114114114214214214214314314314314414414414 414514514514514614614614614714714714714814814814814 914914914 9150150150150151151151151152152152152153153153153154154154154155155155155156156156156157157157157158158158158159159
33
635636637638639640
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-.20285
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-.20285
.38397-.21819.23953.01775.34 354
-.20285
XSH12YSH12XSK12YSH12XSH12YSH12
159159160160160160
All data listed in Appendixes A and B refer to room temperature measurements of a six-
block dipole cross-section. The same procedure may be applied to liquid nitrogen
measurements. In Fig. Bland B2 the keystone lengths at room and liquid nitrogen
temperatures are compared.
34
15.6
O 50 100
Keystone Number
Fig. IB. Keystone lengths at room temperature
150
mm
)ng
th
1b
15
15
15
15
15
. 0 -
.5 -
.4 -
.3 -
.2 -
1 -
15 -50 100
Keystone Number
150
Fig. 2B. Keystone lengths at liquid nitrogen temperature
35