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

2 8,30.0702,4.65719,30.2608,2.8 90 68,45.6021,3.62928,45.34 61,5.7925929,2 9.7604,6.65555,2 9.9105,4.8 4539,45.3251,5.97013,45.0684,8.0347830,29.2647,8.58697,29.5497,6.81591,44.7892,8.29739,44.4553,10.400631,27.8161,10.8477,28.6361,9.28428,42.535,15.6678,41.603,17.552732,2 6.9646,12.6698,27.7855,11.0902,41.54 9,17.7323,40.5 4 64,19.661733,26.0065,14.4421,26.8651,12.8858,40.3685,19.8542,39.5061,21.750134,24.9732,16.1822,25.7503,14.5987,39.1654,21.7605,38.1628,23.673335,23.6138,17.6997,24.6798,16.1767,37.953,23.737,3 6.72 96,25.52733 6,20.1642,20.74 01,21.5552,19.6009,31.6644,30.9988,30.1122,32.410237,18.5158,21.9645,19.9105,2 0.7958,29.9978,32.614,28.3455,33.8 64238,16.8904,23.15 85,18.268,22.128 6,28.0482,33.9355,26.4313,35.310 639,12.09,25.25 69,13.7733,2 4.6165,19.3413,38.8824,17.37 67,39.772140,10.1612,2 6.0651,11.9034,25.3102,17.2287,39.8824,15.083,40.579441,-41.2 907,-1.04432,-41.2505,0.363876,-5 6.6982,0.65 4403,-5 6.6619,-0.97091542,-41.1762,0.567859,-41.2022,1.97937,-5 6.534,2.47837,-5 6.5724,0.8573543,-41.1737,2.16093,-41.0016,3.55 607,-5 6.4 44 4,4.3368 8,-5 6.4332,2.733034 4,-40.927 4,3.70995,-40.825,5.27073,-5 6.22 65,6.10752,-5 6.413,4.6163745,-40.7055,5.48 037,-4 0.6075,6.8865,-55.9956,7.92499,-5 6.1143,6.263446,-40.5285,7.06205,-40.3961,8.50303,-55.578,9.8 6935,-55.7812,8.15 67347,-40.1373,8.65732,-40.0179,10.107,-55.2 641,11.6835,-55.3971,10.02648,-39.773,10.2261,-39.5957,11.6434,-54.8134,13.5131,-55.0022,11.8 81549,-39.3131,11.8369,-39.0409,13.2523,-54.307,15.33 6,-54.6014,13.735150,-41.414 9,-3.03024,-41.34 65,-1.4 6622,-5 6.6513,-1.51932,-5 6.638 9,-3.0285351,-41.324,-4.59038,-41.308 6,-3.20518,-5 6.5 696,-3.25 994,-5 6.5953,-4.9737752,-41.1404,-6.28835,-41.3073,-4.73373,-56.5343,-5.20693,-56.3782,-6.7152753,-40.9545,-7.8 6941,-41.0213,-6.4 437,-5 6.3615,-6.87 634,-5 6.2366,-8.574255 4,-40.6917,-9.3895,-40.7638,-7.98721,-5 6.0788,-8.83595,-55.968,-10.496755,-40.3 621,-11.0897,-40.509,-9.5333,-55.7342,-10.7344,-55.6751,-12.19625 6,-40.0062,-12.7125,-40.1602,-11.3009,-55.3 614,-12.4212,-55.1403,-14.105357,-39.528 8,-14.2772,-39.8439,-12.8201,-54.9601,-14.35 04,-54.718 9,-16.01395 8,-38.998,-15.8 06,-39.2574,-14.3689,-54.5 439,-16.2397,-54.2025,-17.915459,46.44 99,-1.47267,46.4905,-2.87308,61.756,-3.18506,61.8502,-1.5196560,4 6.5413,-3.08511,4 6.5322,-4.5 0379,61.5 679,-5.03775,61.7183,-3.39277

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70,-36.9848,18.1538,-36.30 65,19.4088,-49.5773,26.9495,-50.2651,25.4671,-36.2046,19.6158,-35.473,20.8244,-4 8.52 42,28.60 66,-49.3798,27.17772,-35.4079,21.0343,-34.64 67,22.2531,-47.6937,30.2283,-48.5243,28.765873,-34.5832,22.4516,-33.8018,23.6728,-46.6728,31.7916,-47.5283,30.351774,-33.6912,23.8238,-32.8657,24.9518,-45.4362,33.2499,-4 6.4952,32.000375,-32.7452,25.1021,-31.8402,26.2306,-44.38 61,34.8 408,-45.4149,33.51527 6,-31.723,2 6.3813,-30.8315,27.5283,-43.25 58,36.3349,-44.3317,35.076277,-30.7488,27.6864,-29.8532,28.8383,-42.1338,37.7944,-43.1403,36.485278,-29.6522,28.8333,-28.7211,29.9044,-40.7507,39.2009,-41.855 6,37.978679,-28.5 029,29.9166,-27.5902,31.0376,-39.4 983,40.573,-40.6728,39.39068 0,-27.2785,31.0 616,-2 6.2964,32.1212,-38.1809,41.9144,-39.3342,40.711181,-26.0452,32.1477,-25.0886,33.255,-36.7767,43.212,-38.001,42.080682,-24.8045,33.2823,-23.8586,34.4167,-35.3 624,44.4318,-36.5162,43.24 6883,-23.4423,34.3985,-22.3821,35.3902,-33.9691,45.5 908,-35.0642,4 4.43448 4,-37.5176,-19.0222,-38.1888,-17.7827,-51.8099,-24.6909,-51.0727,-26.209985,-36.938,-20.5709,-37.55,-19.284 8,-51.0241,-2 6.4199,-50.2591,-27.8 938 6,-36.1128,-21.972 6,-36.8768,-20.7791,-50.2 45 6,-28.0929,-49.3 699,-29.578487,-35.2138,-23.3098,-36.1131,-22.2375,-49.3995,-29.8168,-48.393,-31.20588,-34.5052,-2 4.8499,-35.234 4,-23.6255,-48.3931,-31.35 06,-47.5232,-32.70798 9,-33.535 6,-2 6.1554,-34.4169,-2 4.978 6,-47.35 64,-32.9172,-4 6.4292,-34.32 9590,-32.6594,-27.5452,-33.4 015,-2 6.3344,-4 6.3273,-34.58 06,-45.3137,-35.906291,-31.655 9,-2 8.7771,-32.5509,-27.6778,-45.234 6,-36.1349,-44.222 6,-37.454892,-30.687,-30.0141,-31.5472,-28.8948,-44.068,-37.6352,-43.0325,-38.911593,-29.624,-31.2 808,-30.5397,-30.224 9,-42.8919,-39.0713,-41.7916,-40.348594,-28.531,-32.4806,-29.4918,-31.3894,-41.7134,-40.5323,-40.6256,-41.821995,-27.3387,-33.5923,-28.3027,-32.5287,-40.34 62,-41.85 66,-39.2857,-43.087696,-26.133 6,-34.7558,-27.1064,-33.7627,-39.0733,-43.199,-37.9411,-44.48297,-24.827 6,-35.764,-25.8394,-34.7062,-37.6424,-44.5573,-36.4497,-45.749398,-23.6534,-3 6.9251,-24.6602,-35.8 629,-36.2 639,-45.8335,-35.0491,-46.945599,-22.1673,-37.9455,-23.2 407,-3 6.8933,-34.8 076,-47.0393,-33.5785,-48.0936100,43.4965,-17.6417,42.8984,-18.9627,56.4709,-26.094 6,57.24 92,-24.6037101,42.8547,-19.177,42.2168,-2 0.4274,55.6699,-27.7408,5 6.4 44 6,-26.24 87102,42.1852,-20.6033,41.5783,-21.9512,54.7392,-29.4175,55.5083,-27.9794103,41.5023,-22.1199,40.7427,-23.3554,53.8293,-31.0582,54.6237,-29.6528104,40.6503,-23.5078,39.9521,-24.7 601,52.8 683,-32.68 02,53.8165,-31.3171105,39.7502,-24.88 64,39.0657,-26.1533,51.8125,-34.2439,52.7727,-32.9444106,38.8496,-2 6.2905,38.1142,-27.4 84 6,50.6833,-35.7966,51.7159,-34.4578107,37.914 6,-27.5504,37.1676,-28.7978, 49.7022,-37.3634,50.6289,-36.0021108,36.9961,-28.8406,36.1924,-29.9628,48.5223,-38.8002,49.47 67,-37.501109,35.982 6,-30.0841,35.107,-31.263,47.3605,-40.2715,48.333,-38.9724110,34.8548,-31.2735,33.9595,-32.345 9,4 6.008 6,-41.731,47.137,-40.4325111,33.796,-32.4719,32.8261,-33.5511,44.6754,-43.0495,45.8241,-41.8432112,32.5 687,-33.6298,31.6271,-34.6607,43.3934,-44.3576,44.55 62,-43.1712113,31.3438,-34.7424,30.4348,-35.795,41.9781,-45.622,43.1301,-44.3827114,30.1005,-35.7994,29.1383,-36.9298,40.5378,-4 6.9636,41.7611,-45.7496115,28.6922,-3 6.7958,27.7157,-37.9288,39.199, -48.079,4 0.3253,-46.8 823116,-25.2098,-1.02519,-25.1372,0.703073,-40.5322,1.164 43,-40.6088,-1.0 6405117,-25.014,0.92 601,-24.88 48,2.71031,-40.3917,3.4308 8,-40.4752,1.37729118,-25.0352,2.91962,-24.8869,4.7067,-40.212,5.82676,-40.3262,3.66449119,-2 4.6217,4.8 8294,-24.3823,6.61084,-39.8 673,8.094 65,-40.0233,5.9945 4120,-24.2817,6.81611,-23.9664,8.53655,-39.158 4,10.35,-39.5027,8.36747121,-25.3501,-3.23 624,-25.34 08,-1.46272,-40.7112,-1.4 6883,-40.6539,-3.62714122,-25.1477,-5.21291,-25.2622,-3.48 439,-40.6053,-3.8777,-40.5164,-5.95859123,-24.9692,-7.17514,-25.0815,-5.40812,-40.428 6,-6.19659,-40.3162,-8.2514312 4,-2 4.5892,-9.138 65,-24.8461,-7.40072,-40.1421,-8.5554 6,-39.777,-10.631125,-24.039,-11.15 98,-24.2796,-9.31664,-39.5992,-10.8274,-39.2267,-12.8907126,30.5793,-1.44644,30.506,-3.27801,45.8554,-3.64 416,45.855 4,-1.50993127,30.4 877,-3.4 6516,30.3858,-5.27778,45.7202,-5.88852,45.8216,-3.831412 8,30.0501,-5.38 604,29.9126,-7.19769,45.372 8,-8.37215,45.5716,-6.1684 612 9,29.8 907,-7.40321,29.613,-9.10374,45.0479,-10.7595,45.2339,-8.53789130,29.448,-9.28166,29.2803,-11.0581,44.5371,-12.8981,44.8717,-10.8427131,-23.4943,9.29495,-22.6835,10.9347,-36.579,17.6161,-37.265,15.5997132,-22.5 604,11.15 02,-21.6755,12.6992,-35.571,19.7809,-36.4328,17.7713133,-21.65 03,12.8795,-20.8245,14.4268,-34.3505,21.74 49,-35.3481,19.965 4134,-20.5715,14.5908,-19.6745,16.1662,-32.9953,23.6475,-34.0543,21.7745135,-19.4041,16.2679,-18.4 68 6,17.8303,-31.762,25.5369,-32.885,23.8165

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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

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12.26214.04015.77017.43319.025

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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

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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.

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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

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11_

11T_

11T_

1111111_

1i1111

xx1111111111_

11111i_

111111111

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32.12630.98929.80528.57627.30225.983

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' -25.866-26.610

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-.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

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-.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

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-.015

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222222222222222o¿-

2222222222222222222222222?

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949596979899

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2222222222222222222222222222222222222222222222222222222222222222222

-32-30-29-28-27-2540393838373635343332313028272625

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-11-997

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-32-30-29-28-27-2540393838373635343332313029272625

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z14

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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

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1. 9753.892

DIFF-.053-.135-.07 5

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33. 94826.99435.47028.26837.026

29.48338.51830.74739.887

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25.67433.88026.98535.39128.26136.86629.50138.30230.70439.69931.869

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(mm)

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AREA (mm"2)

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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592432845469389423811617172787413942484728234702297543512979588777

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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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XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSK12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12

676767676868686869696969707070707171717172727272737373737 4747474757575757676767677777777787878787979797980808080818181818282828283838383848484848585

29

33934034134234334434534634734834 93503513523533543553563573583593603613623633643653663673683693703713723733743753763773783793803813823833843853863873883893903913923933943953963973983994004014 024034 044 054064 074 08409410411412

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. 007 94

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.064 4 5

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.15230

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. 02757

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XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSK12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSK12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12

/

85 /85 /86 /886 /86 /87 /87 /87 /87 /

/

88 /88 /88 /88 /89 /889 /89 /90 /90 /90 /90 /91 /91 /91 /91 /92 /92 /92 /92 /93 /93 /93 /93 /94 /94 /94 /94 /95 /95 /95 /95 /996 /96 /96 /97 /97 /97 /97 /98 /98 /98 /9899 /99 /99 /99 /

100 /100 /100 /100 /101101101101102 /102 /102 /

102 /103 /103 /103 /103 /

/

/

30

4134144154164174184194204214 224234 244 254264274 2842 94304 314324334344 354364374384394 404414424434 4 44 4544644144844 94 504514524 534544554 564 574584594604614 624634 644654664674 6846947047147247347447547647747847 94 804814824834 84485486

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.14257-.02142.11771.12716.11595

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XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12

1041041041041051051051051061061061061071071071071081081081081091091091091101101101101111111111111121121121121131131131131141141141141151151151151161161161161171171171171181181181181191191191191201201201201211211211211221 22

31

4874884894904 914924934 944954964 974984 9950050150250350450550650750850951051151251351451551651751851952052152252352452552652752852953053153253353453553653753853954 054154254354454554 6547548549550551552553554555556557558559560

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-.02 954-.01519.13539.08550.04071

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122122123123123123124124124124125125125125126126126126127127127127128128128128129129129129130130130130131131131131132132132132133133133133134134134134135135135135136136136136137137137137138138138138139139139139140140140140

32

561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606507608609610611612613614615616617618619620621622623624625626627628629630631632633634

.03276

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-.11397-.28435.08158.07754

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-.10990-.20812.30175.1214 5

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XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12XSH12YSH12

14114114114114214214214214314314314314414414414 414514514514514614614614614714714714714814814814814 914914914 9150150150150151151151151152152152152153153153153154154154154155155155155156156156156157157157157158158158158159159

33

635636637638639640

.38397-.21819.23953.01775.34354

-.20285

.38397-.21819.23953.01775.34354

-.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