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Nuclear Instruments and Methods in Physics Research A 522 (2004) 360370

Manufacturing the Schmidt corrector lens for the

Pierre Auger Observatory

M.A.L. de Oliveira*, V. de Souza, H.C. Reis, R. Sato

Departamento de Raios C!osmicos e Cronologia (DRCC), Instituto de F!sica Gleb Wataghin (IFGW), Universidade Estadual de

Campinas (UNICAMP), Observat !orio Pierre Auger, Cx.P. 6165, CEP 13084-971, Campinas-SP, Brazil

Received 14 August 2003; received in revised form 24 November 2003; accepted 26 November 2003

Abstract

The Pierre Auger Observatory is designed to provide measurements of Extensive Air Showers initiated in the upper

atmosphere by cosmic rays with energies greater than 1018 eV: One of the employed techniques is air fluorescencedetectors with UV filters and a corrector lens. We describe in this article the production process of the corrector lens in

Brazil, starting from the design of the machines up to the final tests in the prototype telescope. We have used diamond

grinding tools to shape a ring of corrector lens with inner radius of 85 cm and outer radius of 110 cm ; divided in 24segments and with aspherical shape. After the production of a first complete set of segments, we measured a segment

shape scanning with a laser. The lens was then installed at the telescope and we measured its overall influence on the

spot size, taking pictures of the Vega star.

r 2003 Elsevier B.V. All rights reserved.

PACS: 96.40.z; 96.40.Pq

Keywords: Cosmic rays showers; Fluorescence detectors; Corrector lenses

1. Introduction

The Pierre Auger Observatory [1] is a large

international effort to try to solve one of the most

puzzling mysteries of nature that has appeared inthe last times: the Ultra High Energy Cosmic Rays

(UHECRs). These cosmic rays are subatomic

particles going through the universe and reaching

Earth with macroscopic energy B1020 eVB16 J:How can these particles gain such tremendous

energy? This is one of the questions that the Pierre

Auger Observatory is aiming to answer. Cosmic

rays with energies above 5 1019 eV were first

observed in 1962 by Linsley [2] in the Volcano

Ranch array. Since then, several events withenergy above 1020 eV have been observed [35].

However, the present arrays, with collecting area

o100 km2; do not provide enough statistics, dueto the extremely low flux (1 event century1km2)

in this energy region [6,7]. The explanation of these

events face theoretical difficulties, since it is

believed to exist a cutoff in the spectra of cosmic

rays around 5 1019 eV due to the interac-

tion with 2:7 K primordial photons, the GZKcutoff [8,9].

ARTICLE IN PRESS

*Corresponding author. Tel.: +55-1937885276; fax: +55-

1937885512.

E-mail address: [email protected] (M.A.L. de Oliveira).

0168-9002/$- see front matterr 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.nima.2003.11.409

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The observatory is a hybrid giant detector using

two different techniques: water Cherenkov tanks

and fluorescence telescopes. The first technique

consists of an array of 1600 tanks separated by1:5 km spread over an area of 3000 km2: TheUHECRs are so rare that even with such a large

area, extrapolating the AGASA spectrum [10]

below 1020 eV; we will have approximately 103events/year. Some advantages of the Cherenkov

tanks are their low cost and the fact that this kind

of detector can operate continuously with any kind

of weather. The ground array samples the lateral

distribution of the shower generated by the

primary UHECRs. The second technique consists

of 24 telescopes overseeing the array of tanks.

These telescopes observe the fluorescence light

emitted by the air nitrogen molecules when they

are excited by the particles of an Extensive Air

Showers (EAS). They operate with clean weather

in moonless nights. This condition corresponds to

only 10% of the available time, but this disadvan-

tage is compensated by the crucial information

that the fluorescence detector gives to us: the

longitudinal distribution profile of the EAS. This

information is used in order to determine the

energy, the arrival direction and to estimate

the composition of the UHECR that originatedthe showers. Each one of the 24 telescopes is

composed by a spherical mirror with 30 30

field of view reflecting the fluorescence light on an

array of 440 photomultiplier tubes (PMTs). The

system adopts Schmidt optics in order to reduce

coma aberration. The basic setup was thought to

have an aperture box consisting of a 85 cm

diaphragm radius to exclude distant off-axis

rays and a band pass filter passing the

300 nmolo410 nm band, which contains the

main emission peaks of the nitrogen fluorescence.However, it was proposed that the inclusion of a

corrector ring in the outer radius part of the

diaphragm would increase the collection area of

the telescopes, increasing the signal to noise ratio

without significant loss in resolution. The logic for

such a design is spelled out in the next section.

Simulations have shown [11] that the use of a

corrector ring would increase the collection area

significantly, still keeping the aberration within the

specified value of 0:5 (which is one-third of the

PMT aperture for the Auger fluorescence tele-

scope). Indeed, it was possible to determine the

most suitable shape of the corrector ring lenses, as

discussed in Ref. [11]. Here, we start from theresults described in this paper and explain the steps

given for the construction of the first prototype

ring, from the machine conception to the final tests

of the sample lenses.

2. Lens construction

The Fluorescence Detector telescopes uses

Schmidt optics following the proposal in [12] and

are sets of spherical mirrors of 340 cm of curvature

radius with a diaphragm limiting the coma

aberration. Due to the telescope geometry, the

spots at the focal surface have spherical aberra-

tions. Their intensity is proportional to the

effective collecting area A and the noise is

proportional to the square root of this quantity,

in such a way that the signal to noise ratio S=N isgiven by

S

Np

ffiffiffiffiA

O

r1

where O is the solid angle covered by a PMT pixel.The diaphragm is introduced to cut rays far

away from the optical axis, avoiding the coma

aberration [13] and allowing a wider field of view

in comparison with a normal telescope.

As the S=N ratio can change with both mirrorand PMTs diameter, one can increase the mirror

diameter or decrease the PMTs pixel diameter to

increase the S=N ratio, but anyone of suchsolutions would raise too much the costs. Thus,

for the designed mirror values (340 cm of curva-

ture radius and 30

30

of aperture) the spotsachieve the required resolution (0:5 diameter inthe focal surface) for a 85 cm diaphragm radius.

The idea of a corrector lens appeared as a way

to increase the telescope area, increasing the spot

luminosity, without increasing the spot size in

excess. The shape of a ring has been chosen instead

of a filled lens to reduce the final cost and because

the simulations showed that it was needed to

correct only the rays beyond 85 cm from the main

optical axis. It has been decided to increase the

ARTICLE IN PRESS

M.A.L. de Oliveira et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 360370 361

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diaphragm radius in 25 cm: Taking into accountthe glass transmittance and losses through the

segment borders, we calculated an overall light loss

of about 20% within the corrector ring. Then,including the shadow of the PMT camera, the

effective collection is 86% larger for an incident

beam parallel to the telescope optical axis 0 and

63% larger for an incident beam inclined of 20

with respect to the telescope optical axis. For

further details, see the reference [11].

In Fig. 1 is shown the geometry of one segment

of the corrector ring, the studied unit vector

normal to the curved surface ~nn and its projec-tions along cylindrical symmetry axes. The graph

in Fig. 2 shows the limits within which the radial

component of the normal vector ~nnr should lie[12], taking into account the chromatic aberra-

tions, which is discussed in the Appendix A.

Some profiles were suggested by the collabora-

tion [14,15] in an attempt to simplify the produc-

tion (see Fig. 3). The comparison of these profiles

with the previous studied limits is also given in Fig.

2. For the circular approximation, case A, the lens

surface is a toroid which goes through itself, in this

plot is a straight line passing through the point

0:8 m; 0: We can see that the lens profile cannot

be approximated by a spherical surface in thewhole segment extension. However, in the case B,

a part of the profile is out of the allowed region,

then the spot size that the telescope will produce

using this type of lens is larger than the required

0:5 0:5 as is written in Ref. [15]. In the case A,it seems to be good enough though a small part of

the profile is out of the allowed region: this

happens because we considered the spot size as

the circle that contains 100% of the light [11],

while in the Ref. [14] it was taken for 90% of thelight. However, our calculation (using 100% of the

light) is more restrictive.

One way to produce lenses for the Schmidt

telescopes is by a vacuum method [16] in which

one deforms a parallel plate and grinds a spherical

surface while the glass is bent. However, we could

not use this method because the deformation

would break the plate that we were using, made

of optical glass. Other difficulty in manufacturing

the lens is its size (220 cm in external diameter).

ARTICLE IN PRESS

Fig. 1. Illustration of the lens surface normal and its

projections.

Fig. 2. Radial projection of the normal unitary vector, nr; tothe curved surface as a function of the distance, r; to the

telescope axis. We compare the limits to maintain the spotresolution with the two proposed profiles (as discussed in

Fig. 3) and the curve produced by our machine.

Fig. 3. Proposed lens profiles for the corrector ring: case A by

Palatka [14] and case B by Cordero [15].

M.A.L. de Oliveira et al. / Nuclear Instruments and Methods in Physics Research A 522 (2004) 360370362

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The problem is not only the machine to produce

this huge lens but also to obtain the appropriate

material and transportation to the site. To solve

these problems the lens was divided in 24 segments

(following the suggestion by Paul Sommers). Fig. 4

shows the layout of each segment. A problem that

appeared with segmentation was the fact that the

center of symmetry is far away from each piece

that could make its production more difficult.One way to solve these problems was suggested

by the enterprise Schwantz Ltd1 that proposed a

machine with a circular base to hold all the 24

segments. The circular base rotates around its

central axis and a circular tool (a disk with small

abrasive diamond cylinders) grinds the material.

Only one edge of this disk is in contact with the

glass. Considering that the position of the tool,

the material and the base are rigidly positioned,

the profile that such machine can produce is shown

in Fig. 2 (see Appendix B). The machine profiledepends on the position, orientation and the

diameter of the tool. The diameter of the tool

was chosen to be 35 cm for two reasons: Schwantz

has technical problems to produce larger tools and

it is impossible to produce the desired surface

profile with a smaller tool (see Fig. 15b and

Ref. [11]).

The process starts with rectangular 296

307 12 mm3 BK7 glass plates from Schott2.

First, one surface is ground and polished to

become as plane as possible using a planning

machine. The planning machine is constituted by a

needle that controls the position and orientation of

a grinding disk with about 20 cm in diameter and

the glass plate rotates around its center. With the

friction between glass plate and grinding disk, thisdisk rotates and grinds the plate almost homo-

geneously. This process does not produce a really

plane surface but it is good enough for our

purposes: deviation of the normal is around

2 mrad:Then the glass is cut to the shape (see Fig. 4) and

is put on the machine to make the profile. The

machine (as illustrated in Fig. 5) was constructed

at Schwantz considering the described ideas. The

base disk can be controlled to spin with a period in

the range of 340 min: The grinding disk isconnected directly to its motor axis and the motorto a base which allows to control the orientation

and the position of the disk by screws. The

frequency of the grinding disk is of about

700 rpm: The produced profile was controlledduring grinding process measuring the curvature

of the surface with a spherometer.

ARTICLE IN PRESS

Fig. 4. The project of the corrector ring segments.

1Schwantz Ferramentas Diamantadas e Com!ercio !Optico

Ltda, Indaiatuba, Brazil. 2Schott Glaswerke, Mainz, Germany.


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However, a problem appeared using this system

(probably because the system is not rigid): the

produced surface had small furrows (see Fig. 6).

Then, another tool was introduced to correct these

defects. It is composed of an iron plate which has

approximately the shape of one lens segment with

grinding pastilles of aluminum oxide. It accom-

modates under the plate and makes pseudo-random movements on the glass while the base

makes a revolution in about 10 min: Before usingthis tool, the produced surface of the lens is copied

putting a sandpaper on the corrector ring surface

while the tool performs the pseudo-random move-

ments on the sandpaper (see Fig. 6).

After all these steps the segments need to be

polished, what is done by both correction tools,

but replacing the diamond cylinders by felts. The

whole process takes about 180 man-hours for the

production of an entire corrector ring, with seven

manual interventions between each step. Although

approximately 75% of this time is consumed by

the grinding machine which is autonomous.

3. Lenses tests

After the completion of the lenses production,

we have performed tests to measure their surfaces

profiles. These tests were done with a laser

scanning method and with a CCD image of a

star, as we will describe below.

3.1. Laser method

When a beam of light impinges on a surface

separating two media with different refraction

indices, it splits in two beams: the reflected and the

refracted. Therefore, impinging a beam on the lens

segment we can see three beams: two going

backward and one going forward, relatively to

the incident beam. This happens because the beam

that goes in the lens can undergo multiple

reflections before getting out the lens. Measuring

the direction of the incident and of the outgoingbeams we can obtain the normal of the lens

surfaces and the lens profile.

In Fig. 7, we have a layout of the system that

was used to study the lens profile. A diode laser

was used as the light source, S; whose wavelengthis between 635 and 670 nm: On the screen, A1; wemeasured the positions, R1 and R2; with amillimeter paper. The scan method consists in

varying the impinging position, L1; on the firstsurface, S1; and reading the arriving points, R1

ARTICLE IN PRESS

Fig. 5. Design of the constructed machine to produce the

curved profile of the lens.

Fig. 6. Left: illustrates the furrows that appeared in the lens

using only the griding disk; Right: shows the system used to

copy the lens profile to the pseudo-random movement tool.


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and R2; on the screen. To make easier themeasurements of the positions L1; we put a paperwith holes of 1 mm of diameter along the lens

x-axis.

Unfortunately, the source has an undesirable

angular divergence (of about 0:5 cm after apropagation of 400 cm). This gives an additional

uncertainty in the measured positions R1 and R2

and consequently in the lens profile. The way wehave treated these uncertainties is described below.

We aligned the system, making the beam to turn

back on itself, restricting the incident light to

propagate on the plane x z: A reference point onscreen A1 was adopted averaging two adjacent

reflections to the laser shadow. With the positions

S; L1 and R1 we can obtain the direction of theincident ~ii S~LL1 and of the reflected ~rr1 L1~RR1 beams. The direction of the normal to thesurface S1 is

~nn1p~rr1

jj~rr1 jj ~ii

jj~iijj: 2

Measuring the normal in some points of the

surface S1 we can obtain its profile. Almost

the same approach can be used to get the profile

of the plane surface, S2; with S; L1 and R2; nowconsidering the direction of the incident and

reflected light inside the lens using the direction

~nn1 ; obtained in the previous step. We adopted arefraction index of 1.514 for the BK7 glass2 to

reconstruct the data, which is the value for the

center of the laser wavelengths band. The main

uncertainties of the laser method come from the

angular divergence of the source. This was treatedby a Monte Carlo method in the following way: we

took randomly distributed points within the spots,

according to a Gaussian distribution with mean

equal to the center of gravity of the spot and

standard deviation given by the spot divergence,

i.e., the points were sorted within S7DS;L17DL1; R17DR1 and R27DR2 and we calcu-lated the normal unit vectors of each surface, n1and n2: We repeated this process several times andwe got a distribution of n1 and n2 for a given

measured datum. The results for n1 and n2 and the

statistical uncertainties are presented in Fig. 8. The

graph of Fig. 8 is a plot in a general reference

system defined by the laboratory walls. We can see

that the component in y-axis of both surfaces

almost vanishes along all segment. It means that

the produced profile is almost symmetric, as

desirable. The other component (x) seems to

follow a straight line. So, as x projection is

changing, we can say that these surfaces have

approximately circular profile, similar to what was

proposed by Palatka (see Fig. 3) where the

curvature radius can be obtained as C dnr=dr

1: As the alignment of lens segment hasbeen done with the reflected light going back to the

source, the plane surface S2 does not coincide with

the plane x y: Consequently, we cannot comparedirectly these results with Fig. 2. But, we must

rotate the results to the frame in which the average

normal of the surface S2 is pointing in the

direction of z- and x-axis is pointing along the

radial direction of lens segment. The new plane

x y of this frame should be very near the plane in

which the segment was holding on the machineduring the production process.

Fig. 9 shows the results for the curved surface of

four segments. The full lines show the limits, given

by the simulation, within which the data must be

and the dotted line is the profile that the machine

should produce if everything (disk tool, base and

glass) were rigid and assuming the following

parameters: R 97:5 cm; rc 17:5 cm; yr 1:10 and yf 1:07

(see Appendix B, Fig. 14,

for their definitions). We can see that the data fit

ARTICLE IN PRESS

Fig. 7. Scanning the surfaces S1 and S2 of the lens with a laser

at the light source S: The reflections R1 and R2 on the screenA1; as well as L1 and S; are used in the ray-tracing

reconstruction.


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very well in the region from 87.5105 cm: Wethink that the disagreement near the edges of the

lens (or outside the region described above) is

mainly due to the introduction of the second

header (random movement header). But, as we will

see further in the next test, this problem does not

poses us serious difficulties. The curvature radiusof the lens can be calculated as the inverse of the

inclination of the line which best describe the data:

C1 dnr=dr: Fitting the available data of Fig. 9in the range 90 cmoro103 cm; we can calculateC 64075 cm:

3.2. Star picture at the Auger telescope

This test was done using the Auger Fluorescence

Telescope in Malarg .ue, Argentina. The data was

ARTICLE IN PRESS

Fig. 9. Data: resulting profiles of four samples shifted by about

90o within the ring (the segments are numbered from 1 to 24 for

the full ring); full curves: the allowed limits given by the

simulation and; dashed line: the best fit for the machine curve.

The errors are smaller than 0.44 in the same ordinate scale.

Fig. 8. Normal unit vectors components as a function of the distance to the diaphragm center for a sample segment. On the left side is

given the projections ofn1 (normal to the curved surface) and on the right side the projections of n2 (normal to the plane surface). In

each sub-figure the projections are designated in the upper left box.


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taken during four nights of March 2002. During

this period the Vega star was in the field of view of

the telescope. Vega (Alpha Lyrae) is a star of

spectral class A0V, with zero magnitude and arelatively flat electromagnetic spectrum within the

wavelengths 350850 nm: The test consisted ontaking pictures with a CCD camera of the star

image formed at the focal surface. The light of the

star enters the system through the aperture

window and is reflected by the mirror into the

camera surface. The camera is covered with a white

UV reflecting screen. The CCD camera is placed in

front of the mirrors aimed at the screen so that we

can get the image of the star (see Fig. 10).

Our intention was to take several pictures of the

star and to determine the spot size of its image in

the camera surface. This measurement was crucial

to quantify the quality of the whole telescope setup

by establishing the total influence of the corrector

ring on the spot size.

In order to increase the S=N ratio avoiding themotion of the star in the camera field of view, we

took 32 pictures of the star in 8 s exposure time

each in two telescopes configurations: without

corrector ring (85 cm of aperture diaphragm

radius) and corrector ring only. For the latter

setup, we masked the inner 85 cm of the aperturein order to get only light that passed through the

lenses. Fig. 11 shows the superposition of the 32

pictures of Vega in both cases.

The analysis procedure consisted in measuring

the light integral as a function of the distance from

the star center. This can be seen in Fig. 12 where it

is possible to notice the effect of the corrector ring.

In each case, the light intensity was normalized to

the own total amount. The light that enters the

telescope passing through the lenses is concen-

trated in the center of the spot while the lightcoming from the inner part of the aperture is

spread in a larger area. The full line in the plot

shows the concentration of light for the total

aperture of the telescope (radius of 1:1 m) with thecorrector ring in place. The figure shows the good

corrector ring performance, approximately 95% of

the light through the corrector ring will end within

the 0:75 cm spot radius, which corresponds to thespecified value of 0:5; or one third of the PMTpixel size.

ARTICLE IN PRESS

Fig. 10. Taking pictures of Vega spot image with a CCD

camera.

Fig. 11. Superpositions of Vega pictures without corrector ring

(above) and with corrector ring only (below).


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4. Conclusion

We described in this article the production of

the corrector ring for the aperture system of the

Pierre Auger Fluorescence Detector. Starting from

its conception and supported by a ray tracing

simulation [11], where the limits of the projections

of one lens surface normal over the another were

established, we detailed the proposals and the

implemented process, describing the machine thathas been constructed to produce the ring. After the

production was completed, we tested some sample

segments by direct laser scanning and the whole

ring by star picture. In the first test, we achieved

the lens profile of one surface, as produced by the

machine, while in the last we evaluated the overall

performance of the corrector ring working to-

gether with one telescope at the site. The results

show that the segments were within the specifica-

tions and that it was possible to increase the

collection area of the detector without increasingthe spherical aberrations.

Acknowledgements

We would like to thank Carlos O. Escobar Paul

Sommers, Hans Klages, Rog!erio Marcon, Ant-#onio C. da Costa and Emerson Schwantz for

important contributions on many aspects of this

work. This work was supported by FAPESP and

CNPq (Brazil).

Appendix A. Chromatic aberration

Let nr be the radial component of the normal to

the curved lens surface and suppose that the plane

surface has its normal along the #z-axis, the allowed

values for nrr were studied in Ref. [11]. As the

lens profile, in that work, was calculated with a

specific refraction index, the chromatic aberrations

were not taken into account. However, we know

that there will be a variation in the refraction index

in the allowed UV filter region of wavelengths. In

the case of the used glass (BK7), the refraction

index ranges from 1:550 to 1.528 (from the shortestto the longest wavelengths). Thus, one needs to

calculate the limits for each refraction index value,

as shown in Fig. 13. So, our goal is reached if we

guarantee that the surface profile is in the region

between the continuous upper line and the dashed

lower line. These limits are adopted throughout

this work.

Appendix B. Lens profile produced by a circulartool

The surface defined by the revolution around

the position O of the circumference with radius rc

ARTICLE IN PRESS

Fig. 13. Chromatic aberration: the limits within which the lens

profile should be produced for the correspondings refraction

indices for l 410 nm n1 and l 300 nm n2:

Fig. 12. Light integral of Vega pictures. This plot determines

the spot size of the telescope configuration.


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and which is in the plane that pass through the

point ~RR and the normal ~nn (see Fig. 14) may bedescribed by the height z and distance r from the

position O since the surface has cylindrical

symmetry.

If we had ~nnp#y we would obtain a toroidalsurface described by equation is z2 r R2 r2c ;that is the profile proposed by Palatka et al. [14]

(see Fig. 3A) with rc 838:3 cm and R 79:527 cm:

Indeed, we would like to analyze the surfaceproduced when the normal ~nn is almost parallel tothe #z-axis. In order to do this, we calculated the

position of the points of the disk writing the

component z as function ofr to a given ~nn; R and rc:With these points we calculated numerically dz=drand then the radial component of the normal,

using the expression of Ref. [11]

zr z0

Zrr0

nrr0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 nrr

0

2q dr

0 B:1

In Fig. 15 we have some of these surfaces within

the tolerance limits for the lens profiles. We can see

that the overall surface is moved byWR when we

change R to R WR (Fig. 15a), while decreasing

(increase) rc the profile becomes more curved

(straight) in the graphic nrr (Fig. 15b). The others

two graphics show how the direction ~nn changes theprofile.

ARTICLE IN PRESS

Fig. 14. System to produce lens profile using a disk with

radius rc:

0.85 0.9 0.95 1 1.05 1.1

-50

-40

-30

-20

-10

0 std

R+

R-

Limits

1000Xn

r

r(m)(a)

1000Xn

r

r(m)

(b)

0.85 0.9 0.95 1 1.05 1.1

-50

-40

-30

-20

-10

0 std

-n

+n

Limits

1000Xn

r

r(m)(c)

1000X

nr

r(m)

(d) 0.85 0.9 0.95 1 1.05 1.1-50

-40

-30

-20

-10

0

0.85 0.9 0.95 1 1.05 1.1-50

-40

-30

-20

-10

0 std

r+

r-

Limits

std

-n

+n

Limits

Fig. 15. Surface profiles produced by the system of Fig. 14

with different parameters. All the graphics show the two

limits of the lens profiles and std the surface produced with

parameters R 0:975 m; rc 0:175 m and normal compo-nents of plane of disk nr 0:021 and ny 0:015: Otherprofiles are identified as x7 means that the parameter x was

changed x-x7Wx; where WR 0:025 m; Wr 0:025 m;Wnr 0:005 and Wny 0:005:


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[15] A. Cordero-Davila, et al., Segmented Spherical Corrector

Rings 1: Computer Simulations; GAP 2000-018, http://

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[16] E. Everhart, Appl. Opt. 5 (1966) 713.

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