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VST Project

Osservatorio Astronomico di Capodimonte Napoli

VST
PRELIMINARY DESIGN REVIEW SECTION 2 OPTICAL DESIGN
Designed by :
Signature

D. Mancini, D. Ferruzzi, G.Marra,

FEA by :
Signature

D. Mancini, F. Perrotta

SW tools by :
Signature

M. Brescia

Prepared by :
Signature

D.Ferruzzi, G.Marra

Supervised by : D. Mancini, G.Sedmak
Signature

Verified by :
Signature

D. Mancini, G. Sedmak, V. Fiume Garelli

Approved by :
Signature

G. Sedmak

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EVOLUTION RECORD

Issue
1.0 2.0 2.1

Revision
0 0 1

Date
15/11/98 18/12/98 22/12/98

Notes
First release for comments Added focus depth and FEA interface analysis Some errors removed

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TABLE OF CONTENTS
2 Telescope Optical Design ......................................................................................... 5
2.1 Introduction ............................................................................................................................. 5 2.2 Optical design requirements ................................................................................................. 5 2.3 Optical layout .......................................................................................................................... 6 2.3.1 Shack Hartmann optical subsystem ...................................................................................... 10 2.4 Optical performance ............................................................................................................. 10 2.4.1 Encircled Energy ...................................................................................................................... 10 2.4.2 Spot diagram ............................................................................................................................. 12
2.4.2.1 Spot diagram with interference filters ........................................................................................ 13

2.4.3 MTF ............................................................................................................................................. 2.4.4 Field curvature and distortion curves .................................................................................... 2.4.5 Analysis of focus depth ........................................................................................................... 2.5 Efficiency curves for the two configurations ..................................................................... 2.5.1 Efficiency with ADC and one lens field corrector ................................................................. 2.5.2 Efficiency with two lenses field corrector ............................................................................. 2.6 Ghost Analysis ...................................................................................................................... 2.6.1 Ghost analysis with ADC and one lens field corrector ........................................................ 2.6.2 Ghost analysis with two lenses field corrector..................................................................... 2.6.3 Analysis of focused ghosts..................................................................................................... 2.6.4 Analysis of sky concentration ................................................................................................ 2.6.5 Ghost analysis summary ......................................................................................................... 2.7 Optical tolerances................................................................................................................. 2.8 First stage of baffles design ................................................................................................ 2.9 Image quality versus mirror deformation ........................................................................... 2.9.1 Image quality versus mirror deformation for two lenses corrector ................................... 2.9.2 Image quality versus mirror deformation for ADC and one lens corrector .......................

14 15 17 18 18 19 20 20 23 25 25 25 26 29 30 31 33

TABLE & FIGURES I
Tab. Tab. Tab. Tab. Tab. Tab. Tab. Tab. Tab. Tab. Tab. Tab. Tab. Tab. Tab.

NDEX

2.1 - Main requirements for the optical design ................................................................................................... 5 2.2 - VST main optical data ................................................................................................................................ 8 2.3 - VST mirrors optical data ............................................................................................................................ 9 2.4 - VST optical data for ADC and one lens, in, B, V, R, I bands ..................................................................... 9 2.5 - VST optical data for two lenses corrector, filter and dewar window in U Â I bands ................................... 9 2.6 - Optical performance for the configuration with two lenses ...................................................................... 10 2.7 - Optical performance for the configuration with the ADC and one lens .................................................... 10 2.8 - Depth of focus versus EE % variation for the configuration with the ADC and one lens at 70°zenith angle .......................................................................................................................................................................... 17 2.9 - Depth of focus versus EE % variation for the configuration with the ADC and one lens at 0°zenith angle .......................................................................................................................................................................... 17 2.10 - Depth of focus versus EE % variation for the configuration with the two lenses at zenith ..................... 17 2.11 - Table of all possible ghosts for ADC and one lens corrector configuration ........................................... 22 2.12 - Table of all possible ghosts for two lenses corrector configuration ....................................................... 24 2.13 - Summary of the brightest focused ghosts ............................................................................................. 25 2.14 - Summary of most focalised ghost for sky concentration ....................................................................... 25 2.15 - Centred tolerances for two lenses field corrector .................................................................................. 26

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Tab. Tab. Tab. Tab. Tab.

2.16 2.17 2.18 2.19 2.20

-

Centred tolerances for one lens field corrector and ADC ...................................................................... Decentred tolerances for two lenses field corrector.............................................................................. Decentred tolerances for one lens field corrector and ADC .................................................................. Performance of polychromatic MTF for two lenses field corrector (320 Â 1014nm) at z=0 ................... Performance of polychromatic MTF for ADC and one lens corrector (365 Â 1014nm) at z=0 ..............

26 27 27 28 28

Fig. 2.1 - VST complete optical layout of telescope with one lens and the ADC, with a curve dewar window ........... 6 Fig. 2.2 - VST zoom of the optical layout of the corrector with one lens and the ADC, with a curve dewar window .. 6 Fig.2.3 - VST optical layout of telescope with two lenses (U Â I bands) ..................................................................... 7 Fig.2.4 - VST zoom of the optical layout of the two lenses (U Â I bands)................................................................... 7 Fig.2.5 - Encircled Energy for two lenses field corrector at zenith ........................................................................... 11 Fig.2.6 - Encircled Energy for ADC and one lens corrector at 0°zenith distance ..................................................... 11 Fig.2.7 - Encircled Energy for ADC and one lens corrector at 70°zenith distance ................................................... 12 Fig.2.8 - Spot diagram for one lens and ADC at zenith from B to I .......................................................................... 12 Fig.2.9 - Spot diagrams for one lens and ADC at z=70°zenith distance ................................................................... 13 Fig.2.10 - Spot diagram for two lenses corrector from U to I bands at zenith .......................................................... 13 Fig.2.11 - MTF two lenses field corrector at zenith .................................................................................................. 14 Fig.2.12 - MTF ADC an one lens corrector at 0°zenith distance .............................................................................. 14 Fig.2.13 - MTF ADC an one lens corrector at 70°zenith distance ............................................................................ 15 Fig.2.14 - Field curvature and distortion curves for the configuration with one lens and ADC at z angle of 70°zenith distance ............................................................................................................................................................. 16 Fig.2.15 - Field curvature and distortion curves for the configuration with two lenses ............................................. 16 Fig.2.16 - Efficiency curves for ADC and one lens corrector at z=0......................................................................... 18 Fig.2.17 - Efficiency curves for two lenses corrector ................................................................................................ 19 Fig.2.18 - ADC and one lens .................................................................................................................................... 20 Fig.2.19 - Two lenses corrector ............................................................................................................................... 23 Fig.2.20 - First stage of baffle design ...................................................................................................................... 29 Fig.2.21 - OAC Telescope optical quality optimisation work flow ............................................................................ 30 Fig.2.22 - Encircled Energy for two lenses field corrector at zenith with M1 gravitational loads applied................. 31 Fig.2.23 - Spot diagram with two lenses corrector at zenith with M1 gravitational loads applied ............................ 32 Fig.2.24 - Field curvature and distortion curves for the configuration with two lenses at zenith with M1 gravitational loads applied ..................................................................................................................................................... 32 Fig.2.25 - Encircled Energy for two lenses field corrector at zenith with M1 gravitational loads applied.................. 33 Fig.2.26 - Spot diagram for one lens and ADC at zenith with M1 gravitational loads applied .................................. 34 Fig.2.27 - Field curvature and distortion curves for the configuration with one lens and ADC at 0° zenith angle with M1 gravitational loads applied ........................................................................................................................... 34

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2 TELESCOPE OPTICAL DESIGN
2.1 INTRODUCTION
In this document, a new optical solution for the VST is reported. As in the baseline of 06/11/98 it has a removable ADC and a curve dewar window, the clear aperture diameter is 2610 mm. It is provided with a corrector made of two lenses from U to I bands (0.320 Â1.014 µm) and a corrector with one different lens and an ADC with curve entrance and exit surfaces from V to I bands (0.365 Â 1.014 µm). The ADC type chosen is constituted of two couples of prisms, which glasses were substituted with PSK3 and LLF1, because the latter, respect to BK7 and LLF6 have the same index of refraction at one wavelength (441.8 nm). In this way the positions of the centroid of spot don't change significantly when observing at different angles. The two double prisms must be suitably counter rotated, to correct the atmospherical dispersion at the different observation angles, respect to zenith. The results of the study of optical quality were reported at zenith angle and at the z angle corresponding to the maximum dispersion of ADC. The parameters of the mirrors were unchanged, with respect to the baseline of 06/11/98, while those of the two correctors, filter and dewar window were re-optimised. In particular the thickness of dewar window was increased, so the distance between M1 and the focal plane. The change of glasses for ADC let to increase the equivalent focal length of the telescope when re-optimising the two correctors. So, respect to the baseline of 06/11/98 it was possible to normalise not only the curvatures of the ADC and one lens corrector, but also all those of the two lenses corrector, still obtaining a good optical quality for both configurations. In particular, the solution found for two lenses corrector shows an optical quality which is close to the goal. It represents a compromise between the maximum achievable distance of last corrector element from the dewar window, and the maximum acceptable percent distortion. If the distance between last lens of the corrector with two lenses is further increased, percent distortion rises critically.

2.2 OPTICAL DESIGN REQUIREMENTS
Table 2.1 summarises the top-level requirements for the nominal design of the telescope optics as well as the dimensional requirements. The additive constraint, coming from the mechanics of the camera on the minimum distance between last corrector element and dewar window was also considered. Telescope diameter Image Scale Pixel size Unvignetted field of view Image quality 2610 mm 0.21 arcsec/pixel 15 µm 1.47° diagonal Required 80% energy within 2 â 2 pixels Goal 80% energy within 1 â 1 pixel Maximum distortion Required 0.3% Goal 0.01% Wavelength range W ithout ADC 0.320 to 1.014 microns W ith ADC 0.365 to 1.014 microns Zenithal distance range Min. 0-60° Max. backfocal distance M1 vertex to focus Min. distance M1 vertex to first optical surface Max. footprint diameter of light beams in M1 center hole Min. backfocal distance last corrector element to image surface Min. backfocal distance last corrector element to dewar window Min. distance back surface of dewar window to image surface Minimum thickness of dewar window Tab. 2.1 - Main requirements for the optical design

1500 400 500 200 245 22.00 20.0

mm mm mm mm mm mm mm

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2.3 OPTICAL LAYOUT
The mirrors parameters are the same of the solutions of 31/07/98 and of 06/11/98, while those of the two correctors and dewar window were modified. As in the solution of November, the last corrector element was moved away from the dewar window in order to have much more space for the mechanics of the camera. The thickness of dewar window was instead modified and increased for safety and the ADC glasses were changed from UBK7 and LLF6 to PSK3 and LLF1 which have the same index of refraction at one wavelength, so the centroid of spot doesn't move substantially at different observing angles. All correctors and dewar window parameters were re-optimised. W ith the change of the glasses of ADC, it was possible to increase the back focal length in order to meet optical quality requirements, also with all two lenses corrector surfaces normalised to DIN tables, keeping percent distortion low. In Fig. 2-1 and 2-2, the complete optical layout of the telescope with one lens and the ADC and the zoom of the corrector are respectively shown.

Fig. 2.1 - VST complete optical layout of telescope with one lens and the ADC, with a curve dewar window

Fig. 2.2 - VST zoom of the optical layout of the corrector with one lens and the ADC, with a curve dewar window

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In Fig. 2-3, 2-4 the complete optical layout of the telescope with the two lenses and the zoom of the corrector are reported.

Fig.2.3 - VST optical layout of telescope with two lenses (U Â I bands)

Fig.2.4 - VST zoom of the optical layout of the two lenses (U Â I bands)

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In Tables 2.2, 2.3, 2.4, 2.5, VST main optical data, the optical data for the mirrors, the optical data with the ADC inserted and with the ADC removed are respectively shown. The glasses of ADC were changed in order to have fixed the position of centroid of spot when observing at different angles respect to zenith. The parameters of the two correctors and of the dewar window were reoptimised in order to satisfy the mechanical constraint on the distance of last corrector element from the dewar window and, in the mean time, to keep percent distortion at low values. The distances between last corrector element and the dewar window were increased, respect to the solution of July, respectively to 290.22 mm and 245 mm, which are greater than the minimum required. All curvatures are normalised also for two lenses corrector, (see Table 2.5) and the optical quality is good. The solution found has the maximum distance achievable between last corrector element and dewar window keeping acceptable the maximum percent distortion. If the distance between last lens of the corrector with two lenses is further increased, percent distortion rises critically.

Vst Main Optical Characteristics Optical configuration Modified Ritchey Chretien Clear aperture 2610 mm Angular field of view 1.47° F# 5.5 Equivalent focal length 14496.93 mm (two lenses) 14395.97 mm (one lens +ADC) Image scale 0.21 arcsec/pixel Overall length 4477.27 mm (fixed) Distance between mirrors -3285.873 mm Spectral Range U Â I bands Distance M1 vertex to first corrector lens in B, V, R, I bands 401.75 mm (>min. req.) 547.35 mm (> min. req.) Distance M1 vertex to first corrector lens in UÂ I bands Distance M1 vertex to CCD plane 1191.4 mm (< max. req.) Footprint diameter of light beams in M1 centre hole 508.5 mm Distance between last corrector element and the image 352.53 mm for one lens +ADC (> min. req.) plane 307.31 mm for two lenses (> min. req.) Distance between last corrector element and dewar window 290.22 mm for one lens +ADC ( 245 mm) 245 mm for two lenses (( 245 mm) Image plane corrector in B, V, R, I bands ADC +one lens Atmospheric Dispersion Corrector (ADC) Two double prisms made of PSK3 and LLF1 Two lenses Image plane corrector in UÂ I bands Focal Plane CCD mosaic 16 k x 16 k CCD pixel size 15µm x 15µm Tab. 2.2 - VST main optical data

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VST MIRRORS OPTICAL DATA Primary Mirror parameters Outer Diameter Clear aperture Inner Diameter Ray of curvature Conic constant K1 Secondary Mirror parameters Clear aperture Ray of curvature Conic constant K2 Distance between mirrors 2658 mm 2610 mm 600 mm -9509 ± 4 mm -1.139899 899.3 mm -4374 ± 2 mm -5.421864 -3285.873 mm Tab. 2.3 - VST mirrors optical data OPTICAL DATA FOR ADC AND ONE LENS CONFIGURATION R1 Tilt S1 R2 Tilt S2 Material Diameter 2511.9 mm R2 Infinity 0° Tilt S2 1.03° infinity R3 infinity 1.03° Tilt S3 0° PSK3 459.7 mm

Element ADC S1,S2 (First prism) ADC S2,S3 (second prism) S3,S4 ADC S4,S5 (third prism) ADC S5,S6 (fourth prism) L3

Thickness 28.57 mm

LLF1 Air gap

457.6 mm

18.30 mm 10 mm

R4 Infinity R5 infinity

0°

R5 infinity R6 10000 mm -10000

-1.03°

PSK3

452.3 mm

18.00 mm

-1.03°

0°

LLF1 air Silica air

450.3mm

24 mm 289.75 mm 48.50 mm 225.22 mm

-1223.2

393.2 mm 391.3 mm

Tab. 2.4 - VST optical data for ADC and one lens, in, B, V, R, I bands OPTICAL DATA FOR TWO LENSES CONFIGURATION R1 R2 Material Diameter Thickness 441.1 mm 1333.5 mm 2304.1 mm Silica 50.00 mm -1295.7 mm Infinity 2304.1 mm -10000 mm Infinity 1223.2 mm Silica Silica Silica
433.4 391.7 390.3 379.1 mm mm mm mm

Element L1 L2 Filter Dewar window

Air thickness 251.74 mm 180 mm 50 mm 36.86 mm

35.00 mm 15.00 mm 25.45 mm

374.8 mm 371.9 mm

Tab. 2.5 - VST optical data for two lenses corrector, filter and dewar window in U Â I bands

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2.3.1 Shack Hartmann optical subsystem
The SH optical subsystem which is necessary for the calibration and close loop control of the active optics system is described in section 3.6.

2.4 OPTICAL PERFORMANCE
In Tables 2.6 and 2.7 the optical performance for the two configurations are reported. The optical quality is better than for solution of 06/11/98. OPTICAL PERFORMANCE FOR THE CONFIGURATION WITH TWO LENSES (WORST CASE) U ÂI bands (0.320 Â 1.014 µm) 80 % in 1.33 pixel (at the edge of the field) 0.013 % (at the edge of the field at = 320 nm) 99%

Diffraction encircled energy Maximum distortion Glass transmission

Tab. 2.6 - Optical performance for the configuration with two lenses

OPTICAL PERFORMANCE FOR THE CONFIGURATION WITH THE ADC AND ONE LENS (WORST CASE) B ÂI bands (0.365 Â 1.014 µm) 80 % in 1.5 pixel at zenith (at the edge of the field) 80 % in 2.88 pixel at z =70°(at the edge of the field) 0.01 % at zenith (at the edge of the field) 0.01 % at z= 70°(at the edge of the field) 88 %

Diffraction encircled energy Maximum distortion Glass transmission

Tab. 2.7 - Optical performance for the configuration with the ADC and one lens

2.4.1 Encircled Energy
In Fig. 2-5, 2-6, 2-7 the curves of polychromatic diffraction encircled energy versus centroid distance, for the different fields of view are reported respectively for two lenses, ADC and one lens correctors at 0°zenith distance The radius of the circle from centroid in which the 80% of encircled energy (normalised to diffraction limit) is enclosed is of 9.9 µm, 11.5 µm and 21.6 µm respectively for two lenses corrector and ADC and one lens corrector at 0°zenith distance and 70°zenith distance.

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Fig.2.5 - Encircled Energy for two lenses field corrector at zenith

Fig.2.6 - Encircled Energy for ADC and one lens corrector at 0° zenith distance

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Fig.2.7 - Encircled Energy for ADC and one lens corrector at 70° zenith distance

2.4.2 Spot diagram
In Fig. 2-8Â2-10, the spot diagrams for one lens and ADC configuration at 0° at 70°zenith distance and the spot , diagrams for the configuration with two lenses at zenith are respectively shown. The configuration is that shown in Figs. 2-2 and 2-4. Note that the filters included are standard units (not interference type)

Fig.2.8 - Spot diagram for one lens and ADC at zenith from B to I

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Fig.2.9 - Spot diagrams for one lens and ADC at z=70° zenith distance

Fig.2.10 - Spot diagram for two lenses corrector from U to I bands at zenith

2.4.2.1 Spot diagram with interference filters
The spot diagrams with interference filters will be determined after the definition of the narrow band interference filters to be used in the camera.

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2.4.3 MTF
In Fig. 2-11Â 2-13 the polychromatic diffraction modulation transfer function curves for two lenses corrector and ADC and one lens corrector at 0°and 70°zenith distance are respectively shown. For two lenses corrector MTF is always greater than 58% until Nyquist frequency of 25 cycles/mm. For ADC and one lens at 0°zenith distance MTF is always greater than 58% until Nyquist frequency of 22.22 cycles/mm, and at 70°zenith distance is greater than 40.7% until Nyquist frequency of 13.33 cycles/mm.

Fig.2.11 - MTF two lenses field corrector at zenith

Fig.2.12 - MTF ADC an one lens corrector at 0° zenith distance

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Fig.2.13 - MTF ADC an one lens corrector at 70° zenith distance

2.4.4 Field curvature and distortion curves
In Figures 2-14, 2-15 the field curvature and distortion curves for the configurations with ADC and one lens at 70° zenith distance and with two lenses are respectively reported. For the ADC and one lens corrector at 70°zenith distance the maximum distortion is 0.01 %, at the edge of the field for =1.014 µm. For two lenses corrector the maximum distortion is 0.013% at the edge of the field for =0.32 µm. The focal plane is flat and it is located in the origin of field curvature diagram between tangential and sagittal curves. The field curvature plot shows the distance from the currently defined focal plane(origin of the graphic) to the paraxial focal plane as function of field view. The plane in which field curvature is zero is the image plane chosen for the system where there is the best focus and the radius in which 80% of encircled energy is enclosed is minimised. The field curvature curves for the tangential and sagittal rays are defined as the distances from the defined image plane of best focus to the paraxial focal planes for those rays, for each field of view. The best focus image plane is the focal plane in which the diameter of spot diagram is minimised and optimised for all the fields of view and is not necessarily coincident with the paraxial focal planes as described in Figs.2.14 and 2.15

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Fig.2.14 - Field curvature and distortion curves for the configuration with one lens and ADC at z angle of 70° zenith distance

Fig.2.15 - Field curvature configuration with two lenses

and

distortion

curves

for

the

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2.4.5 Analysis of focus depth
The analysis of focus depth for two correctors configurations was performed. The depth of focus was calculated respect the best focus image plane of the optical system which is the plane in which field curvature is zero and the radius in which 80% of encircled energy is enclosed is minimised, as discussed in section 2.4.4. In Tables 2.8, 2.9, 2.10 the depth of focus calculated for the two correctors are reported. Depth of focus + 10 µm - 10 µm + 20 µm - 20 µm + 30 µm - 30 µm EE% variation with respect to EE 80% -2.5% 0% -2.8% +0% -6.5% 0%

Tab. 2.8 - Depth of focus versus EE % variation for the configuration with the ADC and one lens at 70° zenith angle Depth of focus + 10 µm - 10 µm + 20 µm - 20 µm + 30 µm - 30 µm EE% variation with respect to EE 80% 0% 0% 6.2% 0% 0% 0%

Tab. 2.9 - Depth of focus versus EE % variation for the configuration with the ADC and one lens at 0° zenith angle Depth of focus + 10 µm - 10 µm + 20 µm - 20 µm + 30 µm - 30 µm EE% variation with respect to EE 80% 0% 0% 0% -2.25 % -4.5 % -4.2 %

Tab. 2.10 - Depth of focus versus EE % variation for the configuration with the two lenses at zenith

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2.5 EFFICIENCY CURVES FOR THE TWO CONFIGURATIONS
In Fig. 2-16, 2-17 the efficiency curves for the two configurations are shown. It was considered a filter of Silica (SQ1 from Zeiss) 15 mm thick and a dewar window of Silica 25.45 mm thick. The coating of the mirrors is aluminium and that one of the correctors is AR coating measured from Zeiss which has a transmission better than 0.985.

2.5.1 Efficiency with ADC and one lens field corrector
In Fig.2-16 the curves of efficiency for VST, for ADC and one lens corrector are shown. The highest curve shows the corrector (PSK3, LLF1, Silica SQ1) with coating efficiency. The maximum residual reflectance for coating measured from Zeiss, (which is less than 1.5% over the whole range from 365 to 1014 nm) was considered. The second curve and the third one from the top are respectively the aluminium coating reflectivity of the two mirrors and the efficiency of corrector with a filter of Silica 15 mm thick, a dewar window of Silica 25.45 mm thick, with corrector coating. The fourth and the fifth are the total efficiencies of the telescope, respectively with and without filter, taking into account, corrector, dewar window, corrector coating and mirrors coating. The last curve downwards is the total efficiency of the telescope with filter, taking into account also the M2 baffle obscuration, which is of 17%. The total efficiency is over 63% without M2 baffle obscuration, and over 52% with baffling the range 365 Â 1014.

Fig.2.16 - Efficiency curves for ADC and one lens corrector at z=0 (* (x (o (+ (* (+ . green) cyan) yellow) yellow) ciano) green) Corrector with AR wideband multilayer coating measured from Zeiss (R<1.5%) Mirrors coated with aluminium Corrector with filter and dewar window, with coating Total efficiency (telescope + corrector + dewar window, with coating) Total efficiency (telescope + corrector +filter+ dewar window with coating Total efficiency (telescope + corrector + dewar window + filter, + M2 baffle obscuration, with coating)

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2.5.2 Efficiency with two lenses field corrector
In Fig.2-17 the curves of efficiency for VST, for two lenses corrector are shown. The highest curve shows corrector (Silica SQ1 from) with coating efficiency. The maximum residual reflectance for coating measured from Zeiss, (which is less than 1.5% over the whole range from 320 to 1014 nm) was considered. The second curve and the third one from the top are respectively the aluminium coating reflectivity of the two mirrors and the efficiency of corrector with a filter of Silica 15 mm thick, a dewar window of Silica 25.45 mm thick, with coating. The fourth and the fifth are the total efficiencies of the telescope, respectively with and without filter, taking into account, corrector, dewar window, corrector coating and mirrors coating. The last curve downwards is the total efficiency of the telescope with filter, taking into account also the M2 baffle oscuration, which is of 17%. The total efficiency is over 66% without M2 baffle obscuration, and over 55% with baffle in the range 320 Â1014 nm.

Fig.2.17 - Efficiency curves for two lenses corrector (* (x (o (+ (* (+ green) cyan) yellow) yellow) ciano) green) Corrector with AR wideband multilayer coating measured from Zeiss (R<1.5%) Mirrors coated with aluminium Corrector with filter and dewar window, with coating Total efficiency (telescope + corrector + dewar window + filter, with coating) Total efficiency (telescope + corrector +filter+ dewar window with coating Total efficiency (telescope + corrector + dewar window + filter, + M2 baffle obscuration, with coating)

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2.6 GHOST ANALYSIS
The ghost analysis has been performed using paraxial rays. This method can be used to select the most critical ghosts. Two kind of ghost image were analysed: the bright focused ghost image and the sky concentration effects..

2.6.1 Ghost analysis with ADC and one lens field corrector
Each surface has a number according to Fig. 2-18, which was used in the analysis. In addition surfaces 1, 2, 3 are respectively M1, M2, the dummy surface at the primary hole. The analysis was limited to two reflections. In the Table 2.11 are reported all possible ghosts. The analysis was done at z =0.

Fig.2.18 - ADC and one lens

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Ghost analysis for ADC and one lens field corrector configuration (365 Â 1014 nm)
REFL 1 2 4 5 6 7 8 9 10 11 12 13 14 15 16 4 5 6 7 8 9 10 11 12 13 14 15 16 5 6 7 8 9 10 11 12 13 14 15 16 6 7 8 9 10 11 12 13 14 15 16 7 8 9 10 11 12 13 14 15 16 8 9 10 11 REFL 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 DBFL -1991.172780 -2100.092044 -2107.840192 -2107.905413 -2107.961226 -2108.025674 -2107.726204 -2110.077621 -2109.779097 -2111.130599 -2111.185905 -2111.439355 -2111.525891 -2111.711344 -1964.466672 -2011.078450 -2011.453305 -2011.773861 -2012.143764 -2010.422639 -2023.780366 -2022.104206 -2029.647838 -2029.954107 -2031.355196 -2031.832667 -2032.854358 -350.689651 -357.530997 -363.505859 -370.547852 -339.083198 -720.750687 -647.823333 -1106.123871 -1134.805778 -1283.122686 -1341.191428 -1481.509286 -31.226640 -57.320664 -86.514483 58.084009 -683.471232 -623.733602 -853.317139 -860.830542 -893.800806 -904.538278 -926.720247 -26.684485 -56.826308 92.616060 -669.865738 -608.800848 -843.144734 -850.798391 -884.372499 -895.302544 -917.875994 -30.718516 123.054701 -658.015405 -595.782028 EFL -323.209465 -17.892368 186.984105 187.103355 187.205287 187.322859 -100.623175 12.527290 -43.070152 -27.985027 -27.897014 -11.290180 -6.381744 -16.919505 -41.842709 524.942616 525.217576 525.452554 525.723529 -220.192727 29.860164 -98.067405 -64.277027 -64.070334 -26.262096 -14.900545 -39.148990 362.515387 362.942539 363.308023 363.730005 571.987557 154.468641 800.209320 1010.728635 999.896207 -1139.522729 -304.027194 2952.436445 -698.496850 -699.343435 -700.321321 -401.442990 216.316258 -270.723498 -200.619242 -199.760696 -101.439594 -61.965719 -137.526645 -698.352046 -699.327159 -403.020042 219.182911 -272.220177 -201.852092 -200.987131 -102.191852 -62.456738 -138.464049 -698.480614 -404.376306 221.691160 -273.511141 DISC -1297.755810 -846.559076 -4235.981959 -4230.830973 -4226.433263 -4221.366723 -3449.590186 -6080.178130 -3390.593327 -3680.223997 -3704.346320 -3638.159443 -3576.343203 -3949.890632 -315.633990 -1685.495091 -1684.334548 -1683.343721 -1682.202204 -1371.323231 -2463.084336 -1370.276985 -1503.314174 -1513.825787 -1489.738862 -1465.420296 -1620.834462 -69.188686 -69.685119 -70.108954 -70.597248 -55.516732 -127.903728 -69.199708 -85.550020 -86.540473 -86.927947 -86.099866 -96.628683 -2.877272 -5.354647 -8.208796 4.155146 -142.872288 -69.049360 -127.122845 -130.103779 -137.443975 -138.351966 -160.478365 -2.452927 -5.307076 6.513145 -138.533484 -66.642756 -124.447219 -127.408003 -134.784613 -135.733846 -157.577450 -2.829701 8.526313 -134.829183 -64.588092 PUPIL RATIO 1.000000 1.000000 1.031508 1.030939 1.030453 1.029893 1.000000 1.514327 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 MAGNIFICATION 0.139085 0.224877 0.045107 0.045164 0.045212 0.045268 0.055387 0.031459 0.056406 0.052000 0.051663 0.052609 0.053521 0.048463 0.564190 0.108160 0.108254 0.108335 0.108429 0.132896 0.074481 0.133770 0.122387 0.121555 0.123606 0.125687 0.113693 0.459465 0.465091 0.470005 0.475796 0.553664 0.510818 0.848627 1.172055 1.188684 1.338052 1.412058 1.389833 0.983804 0.970386 0.955375 1.267169 0.433647 0.818849 0.608487 0.599780 0.589494 0.592660 0.523476 0.986140 0.970641 1.289021 0.438326 0.828107 0.614160 0.605333 0.594784 0.597924 0.528025 0.984065 1.308282 0.442401 0.836179

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REFL 1 12 13 14 15 16 9 10 11 12 13 14 15 16 10 11 12 13 14 15 16 11 12 13 14 15 16 12 13 14 15 16 13 14 15 16 14 15 16 15 16 16

REFL 2 7 7 7 7 7 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 10 10 10 10 10 10 11 11 11 11 11 12 12 12 12 13 13 13 14 14 15

DBFL -834.308635 -842.085166 -876.188040 -887.286626 -910.202566 159.270073 -644.086673 -580.465029 -823.951275 -831.873071 -866.600763 -877.898400 -901.218672 -626.162223 -559.622110 -838.081943 -848.330211 -894.275104 -909.589765 -941.794395 497.196780 -445.613126 -455.137162 -492.429776 -503.202064 -523.664137 -417.245965 -434.027730 -510.632790 -536.676458 -592.298783 -20.242610 -115.771814 -148.975767 -221.168242 -95.950698 -129.392113 -202.095923 -32.074097 -109.494861 -75.778694

EFL -202.916705 -202.046194 -102.842986 -62.882151 -139.274539 -405.950198 224.652996 -275.013706 -204.157238 -203.280245 -103.603510 -63.379504 -140.220136 203.739810 -410.428339 -289.933093 -288.817023 -133.747108 -78.937952 -189.148584 -133.038975 -108.658339 -108.091345 -69.547847 -47.529634 -83.783815 -461.891789 -460.367627 -191.625087 -109.228119 -283.824157 -695.920251 -243.746227 -132.548444 -386.808691 -244.498908 -132.983872 -387.884806 -213.350208 5318.830946 277.555902

DISC -122.162874 -125.106456 -132.514154 -133.498598 -155.100762 10.845656 -130.561509 -62.220942 -119.531112 -122.454875 -129.898390 -130.923399 -152.247405 -122.278364 -59.536712 -107.114518 -109.565718 -115.479202 -116.158478 -134.542277 15.258352 -58.313474 -61.777799 -74.543706 -77.931521 -97.086486 -41.741636 -43.734547 -50.690166 -52.425279 -64.045680 -1.841661 -10.207117 -12.852007 -20.864206 -8.429393 -11.122959 -18.998275 -2.762768 -9.646562 -6.458313

PUPIL RATIO 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000

MAGNIFICATION 0.619087 0.610156 0.599376 0.602492 0.531972 1.331198 0.447191 0.845676 0.624863 0.615808 0.604755 0.607843 0.536592 0.464196 0.852068 0.709255 0.701867 0.701991 0.709838 0.634544 2.953826 0.692713 0.667843 0.598822 0.585320 0.488943 0.906123 0.899616 0.913165 0.927975 0.838331 0.996371 1.028168 1.050773 0.960915 1.031849 1.054513 0.964290 1.052384 1.028929 1.063634

Tab. 2.11 - Table of all possible ghosts for ADC and one lens corrector configuration Keys to Tab. 2.11:
· · · · · · REFL1 - is the number of the surface on which the light is reflected for the 1st time REFL2 - is the number of the surface on which the light is reflected for the 2nd time DBFL - (Delta Back Focal Length) is the distance (mm) from the primary image plane to the reflected image. This is a measure of how far out of focus the ghost image is for this surface pair. If the DBFL is near zero, then the ghost image will be nearly in focus. EFL - (Effective Focal Length) is the focal length (mm) of the system including the two extraneous reflections. This allows to compute the size of the ghost image at the focal plane location indicated by DBFL. DISC - is the semi-diameter (mm) of the reflected beam (from an on-axis object point) at the primary image plane. The smaller this number is, the nearer the ghost image is to being in focus. This will usually only be small when DBFL is also small. PUPIL RATIO - is the maximum ratio of the first order reflected ray heights at the stop surface to the stop semi-diameter. The paraxial marginal ray will pass through the stop surface either once or three times, depending on whether the stop surface is between the reflecting pair of surface or not. If on any of these passes the paraxial ray at the stop surface is larger than the stop diameter, then this ratio will be greater than unity. Since there is by definition an aperture on the stop surface which will limit the rays to the stop diameter, intensity values of ghost images will be reduced for surface pairs whose pupil ratio is greater than unity. MAGNIFICATION - is the size of the reflected image at the image plane indicated by DBFL relative to the size of the primary image. It is the ratio of the EFL, with the reflections, to the nominal EFL of the system.

·

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2.6.2 Ghost analysis with two lenses field corrector
Each surface has a number according to Fig. 2-19, which was used in the analysis. In addition surfaces 1, 2, 3 are respectively M1, M2, the dummy surface at the primary hole. The analysis has been limited also to two reflections. In the Table 2.12 are reported all possible ghosts.

Fig.2.19 - Two lenses corrector

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Ghost analysis for two lenses field corrector configuration (320 Â 1014 nm)
REFL 1 2 4 5 10 11 12 13 14 15 16 4 5 10 11 12 13 14 15 16 5 10 11 12 13 14 15 16 10 11 12 13 14 15 16 11 12 13 14 15 16 12 13 14 15 16 13 14 15 16 14 15 16 15 16 16 REFL 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 10 10 10 10 10 10 11 11 11 11 11 12 12 12 12 13 13 13 14 14 15 DBFL -1970.493875 -2113.336142 -2082.384788 -2085.380286 -2085.168795 -2086.167836 -2086.220097 -2086.460971 -2086.542686 -2086.718682 -2137.686018 -1986.209115 -2003.290531 -2002.104394 -2007.681516 -2007.971460 -2009.305522 -2009.757234 -2010.728662 -241.135825 -596.133624 -535.024835 -1066.359776 -1127.188882 -1535.229059 -1753.112116 -2535.716424 -542.867299 -487.552918 -787.802687 -806.666296 -898.717367 -931.997547 -1007.580487 264.514759 -369.135282 -381.163234 -428.006426 -441.298865 -466.494291 -339.311384 -356.764412 -436.832880 -463.856955 -521.825086 -20.405750 -115.939271 -148.929636 -221.012814 -96.242296 -129.471362 -202.071015 -32.184569 -109.567484 -76.094493 EFL -317.080495 -10.368946 -21.447080 12.601743 -40.829024 -26.849986 -26.765261 -10.887308 -6.148948 -16.174642 -24.360107 -49.892760 30.049373 -93.063444 -61.745716 -61.546553 -25.350725 -14.371253 -37.469404 547.628499 130.974133 266.107209 259.539255 257.738406 319.722763 459.645417 258.623945 171.593555 9720.041296 -2367.153634 -2385.461108 -330.658045 -156.239021 -672.090705 -137.777081 -115.073661 -114.466780 -74.658033 -51.342928 -88.995030 -460.498992 -458.962123 -192.926718 -110.050076 -282.765547 -682.838726 -240.958849 -130.949797 -378.444550 -241.710126 -131.384554 -379.508722 -210.241386 6538.841855 276.845963 DISC -1306.947915 225.250033 -2065.037356 -5707.512689 -3487.213915 -3704.905649 -3729.273599 -3664.945549 -3602.817781 -3978.887906 112.170391 -817.498766 -2316.624408 -1412.964212 -1513.522402 -1524.127282 -1500.781201 -1476.321872 -1632.758561 -36.341242 -90.589447 -55.773421 -57.125586 -57.389238 -55.891728 -54.775012 -60.090029 -90.311958 -51.288871 -74.008573 -75.522553 -78.871951 -79.086120 -91.030562 10.752659 -42.522498 -45.641321 -57.712203 -61.021287 -77.587694 -32.961023 -34.912472 -42.166327 -44.071049 -54.901360 -1.843785 -10.158464 -12.769301 -20.721171 -8.402203 -11.061117 -18.878217 -2.753825 -9.588810 -6.437393 PUPIL RATIO 1.000000 1.000000 1.000000 1.414963 1.000000 1.000000 1.000000 1.000000 1.000000 1.000009 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 MAGNIFICATION 0.135730 -0.844624 0.090781 0.032893 0.053830 0.050691 0.050361 0.051251 0.052137 0.047213 -1.715638 0.218725 0.077848 0.127560 0.119417 0.118603 0.120528 0.122553 0.110864 0.597340 0.592415 0.863588 1.680478 1.768178 2.472780 2.881291 3.798902 0.541138 0.855773 0.958286 0.961562 1.025795 1.060900 0.996443 2.214593 0.781496 0.751818 0.667640 0.651045 0.541269 0.926739 0.919943 0.932630 0.947525 0.855661 0.996327 1.027454 1.049963 0.960203 1.031176 1.053743 0.963614 1.052134 1.028672 1.064151

Tab. 2.12 - Table of all possible ghosts for two lenses corrector configuration

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2.6.3 Analysis of focused ghosts
The brightest focused ghosts are reported in Table 2.13. ADC and one lens corrector
REFL 1 7 13 15 REFL 1 13 15 REFL 2 6 12 14 REFL 2 12 14 DBFL -26.684485 -20.242610 -32.074097 DBFL -20.405750 -32.184569 EFL -698.352046 -695.920251 -213.350208 EFL -682.838726 -210.241386 DISC -2.452927 -1.841661 -2.762768 DISC -1.843785 -2.753825 GHOST AREA (mm2) 18.86 10.6 23.93 GHOST AREA (mm2) 10.64 23.76 PUPIL RATIO 1.000000 1.000000 1.000000 PUPIL RATIO 1.000000 1.000000 MAGNIFICATION 0.986140 0.996371 1.052384 MAGNIFICATION 0.996327 1.052134

Two lenses corrector

Tab. 2.13 - Summary of the brightest focused ghosts

2.6.4 Analysis of sky concentration
The sky concentration is a small image of the telescope pupil located near the detector. The combinations which may create sky concentration which is the pupil ghost are reported in Table 2.14. They are due to reflections between CCD and the back surface of the dewar window. ADC and One lens corrector
REFL 1 16 REFL 1 16 REFL 2 15 REFL 2 15 DBFL -75.778694 DBFL -76.094493 EFL 277.555902 EFL 276.845963 DISC -6.458313 DISC -6.437393 GHOST AREA (mm2) 131 GHOST AREA (mm2) 130.2 PUPIL RATIO 1.000000 PUPIL RATIO 1.000000 MAGNIFICATION 1.063634 MAGNIFICATION 1.064151

Two lenses corrector

Tab. 2.14 - Summary of most focalised ghost for sky concentration

2.6.5 Ghost analysis summary
The first brightest focused ghost is generated between the two flat and parallel surfaces of the ADC, in the region which divide the two couples of thin prisms. The second and third ghosts are generated between the two faces of the filter and dewar window and are present in both optical configurations. The pupil ghost which is the sky concentration is created by the reflections between CCD and the back surface of the dewar window. The maximum area of ghost image and optical system image ratio for the most focalised ghosts is of order of -4 -5 10 , while for sky concentration is of order of 10 .They are negligible and are calculated considering two 4 reflections so they can be reduced of a factor 10 when the two reflecting surfaces are coated with a multilayer wideband coating like that proposed by Zeiss.

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2.7 OPTICAL TOLERANCES
A preliminary study of the tolerances of the two systems is presented. In the following Tables 2.15, 2.16 the centred tolerance for the two lenses corrector and for ADC and one lens corrector are reported. Radius, radius tolerance, thickness and thickness tolerance are given in mm. Fringes of power and irregularity are at 546.1 nm over the clear aperture. Irregularity is defined as fringes of cylinder power in test plate fit.

Centred tolerances for two lenses field corrector
Surface Radius Radius Tol 4.0000 2.0000 0.1000 0.1000 Fringes Pow/Irr 4.0/ 0.25 4.0/ 0.25 4.0/ 4.0/ 4.0 4.0 4.0 4.0 4.0/ 4.0/ 4.0 4.0 4.0/ 4.0/ 4.00 4.00 Thickness -3285.87337 3285.87337 547.35000 50.00000 0.00000 0.00000 0.00000 0.00000 251.74000 35.00000 180.00000 15.00000 50.00000 25.45000 36.86000 Thickness Tol Glass REFL REFL 0.50000 0.25000 SILICA AIR AIR AIR AIR AIR SILICA AIR SILICA SILICA 0.00100 0.04 Index Tol V-NO (%)

1 -9509.00000 2 -4374.00000 3 4 1333.50000 5 2304.10000 6 7 8 9 10 -1295.70000 11 -10000.00000 12 INF 13 INF 14 2304.10000 15 1223.20000

1.0000 1.5000 1.0000 0.7000

4.00 6.00 6.00 6.00

0.50000 0.25000 1.00000 0.05000 0.08000 0.05000 0.05000

0.04 0.04 0.04

Tab. 2.15 - Centred tolerances for two lenses field corrector Centred tolerances for one lens field corrector and ADC
Surface Radius Radius Tol 4.0000 2.0000 0.1000 Fringes Pow/Irr 4.0/ 0.25 4.0/ 0.25 4.0/ 4.0/ 4.0 4.0 4.0 4.0/ 4.0/ 4.0/ 4.0 4.0 4.0/ 4.0/ 4.00 4.00 Thickness -3285.87337 3285.87337 415.60000 30.00000 20.00000 10.00000 20.00000 25.00000 274.24000 38.28000 235.53000 15.00000 50.00000 20.00000 36.69000 0.00000 Thickness Tol 0.50000 0.25000 0.05000 0.05000 0.05000 0.05000 0.50000 0.25000 0.30000 0.05000 0.08000 0.05000 0.05000 Glass REFL REFL BK7 LLF6 AIR BK7 LLF6 AIR SILICA AIR SILICA SILICA 0.00100 0.00200 0.00200 0.00100 0.04 0.04 0.04 0.04 0.04 0.04 0.04 Index Tol V-NO (%)

1 -9509.00000 2 -4374.00000 3 4 2371.40000 5 INF 6 INF 7 INF 8 INF 9 10000.00000 10 -1223.20000 11 -10000.00000 12 INF 13 INF 14 2304.10000 15 1223.20000 16

0.1000 0.5000 1.5000 1.0000 0.7000

4.00 4.00 6.00 6.00 6.00

Tab. 2.16 - Centred tolerances for one lens field corrector and ADC

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In Table 2.17 and Table 2.18 the de-centred tolerances for the two optical configuration are respectively reported. Radii are given in units of mm. For wedge and tilt, TIR is a single indicator measurement taken at the smaller of the two clear apertures. For decentre and roll, TIR is a measurement of the induced wedge and is the maximum difference in readings between two indicators, one for each surface, with both surfaces measured at their respective clear apertures. The direction of measurement is parallel to the original optical axis of the element before the perturbation is applied. TIR is measured in mm. Decentre or roll is measured perpendicular to the optical axis in mm.

Decentred tolerances for two lenses field corrector
Element n° 1 2 3 4 5 6 Front radius -9509.00000 -4374.00000 1333.50000 -1295.70000 INF 2304.10000 Back Radius (MIRROR) (MIRROR) 2304.10000 -10000.00000 INF 1223.20000 Element wedge Tir Arcmin 0.0120 0.0100 0.0500 0.0300 0.1 0.1 0.5 0.3 Element Tilt Tir Arc min 0.0000 0.0 0.0000 0.0 0.0704 0.5 0.1132 1.0 0.1097 1.0 0.1078 1.0 El. Dec/Roll Tir mm 0.0027 0.0100 0.0016 0.0080 0.0146 0.1000 0.0264 0.1000 0.0000 1.0000 0.1413 1.0000

Tab. 2.17 - Decentred tolerances for two lenses field corrector

Decentred tolerances for one lens field corrector and ADC
Element n° 1 2 3 3- 4 4 5 5- 6 6 7 8 9 Front radius -9509.00000 -4374.00000 2371.40000 2371.40000 INF INF INF INF -1223.20000 INF 2304.10000 Back Radius (MIRROR) (MIRROR) INF INF INF INF 10000.00000 10000.00000 -10000.00000 INF 1223.20000 Element wedge Tir Arcmin 0.0120 0.0588 0.0200 0.1284 0.0200 0.0500 0.0300 0.1 0.4 0.2 1.0 0.2 0.5 0.3 Element Tilt Tir Arc min 0.0000 0.0 0.0000 0.0 0.0420 0.3 0.0193 0.100 0.0044 0.0391 0.1095 0.1078 0.1000 0.3 1.0 1.0 0.0282 0.0000 0.1415 0.1000 1.0000 Tir 0.0027 0.0016 El. Dec/Roll mm 0.0100 0.0080

1.0000

Tab. 2.18 - Decentred tolerances for one lens field corrector and ADC

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The values of MTF (Modulation Transfer Function) obtained for the ideal optical system and for the system with tolerances, were computed statistically at the Nyquist frequency of 33 cycles/mm (corresponding to one pixel of 15 µ). The result for the two lenses and ADC and lens corrector were respectively reported in tab. 2-19 and 2-20. The values of MTF obtained considering the tolerances reported in tab. from 2-15 up to tab. 2-18 for each configuration, follow a gaussian distribution. They are reliable with the 97.7% of probability. When the dependence on tolerances is considered, the distance variation between M2 and M1 must be considered as a compensator and it is expressed in mm. Both MTF values with tolerances of the optical system and compensator values for the different fields of view follow a gaussian distribution. They can be considered as mean values with an error range of 2 sigma.

Performance of polychromatic MTF for two lenses field corrector (320 Â 1014nm)
Relative field 0.00, 0.00 0.00, 0.48 0.00, 0.71 1.00, 0.71 0.00, 1.00 Freq L/mm 33.00 33.00 33.00 33.00 33.00 MTF Design 0.543 0.565 0.479 0.409 0.345 MTF Design + Tol 0.496 0.508 0.416 0.330 0.290 Compensator Range (+/-) Displacement S2 (M2) 2.138276 2.138276 2.138276 2.138276 2.138276

Tab. 2.19 - Performance of polychromatic MTF for two lenses field corrector (320 Â 1014nm) at z=0

Performance of polychromatic MTF for ADC and one lens corrector (365 Â 1014nm) Relative field
0.00, 0.00, 0.00, 1.00, 0.00, 0.00 0.48 0.71 0.71 1.00

Freq L/mm
33.00 33.00 33.00 33.00 33.00

MTF Design
0.521 0.606 0.406 0.440 0.312

MTF Design + Tol
0.394 0.501 0.351 0.369 0.263

Compensator Range (+/-) Displacement S2 (M2)
2.135844 2.135844 2.135844 2.135844 2.135844

Tab. 2.20 - Performance of polychromatic MTF for ADC and one lens corrector (365 Â 1014nm) at z=0

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2.8 FIRST STAGE OF BAFFLES DESIGN
In Fig.2-20 a preliminary baffle design reported, in which the whole field of view is unvignetted, so the diameters of the baffle tubes and central obscuration become quite large. The M1 light loss due to M2 obscuration is of order of 7%, with M1 hole diameter of 600 mm . W ith the front baffle tube, on M2, the central obscuration is larger and the corresponding M1 light loss becomes of order of 17%.

Fig.2.20 - First stage of baffle design

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VST Project

Osservatorio Astronomico di Capodimonte Napoli

2.9 IMAGE QUALITY VERSUS MIRROR DEFORMATION
In order to evaluate the optical performance of the telescope after the deformations induced on the primary mirror by gravitational loads, mirror optical data were utilized to create the finite element model described in section 4. The model was performed with MSC PATRAN FEA preprocessor tool and analyzed with the MSC Nastran FEA Solutor tool. For the final optical quality analysis it is necessary to have information about both undeformed and deformed mirror interpolated surface with displacements obtained with MSC-NASTRAN FEA. This data set must be passed to Zemax optical analysis tool in a particular file format. In order to have an automatic and standard interface between the FEA output and Zemax ray tracing tool input, and optimize the real image quality with a control loop, a new procedure was implemented. The output of the finite element analysis model (FEA) was manipulated with a new dedicated software tool implemented in OAC technological laboratories, and constituted the feedback for the mirror optical surface shape deformation. The global mirror with interpolated surface and its appropriate format were obtained by means of an OAC interface data file creation tool made in C++ and running under W indows 95. In Fig.2.21 the flowchart of the procedure implemented for the optimization of the system optical quality is shown.
OPTICAL PERFORMANCE BASELINE OPTICAL DESIGN DATA INPUT

OPTICS DESIGN

AUTOCAD DRAWING TOOL

MSC PATRAN FEA PREPROCESSOR TOOL

MIRROR FINITE ELEMENT MODEL

MIRROR FINITE ELEMENT ANALYSIS

MSC NASTRAN FEA SOLUTOR TOOL

OAC C++ PROGRAM MS_DOS WINDOWS 95 TOOL

OAC INTERFACE DATA FILE CREATION TOOL

MIRROR OPTICAL ANALYSIS

ZEMAX OPTICAL ANALYSIS TOOL

OPTICAL SYSTEM PERFORMANCE ANALYSIS

Fig.2.21 - OAC Telescope optical quality optimisation work flow

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Osservatorio Astronomico di Capodimonte Napoli

2.9.1 Image quality versus mirror deformation for two lenses corrector
The study of optical quality depreciation due to primary mirror surface deformations for gravitation was performed for both correctors. The analysis has been done with telescope at zenith, that represents the worst case. Fig. 2.22 shows the curves of polychromatic diffraction encircled energy versus centroid distance, for the different fields of view. The radius of the centroid in which the 80% of encircled energy (normalised to diffraction limit) is enclosed is 12.5 µm (1.67pxl), so there is a EE% depreciation of 25% in respect to the design value. Spot diagrams are shown in Fig.2.23 where the maximum increment of rms spot radius respect to the design value is about of 11%. Figures 2-24 shows the distance from the best focal plane and the paraxial focal planes of sagittal and tangential rays (field curvature) and distortion curves. The maximum distortion is about 0.013% at the edge of the field for =1.014 µm, so it is unchanged in respect to the design value.

Fig.2.22 - Encircled Energy for two lenses field corrector at zenith with M1 gravitational loads applied

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Osservatorio Astronomico di Capodimonte Napoli

Fig.2.23 - Spot diagram with two lenses corrector at zenith with M1 gravitational loads applied

Fig.2.24 - Field curvature and distortion curves for the configuration with two lenses at zenith with M1 gravitational loads applied

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Osservatorio Astronomico di Capodimonte Napoli

2.9.2 Image quality versus mirror deformation for ADC and one lens corrector
In Fig. 2.25 the the curves of polychromatic diffraction encircled energy versus centroid distance, for the different fields of view are reported when gravitational loads are applied to M1 in horizontal position (telescope at zenith). The radius of the circle from centroid in which the 80% of encircled energy (normalised to diffraction limit) is enclosed at 0° zenith angle including primary mirror surface deformations is 11.25 µm (1.5 pxl), so there no deterioration of EE% respect to the design value. The spot diagrams are shown in Fig.2.26. The maximum increment of rms spot radius respect to the design value is of order of 19%. In Figures 2-27, the distance from the best focal plane designed for the optical system and the paraxial focal planes of sagittal and tangential rays (field curvature) and distortion curves for the configuration are reported. The maximum distortion is 0.011% at the edge of the field for =1.014 µm, so it is comparable with the design value.

Fig.2.25 - Encircled Energy for two lenses field corrector at zenith with M1 gravitational loads applied

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Osservatorio Astronomico di Capodimonte Napoli

Fig.2.26 - Spot diagram for one lens and ADC at zenith with M1 gravitational loads applied

Fig.2.27 - Field curvature and distortion curves for the configuration with one lens and ADC at 0°zenith angle with M1 gravitational loads applied

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