CANESTRARI, Rodolfo

Conconi, Paolo

GIRO, Enrico

RODEGHIERO, GABRIELE

OA@INAF - Istituto Nazionale di Astrofisica

2014Publication Year2023-02-03T14:29:26ZAcceptance in OA@INAFError Budget Tree for the ASTRI prototype: structure and mirrorsTitleCANESTRARI, Rodolfo; Conconi, Paolo; GIRO, Enrico; RODEGHIERO, GABRIELEAuthorshttp://hdl.handle.net/20.500.12386/33136HandleASTRI-SPEC-OAB-3100-002Number  ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 1  All information contained in this document is property of INAF.  All rights reserved.   Error Budget Tree for the ASTRI prototype: structure and mirrors         Prepared by: Name: Rodolfo Canestrari Paolo Conconi Enrico Giro Gabriele Rodeghiero Signature:  Date: 14/01/2014   ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 2  All information contained in this document is property of INAF.  All rights reserved.    TABLE OF CONTENTS  DISTRIBUTION LIST ........................................................................................................................ 3	  DOCUMENT HISTORY ..................................................................................................................... 4	  LIST OF ACRONYMS ....................................................................................................................... 5	  APPLICABLE DOCUMENTS ........................................................................................................... 5	  REFERENCE DOCUMENTS ............................................................................................................ 5	  1.	   INTRODUCTION ........................................................................................................................ 6	  2.	   DEFINITIONS ............................................................................................................................. 7	  2.1	   Reference system .............................................................................................................. 7	  2.2	   Sensitivity ........................................................................................................................... 8	  3.	   ERROR BUDGET TREE RELATED TO M1 .............................................................................. 9	  4.	   ERROR BUDGET TREE RELATED TO M2 ............................................................................ 11	  4.1	   Profile errors .................................................................................................................... 11	  4.2	   Alignment errors .............................................................................................................. 11	  5.	   ERROR BUDGET TREE RELATED TO CAM ......................................................................... 13	  5.1	   Profile errors .................................................................................................................... 13	  5.2	   Alignment errors .............................................................................................................. 13	  5.3	   PDMs tolerances ............................................................................................................. 13	  5.4	   PMMA window tolerances ............................................................................................... 13	  6.	   TOLERANCE STUDY ON ERROR BUDGET .......................................................................... 15	  6.1	   RMS Radius modifications ............................................................................................... 15	  6.2	   Centroid shift estimations ................................................................................................ 19	        ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 3  All information contained in this document is property of INAF.  All rights reserved.  DISTRIBUTION LIST  ASTRI ML astri@brera.inaf.it                          ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 4  All information contained in this document is property of INAF.  All rights reserved.  DOCUMENT HISTORY  Version  Date Modification 1 04/11/2011 first version 2 02/04/2012 Add chapter on Camera 3 14/01/2014 Add chapter on PDMs tolerance New chapter on Tolerance study    ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 5  All information contained in this document is property of INAF.  All rights reserved.  LIST OF ACRONYMS  CAM  Camera, Cherenkov detector FoV   Field of View M1  Primary Mirror M2   Secondary Mirror PDM  Photo Detection Module PMMA  Polymethyl methacrylate PSF  Point Spread Function PV  Peak to Valley R80  Radius containing the 80% of the PSF RMS  Root Mean Square      APPLICABLE DOCUMENTS [AD1]        REFERENCE DOCUMENTS [RD1] ASTRI-IR-OAB-3100-009 “The optical layout of the ASTRI prototype: 4 meter Schwarzschild-Couder Cherenkov telescope for CTA with 10° of field of view” [RD2]       ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 6  All information contained in this document is property of INAF.  All rights reserved.  1. INTRODUCTION This document describes the Error Budget Tree to be used for the design and verification of the structure and mirrors subsystems of the ASTRI telescope prototype. This document is a living document. This means that the numbers adopted for each parameter can be subject of changes depending from the outcomes of the structural analyses and/or technological developments.     ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 7  All information contained in this document is property of INAF.  All rights reserved.  2. DEFINITIONS 2.1 Reference system The reference system is defined as in figure, if not explicitly stated. The z axis is the optical axis and it points toward the M2.  According to the M1 segments numeration, we give the nominal position of the centers of each hexagon. The numbers are in mm unit.  The segments numbered 1, 8 and 13 are used as reference and they correspond to the color index green, light blue and yellow respectively.   ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 8  All information contained in this document is property of INAF.  All rights reserved.   2.2 Sensitivity As described in [RD1] the optical layout of the ASTRI prototype has the energy concentration (ensquared energy) greater then 80% into the Cherenkov pixels along the entire field of view.  This definition is meaningful taking into account the entire telescope optical design and is not referred to the single mirror segments, like in the Davies-Cotton case. Considering this fact the Error Budget Tree hereafter described can be compiled in such a way the global effect of all contributions keeps the energy concentration (ensquared energy) better then (or equal to) 70%. This can be translated in a PV error budget equal to 120 µm and slope error budget equal to 60’’ rms.   ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 9  All information contained in this document is property of INAF.  All rights reserved.  3. ERROR BUDGET TREE RELATED TO M1 Let’s consider the secondary mirror M2 being monolithic, infinitely rigid and having the nominal profile.    Value Units Comments 1. M1 segments profile errors  1.1. Manufacturing   a. Mold 30  10 --  -- µm PV  ‘‘ rms It comes from FLABEG, no/very poor control on it. The rms is sampled at least with a grid of 25 mm of pitch. b. Replication process 50  10 --  -- µm PV  ‘‘ rms It comes from FLABEG, limited control on it.  The rms is sampled at least with a grid of 25 mm of pitch. c. Glass cutting -- 6 ‘  Axial (normal to the surface on the hexagon center) rotation of the glass profile wrt the nominal one. It is equivalent to 0.87 mm over the length of the hexagonal side. d. Integration TBD TBD  -- -- µm PV ‘‘ rms Contribution of the cold shaping step (could be also improvements)   SUBTOTAL 58 -- -- 6 µm PV ‘ Quadratic propagation  1.2. Structural   a. Mounting 40  2 µm PV  ‘‘ rms Contribution of the mounting supports (e.g. gluing of the interfaces, …) The shape will be modified only locally. b. Gravity 30 TBC µm PV ‘‘ rms Contribution of the normal gravity c. Operative wind 30 TBC µm PV ‘‘ rms Contribution of the operative wind d. Operative temp. 1 µm PV Homogeneous temperature shift up to ±20°C    SUB TOTAL 58 µm PV Quadratic propagation  GRAND TOTAL 82 µm PV Error budget in quadratic propagation. 2. M1 segments alignment errors     2.1 Translations   a. x ±2 mm These values are referred to the positions of the centers of the hexagons as reported in Table 1. b. y ±2 mm c. z ±4 mm   ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 10  All information contained in this document is property of INAF.  All rights reserved.   2.2 Rotations   a. z’ ±4 ‘ z’ is defined as the axis parallel to the z (optical axis) passing through the center of the hexagons.  2.3 Tilts   a. x ±30 ‘‘  b. y ±30 ‘‘   Not appreciable degradation (i.e. <5%) of the ensquared energy is reported within these values. There is no need to actively correct with actuators within these ranges. However, these values shall be used to define the accuracy and the range of the actuators.    ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 11  All information contained in this document is property of INAF.  All rights reserved.  4. ERROR BUDGET TREE RELATED TO M2 4.1 Profile errors Let’s consider now the M1 segments being perfectly aligned, infinitely rigid (both the mirrors themselves and the telescope structure) and having the nominal profile.  We consider now the contributions coming from a not perfect secondary mirror.  4.2 Alignment errors The positioning errors along (x, y) and the relative tilts translate almost completely in pointing errors of the telescope (the contribution to the ensquared energy is negligible).  The error along z is a defocusing of the telescope and can be correct adjusting the 3 actuators of M2.   Value Units Comments 3. M2 profile errors  3.1. Manufacturing   a. Mold 120  40 µm PV  ’’ rms It comes from FLABEG, no/very poor control on it. The rms is sampled at least with a grid of 25 mm of pitch. b. Replication process 200  40 µm PV  ’’ rms It comes from FLABEG, limited control on it. The rms is sampled at least with a grid of 25 mm of pitch. c. Glass cutting n.a. ‘  Axial (normal to the surface on the hexagon center) rotation of the glass profile wrt the nominal one. d. Integration TBD TBD µm PV ‘’ rms Contribution of the cold shaping step (could be also improvements)   SUBTOTAL 217 (54) µm PV µm PV Quadratic propagation  (calculated taking into account the demagnification factor, equal to 4)  3.2. Structural   a. Mounting 40  2 µm PV  ‘‘ rms Contribution of the mounting supports (e.g. gluing of the interfaces, …) The shape will be modified only locally. b. Gravity 120 TBC µm PV ‘‘ rms Contribution of the normal gravity c. Operative wind 120 TBC µm PV ‘‘ rms Contribution of the operative wind d. Operative temp. 4 µm PV Homogeneous temperature shift up to ±20°C    SUBTOTAL 174 (44) µm PV Quadratic propagation  (calculated taking into account the   ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 12  All information contained in this document is property of INAF.  All rights reserved.  µm PV demagnification factor, equal to 4)  GRAND TOTAL 278  (69) µm PV  µm PV Error budget in quadratic propagation. (calculated taking into account the demagnification factor, equal to 4) 4. M2 alignment errors     4.1 Translations   a. x ±3 mm This introduces pointing errors to be modeled with T-point. (1 mm = 38’’ pointing error) b. y ±3 mm c. z ±4 ±1 mm mm Relative to M1 Relative to CAM  4.2 Rotations   a. z n.a. ‘   4.3 Tilts   a. x  10 ‘ The tilts do not constrain the design of the telescope structure up to the indicated value.  Obliviously, this introduces pointing errors to be modeled with T-point. b. y 10 ‘    ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 13  All information contained in this document is property of INAF.  All rights reserved.  5. ERROR BUDGET TREE RELATED TO CAM 5.1 Profile errors Let’s consider now the M1 segments and M2 monolithic mirror perfectly aligned, infinitely rigid (both the mirrors themselves and the telescope structure) and having the nominal profile.  We consider now the contributions coming from a not perfect camera mounting.  5.2 Alignment errors The positioning errors along (x, y) translate almost completely in pointing errors of the telescope (the contribution to the ensquared energy is negligible). Nevertheless, we fix the maximum displacements to ±5.5 mm along each axis (x, y).  Tilts errors along (x, y) of the order of 20 arcmin for each axes can be tolerable. The error along z is a defocusing of the telescope and is correct adjusting the 3 actuators of M2.  5.3 PDMs tolerances  5. PDM alignment errors     5.1 Translations   a. x ±1 mm Relative to focal plane mechanical structure b. y ±1 mm c. z ±1 mm  5.2 Rotations   a. z n.a. ‘   5.3 Tilts   a. x  30 ‘ The tilts do not constrain the performance of the telescope up to the indicated value.  Obliviously, this introduces pointing errors to be modeled with T-point. b. y 30 ‘  5.4 PMMA window tolerances The PMMA window positioning (both plane and curved) doesn’t affect significantly the properties, photometric radii and shape, of the telescope PSFs. The main modification is the change in the photons optical path that is proportional to T/n, with T thickness of the window and n its refraction index. The focus shift is about 3.2 mm and it could be compensated by M2 actuators. The PMMA window position is constrained by the mechanical interfaces with the LIDs; the ranges explored with the simulations are:  -­‐ 7.5   ± 2.5   mm   ->      plane window -­‐ 7.75 ± 2.25 mm  ->      curved window Inside this range the relative modifications on R80 is less than 3 %.    ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 14  All information contained in this document is property of INAF.  All rights reserved.  The percentage of PSF enclosed in the Cherenkov pixel for the nominal separation of the PMMA to the central PDM (7.5 mm plane, 7.75 mm curved) is plotted in figure.     ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 15  All information contained in this document is property of INAF.  All rights reserved.  6. TOLERANCE STUDY ON ERROR BUDGET  The tolerances on decentering (x,y,z) and tilts (x,y,z) for M1, M2 and camera PDMs have been put together into a series of simulations to assess the evolution of the RMS radius and centroid of the telescope PSFs. In general the tolerances on the theoretical optical design cause a degradation of the RMS radius and a change of the centroid as can be observed in the example shown in the following figure.    6.1 RMS Radius modifications The effects of tolerances on PSF RMS radius are presented in the follow for different angles into the FoV (0°,1°,2°,3°,4°,4.8°). For each angle about 200 Monte Carlo simulations are randomly run combining the tolerances on M1, M2 and the camera PDMs; a histogram with the quartiles distribution and a scatter plot with the interpolating curve are reported to help results visualization.  The same procedure is applied to the PSF centroid shift estimation reported in section 6.2.   ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 16  All information contained in this document is property of INAF.  All rights reserved.                  ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 17  All information contained in this document is property of INAF.  All rights reserved.                  ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 18  All information contained in this document is property of INAF.  All rights reserved.                 ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 19  All information contained in this document is property of INAF.  All rights reserved.   6.2 Centroid shift estimations              ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 20  All information contained in this document is property of INAF.  All rights reserved.                 ASTRI - Astrofisica con Specchi a              Tecnologia Replicante Italiana   Code: ASTRI-SPEC-OAB-3100-002  Issue: 3 DATE 14/01/2014 Page: 21  All information contained in this document is property of INAF.  All rights reserved.               

Error Budget Tree for the ASTRI prototype: structure and mirrors

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Error Budget Tree for the ASTRI prototype: structure and mirrors

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