1 Calcul FOV function of M3-M4 sizes, taper, with elements from Zemax simulation 2 Current (before 2014) M3 M4 3 Major axis [mm] Minor

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1 1 Calcul FOV function of M3-M4 sizes, taper, with elements from Zemax simulation 2 Current (before 2014) M3 M4 3 Major axis [mm] Minor axis [mm] Semi major axis [mm] Semi minor axis [mm] Size of 45 deg projection of major axis [mm] Wavelength (lambda) [mm] 3 10 HPBW telescope [mm] 29,2 11 Airy radius [mm] 35,0 12 Focus M2 [mm] 0 (influence position image and fields sizes defined below) 13 Distance M3-M4 [mm] Distance mirror - image [mm] (M3-I = 2750 with focus = -1; 3160 with focus = 0) 15 position on minor axis of a 1' diameter FOV [mm] 35,5 37,1 From Zemax Taper from horn on M1 edge [db] Waist radius on image [mm] 21,8 Deduced from taper on M1 edge; see Glodsmith p 19 & 152 => (2/pi)*(ln(10)/20)^0,5 = 0, Waist radius on mirror [mm] Choosen number of w at the mirror minor axis edge Position of encircled energy knee on M (transition steep slope [= by ray tracing coming from pupil] to gentle slope [= effect of diffraction]) 23 Position of Encircled Energy Radius = 97% for lambda = 3mm (3mm >> 2 & 1mm because 97% is beyond encircled energy knee <=> criteria becomes non pertinent) 24 Position of Encircled Energy Radius = 97% for lambda = 2mm (97% encircled <=> >98% on mirror because only half of FOV border field is cut by mirror edge) 25 Position of Encircled Energy Radius = 97% for lambda = 1mm (Attention! In Zemax take measure on surface perpendiculare to optical axis, not on mirror surface!) Distance M2 - mirror [mm] Central field ray tracing radius on mirror [mm] (=> Edge of ray tracing ~ knee of encircled energy) 29 same + Airy radius for safety against diffraction from mirror edge [mm] (Rough margin minimizing effect of 300K diffraction on mirror edge [ other criterias]) position of field which edge = mirror edge for horns [mm] position of field which edge = mirror edge for encircled energy knee [mm] position of field which edge = mirror edge for ray tracing + Airy [mm] FOV diameter fitting criteria for horns [arcmin] 2,5 2,8 36 FOV diameter fitting criteria for encircled energy knee [arcmin] 5,7 5,3 37 FOV diameter fitting criteria for ray tracing + Airy [arcmin] 4,8 4, Waist radius of FOV on edge closer to M Waist radius of FOV on edge closer to image Radius of ray trace + Airy of FOV on edge closer to M Radius of ray trace + Airy of FOV on edge closer to image Position of ray trace + Airy of FOV on edge closer to M lines 44 to 48 used to verif FOV on major axis; done here with ray trace 45 Position of ray trace + Airy of FOV on edge closer to image Position+Radius of ray trace + Airy of FOV on edge closer to M Position+Radius of ray trace + Airy of FOV on edge closer to image verif position + radius FOV on minor axis edge FOV edge on major axis Decentering major axis wrt optical axis to get same FOV edge on both sides 11 12

2 51 52 Position of horn FOV on edge closer to M idem using horn criteria 53 Position of horn FOV on edge closer to image Position+Radius of horn FOV on edge closer to M Position+Radius of horn FOV on edge closer to image verif position + radius FOV on minor axis edge FOV edge on major axis if line 57 = line 49 => OK it's consistent 58 Decentering major axis wrt optical axis to get same FOV edge on both sides line 58 line 50, unless n waist criteria chosen such that n*w give same slope as ray trace (see drawing) Average between ray trace and horn criteria for the decentering Major axis oversize to satisfy both ray trace and horn criterias 3 5

3 1 Calcul FOV function of M3-M4 sizes, taper, with elements from Zemax simulation 2 Futur (after 2014) M3 M4 3 Major axis [mm] Minor axis [mm] Semi major axis [mm] Semi minor axis [mm] Size of 45 deg projection of major axis [mm] (oversizing the major axis gives more margins for the choice of the beam size criteria; see lines 51 & 59) 8 9 Wavelength (lambda) [mm] 3 10 HPBW telescope [mm] 29,2 11 Airy radius [mm] 35,0 12 Focus M2 [mm] -1 (influence position image and fields sizes defined below) 13 Distance M3-M4 [mm] Distance mirror - image [mm] (M3-I = 2750 with focus = -1; 3160 with focus = 0) 15 position on minor axis of a 1' diameter FOV [mm] 35,5 37,4 From Zemax Taper from horn on M1 edge [db] Waist radius on image [mm] 21,8 Deduced from taper on M1 edge; see Glodsmith p 19 & 152 => (2/pi)*(ln(10)/20)^0,5 = 0, Waist radius on mirror [mm] Choosen number of w at the mirror minor axis edge Position of encircled energy knee on M (transition steep slope [= by ray tracing coming from pupil] to gentle slope [= effect of diffraction]) 23 Position of Encircled Energy Radius = 97% for lambda = 3mm (3mm >> 2 & 1mm because 97% is beyond encircled energy knee <=> criteria becomes non pertinent) 24 Position of Encircled Energy Radius = 97% for lambda = 2mm (97% encircled <=> >98% on mirror because only half of FOV border field is cut by mirror edge) 25 Position of Encircled Energy Radius = 97% for lambda = 1mm (Attention! In Zemax take measure on surface perpendiculare to optical axis, not on mirror surface!) Distance M2 - mirror [mm] Central field ray tracing radius on mirror [mm] (=> Edge of ray tracing ~ knee of encircled energy) 29 same + Airy radius for safety against diffraction from mirror edge [mm] (Rough margin minimizing effect of 300K diffraction on mirror edge [ other criterias]) position of field which edge = mirror edge for horns [mm] position of field which edge = mirror edge for encircled energy knee [mm] position of field which edge = mirror edge for ray tracing + Airy [mm] FOV diameter fitting criteria for horns [arcmin] 5,51 6,02 36 FOV diameter fitting criteria for encircled energy knee [arcmin] 8,11 7,78 37 FOV diameter fitting criteria for ray tracing + Airy [arcmin] 7,26 6, Waist radius of FOV on edge closer to M Waist radius of FOV on edge closer to image Radius of ray trace + Airy of FOV on edge closer to M Radius of ray trace + Airy of FOV on edge closer to image Position of ray trace + Airy of FOV on edge closer to M lines 44 to 48 used to verif FOV on major axis; done here with ray trace 45 Position of ray trace + Airy of FOV on edge closer to image Position+Radius of ray trace + Airy of FOV on edge closer to M verif positions champs/bord Zemax 47 Position+Radius of ray trace + Airy of FOV on edge closer to image verif position + radius FOV on minor axis edge FOV edge on major axis Decentering major axis wrt optical axis to get same FOV edge on both sides

4 51 52 Position of horn FOV on edge closer to M idem using horn criteria 53 Position of horn FOV on edge closer to image Position+Radius of horn FOV on edge closer to M Position+Radius of horn FOV on edge closer to image verif position + radius FOV on minor axis edge FOV edge on major axis if line 57 = line 49 => OK it's consistent 58 Decentering major axis wrt optical axis to get same FOV edge on both sides line 58 line 50, unless n waist criteria chosen such that n*w give same slope as ray trace (see drawing) Average between ray trace and horn criteria for the decentering In Zemax I take 20 and 22 = compromise avoid blokage of M2-M3 beam by M4 edge at 20 deg elevation 61 Major axis oversize to satisfy both ray trace and horn criterias 14 15

5 optical axis M3 and M4 adapted to FOV1 with 1w, but when looking at 2w M4 is adapted to FOV2 while M3 is adapted to FOV3 => changing number of w criteria changes relative sizes of M3 and M4!