LAI-FKSI Optical Sensitivity at 2µ wavelength Optics Dennis Evans 22 July 2002

Viewing -Z direction (30001 Random rays, from behind) -X +Y

X-Fan, 301 rays -X 1 2 3 C +Z 4 5

X-Fan, 301 Rays -X 3 C +Z

Spot Diagram for Central Telescope Only EFL = 377877 Spot Diagram for Central Telescope Only EFL = 377877.125 mm 0 and 1 arcsecond

Spot Diagram for 0 and 1 arcsecond

Diffraction Calculations for 2µ 1 meter telescope, EFL = 377877.125 mm Numerical Aperture=n×Sin U (U=slope angle of final limiting axial ray NA = 0.5 ÷ (f/#) or f/# = 0.5 ÷ NA Radius of 1st Dark Ring = (0.61×L)÷NA = 1.22×L×(f/#) [83.9% of energy] Primary Diameter: 1000.00 mm Focal Length: 377877.13 mm Focal Ratio: 377.88 Plate Scale: 0.55 arc-sec/mm Wavelength Airy Radius-1st dk ring (microns) (microns) (arc-sec) ---------- --------- --------- 2.0 922.020 0.503 Limiting Frequency=2 × NA ÷ Wavelength fn[AIRY_MTF] =1÷(Wavelength × FNo[377.877125]) Wavelength Limiting Limiting [micron] Frequency Sample Interval [cy/mm] [mm] 2.0 1.32 0.378

Diffraction Calculations for 2µ 21.5 meter telescope, EFL = 377877.125 mm Numerical Aperture=n×Sin U (U=slope angle of final limiting axial ray NA = 0.5 ÷ (f/#) or f/# = 0.5 ÷ NA Radius of 1st Dark Ring = (0.61×L)÷NA = 1.22×L×(f/#) [83.9% of energy] Primary Diameter: 21500.00 mm Focal Length: 377877.13 mm Focal Ratio: 17.58 Plate Scale: 0.55 arc-sec/mm Wavelength Airy Radius-1st dk ring (microns) (microns) (arc-sec) ---------- --------- --------- 2.0 42.885 0.023 Limiting Frequency=2 × NA ÷ Wavelength fn[AIRY_MTF] =1÷(Wavelength × FNo[17.57568023]) Wavelength Limiting Limiting [micron] Frequency Sample Interval [cy/mm] [mm] 2.0 28.45 0.018

Angular Sensitivity Pixel Spacing for Huygens PSF is 2000÷127 = 15.7480315 microns 15.7480315÷1000 = 0.0157480315 mm pixel spacing 1.832÷0.0157480315 = 116.332 pixels/arc sec ÷116.332 = 0.008596087061 arc sec/pixel stability to about 1/10th pixel or 0.0008 arc sec (0.001 arc sec) is needed 21500×.5×TAN .001÷3600 = 0.00005211747072 mm displacement at full radius (1/20th of a micron) Microarcsecond trackers can be built so milliarcsecond ones would be smaller or the same as microarcsecond trackers working at about 7.5 stellar magnitudes (factor of 1000) fainter. The problem is that the ten meter separation from the outlier collectors to the combiner telescope will really not be stable to this accuracy so the system must be controlled from the focal plane.

Angular Sensitivity The outlier telescopes need to be aligned to second of arc accuracy. This could be done by having a “standard” 6th magnitude star tracker at each telescope or by having a laser interferometric alignment capability (which ever is cheaper). Fine tracking control to the millisecond level can be accomplished using the FKSI itself with a focal plane tracker/instrument. There would need to be the capability of tracking and controlling each optical arm independently.

PSF for 1-meter Central Telescope 3

Default Best Focus 5 Telescope Interferogram First dark ring at 0.043 mm for 21.5-meter telescope First dark ring at 0.922 mm for 1-meter telescope

Path Length (PLEN) Sensitivity analysis ZEMAX is not set-up to easily perform sensitivity analysis when the output is a complex interferogram. The path length was adjusted from the default PLEN value of 31351.011240 to 31350.000000 mm by adjusting the default Return offset from 750 to 749.49438 mm. This allowed the reference path to be an even multiple of 2 microns. Since the geometric ray trace acts like coherent light, there will be a 180 degree phase change every 2 microns of PLEN difference. Because the Huygens PSF algorithm can track on the centroid of the PSF, this shift is not noticeable. The shift was made so that the Merit Function Editor display of path length could be easily read and manually adjusted. It was noticed that the digital randomness of dithered ray tracing resulted in about 0.000 000 5 mm differences in path length each time the prescription was reinitialized. This is an accuracy of about 1 part in 1012.

PLEN=31350.000000mm on all 5

+.001 Sec Space

+0.003 mm Sec Space

PLEN=31350.000000mm on all 5; 5=Absorb

PLEN=31350.000000mm on all 5 First dark ring at 0.043 mm for 1-meter telescope First dark ring at 0.043 mm for 21.5-meter telescope

PLEN=31350. 000000mm on all 5 and PLEN=31350 PLEN=31350.000000mm on all 5 and PLEN=31350.000000mm on all 5; 5=Absorb

Sec Space on 5 = 0, +.001, +0.003, +0.010 mm

Sec Space on 5 = 0, +.001, +0.003, +0.010 mm Signal Intensity Secondary Despace in Z (mm) Pixel 65,64 65,65 65,66 0.000 0.551 1.000 0.552 0.001 0.482 0.993 0.620 0.003 0.360 0.944 0.740 0.010 0.135 0.656 0.939 1 pixel = 15.7480315 microns

“Return” dX spacing sensitivity on 5

Return Space on 5 = 0, +.000 03, +0.000 10, +0.000 30 mm

Return Space on 5 = 0, +.000 03, +0.000 10, +0.000 30 mm Signal Intensity Return Despace in X (mm) Pixel 65,64 65,65 65,66 0.000 00 0.551 1.000 0.552 0.000 03 0.604 0.995 0.498 0.000 10 0.711 0.939 0.380 0.000 30 0.780 0.575 0.242 1 pixel = 15.7480315 microns

PLEN=31351.011240 mm on 1 & 5 only