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

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

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

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

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

6. Spot Diagram for 0 and 1 arcsecond

7. Diffraction Calculations for 2µ
1 meter telescope, EFL = 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: mm
Focal Length: mm
Focal Ratio:
Plate Scale: arc-sec/mm
Wavelength Airy Radius-1st dk ring
(microns) (microns) (arc-sec)
Limiting Frequency=2 × NA ÷ Wavelength fn[AIRY_MTF]
=1÷(Wavelength × FNo[ ])
Wavelength Limiting Limiting
[micron] Frequency Sample Interval
[cy/mm] [mm]

8. Diffraction Calculations for 2µ
21.5 meter telescope, EFL = 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: mm
Focal Length: mm
Focal Ratio:
Plate Scale: arc-sec/mm
Wavelength Airy Radius-1st dk ring
(microns) (microns) (arc-sec)
Limiting Frequency=2 × NA ÷ Wavelength fn[AIRY_MTF]
=1÷(Wavelength × FNo[ ])
Wavelength Limiting Limiting
[micron] Frequency Sample Interval
[cy/mm] [mm]

9. Angular Sensitivity
Pixel Spacing for Huygens PSF is 2000÷127 = microns
÷1000 = mm pixel spacing
1.832÷ = pixels/arc sec
÷ = arc sec/pixel
stability to about 1/10th pixel or arc sec (0.001 arc sec) is needed
21500×.5×TAN .001÷3600 = 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.

10. 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.

11. PSF for 1-meter Central Telescope 3

12. 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

13. 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 to mm by adjusting the default Return offset from 750 to 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 mm differences in path length each time the prescription was reinitialized. This is an accuracy of about 1 part in 1012.

14. PLEN= mm on all 5

15. +.001 Sec Space

16. mm Sec Space

17. PLEN=31350.000000mm on all 5; 5=Absorb

18. 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

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

20. Sec Space on 5 = 0, +.001, , mm

21. 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 = microns

22. “Return” dX spacing sensitivity on 5

23. Return Space on 5 = 0, , , mm

24. Return Space on 5 = 0, , , mm
Signal Intensity
Return
Despace in X (mm)
Pixel
65,64
65,65
65,66
0.551
1.000
0.552
0.604
0.995
0.498
0.711
0.939
0.380
0.780
0.575
0.242
1 pixel = microns

25. PLEN= mm on 1 & 5 only