Sky brightness outside Earth Atmosphere, galactic pole pointing, unit : [W/m^2 um sr].
(Source: Ball Aerospace JWST sensitivity canculations (Dennis Ebbets et al.))
0.5um 1.26e-6
0.63um 1.12e-6
0.79um 8.19e-7
1um 5.15e-7
1.26um 2.9e-7
1.58um 1.5e-7
2um 7.27e-8
Assuming H band, 1.65 um, 20% wide band.
At 1.65um, zero point magnitude = 115e-11 W.m-2.um
2.4m telescope: diffraction limit at 1.65um = 0.142"
Zodi contribution over diffraction spot = 7.09e-20 W.m-2 um
Zodi = star for mH=25.5
Note: same computation for V band gives mV=29.32
Assumptions:
- There is a calibration floor of 2.5 uas per star
- Stars fainter than the zodi limit are excluded
- The precision is 2x photon noise limit
Relative precision ratio between H and V band, equal magnitude. Both assume same bandwidth (20%).
PSF size: x 0.303
Photon noise: x sqrt(0.355) = x 0.596
Overall: factor 30 = 3.7 mag
-> a mH = 20.0 star offers the same astrometric precision as a mV = 23.7 star
Astrometric accuracy per star:
mH=10.0 : 0.1 uas
10 mag -> factor 100
accuracy = 0.1 uas 1.585^(mH-10.0)
awk '{if(($8>15.0)&&($8<18.0)) print $8}' Sources.1degrad.H.txt | sort | awk '{print NR,$1,sqrt(2.5*2.5+(0.2*1.585**($1-10.0))*(0.2*1.585**($1-10.0)))}' | awk '{a=a+1.0/($3*$3); print $0,sqrt(1/a)}' > SourcesH.txt
ASTROMETRIC ACCURACY, 1 SQ DEG
mH range accuracy [uas] #sources/sq deg
10-11 0.40891 38
11-12 0.27721 86
12-13 0.21021 151
13-14 0.174132 241
14-15 0.150903 391
15-16 0.133318 721
16-17 0.12757 1413
17-18 0.116261 3546
18-19 0.123128 6938 # incomplete
19-20 0.44229 989 # incomplete
Correcting for incompleteness, assuming each magnitude bin has 2.5x as many sources as the previous magnitude bin, each faint magnitude bin contributes at the 0.11 uas level.
Up to bin mH=24-25 (above zodi level).
Overall astrometric accuracy, counting from mH=15 to mH=25: 0.03505 uas for 1 sq deg
With 0.3 sq deg FOV -> 0.064 uas