CWS may 27 2024
Consider two rays that enter the telescope dome on opposite sides of the pupil, across a diameter. Assume a planar wavefront arriving at the slit of the enclosure.
Each ray traverses a path length PL as it moves through the dome air. Assume the dome air has a thermal structure so that the average temperature along the two paths differs by delta-T.
This means the two rays see a different average (line-integrated) index of refraction delta-n. The difference in optical path length for the two rays is PL*delta-n. Across a primary mirror of diameter D this induces a wavefront tilt of theta=PL*delta-n/D. We could have seen this from dimensional analysis alone.
Let's put in some numbers. For the Rubin telescope we have D=8m, PL = 10m. The conversion from delta-T to delta-n is dn/dT~-1E-6 per K. Setting the deflection equal to 1 arcsec we can solve for delta-T:
The line-integrated difference in index obeys delta-n=5E-6*(8/10) = 4e-6. So to get less than one arcsec of beam deflection we need to have the line integral of temperatures differ by no more than 4K.
To meet the Rubin dome-seeing spec of 0.08 arcsec we need line-integrated temperature difference to be less than 0.3K. So a measurement objective of 0.1K is very sensible.
For a 10m pathlength of acoustic interrogation we'd see a travel time difference of