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The aperture efficiency of a parabolic dish with uniformly distributed surface errors is
eta_a = eta_0 exp-(4pi sigma/lambda)**2.
Here sigma is the rms surface error and and lambda the wavelength (J. Ruze, 1966, Proc. IEEE 54, 633).
eta_0 is the aperture efficiency at large wavelengths where the surface errors can be neglected.
The following tables give eta_a for eta_0=1.0, and eta_0=0.68 (the value used in the table in the JCMT user guide;
possibly actual values are even lower).

RUZE EFFICIENCIES

RMS 1300 1100 850 750 650 450 350

15 0.98 0.97 0.95 0.94 0.92 0.84 0.75

20 0.96 0.95 0.92 0.89 0.86 0.73 0.60

25 0.94 0.92 0.87 0.84 0.79 0.61 0.47

30 0.92 0.89 0.82 0.78 0.71 0.50 0.31

35 0.89 0.85 0.77 0.71 0.63 0.38 0.21

40 0.86 0.81 0.70 0.64 0.55 0.29 0.13

45 0.83 0.77 0.64 0.57 0.47 0.21 0.07

50 0.79 0.72 0.58 0.50 0.39 0.14 0.04

RMS and wavelength in microns (eta_0=1.0)

RUZE EFFICIENCIES

RMS 1300 1100 850 750 650 450 350

15 0.67 0.66 0.65 0.64 0.63 0.57 0.51

20 0.66 0.65 0.62 0.61 0.59 0.50 0.41

25 0.64 0.63 0.59 0.57 0.54 0.42 0.30

30 0.63 0.60 0.56 0.53 0.49 0.34 0.21

35 0.61 0.58 0.52 0.48 0.43 0.26 0.14

40 0.59 0.55 0.48 0.43 0.37 0.20 0.09

45 0.56 0.52 0.44 0.39 0.32 0.14 0.05

50 0.54 0.49 0.39 0.34 0.27 0.10 0.03

RMS and wavelength in microns (eta_0=0.68)
Values for aperture and main beam efficiencies obtained from planet measurements with the heterodyne receivers
can be inspected in the efficiencies database.

Last modified: 2 October 2002
Jan Wouterloot

j.wouterloot@jach.hawaii.edu

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Contact: Jan Wouterloot. Updated: Tue Nov 9 09:26:00 HST 2004

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