tokens: tests Fig. 11 Reduced distribution for 30 GHz, 44 GHz, 70 GHz, for white noise ( left ), ideal, and realistic simulation ( right ), for 100 realizations. Also shown is the distribution corresponding to an ideal result. The numbers within the plot give the mean value of the distribution. Fig. 12 Reduced distribution for 70 GHz subsets. From top to bottom : full (4 yr) 70 GHz data, years 14 (full frequency), horn pairs 18/23, 19/22, 20/21 (4 yr). From left to right : white noise only, independent destriping ideal/realistic, full destriping ideal/realistic. In the case of full mission, independent and full destriping options are identical. Fig. 13 Effect of various approximations on the result for the worst LFI18/23 case. We add to the ideal simulation one non-ideality at a time: destriping mask, horn-uniform weighting, finite baseline length, and destriping resolution. The result for the ideal simulation case is shown in the background. We validate the noise covariance matrices through tests. We generated 100 realizations of harmonic vectors , as described above. For each vector and corresponding matrix we compute the value Here is the covariance matrix, and is the number of degrees of freedom. Multipole contributes degrees of freedom, except for the monopole and dipole, which are identically zero for and . This yields in total = 3(+1) degrees of freedom, which for = 50 gives = 7795. For a matrix that perfectly describes the noise properties, the results obey the Chi distribution, For large values of the distribution becomes Gaussian, with expectation value 1 and standard deviation of , which for = 7795 is 0.016. We compared the white noise covariance matrix of Eq. ( 11 ) against white noise simulations, and the full noise matrix of Eq. ( 29 ) against ideal and realistic simulations. Results from tests at the three Planck LFI frequencies, 30, 44, and 70 GHz are shown in Fig. 11 . We show a histogram of the values for 100 realizations, and quote their mean. The white noise matrix models the white noise residual nearly perfectly, mean ranging from 0.9992 to 1.0004, Comparison between the full matrix and ideal simulation gives slightly larger values, from 1.0002 at 70 GHz to 1.0037 at 44 GHz, while the expected one-sigma deviation for 100 realizations is 0.0016. Deviations from one are larger in the case of realistic simulation, as expected, given the approximations involved. At 30 GHz we find a mean of 1.0196, at 70 GHz 1.0037. Results for 70 GHz subsets of are shown in Fig. 12 . In the first column we compare the white noise matrix against a pure white noise simulation. Second and third column show results for the full matrix. Results are shown for two destriping options: full 70 GHz destriping, and independent destriping. In all cases, we find very good agreement with the white noise matrix and corresponding simulations. The same can be said about the full matrix and the ideal simulations. The mean
ner_tags: O O O O O O B-Wavelength I-Wavelength B-Wavelength I-Wavelength B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Instrument O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O B-Wavelength I-Wavelength O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O