We report the CO(J=1-0) observations of M51 using both the Combined Array for Research in Millimeter Astronomy (CARMA) and the Nobeyama 45m telescope (NRO45). We describe a procedure for the combination of interferometer and single-dish data. In part
icular, we discuss (1) the joint imaging and deconvolution of heterogeneous data, (2) the weighting scheme based on the root-mean-square (RMS) noise in the maps, (3) the sensitivity and uv-coverage requirements, and (4) the flux recovery of a combined map. We generate visibilities from the single-dish map and calculate the noise of each visibility based on the RMS noise. Our weighting scheme, though it is applied to discrete visibilities in this paper, is applicable to grids in uv-space, and this scheme may advance in future software development. For a realistic amount of observing time, the sensitivities of the NRO45 and CARMA visibility data sets are best matched by using the single dish baselines only up to 4-6 kilo-lambda (about 1/4-1/3 of the dish diameter). The synthesized beam size is determined to conserve the flux between synthesized beam and convolution beam. The superior uv-coverage provided by the combination of CARMA long baseline data with 15 antennas and NRO45 short spacing data results in the high image fidelity, which is evidenced by the excellent overlap between even the faint CO emission and dust lanes in an optical HST image and PAH emission in an Spitzer 8 micron image.
