Classical Cepheids are well-known and widely used distance indicators. As distance and extinction are usually degenerate, it is important to develop suitable methods to robustly anchor the distance scale. Here, we introduce a near-infrared optimal distance method to determine both the extinction values of and distances to a large sample of 288 Galactic classical Cepheids. The overall uncertainty in the derived distances is less than 4.9%. We compare our newly determined distances to the Cepheids in our sample with previously published distances to the same Cepheids with Hubble Space Telescope parallax measurements and distances based on the IR surface brightness method, Wesenheit functions, and the main-sequence fitting method. The systematic deviations in the distances determined here with respect to those of previous publications is less than 1%-2%. Hence, we constructed Galactic mid-IR period-luminosity (PL) relations for classical Cepheids in the four Wide-Field Infrared Survey Explorer (WISE) bands (W1, W2, W3, and W4) and the four Spitzer Space Telescope bands ([3.6], [4.5], [5.8], and [8.0]). Based on our sample of hundreds of Cepheids, the WISE PL relations have been determined for the first time; their dispersion is approximately 0.10 mag. Using the currently most complete sample, our Spitzer PL relations represent a significant improvement in accuracy, especially in the [3.6] band which has the smallest dispersion (0.066 mag). In addition, the average mid-IR extinction curve for Cepheids has been obtained: AW1/AKs ≈ 0.560, AW2/AKs ≈ 0.479, AW3/AKs ≈ 0.507, AW4/AKs ≈ 0.406, A[3.6]/AKs ≈ 0.481, A[4.5]/AKs ≈, 0.469, A[5.8]/AKs ≈ 0.427 and A[8.0]/AKs ≈ 0.427 mag.
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- distance scale
- dust, extinction
- infrared: ISM
- stars: variables: Cepheids