The LOFAR Two-meter Sky Survey: Deep Fields Data Release 1: I. Direction-dependent calibration and imaging

The Low Frequency Array (LOFAR) is an ideal instrument to conduct deep extragalactic surveys. It has a large field of view and is sensitive to large-scale and compact emission. It is, however, very challenging to synthesize thermal noise limited maps at full resolution, mainly because of the complexity of the low-frequency sky and the direction dependent effects (phased array beams and ionosphere). In this first paper of a series, we present a new calibration and imaging pipeline that aims at producing high fidelity, high dynamic range images with LOFAR High Band Antenna data, while being computationally efficient and robust against the absorption of unmodeled radio emission. We apply this calibration and imaging strategy to synthesize deep images of the Bootes and Lockman Hole fields at similar to 150 MHz, totaling similar to 80 and similar to 100 h of integration, respectively, and reaching unprecedented noise levels at these low frequencies of less than or similar to 30 and less than or similar to 23 mu Jy beam(-1) in the inner similar to 3 deg(2). This approach is also being used to reduce theLOTSS-wide data for the second data release.