We report on a Fourier Domain Mode Locked (FDML) wavelength swept laser source with a highly linear time-frequency sweep characteristic and demonstrate OCT imaging without k-space resampling prior to Fourier transformation. A detailed theoretical framework is provided and different strategies how to determine the optimum drive waveform of the piezo-electrically actuated optical bandpass-filter in the FDML laser are discussed. An FDML laser with a relative optical frequency deviation ??nu/nu smaller than 8 x10(-5) over a 100 nm spectral bandwidth at 1300 nm is presented, enabling high resolution OCT over long ranging depths. Without numerical time-to-frequency resampling and without spectral apodization a sensitivity roll off of 4 dB over 2 mm, 12.5 dB over 4 mm and 26.5 dB over 1 cm at 3.5 mus sweep duration and 106.6 dB maximum sensitivity at 9.2 mW average power is achieved. The axial resolution in air degrades from 14 to 21 mum over 4 mm imaging depth. The compensation of unbalanced dispersion in the OCT sample arm by an adapted tuning characteristic of the source is demonstrated. Good stability of the system without feedback-control loops is observed over hours.