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The spatial frequency response of reproduce heads with infinite depth, but finite pole length, is determined to very good accuracy by superposition of conformal map solutions for simpler geometries. This approach yields closed form approximations of the frequency response which are accurate to better than 7% for any head length-to-gap length ratio and any spatial frequency. In particular, the effect of this ratio on the location of the first gap null in the frequency response spectrum is explored for narrow pole length heads. The results lead to design considerations for extending the useful frequency range of thin film reproduce heads.