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A novel cylindrical liquid crystal microlens array with rotary power and tunable capability is proposed and experimentally demonstrated. This structure is capable of generating tunable cylindrical microlenses in two different axis by low voltage control. For this, complex electrical signals are required (electrical phase shift of 180 degrees). A control over the maximum phase shift from 4p to 34p radians has been demonstrated. This effect modifies the effective focal length (from 0.2 to 1.2 mm). Moreover, an OFF-state is also possible (behaving like a transparent medium). The structure is simple and does not require a complex fabrication process. The proposed device has several advantages over the existing microlens arrays and is simple and low cost. The device could contribute to developing new applications and to reducing the fabrication costs of current devices. For example, this device can be used in the next generation of mobile displays with autostereoscopic capability.