We present an ultra compact and high resolution free space optical spectrometer and demonstrate it by using FDTD simulations.The miniature interferometer-based spectrometer is a series of submicron phase objects on a polymethyl methacrylate(PMMA) film with a CCD as the detector.The spectrum is obtained by solving a system of simultaneous linear equations.The Tikhonov regularization method is used to achieve a resolution at the picometer level.Compared with conventional spectrometers,the proposed device is low-cost and easy to fabricate due to its simple structure.Furthermore,its compact feature renders the device ideal for miniaturization and integration as the systems in microfluidics architectures and lab-on-chip designs.