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We report the results of characterization of red blood cell (RBC) structure and its dynamics with nanometric sensitivity using transport of intensity equation microscopy (TIEM). Conventional transport of intensity technique requires three intensity images and hence is not suitable for studying real-time dynamics of live biological samples. However, assuming the sample to be homogeneous, phase retrieval using transport of intensity equation has been demonstrated with single defocused measurement with x-rays. We adopt this technique for quantitative phase light microscopy of homogenous cells like RBCs. The main merits of this technique are its simplicity, cost-effectiveness, and ease of implementation on a conventional microscope. The phase information can be easily merged with regular bright-field and fluorescence images to provide multidimensional (three-dimensional spatial and temporal) information without any extra complexity in the setup. The phase measurement from the TIEM has been characterized using polymeric microbeads and the noise stability of the system has been analyzed. We explore the structure and real-time dynamics of RBCs and the subdomain membrane fluctuations using this technique. [ABSTRACT FROM AUTHOR]