As typical poikilocytes, elliptocytes can indicate underlying diseases and are an important additional diagnostic parameter. The current method is to use a microscope for manual analysis of blood smears, which is non-automatic, time-consuming and requires skilled technicians. Lab-on-a-chip technology using a lensless imaging system provides a better solution. However, diffraction effects and low resolution are the two main problems faced by lensless imaging systems. In this paper, Fresnel diffraction at a straight edge is used to analyse the relationship between the red blood cell edge and diffraction rings. First, the diffraction characteristics of red blood cell edges are given. Next, the measurement accuracy is improved. The super-resolution algorithm proposed in this paper can make the measurement accuracy reach at least 1% of the pixel size, which can meet the needs of elliptocyte detection. Then, the complete elliptocyte detection algorithm is given. Finally, by analysing the diffraction characteristics of a typical elliptocyte in detail, a very good match with the elliptocyte images is achieved under the microscope. This proves that the detection technology is effective.