Improved fractional Fourier transform method based on triangle shrinkage for estimating physical parameters from Newton's rings

Newton's rings serve a crucial role in interferogram analysis for estimating physical parameters, including the radius of curvature of lenses and the centre of the rings. The fractional Fourier transform (FRFT), traditionally employed for extracting physical parameters from Newton's rings, is characterised by its time-intensive nature. This study identified the local symmetry of maximum amplitude within FRFT domains across varying rotation angles associated with Newton's rings. Utilising this local symmetry, an optimisation approach utilising triangle shrinkage was introduced, enhancing the efficiency of FRFT in determining physical parameters from Newton's rings. This innovation significantly reduces the time required for parameter estimation while maintaining the accuracy levels of the FRFT and non-uniform order searching (NOS) methods. Experimental outcomes confirm that our proposed method effectively addresses diverse scenarios and yields superior results. Notably, the method processes 1080 × 1080 pixel images within approximately 3.3 s, significantly faster than both the FRFT and NOS methods, by factors of approximately 1/800 and 1/2, respectively.