Fig. 1

(a) Interferometry setup to generate the forked-shape and planar interferograms, referred to as the forked grating and flattened grating, respectively. (b) designed forked grating of \(\ell =-2\) when Blocker B blocked the Laguerre–Gaussian LG2 beam, (c) designed flattened grating of \(\ell =-2\) and 3, (d) zeroth order of 2D Fourier transform of forked grating of \(\ell =-2\), (e) zeroth order of 2D Fourier transform of flattened grating of \(\ell =-2\) and 3, (f) designing of a Logically Flattened Grating LFG using Binary Forked Gratings BFG of charges \(\ell _1=-2\) and \(\ell _2=3\), and (g) zeroth order of 2D Fourier transform of designed LFG. The phase of the incident plane wave is expressed as \(e^{j k x \tan \theta }\), corresponding to a beam propagating at an angle \((\theta )\) relative to the optical axis of the LG1 beam. This formulation captures the transverse phase gradient introduced by the angular tilt and accurately represents the incident field in the interferometric setup. A tilted plane wave with a tilt angle of \(1^o\) is considered to design the gratings.