The transport-of-intensity equation (TIE) is applied in the reconstruction of two interfering wavefronts by analyzing the interference patterns and their derivatives along their common propagation directions. The TIE is extended from one wave to two waves and is then applied to calculate the phase of the interference field. Finally, the phase shift concept is applied to reconstruct the phase distribution of two waves. The consistency of the method is verified by simulation.
In the last decade, the transport of intensity has been increasingly used in microscopy, wavefront sensing, and metrology. In this study, we verify by simulation and experiment the use of the transport of intensity equation (TIE) in the accurate testing of optical aspheric surfaces. Guided by simulation results and assuming that the experimental setup parameters and the conic constants are known, one can estimate an appropriate defocusing distance Δz that leads to an accurate solution of the TIE. In this paper, this method is verified through the construction of a non-nulled experiment for testing the 2D profile of an aspheric surface. The theoretical method and experimental results are compared to validate the results. Finally, to validate the TIE methodology, the phase distribution obtained by TIE is compared with the phase distribution obtained by a Shack-Hartmann sensor.
We analytically, numerically, and experimentally determine a topological charge (TC) of the sum of two axisymmetric off-axis Laguerre-Gaussian (LG) beams with the indices (0, m) and (0, n). In particular, we find that at m = n, the combined beam has TC = n, which suggests that the sum of two identical off-axis LG beams has the TC of an individual constituent LG beam. At m < n, the TC of the sum is found to take one of the following four values: TC1 = (m + n)/2, TC2 = TC1 + 1, TC3 = TC1 + 1/2, and TC4 = TC1 – 1/2. We also establish rules for selecting one of the four feasible values of TC. For the sum of two on-axis LG beams, TC of the superposition equals the larger constituent TC, i.e. TC = n. Meanwhile following any infinitesimally small off-axis shift, TC of the sum either remains equal to the pre-shift TC or decreases by an even number. This can be explained by an even number of optical vortices (OV) with TC = –1 instantly ‘arriving’ from infinity that compensate for the same number of OV with TC = +1 born in the superposition. We also show that when two LG beams with different parity are swapped in the superposition, the topological charge of the superposition changes by 1. Interestingly, when superposing two off-axis LG beams tilted to the optical axis so that their superposition produces a structurally stable beam, an infinite number of screw dislocations with TC = +1 are arranged along a certain line, with the total TC of the superposition equal to infinity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.