Application of irradiance transport equation in aspheric surface testing

A guide to properly select the defocusing distance for accurate solution of transport of intensity equation while testing aspheric surfaces

“…A series of simulations are carried out based on Ref. [34]. The defocusing distance Δz is varied from 1.0 mm to 400/7.2 mm (because of magnification) and for five pupil diameters: [24, 21, 19, 16.8, and 15] mms corresponding to PV: [255.9, 112.6, 68, 37, and 20.6] radians, respectively.…”

“…In a previous work [34], we presented a theoretical method to accurately estimate the defocusing distance by investigation the error contribution due to Δz in which it is assumed that the radius of curvature (ROC) and conic constant of an aspheric surface is known. We demonstrated that an optimum value for Δz is related to the peak-to-valley (PV) of the phase distribution in which the contribution of piston, tilt, and the quadric term have been removed to accurately estimate the PV [34]. In this study, we demonstrate experimentally how to measure aspheric surfaces of which its conic constant and ROC are known.…”

Accurate testing of aspheric surfaces using the transport of intensity equation by properly selecting the defocusing distance

“…In an earlier work, we assumed that the conic constant (CC) and radius of curvature (RC) of an aspheric surface are known, and a theoretical method was derived to accurately estimate the defocusing distance by investigating the error contribution due to Δz [40]. We concluded that an optimum value for Δz is related to the peak-to-valley (PV) of the phase distribution.…”

“…We concluded that an optimum value for Δz is related to the peak-to-valley (PV) of the phase distribution. The contribution of piston, tilt, and the quadric terms have been eliminated, for making accurate estimation of the PV [40].…”

Numerical evaluation of the intensity transport equation for well-known wavefronts and intensity distributions

“…The phase retrieval based in the ITE is widely used as curvature sensor 3,4 , in optometry 5 , optical metrology [6][7][8] , and in optical microscopy applications 9 . The phase retrieval based in the ITE is very useful in experimental conditions where interferometric techniques cannot be implemented.…”