High resolution optical surface testing using transport of intensity equation

Aberration patterns in the optical testing surfaces using transport of intensity equation

“…It has been shown in previous works that if a wavefront, which propagates in the direction of the optical axis, is considered within the paraxial approximation, we obtain the equation [6]:…”

“…In some works, this equation has been developed proposing that, under specific conditions it can lead to a Poisson equation [3,4]. The recovery of the optical wavefront is thereby reduced to a numerical problem [5], offering the advantage that the spatial resolution of the test will depend on the number of pixels of the detector and not only on the number of elements (stripes, lines, points) obtained by conventional tests that use spatial filters or complex optics like interferometric tests, Ronchi or Hartmann tests [6].…”

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

“…Some of the techniques were based on Green's functions [20], multigrid (MG) approach [21,22], and the Zernike polynomial expansion technique [23,24]. In the last decade, TIE has been used in several areas of optics, such as in adaptive optics and topography retrieval [24,25], quantitative phasesensitive imaging for biological and bioengineering applications [26,27], optical measuring such as refractive index profile measurement and fringe analysis [28][29][30], and high speed optical tomography [31][32][33], just to name a few.…”

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

“…For solving the TIE, many effective numerical methods such as the method based on Green's function [19], multigrid (MG) [20,21], and the Zernike polynomial expansion method [22,23] were presented. Currently, TIE technique is used in different fields of physics such as adaptive optics [24,25], microscopy [26,27], optical measuring [28][29][30], and optical tomography [31][32][33], just to name a few.…”