In order to obtain a rapid estimate of the quality of a lens by observing its behaviour in the interferometer, it is necessary for the observer to be familiar with the characteristic patterns of the various primary aberrations under various conditions of adjustment. A method is described by which these patterns can be easily calculated for any required case; and series of typical patterns are shown together with actual interferograms for comparison.

The interferometer patterns due to the primary aberrations

The conservation equation for a monochromatic field with arbitrary polarization propagating in an inhomogeneous transparent medium is expressed in terms of amplitude and phase variables. The expressions obtained for linearly polarized fields are compared with the results obtained in the eikonal approximation. The electric field wave equation is written in terms of intensity and phase variables. The transport equations for the irradiance and the phase are shown to be particular cases of these derivations. The conservation equation arising from the second-order differential wave equation is shown to be equivalent to that obtained from Poynting's theorem.

/pdf/amplitude-and-phase-representation-of-monochromatic-fields-320xrdjibj.pdf

Amplitude and phase representation of monochromatic fields in physical optics.

A conservation equation for the scalar wave equation is derived from two linearly independent solutions. In the one-dimensional limit the conservation equation yields a previously known invariant. The continuity equation derived for a complex disturbance is shown to yield an equivalent result. The obtention of the second independent solution is discussed using two different schemes that lead either to orthogonal trajectories or to derivative fields. The complementary fields may be visualized as out-of-phase fields where a negative-valued density is interpreted in terms of the leading or lagging field. These results are compared with the usual definition of energy density and flow for scalar waves. In the monochromatic plane wave case, the averages of all the proposed densities and flows converge to the same result. The physical meaning of the different approaches is discussed.

http://iopscience.iop.org/article/10.1088/0305-4470/37/13/013/pdf

Complementary fields conservation equation derived from the scalar wave equation

We have reproduced quantitatively the technique commonly used in optical shop to evaluate surface error from comparison between experimental and simulated Ronchigrams. We used this procedure to evaluate, from Ronchigrams of any number of fringes, the curvature radius and/or conic constant of conic surfaces. The error function is calculated without using integration (numerical or polynomial) so the corresponding problems were avoided. Furthermore, when the error function is described with cubic splines, then the local errors are very well reproduced, which is not the case with the polynomial description. We have described the error functions with conical surfaces or with cubic splines, and for the best reproduction of experimental Ronchigram we used genetic algorithms.

Local and global surface errors evaluation using Ronchi test, without both approximation and integration

By correlating bi-Ronchigram images, surface errors without any supposed symmetry are evaluated. No approximation and interference orders are needed. First, only one experimental bi-Ronchigram (Ronchigram with a square grid) image was recorded. Second, given a surface parameter set (curvature radius, conic constant, and/or symmetric and asymmetric deformation coefficients), a bi-Ronchigram image is simulated and correlated with the bi-Ronchigram experimental image. Third, genetic algorithms are used to find the parameters for which the correlation coefficient reaches its maximum value. Finally, the parameters of the experimental surface are estimated. Evaluations of curvature radius, conic constant, and error functions for reflecting surfaces will be shown.

https://www.spiedigitallibrary.org/journals/Optical-Engineering/volume-54/issue-3/034108/Optical-surface-evaluation-by-correlating-bi-Ronchigram-images/10.1117/1.OE.54.3.034108.pdf

Optical surface evaluation by correlating bi-Ronchigram images

Wavefront Slope Measurements in Optical Testing

Some experimental qualitative results are presented with a setup that uses a knife edge for producing partial interferograms, in order to obtain the quality of a lens under test. However, the same method can be extended to test an optical surface. The knife edge is located near the focal point of the lens, covering almost half of the incident laser light beam. The different observed interferograms correspond to the orientation of the knife edge with respect to the optical axis, and its distance to the focus of the lens.

Knife edge interferometer, part I: with collimated beam

In this paper some experimental results will be presented with a setup that uses a knife edge for producing partial interferograms, with information about the quality of a lens under test. However the same method can be extended to test an optical surface. The knife edge is located near the focal point of the lens, covering almost half of an incident laser light beam. The different observed interferograms correspond to the orientation of the knife edge with respect to the optical axis, and focus of the lens.

https://iopscience.iop.org/article/10.1088/1742-6596/274/1/012063/pdf

Fermín S. Granados Agustín

Papers

Wavefront Slope Measurements in Optical Testing

Knife edge interferometer, part I: with collimated beam

Optical Testing with a Knife Edge Interferometer

Medición de la fase o frente de onda con un banco nodal