A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Mathematical Handbook for Scientists and Engineers

An imaging lens substantially consists of a first lens-group, a stop and a second lens-group in this order from an object-side. The first lens-group substantially consists of three or less lenses including at least one negative lens and a positive lens. The second lens-group substantially consists of a 21st lens-group and a 22nd lens-group in this order from the object-side. The 21st lens-group substantially consists of three or less lenses and has positive refractive-power. The 22nd lens-group substantially consists of two lenses of a negative lens and a positive lens in this order from the object-side. Predetermined conditional formulas about distance on an optical-axis from a most-object-side lens surface in an entire system to an image-plane, maximum image height, distance on the optical-axis from a most-object-side lens surface in the first lens-group to a most-image-side lens surface in the second lens-group, and focal-length of the entire system are satisfied.

Imaging lens and imaging apparatus

Interferometric measurement methods are based on the principle of interference of two coherent wave fields (object and reference) and consequent evaluation of the interference pattern. The measured quantity, e.g. deformation, is related to the optical path difference between both wave fields, which depends on the phase of the object wave field. The phase can be obtained from the values of the intensity of the interference field with phase measuring techniques. In the work there was proposed an optical method for measuring of static deformations based on the interference of coherent wave fields and phase shifting procedure. Detailed analysis of the measurement and evaluation process with respect to most important factors is performed.

Interferometric method for deformation measurement of structures in industry

This paper is focused on a theoretical general description of membrane deformation in membrane liquid lenses, which is
based on the theory of large deformations of thin plates under uniform hydrostatic loading. The general formulas are
derived, leading to a system of differential equations that describe the shape of a deformed membrane. Since an
analytical solution cannot be found, numerical methods are applied and the membrane shape is calculated for given
practical examples. Further, the dependency of maximal deflection of the membrane on the applied hydrostatic pressure
is analysed. For a better understanding and possibility of modelling the membrane shape in an optical design software,
the shape is depicted as aspherical. Finally, the theoretical simulations are compared with experimental results for a
given membrane and applied loadings. It is clearly seen that the shape of the membrane does not correspond to a sphere
even under low applied pressures. Therefore, the presented analysis could have a significant impact in optical design.
Using the results of the paper and numerical examples, one can easily model many cases of membrane liquid lenses and
exploit the results of the simulation for precise description of optical systems with active components.

Numerical solution of deformation of circular membrane of liquid lens under uniform hydrostatic pressure

Flat mirrors are often used for designing many optical measurement systems. These mirrors can be generally deformed with respect to environmental conditions during measurements. The detailed theory of deformation of the thin flat mirror, which vibrates in the direction of the normal to its surface, is introduced in our work. It is also derived the relation for the dynamic wave aberration. On the basis of this relation, it is carried out the calculation of the Strehl definition of the deformed mirror. Obtained results can be used for analysis of the influence of mechanical vibrations on the accuracy of optical measurement systems in various practical applications.

Imaging properties of vibrating flat mirror

This paper develops a methodology for a design of zoom-systems, which are composed of thin optical components with a variable focal length (e.g., membrane lenses). The proposed procedure allows us to design not only the outer parameters of the system (focal lengths and separation of lenses), but the inner structure of individual components of the system can be calculated as well (radii of curvature, thicknesses, and refractive indices) i.e., the starting values of the mentioned parameters can be calculated and used for the next optimization.

Antonin Miks

Papers

Interferometric method for deformation measurement of structures in industry

Numerical solution of deformation of circular membrane of liquid lens under uniform hydrostatic pressure

Imaging properties of vibrating flat mirror

Design of zoom systems composed of lenses with variable focal length

Design of membrane thickness for a focus-variable liquid lens with a defined shape of the membrane’s outer surface