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

Optical systems with variable optical characteristics (zoom lenses) find broader applications in practice nowadays and methods for their design are constantly developed and improved. We describe a relatively simple method of the design of zoom lenses using the third-order aberration theory. It presents one of the possible approaches of obtaining the Seidel aberration coefficients of individual members of a zoom lens. The advantage of this method is that Seidel aberration coefficients of individual elements of a given optical system can be obtained simply by solving of a set of linear equations. By using these coefficients, one can determine residual aberrations of the optical system without detailed knowledge about the structure of its individual elements. Furthermore, we can determine construction parameters of the optical system, i.e., radii of curvature and thicknesses of individual elements of a given optical system. The proposed method makes it possible to determine which elements of the optical system can be designed as simple lenses and which elements must have a more complicated design, e.g., doublets or triplets.

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Method of zoom lens design

Noncontact optical metrology based on the chromatic confocal principle is becoming increasingly important for fast and accurate measurements of surface topography, distance, and layer thickness in engineering and industry. These sensors are based on the wavelength dependence of longitudinal chromatic aberration of optical systems, and the distance or thickness of the measured sample is coded into spectral information. We provide a theoretical analysis of a problem of the thickness measurement of transparent samples (glass plane-parallel plates or lenses) with respect to material dispersion. Our work deals with a description and analysis of induced measurement errors in the cases of measurement of the thickness of a plane-parallel plate and the central thickness of a lens. Relations are derived for a quantitative evaluation of these errors and a method is presented for minimizing the influence of these errors on the accuracy of measurement.

Analysis of method for measuring thickness of plane-parallel plates and lenses using chromatic confocal sensor

Multi-step phase-shifting algorithms insensitive to linear phase shift errors

Traditional optical systems with variable optical characteristics are composed of several optical elements that can be shifted with respect to each other mechanically. A motorized change of position of individual elements (or group of elements) then makes possible to achieve desired optical properties of such zoom lens systems. A disadvantage of such systems is the fact that individual elements of these optical systems have to move very precisely, which results in high requirements on mechanical construction of such optical systems. Our work is focused on a paraxial and third order aberration analysis of possible optical designs of two-element zoom lens systems based on variable power lenses with a variable focal length. First order chromatic aberrations of the variable power lenses are also described. Computer simulation examples are presented to show that such zoom lens systems without motorized movements of lenses appear to be promising for the next-generation of zoom lens design.

Analysis of two-element zoom systems based on variable power lenses

A method is presented for the calculation of paraxial design parameters of a double-sided telecentric zoom lens with easy variation of the magnification range. The telecentric lens consists of a zoom lens with a fixed distance between focal points and a lens with a fixed focal length. The third-order aberration analysis is also performed, and spot diagrams are calculated for two f-number values.

Antonin Miks

Papers

Method of zoom lens design

Analysis of method for measuring thickness of plane-parallel plates and lenses using chromatic confocal sensor

Multi-step phase-shifting algorithms insensitive to linear phase shift errors

Analysis of two-element zoom systems based on variable power lenses

Design of a double-sided telecentric zoom lens