The optical components employed in high power density solid-state laser for inertial confinement fusion (ICF) must be measured accurately to provide the high resolution measurement neccessary to detect mid-spatial-frequency errors in the wavefront. The use of a Fresnel zone plate (FZP) technique to measure lens transmission wavefront power spectral density (PSD) in mid-frequency domain is disscussed. FZP can provide reference sphere with high-precision, in the meantime greatly shorten air space, thus reduce the effect of vibration and air turbulence, therefore is of great importance for lens transmission wavefront PSD measurement, especially for lens with long focal length used in the ICF facility. To verify the accuracy of the measurement, a comparison experiment of the FZP measurement with results from a Fizeau sphere interferometry method is carried out. Measurement results show excellent agreement, which proves the validity of this method. Finally, measurement uncertainty due to FZP fabrication process is analyed. Analysis of the FZP test showed the overall accuracy of 4.5nm RMS for a sphere lens with 1.5 m focal length and Φ70mm clear aperture. Thus, the measurement accuracy using the proposed FZP method is proved to be very high, FZP can therefore be used to measure lens transmission wavefront PSD accurately.
Computer generated holograms (CGHs) are state-of-the-art components in optical systems, and are widely used in combination with standard Fizeau interferometers. The primary role of the CGHs is to generate reference wavefront with any desired shape. A method of interferometrically measuring large convex lens with CGHs is adopted, and the results from a set of experiments that demonstrate the accuracy and simplicity of performing the holographic test are presented. A direct comparison of the CGH measurement with results from a compensation method shows excellent agreement. Finally, measurement uncertainty due to substrate error and hologram fabrication processes is analyzed.
A new reconstruction algorithm for absolute shape calibration in two-flat test is proposed. The shift-rotation method is applied to absolute shape calibration in two-flat test. Relying on the decomposition of the reconstructed shapes into rotationally asymmetric and symmetric components, an iteration algorithm is presented to reconstruct the rotationally asymmetric components, and Zernike polynomial fitting algorithm is used to calculate rotationally symmetric components. Compared to the traditional algorithms, the proposed algorithm has the characteristics of considerable accuracy and less computational effort. A simulation experiment proves the validity of the presented algorithm.
KEYWORDS: Stitching interferometry, Plano, Data fusion, Interferometers, Optical engineering, Data corrections, Interferometry, Detection and tracking algorithms, Process modeling, Lithium
The paper will describe an automated subaperture stitching interferometry for large plano surface based on relevant algorithm, which restruct the whole surface without recording the position of every subaperture. Both correction and data fusion algorithm are used to minimize the stitching error.
Zernike Polynomial fitting method is an effective way to reconstruct absolute surface for three-flat test. However, the Zernike circle polynomials are not orthogonal over the circular area, hence they are not suitable for square flat. We present an absolute testing of a square flat with Legendre polynomial fitting method, which relies on calculating the coefficients of the Legendre terms by least-square fitting method. To obtain the three-dimensional surface data, one additional measurement that rotate the test flat through 90° should be introduced. The formulas are derived theoretically in detail, and validity has been proved by simulated experiment. Vertical profiles of the three surfaces are compared with the measurement results obtained by three-flat test. Good agreement validates our method.
A new technique for precise wavefront measurement of lens with a hologram is presented. In diffraction, the Fresnel-zone plate hologram emulates the reflective properties of a spherical mirror for use during transmission null tests of an optic by use of a phase-shifting interferometer. Experiment shows that the Fresnel-zone hologram method result is quite similar with that of the traditional interferometry testing method, in which retroreflecting spherical surfaces are used as the reference. The benefit of this methodology is the higher degree of precision at lower cost of manufacturing the reflecting hologram, compared with retrospheres capable of delivering similar precision. This technique is widely applicable and is particularly useful for measuring long focus lens.
The corresponding author for this article [Opt. Eng.. 53, (9 ), 092004 (2014)] has been changed from Bo Gao to Liqun Chai. The paper was corrected online on 4 June 2014.
An iterative algorithm has been successfully used to process data from the three-flat test. On the basis of the iterative algorithm proposed by Vannoni, which is much faster and more effective than the Zernike polynomial fitting method, an improved algorithm is presented. By optimizing the iterative steps and removing the scaling factors, the surface shape can be easily computed in a few iterations. The validity of the method is proved by computer simulation, and the interpolation error and principle error are analyzed.
A three dimensional (3-D) measurement method with orthogonal composite grating aided by fringe contrast and background calibration is proposed. Due to spectrum overlap, we find that the contrast and background of each deformed phase-shifting fringe demodulated from the captured composite fringe image is changed differently, which violates the principle that the contrast and background between any two deformed fringes must be uniform in the traditional 3-D measurement method with orthogonal composite grating, and therefore results in measurement error. We acquire the phase-shifting sinusoidal fringes from the composite fringe image captured on the reference plane, and the zero- and first-order spectra of the sinusoidal fringes can be obtained by filtering in the spatial frequency domain. Then the ratio contrast and background coefficients between the phase-shifting sinusoidal fringes can be calculated. When an object is measured, the contrast and background of the demodulated deformed fringes can be calibrated by these ratio coefficients. A new 3-D measurement mathematical model is set up to reconstruct the object. Experiments prove the new method can effectively restrain the effect of spectrum overlap, and can improve the measurement accuracy more than 1 time.
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