In order to realize large-scale absolute surface reconstruction, a generalized iterative optimization method for solving the three-flat problem is studied. First, the idea of model-based absolute surface reconstruction is proposed, which considers the problems of absolute surface reconstruction as inverse problems. Then we take the three-flat problems as an example, we introduced two generalized iterative optimization methods for three-flat model. Finally, by both simulation and experiment, it is concluded that the block SOR method with an optimal relaxation factor converges much faster and saves more computational costs and memory space without reducing accuracy. Both simulation and experimental results indicate that the proposed iterative optimization methods are effective for solving the three-flat problem with pixel-level spatial resolution and the measuring precision of two separate measurements is 0.6 nm rms, and the cross-check test result is 0.8 nm rms. It is concluded that the proposed method can correctly reconstruct absolute figures with high efficiency and pixel-level spatial resolution.
Generally, in order to gain high accuracy in aspheric testing, a piece of high-quality CGH (computer generated hologram) is inserted behind transmission sphere to generate specified wave-front to match aspheric part. According to the difference in function, the CGH is divided into 2 parts: the center region, called as testing hologram, is used to generate specified aspheric wave-front; the outer ring, called as alignment hologram, is used to align the location of CGH behind transmission sphere. Although alignment hologram is used, there is still some adjustment error from both CGH and aspheric part, such as tilt, eccentricity and defocus. Here we will stimulate the effect of these error sources on the accuracy that is rms after the piston, tilt and power are removed, when testing a specified aspheric part. It is easy to conclude that the total measurement error is about 2 nm and the defocus of CGH contributes most.
Freeform optics provide excellent performance for a wide variety of applications. However, obtaining an accurate freeform surface measurement is highly challenging due to its large aspheric/freeform departure. It has been proven that SCOTS (Software Configurable Optical Test System), an advanced deflectometry system developed at the University of Arizona, can measure the departure of a freeform surface from the desired shape with nanometer accuracy. Here, a new data processing technique was used to measure a freeform surface without any prior knowledge of the shape of the surface. Knowing only the geometry of one point on the test surface, this method can take a blind measurement of a freeform surface and arrive at the true surface through iterative construction.
Absolute testing methods have been widely employed in the accurate metrology of optical surface deviation. As a general method, the shift-rotation method requires several rotations and translations of the surface under test. And the surface deviation of the reference and the surface under test can be both calculated in terms of Zernike polynomials. The validity of the shift and rotation procedure was proved through experiments. Two different transmission spheres (with the same F number but different quality of the reference surfaces) were used to test the same spherical surface under test. The test results of the spherical surface under test are in good agreement.
We propose a sampling method to measure surface roughness of circular flat in this paper. The steps of this method are described in following. First, the number of sampling points is determined based on the radius of the circular flat; then the sampling points are selected by a certain angle in helical line; at last we use instrument like white light interferometer to measure the surface roughness of these sample points. The sampling method can effectively use the surface roughness of sampling points to estimate the surface roughness of the overall optical surface. According to mathematic derivation and simulation analysis, this method has a good sampling results, thus it can be widely used to measure the surface roughness of the circular flat.
We have provided a comparative analysis of methods that involves multi-angle averaging, pseudo
multi-angle averaging, single-rotation and variants based on the combinations. All these methods
require measurement results being determined at rotational positions, serving for the interferometric
measurement of rotationally asymmetric surface deviation of a specimen. Zernike coefficients and
power spectral density (PSD) are computed and used for detailed comparison. The experimental results
show that single-rotation method gives noticeably smoother result, thus it is limited to applications of
measuring low spatial frequency deviations, taking the advantage of quick measurement time with
fairly accurate rms results and potentially less influence of environment; in contrast, the result with
multi-angle averaging contains more information of mid and high spatial frequency but it’s
time-consuming. The pseudo multi-averaging method is the concise variant with fewer measurements.
Its result contains more noise errors depending on the number of rotational measurements of
multi-averaging method.
We present an absolute testing of a spherical reference surface of a Fizeau interferometer with the method of shift-rotation, which relies on the decomposition of the surface deviation into rotationally asymmetric and symmetric components. With a new procedure to measure the rotationally asymmetric component and an iterative algorithm to calculate the symmetric component, the method can calibrate the spherical reference surface with high accuracy. An experiment is presented to verify the validity of the absolute testing method. The reference surface deviation measured with the absolute testing method agrees well with that of random-ball-averaging testing method; the root mean square of the residual figure between them is ∼0.8 nm .
The absolute measurement of spherical surface with multiple relative measurements is used widely in high accuracy interferometry, which can obtain the absolute surface data of the tested spherical surface. We present an experimental study on the different absolute methods of two-sphere, random-ball-averaging and shift-rotation to calibrate the spherical reference of a same transmission sphere with high accuracy. The experimental results show that the reference surface deviation measured with the different absolute methods agrees well with each other, with the fact that the difference of rms is ~0.6nm.
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