Lei Chen

Computer-aided alignment for a reference transmission sphere of an interferometer

A reference transmission sphere is an important device to measure the spherical surfaces, and it offers a high-quality spherical wave and a reference spherical surface with peak-to-valley less than l/20 (l50.6328 mm). For this value, only the manual alignment is difficult to manage it. Thus, we study the computer-aided alignment (CAA), which can provide a guide to align the individual lens. We describe the following works concerning the CAA with no iteration for the transmission spheres: (1) by analysis of the relationship between the Zernike polyno- mial coefficients and the sensitive variables, for example, the air thick- ness error, the tilt, the decenter of the transmission sphere with an analy- sis program written in Zemax program language, only several Zernike coefficients that change linearly with these sensitive variables are cho- sen; (2) the magnitude and direction of the correction are found using the Moore-Penrose generalized inverse matrix; and (3) a numerical simula- tion and successful alignment are processed for a 4-in.-diam, f/5 trans- mission sphere.

Absolute measurement of optical flat surface shape based on the conjugate differential method

In this paper the conjugate differential method is proposed to measure the absolute surface shape of the flat mirror using a phase-shifting interferometer. The conjugate differential method is derived from the differential method, which extracts absolute phase differences by introducing the slight transverse shifts of the optic. It employs the measurement schemes making transverse shifts on the orthogonally bilateral symmetry positions. So the measurement procedures have been changed into four-step tests to get the phase difference map instead of three-step tests for the differential method. The precision of the slope approximation is enhanced by reducing couplings between multi-step tests, and the reliability of the measurements can be improved. Several differential wavefront reconstruction methods, such as Fourier transform, Zernike polynomial fitting and Hudgin model method, can be applied to reconstruct the absolute surface shape from the differencing phase maps in four different simulation environment. They were also used to reconstruct the absolute surface shape with the conjugate differential method in the experiment. Our method accords with the classical three-flat test better than the traditional differential method, where the deviation of RMS value between the conjugate differential method and the three-flat test is less than 0.3 nm.

New algorithm on phase-shifting interferometry: the overlapping averaging 4-frame algorithm

Phase shifting interferometry (PSI) is a highly efficient and accurate phase measuring method. The accuracy of PSI is most seriously impaired by calibration error and nonlinearity in the phase shifter. This paper presents a new algorithm, the overlapping averaging 4-frame (OAF) algorithm, which can reduce the phase error due to phase shifter errors. The relationship between the accuracy of OAF algorithm and phase shifter errors is given. From this relationship, it is verified that the OAF algorithm can reduce the phase error due to phase shifter errors. The computer simulation providing the magnitude of a calibration error and nonlinearity in the phase shifter are shown for a number of different phase-measurement algorithms. From the analysis, the result is obtained that the OAF algorithm is more highly accurate than other phase-measurement algorithms.

Assessment of optical freeform surface error in tilted-wave-interferometer by combining computer-generated wave method and retrace errors elimination algorithm

Abstract. As is well-known, optical testing has begun to emerge as a limiting factor in the application of freeform surfaces. In all kinds of published freeform optical metrology, the tilted-wave-interferometer (TWI) is the precise and flexible method for testing a freeform surface as it can compensate the local surface’s deviation from its best fit sphere by using a set of tilted waves. In the process of measurement with TWI, accurate assessment of the test surface error from the fringes plays a key role. We present a method for evaluation and characterization of surface aberrations in TWI by combining computer-generated wave technology and a retrace errors elimination algorithm. The feasibility of the method is proved by the simulation and experimental results.

Problems on fabrication of computer-generated holograms for testing aspheric surfaces

Interferometric optical testing using computer-generated hologram (CGH) can give highly accurate measurement of aspheric surfaces has been proved. After the system is designed, a phase function is obtained according to the CGHs surface plane. For the requirement of accuracy, an optimization algorithm that transfers the phase function into a certain mask pattern file is presented in this letter, based on the relationship between the pattern error of CGH and the output wavefront accuracy. Then the writing machine is able to fabricate such a mask with this kind of file. With that mask, an improved procedure on fabrication of phase type CGH is also presented. Interferometric test results of an aspheric surface show that the whole test system obtains the demanded accuracy.

Processing technique for interference pattern with step using phase-shift interferometry

Based on introducing the principle and method of processing technique for interference pattern with step using the characteristic of phase-shift interferometry. The paper has discussed a new phase-unwrapping algorithm for the phase map containing discontinuities. The correct phase values in the presence of discontinuities, especially those caused by the object with height steps, can be obtained. This algorithm is fast and accurate. The results of the measurement of three- dimensional object with height steps are presented. These techniques have been successfully applied to measure the surface and wave aberration of the system with step.

Ronchi test using overlapping averaging 4-frame algorithm

An automatic technique to process Ronchigrams is presented. The phase shifting error introduced by a phase shifter is reduced using overlapping averaging four-frame algorithm. A standard plano-convex lens is tested to verify the accuracy of this technique.

Measurement for 90-deg error of dihedral angles of glass cubes

A method for testing the 90-deg error of dihedral angles of glass cubes is proposed. The test beam of a Fizeau interferometer enters the cube and is retroreflected by a dihedral angle to interfere with the reference beam. The angle between different regions of the retroreflective wavefront can be obtained using a phase-shifting interferometer. The relation between subwavefronts and the dihedral angle error is deduced, so the latter can be calculated. It does not need any extra auxiliary optical components. In the experiment, a glass cube is tested on the phase-shifting interferometer, and its four dihedral angle errors in the same principal section are obtained. The results obey the angle sum of a quadrangle principle with a tolerance of 0.04″. Moreover, the result is validated by another method, as the differences between them are less than 0.06″.

Effect of crystalline lens surfaces and refractive index on image quality by model simulation analysis

The surfaces and refractive index of crystalline lens play an important role in the optical performance of human eye. On the basis of two eye models, which are widely applied at present, the effect of lens surfaces and its refractive index distribution on optical imaging is analyzed with the optical design software ZEMAX (Zemax Development Co., San Diego, USA). The result shows that good image quality can be provided by the aspheric lens surfaces or (and) the gradient-index (GRIN) distribution. It has great potential in the design of intraocular lens (IOL). The eye models with an intraocular implantation are presented.

The position relationship in multi-interferograms

In the high accuracy absolute interferometry, several interferograms from different objects has to be calculated. This paper introduces a technique that ensures the spatial positions of the interferograms coinciding correctly (spatial unity). In this technique the characteristic parameters of interferograms’ position are picked up in the sample matrix coordinates system. And all these characteristic parameters are compared and fed back to the operator. Then the operator aligns the optical path precisely until it achieves the conditions for the absolute measurement. Computer guards the whole process, so the results are more reliability. The absolute measurement of cylindrical surface using this method has been realized and high-accuracy results are obtained.