Jinlong Cheng

Bio: Jinlong Cheng is an academic researcher from Nanjing University of Science and Technology. The author has contributed to research in topics: Interferometry & Phase (waves). The author has an hindex of 5, co-authored 13 publications receiving 67 citations.

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture

Abstract: Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on the modal method are currently available, namely, the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, as are 2D Legendre polynomials. Zernike square polynomials are derived by the Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to the other three polynomials because of its high accuracy and robustness even in the case of a wavefront with incomplete data.

Large radius of curvature measurement based on virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer.

Abstract: We have proposed a virtual quadratic Newton rings phase-shifting moire-fringes measurement method in a nonnull interferometer to measure the large radius of curvature for a spherical surface. In a quadratic polar coordinate system, linear carrier testing Newton rings interferogram and virtual Newton rings interferogram form the moire fringes. It is possible to retrieve the wavefront difference data between the testing and standard spherical surface from the moire fringes after low-pass filtering. Based on the wavefront difference data, we deduced a precise formula to calculate the radius of curvature in the quadratic polar coordinate system. We calculated the retrace error in the nonnull interferometer using the multi-configuration model of the nonnull interferometric system in ZEMAX. Our experimental results indicate that the measurement accuracy is better than 0.18% for a spherical mirror with a radius of curvature of 41,400 mm.

Design, assembly and calibration of white-light microscopy interferometer

Abstract: A white-light microscopy interferometer was developed for measurement of the 3D profile and roughness.10X, 20X and 50X Mirau interference microscope objectives with the numerical aperture of 0.3, 0.4 and 0.55 were designed, manufactured and then provided as the accessories. Thickness deviation between beam splitter plate and reference mirror plate as well as the numerical aperture will both affect the contrast of interference fringe, according to optical modeling and image evaluation. The former would generate dispersion and then decrease the fringe contrast, while the latter would not produce dispersion separately but impact the amount of dispersion when thickness deviation exists, and their influence on fringe contrast was based on the expression of white-light interference intensity. Simulations for interference fringes from Mirau interference microscope objectives with different NA and thickness deviation were implemented, demonstrated that the fringe contrast will be falling with NA and thickness deviation increasing. A standard step with the nominal step value of 110 nm was used to calibrate the white-light microscopy interferometer, showing that less than1nm deviation can be reached.

Carrier squeezing interferometry with π/4 phase shift: phase extraction in the presence of multi-beam interference.

Abstract: Multi-beam interference exists in testing high-reflectivity surfaces with a Fizeau interferometer. In this paper, the multi-beam interference intensity was estimated as the sum of the first six order harmonics using the Fourier series expansion. Then, by adopting carrier squeezing interferometry with a π/4 phase shift, an algorithm was proposed to extract the phase from multi-beam interferograms. To ensure the separation of the lobes of phase-shift errors and the phase in the frequency domain, conditions of the necessary linear carrier in the proposed algorithm were derived. Simulation results indicated that the phase retrieving precision is better than PV 0.008λ and RMS 0.001λ, even when the reflection coefficient of the test surface is as high as 0.9 and the phase shift varies within π/4±π/20. Compared with the other algorithms, the proposed algorithm for multi-beam interference was validated by its good performance in the experiments, especially when the phase-shift error exists.

Review of optical freeform surface representation technique and its application

Abstract: Modern advanced manufacturing and testing technologies allow the application of freeform optical elements. Compared with traditional spherical surfaces, an optical freeform surface has more degrees of freedom in optical design and provides substantially improved imaging performance. In freeform optics, the representation technique of a freeform surface has been a fundamental and key research topic in recent years. Moreover, it has a close relationship with other aspects of the design, manufacturing, testing, and application of optical freeform surfaces. Improvements in freeform surface representation techniques will make a significant contribution to the further development of freeform optics. We present a detailed review of the different types of optical freeform surface representation techniques and their applications and discuss their properties and differences. Additionally, we analyze the future trends of optical freeform surface representation techniques.

Orthonormal Polynomials in Wavefront Analysis: Analytical Solution

Abstract: This paper derives closed-form orthonormal polynomials over noncircular apertures using the Gram-Schmidt orthogonalization process. Isometric plots, interferograms, and point-spread functions are illustrated. Their use in wavefront analysis is discussed.

Combining freeform optics and curved detectors for wide field imaging: a polynomial approach over squared aperture.

Abstract: In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which are very compact and free of obscuration. However, the field of freeform surfaces design techniques still remains underexplored. In the present paper we use the mathematical apparatus of orthogonal polynomials defined over a square aperture, which was developed before for the tasks of wavefront reconstruction, to describe shape of a mirror surface. Two cases, namely Legendre polynomials and generalization of the Zernike polynomials on a square, are considered. The potential advantages of these polynomials sets are demonstrated on example of a three-mirror unobscured telescope with F/# = 2.5 and FoV = 7.2x7.2°. In addition, we discuss possibility of use of curved detectors in such a design.

Modal wavefront estimation from its slopes by numerical orthogonal transformation method over general shaped aperture.

Abstract: Wavefront estimation from the slope-based sensing metrologies zis important in modern optical testing. A numerical orthogonal transformation method is proposed for deriving the numerical orthogonal gradient polynomials as numerical orthogonal basis functions for directly fitting the measured slope data and then converting to the wavefront in a straightforward way in the modal approach. The presented method can be employed in the wavefront estimation from its slopes over the general shaped aperture. Moreover, the numerical orthogonal transformation method could be applied to the wavefront estimation from its slope measurements over the dynamic varying aperture. The performance of the numerical orthogonal transformation method is discussed, demonstrated and verified by the examples. They indicate that the presented method is valid, accurate and easily implemented for wavefront estimation from its slopes.