S. L. Zhuang

Bio: S. L. Zhuang is an academic researcher from Pennsylvania State University. The author has an hindex of 1, co-authored 1 publications receiving 3 citations.

Optimal balance of aberrations under partially coherent illumination

Abstract: An optimal balance of spherical aberrations under partially coherent illumination is presented. The visibility of a two-point image as a merit function is used to estimate the image aberrations. Although the optimal balance of aberrations has been evaluated by Marechal [ Rev. Opt.2, 257 ( 1947)] and Wang [ Proc. Phys. Soc. London53, 157 ( 1941)] for incoherent illumination, it has not been treated for partially coherent illumination. In this paper, a general relationship between the optimal balance of aberrations and the degree of mutual coherence under partially coherent illumination is discussed. The result obtained for incoherent illumination turns out to be a special case of that for partially coherent illumination. In other words, the result of optimal balance of aberrations under partially coherent illumination is a general case that includes coherent, incoherent, and partially coherent illumination.

On the diffraction theory of optical images

Abstract: The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

The concept of partial coherence in optics

Abstract: It is shown that a 'phase-coherence factor' may be defined in a manner which leads, without recourse to explicit statistical analysis, to the theorems established by van Cittert (I934) and Zernike (I938) for analogous factors. An invalid approximation made in their calculations of the phase-coherence factor for a plane illuminated directly by a source is corrected. The new treatment is applied to the theory of Young's experiment, the stellar interferometer, and illumination in the microscope. The phase-coherence factor defined here enables a general theory of the formation of optical images to be formulated. Further, it is shown that the diameter of the area of coherence on a plane illuminated by a source of angular radius α is given by d = 0.16λ/N sin α, where N is the refractive index of the intervening medium.

Aberration-variance-based formula for calculating point-spread functions: rotationally symmetric aberrations

Abstract: By using exponential evaluations of the Strehl ratio and appropriate Dini-sampling formulas in concert, an approximate formula is derived for fast calculation of intensity distributions in the central bright core of rotationally symmetric aberrational diffraction patterns. Since the formula involves no special functions, it is convenient both for numerical and analytical purposes. Numerical examples show that for moderate amounts of rotationally symmetric aberrations, the formula gives excellent results inside the unity disk (compared with a radius of 1.22 for the Airy disk) at the image plane. In the case of balanced (Zernike) spherical aberrations, our formula reduces to the perfect Airy pattern multiplied by corresponding Strehl ratio. A useful tool for the optical system designer, it can easily be implemented using any desk-top calculator for evaluating parameters as encircled energy, truncated radius of gyration, or to compute the central part of polychromatic diffraction patterns.