B.R.A Nijboer

Bio: B.R.A Nijboer is an academic researcher. The author has contributed to research in topics: Coma (optics) & Diffraction. The author has an hindex of 1, co-authored 1 publications receiving 63 citations.

Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy.

Abstract: Oil-immersion microscope objective lenses have been designed and optimized for the study of thin, two-dimensional object sections that are mounted immediately below the coverslip in a medium that is index matched to the immersion oil. It has been demonstrated both experimentally and through geometrical- and physical-optics theory that, when the microscope is not used with the correct coverslip or immersion oil, when the detector is not located at the optimal plane in image space, or when the object does not satisfy specific conditions, aberration will degrade both the contrast and the resolution of the image. In biology the most severe aberration is introduced when an oil-immersion objective lens is used to study thick specimens, such as living cells and tissues, whose refractive indices are significantly different from that of the immersion oil. We present a model of the three-dimensional imaging properties of a fluorescence light microscope subject to such aberration and compare the imaging properties predicted by the model with those measured experimentally. The model can be used to understand and compensate for aberration introduced to a microscope system under nondesign optical conditions so that both confocal laser scanning microscopy and optical serial sectioning microscopy can be optimized.

On the circle polynomials of Zernike and related orthogonal sets

Abstract: The paper is concerned with the construction of polynomials in two variables, which form a complete orthogonal set for the interior of the unit circle and which are ‘invariant in form’ with respect to rotations of axes about the origin of coordinates. It is found that though there exist an infinity of such sets there is only one set which in addition has certain simple properties strictly analogous to that of Legendre polynomials. This set is found to be identical with the set of the circle polynomials of Zernike which play an important part in the theory of phase contrast and in the Nijboer-Zernike diffraction theory of optical aberrations.The results make it possible to derive explicit expressions for the Zernike polynomials in a simple, systematic manner. The method employed may also be used to derive other orthogonal sets. One new set is investigated, and the generating functions for this set and for the Zernike polynomials are also given.

Zernike polynomials: a guide

Abstract: In this paper we review a special set of orthonormal functions, namely Zernike polynomials which are widely used in representing the aberrations of optical systems. We give the recurrence relations, relationship to other special functions, as well as scaling and other properties of these important polynomials. Mathematica code for certain operations are given in the Appendix.

The diffraction theory of aberrations

Abstract: A historical and critical survey is given of investigations concerned with image formation in optical instruments in the presence of aberrations. The development of the subject is traced from the early researches of Airy on an aberration-free image. The advances made in recent years are discussed in greater detail; these mainly concern the effects of small aberrations, tolerance criteria, and the asymptotic treatment of diffraction problems. A section is also included on investigations into the effects of waves of non-uniform amplitude. The detailed light distribution in typical images is illustrated by isophote-diagrams and photographs.

Analytical solution of the diffraction integrals and interpretation of wave-front distortion when light is focused through a planar interface between materials of mismatched refractive indices

Abstract: The treatment of the diffraction of electromagnetic waves for light focused by a high numerical aperture lens from a first medium into a second medium [ J. Opt. Soc. Am. A12, 325 ( 1995)] is extended so as to provide an analytical solution for the diffraction integrals by means of polynomial expansion. Methods are proposed and used to eliminate strong oscillations from the diffraction integrals. The aberration function is analyzed and expanded in terms of Zernike polynomials. The Zernike coefficients are obtained, and the error of the expansion is determined. It is shown that when the relative refractive index of the second and first media is larger than unity, the higher-order Zernike coefficients are independent of the refractive index of the second medium. A physical interpretation is given to explain this behavior. Pictorial representation of the first 25 Zernike polynomials is also presented.