Multielement Optical Systems Research Articles

Fifth-order aberration for soft x-ray and vacuum ultraviolet multi-element optical systems.

Based on the recently developed fifth-order intrinsic aberration of a soft x-ray and vacuum ultraviolet single-element optical system, this paper proposes a fifth-order aberration (including intrinsic aberration and extrinsic aberration) calculation method for this kind of optical system with multiple elements. First, the fifth-order intrinsic aberration expressions of soft x-ray and vacuum ultraviolet multi-element optical systems are studied; second, the extrinsic aberration calculation method of this kind of optical system is discussed, and corresponding calculation expressions are derived; third, to improve aberration calculation accuracy, the modification of aberration expressions due to the transfer relationship of aperture-ray coordinates with second-order accuracy on the reference exit wavefront between adjacent optical elements is obtained. Finally, the resultant aberration expressions are applied to calculate the aberration of two design examples of soft x-ray and vacuum ultraviolet double-element optical systems with large apertures, and their images are compared with ray-tracing results using Shadow software to validate the aberration expressions. The study shows that the accuracy of the aberration expressions derived in this paper is satisfactory.

Focus on software, data acquisition, and instrumentation

Focus on software, data acquisition, and instrumentation

Three-dimensional polarization aberration functions in optical system based on three-dimensional polarization ray-tracing calculus

The polarization aberrations of a complex optical system with multi-element lens have been investigated using a 3D polarization aberration function. The 3D polarization ray-tracing matrix has been combined with the optical path difference to obtain a 3D polarization aberration function, which avoids the need for a complicated phase unwrapping process. The polarization aberrations of a microscope objective have been analyzed to include, the distributions of 3D polarization aberration functions, diattenuation aberration, retardance aberration, and polarization-dependent intensity on the exit pupil. Further, the aberrations created by the field of view and the coating on the distribution rules of 3D polarization aberration functions are discussed in detail. Finally a novel appropriate field of view and wavelength correction is proposed for a polarization aberration function which optimizes the image quality of a multi-element optical system.

Refracting the k-function: Stavroudis’s solution to the eikonal equation for multielement optical systems

The k-function of Stavroudis describes a solution of the eikonal equation in a region of constant refractive index. Given the k-function describing the optical field in one region of space, and given a prescribed refractive or reflective boundary, we construct the k-function for the refracted or reflected field. This procedure, which Stavroudis calls refracting the k-function, can be repeated any number of times, and therefore extends the usefulness of the k-function formalism to multielement optical systems. As examples, we present an analytic solution for the k-function, wavefronts, and caustics generated by a biconvex thick lens illuminated by a plane wave propagating parallel to the symmetry axis, and numerical results for off-axis plane-wave illumination of a two-mirror telescope.

Aberrations of plane-symmetric multi-element optical systems

Based on a recently developed aberration theory of plane-symmetric grating systems, its aberration coefficients are firstly extended to be applicable to the plane-symmetric refractive optical surface. To justify the linear approximation of aperture ray in a multi-element system, the ray aberrations of double-element systems with the third-order accuracy of aperture ray are derived and expressed as the form of wave aberrations. The numerical comparisons are then made between the ray tracing, the aberration expressions with the linear and with third-order accuracy of the aperture ray. Moreover, the modifications of the wave and ray aberrations are discussed in the paper when the position of the principal ray changes.

The van Cittert–Zernike theorem: a fractional order Fourier transform point of view

The transfer of the coherence by a multielement optical system is studied, within the framework of the fractional Fourier transform. The results show that, the van Cittert–Zernike theorem can be expressed in terms of the fractional order Fourier transforms of the mutual intensities over surfaces M 1 and M 2; which allows, among others, to situate this theorem in a quite general context.

Calculating and correcting the chromaticity of multilens telescopes for endoscopes

A comprehensive program has been developed for calculating the optical characteristics and chromaticity of multielement optical systems. An analysis is given of how the chromaticity of multilens telescopes for endoscopes depends on the optical characteristics of the glasses that are used and the design of the antireflection coating. It is established that the main reason that chromaticity appears in the telescopes is the selective absorption of glasses that are used. A stepwise technique has been developed for choosing the antireflection coating to correct the spectral characteristics of the transmittance of the telescopes in such a way as to minimize the chromaticity while maximizing the total transmittance. Using the results of the calculations under production conditions, colorless multilens telescopes containing thirty-eight and thirty antireflection-coated surfaces have been fabricated.

Aperture efficiencies of large axisymmetric reflector antennas fed by conical horns

It is shown how the radiation patterns of conical horns can be understood in terms of Laguerre-Gaussian beam modes. This approach provides a simple method for calculating the horn radiation pattern as it propagates through a multielement optical system consisting of lenses or offset mirrors with large focal ratio and/or a small angle of incidence, and can be used in quantitatively determining aperture efficiencies for systems where conical horns are coupled to antennas via tertiary optics. The resulting aperture efficiency results and a practical quasioptical system fed by a conical horn are discussed. >

Plastics optics for opto-electronics

Special moulding techniques result in single- and multi-element optical systems which can create entirely new options for both optical designers and production engineers.

Holographic representation of multielement optical systems

Holographic representation of multielement optical systems