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Topological pupil segmentation and point spread function analysis for large aperture imaging systems
With the widespread availability of electromagnetic (vector) analysis codes for describing the diffraction of electromagnetic waves by periodic grating structures, the insight and understanding of nonparaxial parametric diffraction grating behavior afforded by approximate methods (i.e., scalar diffraction theory) is being ignored in the education of most optical engineers today. We show that the linear systems formulation of nonparaxial scalar diffraction theory enables the development of a scalar parametric diffraction grating model [for transverse electric (TE) polarization] for sinusoidal reflection gratings with arbitrary groove depths and arbitrary nonparaxial incident and diffracted angles. This scalar parametric analysis is remarkably accurate as it includes the ability to redistribute the energy from evanescent orders into the propagating ones, thus allowing the calculation of nonparaxial diffraction efficiencies to be predicted with an accuracy usually thought to require rigorous electromagnetic theory. These scalar parametric predictions of diffraction efficiency are compared to paraxial scalar and rigorous electromagnetic (vector) predictions for a variety of nonparaxial diffraction grating configurations, thus providing quantitative limits of applicability of nonparaxial scalar diffraction theory to sinusoidal reflection gratings as a function of the grating period-to-wavelength ratio (λ /
With the wide-spread availability of rigorous electromagnetic (vector) analysis codes for describing the diffraction of electromagnetic waves by specific periodic grating structures, the insight and understanding of nonparaxial parametric diffraction grating behavior afforded by approximate methods (i.e., scalar diffraction theory) is being ignored in the education of most optical engineers today. Elementary diffraction grating behavior is reviewed, the importance of maintaining consistency in the sign convention for the planar diffraction grating equation is emphasized, and the advantages of discussing “conical” diffraction grating behavior in terms of the direction cosines of the incident and diffracted angles are demonstrated. Paraxial grating behavior for coarse gratings (
Linear systems formulation of image analysis in the presence of both aberrations and surface scatter
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This course provides a basic understanding of X-ray imaging systems and the fundamental physical mechanisms that limit image quality. A complete engineering systems analysis is presented. The relative effect of these mechanisms upon image quality is discussed for a variety of applications including soft X-ray microscopy, high-energy astrophysics, X-ray microlithography, and X-ray synchrotron beam lines.
In this short course, a linear systems approach to modeling non-paraxial scalar diffraction theory is developed and shown to be shift-invariant with respect to changes in incident angle only when expressed in terms of the direction cosines of the propagation vectors. It is the diffracted radiance (not intensity or irradiance) that is shift-invariant in direction cosine space. This realization extends the range of parameters over which simple Fourier techniques can be used to make accurate calculations concerning wide-angle diffraction phenomena. Diffraction grating behavior and surface scattering effects are two applications that are not limited to the paraxial region and benefit greatly from this new development.
After an explanation of astronomical optics from Galileo to the Hubble Space Telescope, the geometrical theory of image formation is reviewed. The image degradation effects of diffraction, geometrical aberrations, and scattering are presented with emphasis on obtaining physical insight while retaining some degree of mathematical rigor. A systems approach to image formation leads to a discussion of various image quality criteria appropriate for different applications. Optical transfer function (OTF) in optical performance analysis is discussed for diffraction-limited situations and optical fabrication and environmental errors. The characteristics of reflective telescope configurations are discussed in detail.
This course provides a basic understanding of UV/EUV and X-ray optical systems and the fundamental physical mechanisms that limit image quality. A complete systems engineering analysis is presented. The relative effect of these mechanisms upon image quality is discussed for a variety of applications including soft X-ray microscopy, high-energy astrophysics, EUV/X-ray microlithography, and X-ray synchrotron beam lines.
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