Aberrations In Imaging System Research Articles

Imaging system aberrations through optical windows with nonuniform laser heating.

An optical window is a critical component of an imaging system. When operating in harsh environments with extreme heating, nonuniform temperature changes occur throughout the window and cause nonuniform refractive index changes and mechanical deformations due to thermal expansion, which can degrade the imaging system's performance. In this paper, we present results collected from an experimental setup developed to characterize these aberrations. This setup includes a C O 2 laser for sample heating, an infrared camera for measuring front and back surface temperatures, and a visible imaging system and a wavefront sensor for measuring degradations of a collimated beam from a point source transmitted through the heated window. Sapphire samples are laser heated with a Gaussian profile to temperatures in excess of 500K with surface temperature gradients in excess of 15K/mm. These measurements are compared with first principles models, which show quantitative agreement for window temperatures and qualitative agreement with the transmitted wavefront and imaged point source.

Quantitative Jones matrix imaging using vectorial Fourier ptychography.

This paper presents a microscopic imaging technique that uses variable-angle illumination to recover the complex polarimetric properties of a specimen at high resolution and over a large field-of-view. The approach extends Fourier ptychography, which is a synthetic aperture-based imaging approach to improve resolution with phaseless measurements, to additionally account for the vectorial nature of light. After images are acquired using a standard microscope outfitted with an LED illumination array and two polarizers, our vectorial Fourier ptychography (vFP) algorithm solves for the complex 2x2 Jones matrix of the anisotropic specimen of interest at each resolved spatial location. We introduce a new sequential Gauss-Newton-based solver that additionally jointly estimates and removes polarization-dependent imaging system aberrations. We demonstrate effective vFP performance by generating large-area (29 mm2), high-resolution (1.24 μm full-pitch) reconstructions of sample absorption, phase, orientation, diattenuation, and retardance for a variety of calibration samples and biological specimens.

Three Dimensional Single Molecule Localization using Phase Retrieved Pupil Functions

Single particle tracking and single-molecule localization based super-resolution techniques rely on the precise and accurate localization of single fluorescent molecules. For two dimensional imaging, relatively simple models of a microscope point spread function (PSF), such as the two dimensional Gaussian, are adequate for most common imaging approaches. However, three dimensional localization is hampered by the fact that the image of a molecule near the focal plane contains little information about its axial position. In recent years, several three dimensional (3D) imaging techniques have been demonstrated that improve the localization of single fluorescent molecules along the axial direction, such as astigmatic imaging[1], a double helix point spread function (DH-PSF)[2], and dual focal plane methods[3]. Although these methods implement very different optical setups, they use either a simple Gaussian models, theoretical PSFs that do not account imaging system aberrations, or large, unwieldy, experimentally acquired 3D PSFs that can be prone to artifacts. Here we introduce a localization algorithm based on phase retrieved pupil functions. Pupil functions can contain information about specific aberrations present in the imaging system and can be used to calculate realistic 3D PSFs from a small set of Zernike polynomial coefficients that describe the pupil magnitude and phase. This compact representation of the 3D PSF allows the PSF to be efficiently calculated as needed in an iterative update method implemented on GPU hardware. We demonstrate the use of phase retrieved pupil functions for 3D localization in both the astigmatic and dual focal plane setups.Reference[1] Bo Huang, Science, 2008[2] Pavani, App.Phy.Sci, 2009[3] Manuel F Juette, NMETH, 2008

Adaptive phase plates for optical encoding systems invariant to second-order aberrations

Certain optical aberrations of imaging systems yield low resolution images. Wavefront coding has proven to minimise this problem by means of hybrid optical-digital imaging systems. The optical part usually involves a phase plate described in terms of cubic polynomials whose shape is a linear combination of ( x 3 + y 3) and ( x 2 y + xy 2). Optimization is achieved by seeking the most appropriate linear combination with respect to the optical system's constraints. Here, we propose the shape of two pairs of phase plates such that by means of relative rotations they allow for variation of the linear combination of the cubic terms. This will enable adaptive optimization of the cubic phase to the optical system's constraints when these vary in time. Results will be illustrated with numerical simulations.

Reconstruction of refractive-index distribution in off-axis digital holography optical diffraction tomographic system

In the paper the optical diffraction tomographic system for reconstruction of the internal refractive index distribution in optical fiber utilizing grating Mach-Zehnder interferometer configuration is explored. The setup applies afocal imaging. Conventional grating application gives, however, highly aberrated object beam producing incorrect refractive-index reconstructions. The grating inherent aberrations are characterized, its influence on both image projections and refractive index reconstructions is presented. To remove aberrations and enable tomographic reconstruction a novel digital holographic algorithm, correcting optical system imaging, is developed. The algorithm uses plane wave spectrum decomposition of optical field for solving diffraction problem between parallel and tilted planes and enabling correction of imaging system aberrations. The algorithm concept was successfully proved in simulations and the experiment.

Criteria for correction of quadratic field-dependent aberrations.

Aberrations of imaging systems can be described by using a polynomial expansion of the dependence on field position, or the off-axis distance of a point object. On-axis, or zero-order, aberrations can be calculated directly. It is well-known that aberrations with linear field dependence can be calculated and controlled by using the Abbe sine condition, which evaluates only on-axis behavior. We present a new set of relationships that fully describe the aberrations that depend on the second power of the field. A simple set of equations is derived by using Hamilton's characteristic functions and simplified by evaluating astigmatism in the pupil. The equations, which we call the pupil astigmatism criteria, use on-axis behavior to evaluate and control all aberrations with quadratic dependence on the field and arbitrary dependence on the pupil. These relations are explained and are validated by using several specific optical designs.

Aberrated foci in the time and frequency domains and experiments with acoustical diffraction catastrophes.

Properties of wave fields at and near foci are considered for situations in which the amplitude is limited by the shape of an initial wave front rather than its aperture or initial dimensions. Such aberrated foci are relevant to high-frequency scattering from curved surfaces and to understanding the response of source and receiver arrays. Caustics classified by generic catastrophes are considered such as produced by random phase perturbations or by aberrations of imaging systems [M. V. Berry and C. Upstill, Prog. Opt. 18, 258 (1980)]. Experiments were carried out in which ultrasonic transients and tone bursts were reflected from a curved metal sheet in water such that the resulting caustic surface was a cusp which opens up generally transverse to the propagation direction of the reflected wave front [C. K. Frederickson, Ph.D. dissertation, Washington State University (1991)]. The results illustrate several more general properties of transient responses and diffraction patterns near weak foci. For example, the singular part of the travel time surface describing the merging of echoes has a shape like that of the next higher cuspoid catastrophe: a swallowtail catastrophe. Conditions for neglecting the effects of apertures on catastrophe diffraction patterns are examined. [Work supported by ONR.]

Chromatic Correction of Two- and Three-element Holographic Imaging Systems

This paper gives a comprehensive survey of the chromatic correction, imaging quality, and spherochromatic aberrations of imaging systems consisting of two or three holographic optical elements (HOE...

Zernike annular polynomials for imaging systems with annular pupils

The aberrations of imaging systems with uniformly illuminated annular pupils are discussed in terms of a complete set of polynomials that are orthogonal over an annular region. These polynomials, which we call Zernike annular polynomials, are similar to the Zernike circle polynomials and reduce to them as the annulus approaches the full circle. The Zernike-polynomial expansion of an aberration function is compared with its power-series expansion. The orthogonal aberrations given by Zernike annular polynomials describe how a higher-order classical aberration of a power-series expansion is balanced with one or more lower-order classical aberrations to minimize its variance. It is shown that as the obscuration ratio increases, the standard deviation of an orthogonal as well as a classical primary aberration decreases in the case of spherical aberration and field curvature and increases in the case of coma, astigmatism, and distortion. The only exception is the case of orthogonal coma, for which the standard deviation first increases and then decreases. The orthogonal aberrations for nonuniformly illuminated annular pupils are also considered, and, as an example, Gaussian illumination is discussed. It is shown that the standard deviation of an orthogonal primary aberration for a given amount of the corresponding classical aberration is somewhat smaller for a Gaussian pupil than that for a uniformly illuminated pupil.

Fourier treatment of near-field scalar diffraction theory

A general treatment of scaler diffraction theory is presented and some interesting concepts are discussed which yield new insight into the phenomena of diffraction throughout the whole space in which it occurs. The direct application of Fourier transform theory to the diffraction process results in two equivalent descriptions of the diffracted wave field: one describes the wave field as a superposition of plane-wave components and corresponds to the transfer function approach in linear systems theory, and the other describes the wave field as a superposition of hemispherical-wave components (or Huygen wavelets) and corresponds to the impulse response approach in linear systems theory. The convolution of the initial disturbance with the impulse response results in the well-known Rayleigh-Sommerfeld formula for near-field diffraction. This formula is then rewritten in the form of the Fourier transform integral of a generalized pupil function which includes phase variations in the diffracting aperture. Any departures of the actual diffracted wave field from that predicted by the Fourier transform of the aperture function are shown to have the same functional form as the conventional wave-front aberrations of imaging systems. These aberrations are precisely the effects ignored when making the usual Fresnel and Fraunhofer approximations.