Arbitrary Optical System Research Articles

Geometrical concept of the propagation of general Gaussian beams

The propagation of a general Gaussian light beam in free space and through an arbitrary optical system in paraxial approximation is described in terms of a pure geometrical optics concept. Also, several parameters that are introduced to express the general Gaussian beam are described more clearly. In general case some parameters compose a non-symmetric matrix which sense is explained through analysis of footprints with the help of ray tracing.

Polarization eigenstates of nondepolarizing optical systems

The characteristic equation for the Mueller matrix of an arbitrary nondepolarizing optical system is obtained and solved. Polarization eigenstates for all types of nondepolarizing systems are studied. An efficient method for obtaining eigenvectors of matrices as functions of eigenvalues is described.

Photographic reproduction of out-of-focus and distorted ocular imagery

The necessary settings and parameters were determined for ordinary camera and lens systems to faithfully reproduce out-of-focus and distorted imagery as it falls upon the retina of the human eye. Theoretic considerations of both geometric and physical optics were used to calculate the ‘relative blur’ and distortion produced by refractive error added to ordinary camera lenses as opposed to refractive error in an arbitrary thick-lens optical system bounded by air and fluid (i.e. the eye). In both the camera and the eye, ‘relative blur’ was determined to be directly proportional to dioptric defocus and to aperture size, and effectively independent of the focal length. Distortion of imagery was also found to be independent of the focal length. Photographs corroborate the theoretic findings. A given amount of relative blur, however, appeared somewhat greater when recorded on photographic film than when appreciated by the human eye. The Stiles–Crawford effect, the chromatic aberration of the eye, and neural processing probably each contribute to this difference. Previous investigators have grossly exaggerated blur and distortion in photographs intended to simulate ocular imagery and have drawn misleading conclusions from their results.

Polar forms of Mueller matrices of nondepolarizing optical systems

Polar forms of the Mueller matrix of an arbitrary nondepolarizing optical system are constructed and physically interpreted.

Dynamic laser speckle in complex ABCD optical systems

Within the framework of ABCD matrix theory an exact analytical expression is derived for the space–time-lagged photocurrent covariance that is valid for arbitrary (complex) ABCD optical systems, i.e., systems that include Gaussian-shaped apertures and partially developed speckle. General expressions are derived for the mean spot size and both the mean speckle size and the temporal coherence length. Additionally, a general description of both speckle boiling and speckle translation in an arbitrary observation plane is given. Included in the analysis is the effect of a finite wave-front-curvature radius for the Gaussian-shaped laser beam illumination of the target. The effects of diffraction and wave-front-curvature radius are discussed for both imaging systems and a Fourier transform system. It is shown that, whereas diffraction affects the speckle dynamics in both cases, a finite wave-front curvature affects only the speckle dynamics in the Fourier transform system. Further, the effects of finite detector apertures are considered, in which the effects of speckle averaging are included and discussed. In contrast to previous work, the obtained analytical results are expressed in a relatively compact form yet fully contain all diffraction effects and apply to an arbitrary ABCD optical system.

Simple model for calculation of distortion in an optical analogue subcarrier multiplexed CATV system

Composite triple beat and composite second order values of an arbitrary optical multichannel system are deduced from the results of two-tone measurements. The calculated results will be compared with results from measurements on multichannel systems.

Second-order statistics for wave propagation through complex optical systems

Closed-form expressions are derived for various statistical functions that arise in optical propagation through arbitrary optical systems that can be characterized by a complex ABCD matrix in the presence of distributed random inhomogeneities along the optical path. Specifically, within the second-order Rytov approximation, explicit general expressions are presented for the mutual coherence function, the log-amplitude and phase correlation functions, and the mean-square irradiance that are obtained in propagation through an arbitrary paraxial ABCD optical system containing Gaussian-shaped limiting apertures. Additionally, we consider the performance of adaptive-optics systems through arbitrary real paraxial ABCD optical systems and derive an expression for the mean irradiance of an adaptive-optics laser transmitter through such systems.

Optical system defect propagation in ABCD systems

We describe how optical system defects (tilt/jitter, decenter, and despace) propagate through an arbitrary paraxial optical system that can be described by an ABCD ray transfer matrix. A pedagogical example is given that demonstrates the effect of alignment errors on a typical optical system.

Optical beam wave propagation through complex optical systems

20We describe a novel formulation of light beam propagation through any complex optical system that can be described by an ABCD ray-transfer matrix. Within the paraxial approximation, optical propagation can be formulated in terms of a Huygens principle expressed in terms of the ray-transfer ABCD matrix elements of the optical system. We extend and generalize previous treatments to include the effects of finite-sized limiting apertures (i.e., diffractive screens) in the optical train, tilt and random jitter of the optical elements, and distributed random inhomogeneities along the optical path (e.g., clear air turbulence and aerosols). In the presence of limiting apertures the ABCD matrix elements of the optical system are complex. For the case of laser beam propagation and Gaussian-shaped limiting apertures in the optical train, we obtain analytical expressions for both the spot radius and the wave-front radius of curvature at an arbitrary observation plane and give illustrative examples of practical concern. In particular, analytical expressions for the fringe visibility obtained in a coherent laser interferometric system are presented. An analytical expression for the mean spot radius of a laser beam propagating through an optical system in the presence of tilt and random jitter is obtained. We also consider the propagation of partially coherent light through optical systems. In particular, we derive a generalized van Cittert–Zernike theorem that is valid for an arbitrary optical system that can be characterized by an ABCD ray-transfer matrix. Finally, the propagation of laser beams through a general optical system in the presence of distributed random inhomogeneities is considered. An explicit expression for the mean irradiance distribution of a Gaussian-shaped beam is derived that is valid for an arbitrary optical system. In addition, we derive an expression for the mutual-coherence function for wave propagation through an arbitrary optical system. In all cases the results are expressed in terms of the ABCD matrix elements of the complete optical system. The formulation of optical propagation presented here is a rather simple and straightforward way of determining the effects of finite-sized optical elements, tilt and random jitter, and distributed random inhomogeneities along the optical path. It is merely necessary first to multiply the relevant ray matrices together to find the complete system matrix and then to substitute this matrix into the expressions given in this paper.

Expansion of Coherence Functions of Stationary, Partially Coherent, Polychromatic Fields

The self-coherence function of stationary, partially coherent, polychromatic optical fields is written as sum of totally coherent fields and an autocorrelation term. Also, it is shown that spatially fully coherent fields (whose mutual coherence function corresponds to the autocorrelation term of the former expansion) may be written as sum of cross-spectrally pure fields. As an illustrative example of these developments, a Young's interference arrangement is analysed. The behaviour of each term of the foregoing expansion with respect to an arbitrary optical system is examined.

Geometrical optics field of general optical systems

Using the stationary phase approximation of the Kirchoff diffraction integral, we derive a general expression for the field in the image space of a point source for an arbitrary optical system. The concept of an “optical path matrix” (OPM), which is the Hessian of the point eiconal, is introduced. Luminosity, caustic surfaces, and evanescent fields are defined in terms of the OPM. Detailed consideration of the single-interface problem yields solutions in terms of the Gaussian, mean, and normal curvatures of the interface. A complete solution of the simple lens is given as an example of a system with two refracting surfaces.

First-Order Optics of the General Optical System

First-order imagery by rays in the neighborhood of some base ray traversing an arbitrary optical system is anamorphotic and characterized by the presence of astigmatism and image rotation. The relationships among these three attributes is discussed; in particular, the effects of requiring that there exist one or more pairs of conjugate points on the base ray. Some inaccuracies in the literature pertaining to the torsion of the image by a general system are cleared up.

A Class of Aplanatic Optical Systems

An arbitrary centred optical system is followed by two aspherical mirrors which are such that the complete system is exactly aplanatic. It is shown that the equations specifying these mirrors can be reduced to a first order linear differential equation and so the solution involves two quadratures. If these integrals can be evaluated then the mirrors can be specified exactly. If the arbitrary optical system is axially stigmatic then a particular solution of the differential equation can be found by inspection and the solution then involves only one quadrature. As an example the combination of two aspherical mirrors following a parabolic reflector to form an aplanatic telescope is solved exactly.