Nicholas George

Hybrid diffractive-refractive lenses and achromats

Hybrid elements containing optical power with both diffractive (holographic) and refractive components are shown to be useful for obtaining arbitrary or, in special cases, achromatic dispersive characteristics. In one configuration a volume holographic element is coated on the surface of a crown glass lens, and by varying the power distributions among the refractive and holographic components while maintaining constant overall optical power the effective Abbe V numbers of the resultant hybrid element are shown to span all real numbers excepting a narrow interval around zero. In the achromat case (V number = infinity), both refractive and diffractive components are of the same sign resulting in much smaller glass curvatures than in all-refractive achromat doublets or apochromat triplets. The large separation between holographic partial dispersions and available glass partial dispersions is shown to lead to hybrid three-color achromats with greatly reduced glass curvatures. Applications are expected to include broadband achromatic objectives and chromatic aberration corrector plates in high performance optical systems. Such corrector plates may have any net power (including zero) while exhibiting effective V numbers that are positive or negative and that span a wide range, e.g., +/-1 or +/-1000. Further advantages include reducing the need for choosing high dispersion glasses, which may be costly and difficult to grind or polish. High diffraction efficiency and broad spectral bandwidths (in excess of 3000 A) are obtained in the holographic optical elements using single-element central-stop and cascaded element designs.

Electronic imaging using a logarithmic asphere

Transmission functions are derived that are valid in the nonparaxial case for a class of lenses that will image a continuum of points along an optical axis to a single image point. This lens, which we call a logarithmic asphere, is then used in a digital camera. The resolution of the camera is limited by the pixel size of the CCD; i.e., it is not diffraction limited. Digital processing is used to recover the image, and image-plane processing is used for speed. We find a tenfold increase in the depth of field over that for the diffraction-limited case.

Theory of low-threshold optical switching in nonlinear phase-shifted periodic structures

The theory of phase-shifted nonlinear periodic structures operating in the stationary regime is presented. The transmissive properties of the structure are analyzed by solution of the corresponding set of nonlinear coupled-mode equations exactly. Extremely low switching intensities are found for the special case of λ/4-shifted structures. An all-optical low-intensity switching configuration that uses a wavelength-tunable source and a λ/4-shifted nonlinear structure is proposed. Advantages of the phase-shifted distributed-feedback design in all-optical switching applications are discussed.

Extended depth of field using a logarithmic asphere

Imaging systems are described which use a logarithmic asphere and image processing in order to increase the depth of field substantially beyond classical limits. A nonparaxial form of the diffraction theory integral for an impulse response is derived and evaluated in order to establish a precise expression for the transmission function of this asphere. This nonparaxial physical optics formulation provides results of fractional wavelength accuracy that enable one immediately to complete the design and fabrication of the optical system. Circularly symmetric aspherical lenses, either for single-lens cameras or blurring phase filters for use with commercial photographic lenses, have been fabricated using advanced grinding and finishing machines. Computer simulation studies are presented to show that a logarithmic asphere is capable of diffraction-limited performance over an extended depth of field. Experimental imaging results including digital processing by an inverse filter show a tenfold increase in the depth of field.

Computational imaging with the logarithmic asphere: theory.

A theory for an integrated system is described that combines a logarithmic aspheric imaging lens with maximum-entropy digital processing to extend the depth of field ten times over that of a conventional lens and to provide near-diffraction-limited resolution. Two types of logarithmic aspheres are derived that are circularly symmetric lenses with controlled continuous radial variation of focal length. The details of an iterative maximum-entropy algorithm are also presented. The properties of convergence and speed of the algorithm are greatly improved by introducing a metric parameter to adjust the weight of different pixel values of the recovered picture in each loop properly.

Optical switching in lambda/4-shifted nonlinear periodic structures.

We show that lambda/4-shifted distributed-feedback nonlinear devices can be used as an all-optical switch at relatively low input intensities. The lambda/4 shift opens a narrow transmission window whose peak position within the stop band depends on the input intensity, a feature that can be used for low-power optical switching. The nonlinear coupled-mode approach is used to analyze the stationary operating regime of such a device and determine the transmittivity as a function of the input intensity. A closed-form solution, rather than a numerical one, is found for what we believe is the first time.

Neural networks applied to diffraction-pattern sampling

While diffraction-pattern sampling has been widely applied in the classification of patterns, still its usage has been limited somewhat by the need to devise rather sophisticated algorithms. In this paper we describe sorting or classification of a variety of patterns with commercially available neural-network software together with the ring-wedge photodetector to supply optical transform data for the input neurons. With this combination of neural networks and diffraction-pattern sampling it is no longer necessary to write specialized software. The training and testing methodology is carried out for this new system, and excellent results are obtained for sorting thumbprints. In sorting thumbprints the neural network can be trained for orientation-independent or wide-scale size-independent classifications by use of ring-only or wedge-only input neurons, respectively. Separate experiments are described for the sorting of particulates. Again, these are cases in which writing appropriate software based on diffraction theory would be extremely difficult. Two interesting novel neural networks are obtained: one is for real-time control of a submicrometer colloidal suspension of CdS, and the second is for concentration measurements of 2.02-µm polyvinyltoulene spheres in methyl alcohol. Widespread new applications are predicted for this hybrid system that combines diffraction-pattern sampling and the neural network.

Analysis of nonuniform nonlinear distributed feedback structures: generalized transfer matrix method

A new method for the analysis of almost-periodic, nonuniform, nonlinear distributed feedback (NLDFB) structures is presented. A grating segmentation technique used for linear DFB devices is combined with the analytic solutions corresponding to a strictly periodic, uniform NLDFB device. The method is demonstrated for tapered, chirped, and phase-shifted structures. New results describing the operation of single- and multiple-phase shifted NLDFB are reported. NLDFB structures with a axially-varying effective Kerr index are also considered. >

Wavelength performance of holographic optical elements

A comprehensive treatment is presented for the diffraction efficiencies of transmission holographic elements and cascade lenses when subject to broad spectral and field angle detunings. Experimental measurements are made in support of our theory on holographic optical elements fabricated in bleached silver-halide emulsions and in dichromated gelatin. The theory of holographic grating diffraction efficiency is studied through two approaches. A numerical treatment based on the theory of thin grating decomposition is implemented and shown to be in close agreement with other theories. Additionally, a more approximate approach is pursued in which the volume grating is treated as a phased array of scatterers. The latter approach leads to closed-form formulas in addition to a simple physical picture of volume effects. It is found that three-element cascades can exhibit spectral and field angle bandwidths essentially as broad as two-element cascades and that these bandwidths are in excess of 2300 A and 7° respectively.

Cosinusoidal transforms in white light

Theory and techniques of white light interferometry have been studied to devise an optoelectronic hybrid for diffraction pattern sampling. For an incoherently illuminated input scene, we obtain an output intensity that is the 2-D spatial cosine transform of the input plus a bias term. The bias can be subtracted electronically to within shot noise fluctuation limitations. The optical system consists of a double-imaging interferometer with a beam-splitter cube and crossed right-angle-prism reflectors followed by an achromatic-optical-transform lens pair. A photodiode array is placed in the optical transform plane, and this is coupled to a digital computer for further signal processing. Theoretical results are presented for the synthesis of the cosinusoidal transform configuration. From Fresnel-zone theory, a general form is derived for the impulse response of a cascade of ideal thin lenses, and this is used to design Fourier transform achromats that are well suited to this application. Experiments are presented showing cosine transforms for rough objects and for objects in reflection using illumination of negligible spatial coherence at the object. Excellent sensitivity is obtained with the bias subtraction, and a high space–bandwidth product is attained for the system.