Michael A. Golub

Infra-red radiation focusators

Abstract This paper presents the results of investigations in the field of diffractive or ‘binary’ computer-generated optics for the infra-red region of the spectrum. The problem of a CO 2 -laser beam focusing into a complicated focal domain is considered in detail. Special ray-tracing methods are elaborated to calculate the new analytic functions of diffractive optical elements, called focusators. The development of IR focusators into a ring, uniform planar spots, segments of a straight line, and other focal domains for the CO 2 lasers powered from several watts up to 3 kW is reported. Reflective-type focusators are manufactured by a specific microrelief technology that has some features in common with normal microelectronic technology. Experimental results for focused-beam interaction with rubber, wood, fabric, and plastics are presented for the case of a 30 -W laser. Effective laser heat-hardening of steel is achieved by 3 -kW CO 2 laser by means of a computer-generated reflective focusator.

Computer Generated Diffractive Multi-focal Lens

The method has been proposed for computing Fresnel-type multi-focal lenses on the basis of special-type phase nonlinearity. A multi-focal lens is represented as a mathematical superposition of a thin lens and nonlinearity distorted Fresnel lens. Selection of the nonlinearity type is reduced to the problem of the groove form determination for the phase diffraction grating with pre-set energy distribution between orders. In particular, bi-focal lens and seven-focal lens have been investigated.

Software on diffractive optics and computer-generated holograms

The `Quick-DOE software for an IBM PC-compatible computer is aimed at calculating the masks of diffractive optical elements (DOEs) and computer generated holograms, computer simulation of DOEs, and for executing a number of auxiliary functions. In particular, among the auxiliary functions are the file format conversions, mask visualization on display from a file, implementation of fast Fourier transforms, and arranging and preparation of composite images for the output on a photoplotter. The software is aimed for use by opticians, DOE designers, and the programmers dealing with the development of the program for DOE computation.

Experimental investigation of mode coupling in a multimode graded-index fiber caused by periodic microbends using computer-generated spatial filters

Abstract The results are described of an experimental investigation of mode coupling in a multimode graded-index fiber as a function of the periodic microbend amplitude. Computer-generated holograms were used as mode selecting spatial filters for measurements of the modal power distribution. The experimental data are in a good qualitative agreement with theoretical predictions. The results obtained may be helpful in the development of amplitude-type graded-index fiber sensors with high sensitivity.

The technology of fabricating focusators of infrared laser radiation

The possibility of fabricating focusators of infrared laser radiation, based on photolithographic technology, is analysed. The realizability of focusator fabrication is based on the possibility of producing a set of binary photomasks and achieving the necessary depth of etching the substrate of the pattern while forming the microrelief. The possibility of producing these photomasks is evaluated with regard to the focusators extremal zone width and the appearance of photomasks displayed on the screen. Forming of step-by-step microrelief is achieved using plasma etching or wet etching and depends on the minimum elements dimension and the etching depth. Examples of the microreliefs profiles, of focusators fabricated using photolithography, and the result of the transformation of a focusators radiation into a straight line segment, are discussed.

Computational experiment for computer-generated optical elements

The estimation of performance of computer-generated optical elements (CGOE) at the design stage is the actual task. In this paper the mathematical model of laser beam focusing by CGOE is suggested. On the basis of this model, the following results have been obtained: a numerical method for the diffraction computing of the field at the focal region, and also algorithms and software for investigating diffraction characteristics of focusators within the scope of computer simulation. The estimations of power efficiency, focal line width, and light intensity distribution at a focal region for various types of focusators vs physical parameters, number of samples, and number of quantization levels are obtained as a result of computational experiments. CGOE with an elevated depth of focus and focusator at semi-ring are investigated.

Phase coding in iterative synthesis of computer-generated holograms

A new method is investigated for phase-only hologram synthesis. The method combines iterative calculation of the hologram phase function with the coding of the amplitude-phase characteristics of the complex transmission function into phase characteristics. The results of computational experiments are presented. The phase masks and reconstructed object images are also presented.

Focusators at letters diffraction design

A new method is investigated for synthesis of computer-generated optical elements to focusate the radial-symmetrical laser beam into the complex focal contours--in particular, into the alphabetical-digital symbols. The method is based on decomposition of the focal contour by segments of the straight lines and half-circumferences, following corresponding spacing out of the focusator on elementary segments with a ring shape and solution of the inverse task of focusing from focusator segments into corresponding element of the focal contour. It was determined in the computer experiment that the theoretical efficiency of synthesized focusators into the letters is above 85%.

Phase quantization and discretization in diffractive optics

Theoretical description of phase discretization and quantization is provided for coaputer generated optical eleients (CGOK). Suitable estiiations of seanaquared and iaxiaui aberrations, Strehl nuaber and aean wavefront deviation are derived in dependence of discretization and quantization paraieters. A diffractive aberration corrector for thin len5 and also phase diffractive coipensator for aspheric wavefront foriation are investigated as exasples, 1 . PROBLEM OF CGOE D ISCRETI ZAT ION AND QUANTI ZAT ION. Wide-range possibilities of coaputer generated holograis and optical eleients1 are soietiies liiited by discretization of their phase transfer function. The known aethods for studying phase nonlinearities treat quantization as a superposition of iany diffraction orders but do not take discretization into account. In this paper coibined studying of discretization and quantization is perforied for siooth phase functions such as of zoned phase plates, coipensators, Fresnel lenses and siiilar type CGOK. Digital holography applications provide us coiputer generated optical elesents including kinoforis with purely phase-type transfer function r (t) exp{L.treod25rrrt (p(a)] (1) where • : (u,v) are 2-D Cartesian coordinates in the CGOIs plane, f (ii) is the phase shift perforied in point IT, iod2,,,tf ) is the value of p the aodulo (2ira), 1:1 or another positive nuiber. Coiputer-aided design of CGOK includes calculation of digital saiples for P function brought to [O,2%a) interval, driving suitable nak generator to access grey-level or binary iasks. Grey-level iasks used in bleaching or photopolyaer technology yield a CGO with variable iicrorelief thickness. Optical lithography with a set of binary aasks or iulti-stepped electron-beaw lithography yields aulti-level COOK described by quantization of P . Raster scanning iask generator set up all saska iI the field G fros so called resolution cells G7that are centered in i;point, enuierated by double index 1 : (i,,i) froi J set and obey the equations Q=,U G; , &!;flp=O if T (2) Masks spatial resolution is fully deteriined by the size of cell. This is the way that discretization of takes place and results in piecewise approxiiation of 1. Thus discretization and quantization are specific for CGOK and cannot be resoved. It should be noted that quantization take place also in holographic optical elesents lithographically fabricated fro. physical holograss used as aasks. Next parts of this paper are placed in the following sequence. For the first, zoie iatheaatical iodel is presented for phase discretization and quantization in CGOK. For the second, phase fluctuations are evaluated only on the CGOKs plane. For the third CGOKs light field is transforied to the plane at a soie distance fros CGOKs plane, soae characteristic are evaluated in general case and for such applications as iiage foriation and aspheric wavefront foraing.

Computer-generated optical elements for optical testing

Diffractive optical elements - compensator - permit to -form complicated optical wavefronts for tetinci complex optical surfaces in mirrors and lenses. In this paper the optical testing scheme has been considered as a transformator of optical transfer function of diffractive compensator into wavefronts with demanded form.