It is the declared goal of the EUREKA project CHOCLAB (characterization of optical components and laser beams) to support standardization efforts in the area of laser beam radiation and laser optics as well as to contribute to the implementation of those standards in industry. The interaction and the benefits of development-related standardization and the pre-normative research accomplished in CHOCLAB are explained, particularly focusing on standardization efforts for test methods for beam widths, divergence angle and beam propagation. The standards system for test methods for laser beam parameters and laser optical components is described in order to provide information on ongoing activities as well as on already published standards and in order to encourage people to make use of these standards.

We have demonstrated both experimentally and theoretically that applying nonlinear optical processes can enable new devices to be realized which allow direct measurement of the power density of laser beams, determination of focal spot location and the beam waist size, as well as visualization and analysis of complex beams' profiles, determination of the beam quality factor and the Strehl ratio. Materials with non-absorptive nonlinearity allow in-line non-distorting measurements. Furthermore, the absence of absorption makes the devices applicable to high power laser beams, and in the focal plane. The resolution of the method is extremely high and is principally limited by the wavelength making possible parallel measurements for a large number of beams. Use of 'intrinsic interference' allows one to obtain high accuracy with simple schemes. We have identified liquid crystals as a highly suitable medium for these purposes due to their giant, non-resonant, and non-absorptive orientational optical nonlinearity.

We report preliminary experimental results on the use of a filter with a parabolic transmission profile for a direct measurement of the spatial variance of the intensity distribution of a laser beam. It is shown that by recording, at various planes, the maximum transmitted power through such a filter, one can characterize the beam without having to determine the corresponding intensity profiles. A simple parabolic fit of the data allows the determination of the required parameters for a second-moment-based beam characterization.

The accuracy in the measurement of beam parameters based on irradiance moments using CCD cameras and other matrix detectors has been the subject of several experimental investigations and round robin experiments. It turned out that the obtainable accuracy depends strongly on the detector system (signal-to-noise ratio, resolution) and on properties of the power density distributions to be measured. It is known that the width of slow decaying distributions (e.g. the far field of unstable resonators) is more difficult to be measured than the width of steep decaying distributions (as top-hat fields and super-Gaussian profiles) and that the measurement error increases with the size of the integration area. It has also been recognized that the determination of the offset level might be crucial for accurate results. But all of this knowledge is rather qualitative. In this paper we deduce analytically the obtainable accuracy in measuring moment based parameters as of function of the crucial parameters of the detector and the signal (the power density distribution). The statistical noise of the matrix detectors is assumed to be the fundamental cause of the finite accuracy, though there are some more potential sources of errors. Thus only an estimation of the lower bound of the obtainable accuracy will be given. When measuring beam parameters these results may be used to estimate the accuracy of the measured values.

This paper presents recent results on the experimental testing of characterization methods for laser beam power and energy density distribution as described in draft ISO standards ISO 11146 and 13694. The tests were carried out using various laboratory and industrial laser sources. The accurate and repeatable measurement of distributions is of particular concern. Attention has been paid to background compensation and noise reduction methods. Tests were made to calculate beam uniformity, goodness of fit, beam size and the higher order moments of beam profile data derived from various CCD array detectors. These methods are evaluated in the context of their usefulness for on line monitoring, final laser test, and laser R&D.

The characterization of light beams has devoted a lot of attention in the past decade. Several formalisms have been presented to treat the problem of parameter invariance and characterization in the propagation of light beam along ideal, ABCD, optical systems. The hard and soft apertured optical systems have been treated too. Also some aberrations have been analyzed, but it has not appeared a formalism able to treat the problem as a whole. In this contribution we use a classical approach to describe the problem of aberrated, and therefore apertured, light beams. The wavefront aberration is included in a pure phase term expanded in terms of the Zernike polynomials. Then, we can use the relation between the lower order Zernike polynomia and the Seidel or third order aberrations. We analyze the astigmatism, the spherical aberration and the coma, and we show how higher order aberrations can be taken into account. We have calculated the divergence, and the radius of curvature of such aberrated beams and the influence of these aberrations in the quality of the light beam. Some numerical simulations have been done to illustrate the method.

An aberration factor, that is a general characteristic of the wavefront of the beam, is defined in order to quantify the aberrations of a beam, using the second moment method. This parameter can be easily calculated and measured from intensity measurements. Some examples are given and it is compared with the aberration variance, and related to the Strehl ratio.

We have developed a two-dimensional Shack-Hartman wavefront sensor that uses binary optic lenslet arrays to directly measure the wavefront slope (phase gradient) and amplitude of the laser beam. This sensor uses an array of lenslets that dissects the beam into a number of samples. The focal spot location of each of these lenslets (measured by a CCD camera) is related to the incoming wavefront slope over the lenslet. By integrating these measurements over the laser aperture, the wavefront or phase distribution can be determined. Since the power focused by each lenslet is also easily determined, this allows a complete measurement of the intensity and phase distribution of the laser beam. Furthermore, all the information is obtained in a single measurement. Knowing the complete scalar field of the beam allows the detailed prediction of the actual beam's characteristics along its propagation path. In particular, the space-beamwidth product, M², can be obtained in a single measurement. The intensity and phase information can be used in concert with information about other elements in the optical train to predict the beam size, shape, phase and other characteristics anywhere in the optical train. We present preliminary measurements of an Ar⁺ laser beam and associated M² calculations.

Reconstruction of the complex field of a laser beam or of the complex field strength of a single ultrashort pulse ap0plying the page distribution function are discussed for two experimental examples.

It is known that the Fourier transform of an infinitesimally thin circular ring is a Bessel function. By fabricating a mask with zero transmittance except at a given number of concentric thin rings, we have generated a series of Bessel beams, each of which constitutes a diffraction-free beam. We show theoretically and experimentally that a proper selection of Bessel beams leads to a periodic pattern along the propagation axis, e.g. a self-imaging field is produced. The on-axis profile of the field is then expressed as the discrete Fourier transform of the beam incident on the mask. The position of the intensity maxima along the propagation axis provides a direct measurement of the curvature of the wavefront of the incident laser beam. We further propose to use a transmission mask with a specific distribution of thin rings as a method to measure the second-order moment of laser beams.

We report on the measurement of the output beam phase distribution of the high power, 30 cm aperture, Nd:glass laser HELEN using a self referencing cyclic radial shear interferometer. This near field interferometry technique for beam quality measurement is evaluated by comparison with measurements of the far-field intensity distribution. Results are also presented on the evolution of the thermal gradients and their effects on the transmitted wavefront quality through the final disc amplifiers following a laser shot.

We discuss the use of the truncated second-order moment as an appropriate way of getting rid of the troublesome divergence problem caused by hard-edge diffraction. This approach preserves the simplicity of the propagation law of the beam size and makes the beam-propagation factor nearly invariant when propagation in ABCD systems is considered.

Generalized moments for beams with or without diffraction influence are introduced. Their ABCD-transformation laws are shown theoretically as well as experimentally. The generalized moments are defined from the Wigner function with a window function which improves convergence of the moments integrals. The window function is applied in a covariant way so that the ABCD-transformation properties of the moments become evident. The determination of the generalized moments from beam intensity measurements and their behavior in optical systems is shown from numerically simulated data.

A liquid nitrogen cooled high precision CCD camera is used for a systematic investigation of the propagation properties of hard edge diffracted beams. The diffraction effects are generated by propagating a nearly Gaussian beam (K equals 0.98, lambda equals 632.8 nm) through circular apertures of different sizes. The apertures are chosen so that 1.5%, 5.9% and 14.1% of the total beam power are truncated. Propagation measurements are performed for two different beam caustics which are connected by a transformation with a nearly aberration-free focusing element. As a consistency test, based on the measured data of the first beam caustic the propagation properties of the second beam caustic are calculated, the results are then compared with the measured data of the second beam caustic. Furthermore the influence of the size of the integration area, taken into account in the calculation of beam parameters, on the results and their self-consistency are investigated in detail.

The characterization of non-paraxial radiation by moments is worked out. The Helmholtz equation is reformulated in terms of two equivalent first order equations of Schroedinger type. Left and right traveling parts of the solutions are separated and used to extract physically meaningful parts of generalized moments of the wave field. Based on the Schroedinger formulation the propagation behavior of nonparaxial moments is found.

Making use of the angular-spectrum representation of a radiation field a formula for the second moments 2(z)> is given, which applies to the propagation of non paraxial beams. The formula was originally derived by Belanger et al. [Bel94] for coherent fields and here it is extended to partially coherent fields. Formally a quadratic propagation law for the second moments 2(z)> is obtained. With the help of an equation of motion for the Wigner distribution function that accounts for non paraxial fields, analogous propagation equation for the second moments 2(z)> is derived, which yields a quadratic z-dependence of the moments as well. The coefficients, which in the paraxial approximation are identified as measures of the beam parameters, suffer in the general case from convergency problems. Therefore the field descriptions are modified in such a way that finite beam parameters exist. The effects of extending the beam propagation formalism form the paraxial approximation to the non paraxial region are studied with sample fields.

Reciprocal quantities are introduced in terms of the second moments associated with the near and far fields in wide- angle scalar wave propagation. Free fields are considered and conditions for the finiteness of the second moments are analyzed. Relations of the exact full-wave far field to the corresponding paraxial solution are established. Effects of polarization on wide-angle divergence are also briefly addressed.

In previous work, a new family of exact, closed-form, analytic solutions to the scalar Helmholtz equation was derived in the oblate-spheroidal coordinate system. The 0,0 order of this family represents a new mathematical model for the fundamental mode of a propagating Gaussian beam which is not limited to the paraxial region, but reduces to the traditional Kogelnik and Li model in the paraxial limit. This present work compares the higher-order terms of the spheroidal-Gaussian modes with both the Hermite-Gaussian and Laguerre-Gaussian modes. Distinction is made between magnitude and phase results for paraxial modes (Hermite, Laguerre, and spheroidal) and nonparaxial ones (spheroidal only).

It is known that only a single-mode beam is completely spatially coherent. In general, beams generated by lasers and other sources consist of several modes and consequently are spatially only partially coherent. In this tutorial paper we first review the basic concepts which are needed to characterize beams of any state of coherence. We then discuss some of their main properties and we show that partially coherent beams can have very rich behavior. For example, two beams may have different spatial coherence properties at the source and yet may give rise to the same intensity distribution in the far zone; or they may have different intensity distributions at the source but may generate far fields with the same spatial coherence properties. We also discuss some recent developments which have demonstrated that the superposition of two beams with broad spectra (low temporal coherence) may result in a light distribution with a completely different spectrum; and that, moreover, the spectrum may be different at different points in the region of superposition. Both theoretical predictions and their experimental verifications are discussed.

The propagation of partially coherent beams through optical systems is modelled numerically in one transverse dimension. The systems are divided into different elementary elements, through which the propagation of light can be calculated by appropriate operators, working on the coherence function or the Wigner distribution function respectively. For the necessary changes between these two functions describing the partially coherent beams, the use of the remarkable z- transform seems to be an advantage. With this algorithm the grid and the resolution in the spatial frequency domain can be chosen arbitrary in contrast to the usual Fourier transform. The influence of phase aberrations on the focusability of Gauss-Schell model beams is discussed as an application example of the numerical model. With the help of this tool practical beam guiding systems can be simulated for the use with multimode laser radiation.

Different kinds of coherent Bessel-Gauss beams have been defined. We first analyze how these different sets of fields can be physically transformed into one another with simple optical means and illustrate how a superposition model of Gaussian beams allows this transformation to be clearly interpreted. This procedure leads to a complete characterization of these beams. We then recognize that partially coherent beams radiated by JO-correlated sources endowed with a Gaussian profile of the intensity are a mixture of coherent Bessel-Gauss beams and therefore can be considered their partially coherent extension. With the same procedure used with the coherent beams we characterize the partially coherent beams. In the last case the influence of the degree of coherence is clearly evidentiated.

In This paper, on the basis of the generalized Huygens- Fresnel diffraction integral and by using the statistical- optics model of high-power lasers presented by Manes and Simmons at LLNL, the propagation and focusing properties of high-power lasers with amplitude modulations (AMs) and phase fluctuations (PFs) have been studied in detail. Numerical calculations for the apertured case have been performed, showing the dependence of focused field characteristics on the truncation parameter, Fresnel number of the system, phase fluctuations and amplitude modulations of high-power laser beams.

Laser beam profile measurements always involve integration of the incoming intensity profile over a finite time interval. Under this condition, the measured moments of the spatial profile of a time-varying laser beam are shown to follow the simple algebraic laws of propagation obeyed by the moments of the intensity profile of a purely monochromatic laser field. Transverse shifts of the intensity profile and angular tilts of the axis of propagation of a wandering beam, expressed as fluctuations of the first order moments of the beam, obey similar laws of propagation. The time-variance of first order moments actually propagate the same way as do second order moments. The moment approach thus provides a consistent description of the propagation of a wandering laser beam. Invariants can be defined to quantify the extent of the wandering, taking into account both transverse shifts and angular tilts. It is also possible to define a time-integrated M² factor, obtained by measuring the second order moments of the time- integrated fluence profile of a laser beam. The increase of this factor, as a function of the time of integration, provides a sense of the time scale and amplitude of the beam wandering.

Experiments have been conducted to evaluate the feasibility of conducting pointing stability measurements with a relatively low cost stand alone apparatus. These experiments also aimed at collecting beam wandering data for pointing stability measurement system engineering purposes. The system consists of two dual-axes position sensing detectors (PSDs) that simultaneously measure variations of the beam position in two different planes. Sample-and-hold circuits are used to synchronize measurements taken by both PSDs. Detector signals are amplified and processed analogically in order to obtain voltage outputs directly related to beam position. The output signals are then A/D converted for computations. Software allows pointing stability calculations as well as frequency spectrum analysis of position fluctuations.

A laser beam diagnostic device is presented, which allows the determination of the intensity profiles of high-power carbon-dioxide lasers with high time-resolution. The detector of this device consists of two linear arrays of room-temperature HgCdTe-detectors, arranged perpendicularly to each other across the center of the beam. The data of the 70 detector elements is acquired simultaneously at rates up to 15 kS/sec for single shot events and several 100 kS/sec for repetitive laser pulses. Due to a use of a digital signal processor (DSP) and an especially adapted software, the device is capable of analyzing the temporal behavior and the stability of the intensity distribution on-line. The calculation of the local variance and mean values enables the dependence of the laser's short- and long-term stability to be investigated due to changes in the resonator alignment, the stability of the power supply, the gas composition, etc. For the pulse-mode of a laser, its transient behavior, for example changes in the intensity distribution, can be determined with high time-resolution. This is achieved by the method of sequential equivalent time sampling. The calculation of further statistical functions by the DSP makes it possible to estimate the uniformity of the laser pulses on-line as well. Using a partially transmitting mirror in the beam delivery system, measurements can be performed during material processing.

We investigate from both a theoretical and an experimental point of view the dependence of the spatial parameters (integrated along the pulse length) of TEA carbon dioxide laser pulses on the presence of nitrogen in the gas mixture and also on the size of an intracavity diaphragm used to attenuate higher-order modes.

By taking the vectorial property of the (time average) energy flow density into account, the first and the second intensity moments of the nonparaxial vector beams are defined. The parabolic propagation law of the second intensity moment in free space is deduced by employing the Maxwell's equations. And then, as an extension of the M² factor of the paraxial scalar beams, the M² factor of the nonparaxial vector beams is introduced. In the condition that the beam width is greater than a few wavelength, the relation M² greater than 1 is proven by using the Schwarz inequality. Finally, the intensity moment theory is generalized for the propagation of general polychromatic and nonparaxial pulsed vector beams in free space except that the M² factor of the static beams is replaced by the characterization width W_c which is defined as the product of the minimum beam width in the near field and the divergence in the far field.

Loss-guided optical waveguides have propagation operators which are linear but not self-adjoint. The eigenmodes of such nonHermitian systems are then not orthogonal but rather are biorthogonal to a set of adjoint functions. If one wishes to expand an arbitrary wave in the eigenmodes of the system, it is tempting to find the expansion coefficients using the biorthogonality relation to obtain quadrature integrals between the propagating wave and the adjoint functions. We show however that a minimum least-square error expansion is obtained not by using these adjoint integrals, but by a more complex procedure based on inverting the eigenmode orthogonality matrix. For the particular case of Hermite-Gaussian functions having a complex-valued scale factor, expansions using the adjoint coefficients fail to converge under a wide range of circumstances, whereas the minimum-error coefficients converge and give much smaller errors under all circumstances.

An optical system is presented which transforms an arbitrary astigmatic beam into one of circular symmetry with twist. This holds for coherent and partially coherent fields. Experiments were performed with Gauss-Hermitian modes TEM_no, transforming them into ring-like structures of Gauss- Laguerre type modes. The theoretical results concerning intensity structure and beam propagation factor were confirmed.

As is well-known, pure-phase transmittances are not, in general, first-order optical systems. It thus seems that a simple ABCD-propagation law cannot be applied to this kind of transmittance. In other words, such optical elements could not be characterized by an overall ABCD matrix. The aim of the present contribution is to overcome this trouble. In fact, the propagation laws of the intensity moments of a laser beam through ABCD optical systems are generalized to include pure phase transmittances. This is done by representing the behavior of such transmittances by means of a 4 by 4 matrix, M, which can be handled, to some extent, as the ABCD-matrices associated with ordinary first-order optical systems. This formalism enables the application of ABCD propagation formulae to cascaded optical systems containing pure phase transmittances. Matrix M is applied, in particular, to determine the intensity moments and the beam quality parameter at the output of special quartic phase transmittances, namely, thin and thick spherically aberrated lenses.

A typical axially symmetric beam on paraxial free propagation maintains the same transverse shape as at its waist plane for a certain range along its axis. We introduce a general procedure for estimating this range.

In the present work we extend the intensity-moment spatial characterization to partially polarized beams by means of a generalization of the Stokes-Mueller formalism. A simple classification scheme of partially polarized beams is proposed and propagation laws through non-polarizing and polarizing optical systems are provided. Some invariant parameters are investigated and a general measuring procedure is pointed out.

We study the three-dimensional field distribution of a focused axially symmetric flattened Gaussian beam. As particular cases, we give the expressions of the intensity along the optical axis and at the focal plane. All our results are compared with those pertinent to the case of a converging spherical wave diffracted by a circular hole.

A continuously measuring carbon-dioxide laser power calorimeter designed for laser powers up to 25 kW is presented. The absorption of the detector is shown to be 99.98% at 10.6 micrometer and 99.1% at 1.06 micrometer. The flow-rate of the coolant is measured by determining the temperature increase due to an equivalent electrical heating of the coolant before the detector. An electrical calibration proves an accuracy of plus or minus 1% in the range from 40 W to 4 kW. A comparison with an instrument calibrated at the Physikalisch Technische Bundesanstalt (PTB) reveals a deviation of less than 0.5% at 850 W. The online-precision is limited by a relative and an absolute noise signal of 0.5% and 5 W, respectively. Methods to reduce the measurement errors occurring in the calorimetric design are presented.

Within the EUREKA-project 'CHOCLAB' a workshop was organized, where several partners analyzed the beam of an industrial carbon-dioxide laser device. The goal was to qualify the ISO 11146 standard by using different measurement techniques. This paper compares the results of the determination of the beam propagation factor and beam widths. The following test methods for measuring the beam width were applied: (1) determination of the power density distribution with a rotating pinhole device and subsequent evaluation of beam widths, (2) determination of the power density with a pyroelectric camera and subsequent evaluation of beam widths, (3) moving knife edge method. For the measured data various methods of evaluation were used. These include data processing with different filters, evaluation of averaged power density distributions as well as different algorithms for curve fitting. Despite the different methods of measurement and evaluation the results showed reasonable agreement. This proves the applicability of the ISO 11146 standard to an industrial carbon-dioxide laser device.

In the industrial application of high power lasers, the knowledge of the properties of the laser beam is of great importance. The definitions given in ISO 11145 and ISO 11146 are rather sensible and efficient from a mathematical point of view and as long as more or less perfect beams are considered. In real life, however, there are some problems. The major problems with beam characterization according to ISO 11145 and ISO 11146 are discussed on a basis of examples taken from measurements of high power carbon-dioxide lasers in industrial applications and environments.

A high power carbon-dioxide laser beam, sampled by a diffraction grating, is monitored simultaneously by a Hartmann sensor to measure the wavefront and by a pyroelectric matrix camera to obtain the far field distribution. The maximum sampling frequency of the Hartmann sensor is 1 kHz with a resolution of 10 (mu) rad for the measurement of the beam direction. The data of the pyro- camera can be analyzed with a maximum frequency of 5 Hz and the beam direction in the far field can be measured with an angular resolution of 50 (mu) rad. Both methods reveal a periodic change of the beam direction with an amplitude of nearly 50 (mu) rad and a periodic change of the beam divergence with an amplitude of about 150 (mu) rad. Far field profiles measured with the matrix camera show that the angular stability is limited by fluctuations of the power density distribution. These changes of the transverse beam profile are closely connected to fluctuations of the laser gas pressure, which are due to the gas pressure regulation system.

In the context of the international EUREKA project CHOCLAB 'Instruments and Standard Test Procedures for Laser Beam and Optic Characterization', it is especially important that work on new standards and test methods for the characterization of laser radiation and optical components should take account of the appropriately standards-oriented measuring technology which will be needed to realize and implement the new standards. The paper presents the latest results of research and development aimed at creating a metrological basis for the characterization of carbon- dioxide laser beams. It describes the current research status of a new, standards-oriented laser beam diagnostics unit capable of determining the power density distribution of the laser beam in the unfocused or focused beam, and based on the hollow needle principle. The paper indicates special features which need to be allowed for when using the moments method for a measuring system and discusses planning for this new measuring system with special reference to automatic measurement of the beam caustic and to the computation and graphic presentation of the beam parameters.

A laser beam may be regarded as a tool when it is used to cut, weld or harden metals. It is essential to achieve optimum, constant adjustment of the laser beam parameters, e.g. focal radius, focal position, intensity distribution, etc. Within relatively narrow limits in order to increase the quality and reliability of the products manufactured in laser beam machining units. A laser unit can be set-up and monitored optimally for a machining task by means of diagnosis and monitoring of the unfocused and focused laser radiation. This form of laser characterization forms the basis for constant product quality and process reliability. The power density distribution of a laser beam can be determined and the laser beam characterized with the aid of a hollow needle measuring system which has been developed for this purpose. By using suitably matched hollow needles, it is possible to perform such measurements in the free beam, but also in the laser beam focus, enabling us to measure the beam caustic. A variety of different types of projection are available for displaying the power density distribution, ranging from isometric projection to contour line displays. A modified form of contour line displays is especially suitable for determining beam parameters, e.g. the beam radius. Further laser beam or working beam parameters, like iterative determination of the caustic, short-short-term stability of the laser, Rayleigh length, etc., can be obtained using this method of measurement.

This paper describes the specific requirements for measurement of excimer laser beam profiles for standardized characterization 'of commercial excimer lasers. A corresponding measurement system is presented which allows a simultaneous characterization of energy density distribution in the near field as well as in the focal plane of a lens (far field). Specially adapted UV-cameras make possible sings pulse diagnostic. Beam widths are calculated from the digitized camera data by different methods corresponding to the proposals of ISO 11146 (second moment, moving knife edge, and moving slit) and the results are compared. In particular, the influence of background signals as well as the typical shape of energy density distribution in the near field to the determined beam widths are analyzed.

Based on the results obtained from two high peak power excimer lasers developed in the ENEA Research Centre of Frascati, equipped with different hard-edge unstable resonators, a comparison is made between the widely used M² beam quality parameter and a newly defined 'times- diffraction-limit' (TDL) factor, pointing out the different meaning of the two coefficients, the respective limitations, and their range of applicability. A simple setup for the beam pointing stability estimation is also proposed.

A laboratory system for comprehensive characterization of excimer laser beam parameters in both near- and far-field is presented, along with a description of calibration procedures for spatially resolving UV detectors which were tested with respect to linearity, sensitivity, uniformity and stability. The investigations also comprise improvements in the standardized evaluation of beam characteristics. A semi-analytical method for accurate background substraction based on the requirement that the integral pulse energy must not depend on the size of the integration area is described. This algorithm allows high-precision determination of beam diameters for both 'moving slit' and 'second moment' methods. Definitions for unambiguous evaluation of relevant excimer laser beam properties like plateau uniformity and edge steepness of homogenized profiles are proposed.

We have conducted thorough analysis of a vertical-cavity surface-emitting laser (VCSEL) diode which produces TEM_01* (donut) and higher-order modes. Our analysis includes the following quantities as a function of drive current: optical power, spectral content, relative intensity noise (RIN) up to 100 MHz, and beam characterization parameters. While this VCSEL produces higher-order modes which are not affected by optical feedback, its optical power (0.05 mW for TEM_01*), long term stability, and sensitivity to collimating lens position make it a doubtful candidate for use in a beam characterization round robin. Also, we hope to present recently acquired data from the diode-pumped tunable transverse mode laser developed in Berlin and tested at NIST.

Higher power laser diodes have been aged under various operating conditions to gain information on the long-term output power behavior. In particular, the degradation of cw diode lasers that are operated at constant output power or at a constant driving current are compared to each other. It turns out that the lifetime results and their comparability strongly depend on the 'end-of-life' criterion. Especially for constant power operation extrapolation of the lifetime for longer intervals might give inconsistent results if the degradation of threshold current and slope efficiency are not known. Aging tests at increased temperature have been performed to investigate whether accelerated lifetime tests give reliable results to estimate lifetime and degradation rate at nominal operating conditions.

The acceptance of laser material processing in industry is often detracted by relatively high costs. A generally adopted approach to overcome this drawback is the search for laser sources with higher efficiency and optical components with improved performance. A quite different and even more successful measure, however, is the purposive choice of beam properties for the particular task. As the interaction phenomena at the workpiece decisively depend upon them, quality and speed of the progress can be considerably increased. On the basis of several examples, the role of properties such as wavelength, polarization and 'beam quality' are discussed and the potential enhance the process efficiency by their proper use is demonstrated.

A simple model for a shape varying beam is evaluated with respect to the description of these beams by moments of second and fourth order. The influence of the beam shape parameterized by the fourth moments or the kurtosis on the power transmission of shape varying beams e.g. from unstable resonator lasers through step index fibers is studied in a simple approximation.

Laser beam characteristics related with the design of laser engraving systems combining scanning of a material surface together with mask projection techniques are studied in this paper. The laser beam intensity distributions have been displayed for different positions of the mask in the optical device, showing the ranges of movement at which it is possible to work with a high reliability of this type of laser systems. The concept of an effective circle of confusion from optical imaging is applied for determining a good image formation in laser engraving systems.

The geometric law of energy conservation is utilized in evaluating the phase transmittance function for Gaussian beam homogenizer. Numerical computation of the Fresnel diffraction integral leads to results very close to geometrical-optics predictions and confirms validity of this method of designing.

Optical and laser beams do not necessarily have smooth spatial and temporal distributions. These distributions may arise from the source itself -- e.g., multilongitudinal and/or transverse mode laser beams. They may be affected by the physical properties, distortions, refractive index variations and surface finish of the optical components and the optical coatings in the beam path. This paper discusses and shows examples of the influence of the various parameters on the transmitted beam quality and ultimately on the laser induced damage threshold and usefulness of the optical components themselves.

Hafnia-silica multilayer mirrors and polarizers were deposited by e-beam evaporation onto BK7 glass substrates. The mirrors and polarizers were coated for operation at a wavelength of 1053 nm at 45 degrees and at Brewster's angle (56 degrees), respectively. They were tested with a single 3-ns laser pulse. The morphology of the laser-induced damage was characterized by optical and scanning electron microscopy. Four distinct damage morphologies were found: pits, flat bottom pits, scalds, and delaminates. The pits and flat bottom pits (less than 30 micrometer in diameter) were detected at lower fluences (as low as 5 J/cm²). The pits seemed to result from ejection of nodular defects by causing local enhancement of the electric field. Scalds and delaminates could be observed at higher fluences (above 13 J/cm²) and seemed to result from the formation of plasmas on the surface. These damage types often originated at pits and were typically less than 300 micrometer in diameter; their size increased almost linearly with fluence. Finally, the effects of the damage on the characteristics of the beam (reflectivity degradation and phase modulations) were measured.

Two different damage mechanisms are observed in laser damage experiments in the long-pulse regime for coated metal mirrors, partial reflectors and transmissive windows. These damage mechanisms can be distinguished by their time of damage behavior and are interpreted as induced by either defects or stresses in the coating. For both mechanisms, analytical calculations of the temperature evolution show a good agreement with the experimental data. Some samples show both damage mechanisms. The separation of these mechanisms by the time of damage analysis is used to study degradation effects due to an S on 1 irradiation. The experiments show that the defect induced damage threshold is in most cases independent of S, while the threshold of the stress induced damage decreases in a first approximation logarithmically with S. The integration of the Nomarski-microscope in the experimental setup allows for an effective evaluation of the experimental data according to the damage probability method of the ISO-standard ISO-DIS 11254-2. Microscopic inspection reveals noncumulative damage phenomena during S on 1 testing, which may prohibit the use of non-microscopic online detection techniques.

There is a growing requirement for high power laser pulses to be delivered from the laser to the workpiece via a fiber optical cable. The power and energy handling capability of these fibers are affected by both linear and nonlinear effects including Raman and Brillouin scattering and are ultimately limited by the laser induced damage threshold of the fiber itself. This paper summarizes the power handling capability limits of such fibers and includes comments on recommended launching and delivery procedures.

The faulty microstructure of KDP samples having different bulk laser damage threshold (4 multiplied by 10¹⁰ W/cm² - 5.4 multiplied by 10¹¹ W/cm² was studied using the methods of the three-crystal x-ray diffraction and two-crystal topography on reflection. A correlation between the dispersion of the structure-sensitive parameters characterizing the microfaultness and the value of bulk laser threshold of samples cut off large KDP crystals was established.

A laser calorimetric technique is employed to measure absorptance and laser-induced changes therein on optical components at 248 nm. In BaF₂ a linear increase of absorptance with intensity is observed, but a pure two- photon absorption mechanism can be ruled out because the slope lessens towards shorter pulse lengths. Fused silica, at moderate energy densities, exhibits a reversible, linear absorption increase with energy density; an AR-coated sample mirrors the behavior of the uncoated substrate but discloses an added offset due to coating imperfections. In a series of measurements at constant irradiation parameters, uncoated substrates of Suprasil and CaF₂ reveal a slight exponential decrease in absorptance which might be attributed to surface cleaning or conditioning effects, and absolute absorptance is virtually independent of the sample thickness.

The intention of this paper is to contribute to the discussion on the characterization methods for laser components within the framework of CHOCLAB. We report on absorption measurements performed with a highly sensitive laser calorimeter at the wavelengths 532 nm and 1064 nm. Several types of sample holders have been tested for their performance and the results were studied with special regard to the influence of scatter light and other signal distortions. For the evaluation of the temperature data, different methods are employed and compared. Based on our practical and theoretical investigations, the practicability of the ISO/FDIS 11551 for calorimetric measurements in the visible and near infrared spectral range is discussed and possible refinements are suggested.

We present significant differences in absorption measurements at the wavelength 10.6 micrometer and in the near infrared or UV region. This behavior is due to the different materials and their thermal properties. Zinc selenide and copper optics and optics made of various salts have been investigated at 10.6 micrometer. In these cases negligible problems with the measurement and evaluation procedures were observed. At the other wavelengths of 1.06 micrometer and 248 nm the measurements were carried out on BK7 or silica substrates. The evaluation corresponding to the ISO/DIS 11551 was not clear. One reason for this behavior is the low thermal wave velocity, so that the signal will arrive with long delay at the detectors. Furthermore the spatial and the temporal temperature profiles depend on the substrate material and sample geometry our measurements and computer simulations show the influence of the temperature conductivity of the substrate material, the sample thickness and diameter and the distance between the sensors and the laser irradiated area on the obligatory calibration factor.

High quality optical components are of major importance for the development of new concepts and applications of carbon- dioxide lasers. Especially, as a consequence of the ever increasing output power of new laser systems, optical absorption has become a crucial topic for the production and commercialization of laser components. Therefore, activities for the standardization of optical absorption measurements were initiated in ISO/TC 172/SC 9/WG 6, which is dedicated to optics and optical instruments in lasers and laser related equipment. Recently, the corresponding standard document ISO/DIS 11551 on test methods for absorptance of optical laser components has passed the international voting procedure. For an evaluation of this standard practice, which is based on laser calorimetry, a round-robin test on optical absorption at 10.6 micrometer was started. In order to cover a broad range of carbon-dioxide laser optical components, different types of metal mirrors and transmissive ZnSe-optics were selected for the sample set, which was circulated between manufacturers and optical laboratories in the United States, the United Kingdom and Germany. This paper reports on the results of this experiment in respect to the new standard procedure described in ISO/DIS 11551. The contributions of the laboratories, which are based on a variety of different calorimetric measurement facilities, are compared and evaluated.

The development of a high repetition rate TEA-CO₂ laser chain has a number of difficulties that must be overcome. One of these difficulties is to predict the free space propagation of the beam. A low energy (approximately 100 mJ/pulse), high-quality, carbon-dioxide beam is amplified in a number of carbon-dioxide amplifiers to more than 1 J per pulse. On propagation through the amplifier chain the primary beam encounters several transmission optics. It was found that the beam parameters of the primary beam change dramatically for high repetition rate operation (greater than 100 Hz). The alteration in beam parameters is brought about by thermal expansion and refractive index variations known as thermal lensing. This phenomenon is caused by the thermal gradient introduced to an optic by absorption of a laser beam with a Gaussian profile. Thermal lensing caused by the aforementioned laser system in transmission optics was investigated. The influence of several types of transmission optics in the amplifier chain was studied and compared. It was found that the use of a specific substrate (KCl or ZnSe) is determined by the position in the chain. A marked increase in thermal lensing effects was observed with damaged or contaminated optics.

We report on the characterization of infrared materials using a phase measuring Twyman Green interferometer at 10.6 micron. Parameters studied are refractive index, wavefront distortion and optical homogeneity. The materials which were considered are CVD diamond, germanium and zinc selenide. Residual stresses coming from the manufacturing process and thermal stresses generated by absorption of carbon-dioxide laser light were measured and modeled.

Photothermal deflection measurements on optical components for 10.6 micrometer are presented. This technique is used to measure the photo induced deformation of the coated surface. The experimental results are compared to finite element calculations which allows the determination of the temperature and deformation profile at every point on the surface and within the sample. This comparison allows the determination of the thermal conductivity of the coatings. Although in the finite element calculations the coatings are approximated as only one single layer, we find a good agreement with the experimental results. The thermal conductivity of typical coated copper mirrors for 10.6 micrometer is found to be up to an order of magnitude lower than those of the corresponding bulk material.

Deviations of an x-ray mirror from its ideal shape, with errors as small as one arcsec, can severely degrade its overall performance. Because the mirrors in third-generation synchrotron sources are typically exposed to extremely high power and power density, their surfaces are very susceptible to heat-induced distortions, imposing demanding constraints on both the mirror design and construction. These x-ray mirrors are routinely measured off-line for their surface roughness and figures; however, in-situ diagnostics are much more rare. Knowledge about the deformation of these mirrors under high heat load enables one to check the mirror performance, to improve upon the mirror design and construction, and to verify the thermal deformation calculations as predicted by theoretical and finite-element analysis. In response to this crucial need, we have developed at the Advanced Photon Source a portable electro- optical system for real-time, in-situ monitoring of thermally induced surface distortions of synchrotron mirrors under high heat load. We employ multipass technique to magnify (mu) rad angular (or slope) deviations to within the resolution of a commercially available CCD camera (with 9- micrometer square pixels). This system has been demonstrated to have angular resolution of less than 1 (mu) rad (or 0.2 arcsec) and long-term stability of less than 2-(mu) rad) fluctuation over a period of 12 hrs., after digital signal processing. With the present camera, the system is capable of sampling one surface profile (at 8 discrete points) about every 2 minutes and can readily be modified into an adaptive mirror system with the necessary actuator hardware. The prototype system has been installed and tested, and those results are presented.

Characterization techniques that are appropriate for detecting surface topographic features on ultra-smooth laser optics are described. Thee include various types of microscopes, optical and mechanical profilers, and instruments to measure light scattering. Two special techniques are emphasized -- total internal reflection microscopy (TIRM) and scanning force microscopy (SFM). The importance of keeping laser optics contamination-free is emphasized.

Accurate interferometric measurement of large laser slabs requires spatial frequencies of 1 mm/cycle to 33 mm/cycle over a 100 mm field of view to be passed by the system with no more than 25% loss in modulation. To eliminate noise and artifacts due to strictly coherent imaging, many commercial interferometers employ a rotating diffuser on an intermediate image plane and relay this image incoherently onto a detector. Unfortunately, this process may adversely affect the resolution of the instrument. Through measurement of a sinusoidal phase grating and fused silica step, the transfer function a laser Fizeau interferometer was measured for both a system with and without the incoherent relay system. Results are compared to those predicted by diffraction theory. Studies of the effects of defocus and propagation on the measurement were also made. Using strictly coherent imaging dramatically increases the system's ability to measure features of high spatial frequency and allows the measurement requirements for laser slabs to be met.

The power spectral density function (PSD) is being employed to specify the surface finish and transmitted wavefront in the mid-spatial frequency regime for laser beam optics of the National Ignition Facility (NIF). The instrument used to measure the PSD is a phase measuring Fizeau interferometer. The phase map produced by the interferometer is digitally processed to create the PSD. Before one can use the PSD information, it is necessary to evaluate the fidelity of the interferometer spatial frequency response. Specifically, one must measure the overall transfer function of the instrument. To accomplish this, we perform a two-step 'calibration' process. We first measure a known precision phase object with the interferometer and then compare the measured PSD to an ideal numerical simulation which represents the theoretical PSD. The square root of the ratio of the measured function to the simulation is defined as the transfer function of the instrument. We present experimental results for both reflective and transmissive test objects, including effects such as the test object orientation and longitudinal location in the interferometer cavity. We also evaluate the accuracy levels obtained using different test objects.

The profile of a laser beam was transformed into a rectangular uniform profile using a fabricated mirror. However, intensity ripples in the transformed beam were observed. These intensity ripples resulted from small ripples on the fabricated mirror surface. The peak-to-valley height and the peak-to-peak distance of the ripples on the mirror surface due to the fabrication error are 1.2 mm and about 10 nm, respectively. We evaluated the effect of these small ripples on the transformed intensity profile by calculating the laser beam propagation characteristics. The calculated laser beam profile was similar to the actual beam profile, and exhibited intensity ripples. Therefore, the intensity ripples of the reshaped beam resulted from the small ripples on the fabricated surface with the peak-to- valley height of 1/60 lambda. These ripples on the fabricated surface were probably caused by the feed speed error of the x-y stage of the fabrication machine.

WYKO Corporation is designing and building 24' (61 cm) aperture phase shifting interferometers to aid in the manufacture and qualification of optics for the NIF (U.S. National Ignition Facility). The first interferometer is scheduled for delivery in early 1997. The 24' systems will be the largest commercially available phase shifting interferometers, and will use a megapixel CCD camera to give high lateral resolution. Some of the NIF optics will be tested at Brewster's angle, and that condition places unusual design requirements on the interferometer. The main effect of testing a planar optical element in transmission at Brewster's angle is that there is a large separation between areas of the element and the return flat, so that optical propagation effects become important. We describe our design of a large aperture phase shifting interferometer, and how it will be used to test the NIF optics.