This paper is a summary of the International Standards Organization Working Draft covering laser beam width and propagation measurements. Included is a summary of the draft and discussion of the reasons for the recommended measurement methods. Problem areas and limitations are also presented.

A method is presented for describing the propagation of axisymmetric beams by expansion into Gaussian beams which are displaced axially relative to the entrance plane. If the position of the Gaussian beams' waists and their widths are properly chosen, the coefficients of the expansion can be found by means of fast Fourier transform (FFT) procedures. One disadvantage of propagation algorithms based on FFTs is that their range is limited by aliasing effects. The propagation length is then enhanced usually by enlarging the entrance plane and padding with zeros the transverse field range thus enlarging the size of vectors without increasing field details. An alternative approach is that of subdividing the propagation length into smaller steps and eliminating the leaking aliased field by introducing absorbing layers close to the boundaries of the transverse range. The method described here has significantly reduced aliasing effects due to the bound character of the Gaussian functions, thus enlarging the range of propagation of a single step. Another advantage of the method is that the sampling points are evenly distributed in the r² coordinate, following linearly the power distribution across the radius of axisymmetric beams.

Laser light through a very small aperture is magnified by a lens, and beam profiles are measured at various points on each side of the image plane. The profiles are compared with the calculations done on several computer propagation programs in common use. While useful results were obtained from all the programs, there were significant differences in the fine structure of the calculated profiles. This was true when comparing programs and also when using the same kind of program with different numbers of transformation points or range of the transform. The difficulty of using simple Gaussian beam propagation theory on diffracted beams is pointed out.

Measurement of the beam profile and/or beam width of a laser source is complicated by the fact that most detectors available are just too sensitive. Typical lasers measured in millijoules/cm² must be attenuated to a few 10s of nanojoules/cm². To maximize the photoreceptor's digitizer range and operate at a maximum signal-to-noise ratio, it is preferred that the input energy is controlled to just below the detector saturation point. The most common attenuation methods are either discrete in increment, narrow in wavelength range, or operate on a polarization principle that can produce erroneous results for many mixed-mode lasers. Metalized gradient pair attenuators suffer from nonlinear attenuation across the beam and/or multiple interference fringes. What is described here is a novel technique to continuously attenuate an incident laser beam over a ratio of 6300:1 or more (3.8 orders of magnitude). It can be adjusted to the nearest incremental transmission value of 0.005 (0.5 percent). It achieves this at near normal incidence, which is very important if the source contains polarization-dependent laser mode components. Photon, Inc.'s ATP attenuator package achieves this performance without interference fringes, bubbles, or stria and with a minimum of deflection or redirection. A broad wavelength performance also is achieved that ranges from 360 to 2,500-plus nanometers. ATP's primary application is with very sensitive CCD or vidicon array detectors that are capable of measuring beam sizes of a few hundred microns. ATP does this with virtually no root mean square wavefront errors. This device coupled with a high accuracy beam profiler will produce true accurate profiles and beam widths.

A high-speed imaging device based on a streak camera has been demonstrated, which provides multiple images from non-repeatable transient events of time scale >= 1 ns. It can be employed for pulsed laser beam diagnostics, measuring laser beam spatial and temporal structure on a single-pulse basis. The system currently has angular resolution of 16 X 16 pixels, with a time resolution of 250 ps. The laser beam width is sized to fill the input optic, and the image is dissected by a square array of optical fibers. At the other end of the fiber optic image converter, the 256 fibers form a line array, which is input to the slit of a streak camera. The streak camera sweeps the input line across the output phosphor screen so that position is directly proportional to time. The resulting 2-D image (fiber position vs. time) at the phosphor is read by an intensified (SIT) vidicon TV tube, and the image is digitized and stored. A computer subsequently decodes the image, unscrambling the linear pixels into an angle-angle image at each time. We are left with a series of snapshots, each one depicting the laser beam spatial profile (intensity cross-section) at succeeding moments in time. The system can currently record several hundred images over a span of 25 to 400 ns. This detector can study lasers of pulse width >= 1 ns and with a visible wavelength (200 - 900 nm). Candidate lasers include doubled Nd:YAG, excimer, ruby, nitrogen, metal vapor, and Ti:Sapphire. The system could also be simply configured as an 8 X 8 element wavefront sensor to record the cross-sectional distribution of phase, as well as amplitude. Finally, suggestions for system improvement are detailed, and the ultimate limitations of the method in terms of spatial and temporal resolution are discussed.

The energy distribution of Airy disk includes a lot of usef ul information of optical systems, through researchers and engineers in the field have developed several kinds of systems to measure the distribution < )). More convenient and low cost system is still required for general optics-related lab. In this paper , a microprocessor-based system for displaying three dimensional energy distribution of Airy disk on oscilloscope is discribed. A laser beam (to be measured ) goes on to a linear CCD camera which is on a table driven by a stepping motor. The output of the camera is received by a signal condition ing circuit and then to an A/D converter which is one of the interfaces of the microprocessor . CCD sensor drive and control , signal processing and signal output to an oscilloscope through D/ A converter is the task of the microprocessor. The sensor pixel area is l 4µm X 14µm , the resolution in X direction is 14µm , a superresolution arithematic method is emploied in Y direction , it leads to 2µm resolution , the method is discribed in detail in this paper. An experimental setup has also been developed • the Airy disk of a 0. 1mm diameter microhole dif fraction pattern has been measured with this setup , the resu lt has been analysed.

We present the results of a round robin in which six U.S. manufacturers of beam analysis instruments participated. Following a procedure recommended by the International Organization for Standardization (ISO), participants used a camera, pinhole, slit, or knife-edge to determine several parameters characterizing the beam of a common laser source. Their results and ours are displayed graphically and analyzed statistically. Agreement on beam width measurements is in a range around five percent relative standard deviation while significantly less agreement exists for other quantities calculated within the ISO procedure.

The spatial behavior of a certain class of depleted-center intensity beams is analyzed by introducing a number of characteristic parameters, including the concept of lateral mean position, lateral beam width, and lateral far-field divergence.

We show how FWHM, FW1/e², Strehl ratio, and encircled energy figures of merit vary with different types of aberration and measurement methods. We examine in detail the array sampling method and the slit-scan method. Our irradiance in the exit pupil of the optical system is a simple Gaussian. We found that in general the slit-scan method and the array method do not yield the same result. The width measurements for the central lobe of the diffraction pattern are very insensitive to aberration.

At present, the quality of a laser beam is defined by the parameter M² or divergence ratio. It is the ratio of the actual far-field divergence of a beam to that of an ideal TEM₀₀ Gaussian beam with the same size waist. It is important because it provides information on beam size for the design of beam delivery systems and on beam focusability for the design of applications which require a small spot size. This parameter, however, relates to the beam size which contains no information on energy distribution within the beam. By defining an additional parameter called the intensity or Strehl ratio which is related to the on-axis, far-field intensity of the beam, one has further information on the smoothness or sharpness of the beam. From an analysis of multimode beams composed of pure Laguerre-Gaussian (L-G) modes, this paper shows that the divergence ratio and Strehl ratio are independent and concludes that both ratios would be beneficial in specifying the `quality' of a beam. For specific cases, these two ratios uniquely determine the energy distribution of a multimode beam, even though the combination of L-G modes is not unique.

A novel method for measuring the beam quality of short, powerful laser pulses is presented. It is based on the Z-scan technique used to investigate the nonlinear susceptibilities of optical materials. We show that both two-photon absorption and nonlinear refraction of a nonlinear sample can be used to obtain information about the spatial quality of the pulses.

Accurate quantitative measurement of the spatial mode distributions of high power pulsed Nd:YAG lasers and their harmonics presents many challenges. This paper describes efforts to date on the characterization of near, mid, and far field beam distributions from Quanta- Ray^R GCR Series^R lasers.

As a leading manufacturer of pulsed lasers that vary from one millijoule femtosecond systems to 120 joule glass lasers, beam quality is very important to us as a measure of performance of the systems. Beam quality in the form of near and far field images are obtained for most of our systems and incorporated into our final acceptance test before leaving the factory, contributing to the total quality program we have initiated. Measurement of beam quality relies heavily on CCD cameras and supporting software that allow us to directly measure intensity profiles, pointing stabilities, and calculate M² and Fresnel numbers.

Most excimer beams are rectangular and have a top hat profile (flat top, steeply sloped sides) in the longer, horizontal dimension, with a near Gaussian profile in the vertical dimension. These rectangular beams are suitable for large area materials processing applications that require a certain degree of beam uniformity at the workpiece. Beam uniformity is usually described in terms of an allowable percentage variation in the energy density, or fluence, at the workpiece. This allowable variation is often referred to as the process window, which is often used to define the uniformity requirements of the excimer beam. But all excimer beams are not equal, and a beam which may be suitably uniform for one application may not be uniform enough for a different application. Thus, a knowledge of the degree of beam uniformity is very important when evaluating a laser for a given application. We have developed two beam uniformity specifications: the Top Hat Factor and Energy Fraction at 80% of peak fluence. We describe the development of these specifications and how they can be used to evaluate an excimer laser beam.

We present simple formulas for the degradation in beam quality factor M² of a laser beam caused by quartic phase aberrations, such as may occur in spherically aberrated optical components, thermally aberrated rods or windows, or divergent beams passing through planar dielectric interfaces, as in unstable-resonator diode lasers. The beam quality degradation in all cases is found to be small for beams smaller than a certain critical spot size w_q, but degrades as M² approximately equals (w/w_q)⁴ for beam sizes greater than w_q. Experimental results confirming the beam quality degradation from an uncorrected plano- convex lens are also given.

Diffractive focusing elements which eliminate spherical aberration in industrial CO₂ laser beam delivery systems are being manufactured. The theory of these elements as well as the experimental verification of diffraction limited performance are discussed.

Beam quality behavior of Hermite-Gauss modes and Gauss Schell-model fields propagating through super-Gaussian apertures are analyzed.

Two main approaches exist in order to generate laser beams with transverse profiles which depart from the common Gaussian shape: The use of graded transmission resonator mirrors and the use of aspheric mirrors. Aspheric, fully reflecting mirrors have the advantage of better power and energy handling and availability of reflecting surfaces at wavelengths where transparent materials are inconvenient to handle and eventually nonexisting. A beam synthesis method was developed by means of which it can be proven that any prerequired beam profile can be supported by a resonator based on either variable transmission mirrors or aspheric mirrors, in the empty-cavity approximation. The cavity will not, however, necessarily support the pre-required mode as the lowest-loss mode, and the gain profile of the amplifying medium has to be taken into account. Examples are presented in which cavity design improves the efficiency of the laser by coupling between the mode profile to the gain profile of the medium. Additional applications of aspheric mirror resonators include the matching of free-space modes to waveguide modes and shaping of beams according to subsequent beam handling requirements like focusing to preferred spot shapes for materials processing.

Using phaseconjugating mirrors (PCMs) the beam quality of solid state lasers can be improved by compensating the thermal lens of the rods at high average powers. Oscillators with one PCM as a highly reflecting mirror and double-pass amplifiers with PCMs have been investigated. PCMs are realized by stimulated Brillouin scattering (SBS). Nd:YAG and Nd,Cr:GSGG oscillators have been built with pulse repetition rates up to 45 Hz. Stable TEM₀₀-mode operation has been obtained. Average output powers of 10 watts for 15 ns Q-switched pulses of a Nd:YAG laser and 7 watts for Nd,Cr:GSGG have been achieved. In a double pass Nd:YAG amplifier the thermal lens was compensated leading to a nearly diffraction limited beam with a maximum output power of 40 watts.

The special requirements and possibilities of laser spatial intensity profiling in the UV spectral range are discussed in this paper, along with a description of a high resolution beam monitoring system. Especially developed for excimer lasers, this device allows real-time acquisition of beam profiles with various cross-sections from about 100 mm down to 100 micrometers . The acquired intensity distributions can be comprehensively analyzed, e.g., with respect to homogeneity, energy density, and energy fraction above a given threshold. In addition, we report on experiments with a highly integrating and high efficiency beam homogenizer consisting of crossed cylindrical lenses. It can be used to generate flat-top intensity distributions for nearly any type of input profile, also Gaussian. In combination with the laser beam monitor a high precision adjustment of the employed optics can be performed. The remaining non-uniformity of the obtained beam profile is in the range of 1%, allowing a variety of applications in material processing, medicine and spectroscopy, which strongly require a laterally constant energy density.

The results of solving the self-matching scattering problem of a p-polarized Gaussian beam on a diffraction grating of finite length near surface electro-magnetic wave excitation resonances are presented. The role of dismatching between surface electromagnetic wave lines on the grating and a plane surface, an incident beam plane-wave spectrum and a Fraunhofer factor of grating in finite size effects is defined.

The presented sensor for monitoring a high-power laser beam is based on an extension to a bending mirror in the beam path. The fraction of the light absorbed by the mirror causes a heat flow into the mirror. The laser beam intensity distribution can be determined by a spatial and temporal resolved measurement of this heat flow (or the resulting temperature gradient). A multi-element thermal detector has been applied onto the mirror surface in the form of a thin film system. The structured sensor film has a thickness of about (lambda) /100 and is embedded in the insulating layers. An additional metallic layer leads to a reflective surface. With this sensor beam characteristics, like the beam position, can be determined. Further applications have been mentioned.

A measuring device for the intensity profile of high-power CO₂ laser beams based on a linear pyroelectric detector array is presented. It enables the user to measure variations of the mode structure up to several kHz with a one dimensional spatial resolution. Periodic as well as stochastic fluctuations of the local intensity are analyzed, leading to fundamental considerations to characterize the temporal stability of laser beams. Simultaneously to the laser beam diagnostic, signals obtained from the cutting and welding process have been detected. By the comparison of these signals with the time-resolved measurement of the intensity profile, the influence of laser mode instabilities on the material processing is documented.

The main parameters used for describing the beam quality of CO₂ lasers are the Beam Quality Number, energy distribution, the geometry of the beam path including the beam waist diameter, position of the beam waist and the divergence of the beam. In this paper experimental investigations of the relationship between the beam geometry parameters and the processing performance are presented. The experiments have been carried out with a portable beam analyzing system developed at the Technical University of Denmark. The beam parameters are automatically detected within a few seconds from one single measurement in an arbitrary point in the beam path of the laser, and from these parameters the focus conditions of the beam are calculated. The experiments were made on a number of industrial used laser cutting systems in the power range 1 - 2 kW and a strong correlation between the beam parameters and the cutting performance is demonstrated. The investigations have furthermore demonstrated large possibilities for optimization of the optical systems when the beam parameters are known.

The performance of a high power laser in material processing is strongly dependent on the laser beam intensity distribution. In particular, the uniformity of the beam intensity during laser transformation hardening is a critical factor in the success of the process. The results of tests on a new class of beam-integrating infrared optics used in the transformation hardening process are presented here. These complex, multi-faceted lenses have been manufactured, assembled in laser processing systems, and tested in optical experiments that correlate laser beam characteristics, integrator performance, and successful process completion.

Measurements with a beam propagation analyzer of the mode characteristics of the cw dye laser as a function of pump laser input power and mode quality, indicate that the thermal lens (of cylindrical form, induced by pump absorption in the flowing dye) controls the dye beam mode quality. At high pump power, if the dye laser resonator is adjusted for maximum output power, a degraded quality dye mode results, which is lower for lower quality pump modes. When the dye resonator is adjusted for maximum output power density (a direct output of the analyzer), typically a 12% power drop is sufficient to produce a nearly perfect beam quality (M² < 1.1) and a +27% increase in beam power density for a multimode pumped dye laser.

With this paper a newly developed optical device for an active beam guidance and forming in CO₂ laser systems is presented. The availability of this additional tuning element in processing will solve current problems in beam delivery as well as offer new laser processing options. By integrating this optic in the beam delivery: (1) the process conditions can be improved, (2) the process influencing effects in beam propagation or delivery can be compensated, (3) the workpieces with complex structures and difficult accessibility can be processed in conformance with high quality standards, and (4) new laser processing options are possible.

A two wave mixing experiment using a Nd:YAG laser, operating at 1064 nm, and a photorefractive InP:Fe crystal resulted in a gain coefficient (Gamma) of 17 cm^-1 and a signal gain (gamma) of 15. In the case of a (pi) /2 spatial phase shift between the light interference fringes and the refractive index grating, phase cross talk is eliminated. Amplitude cross talk can be eliminated using volume hologram averaging of the beams. With this scheme a weak Gaussian beam is amplified by a pump beam containing strong phase and amplitude aberrations. Energy efficiencies of 27% were obtained under preservation of the nearly diffraction limited beam shape.