Precise Laser Beam Analysis
November 25, 2008
High-resolution wavefront sensors help improve the alignment of the optical systems involving lasers; control and predict the shape of laser beams; measure collimation of the beam and detect the tiniest aberrations caused by optical elements in the optical setup, thus protecting sensitive components of laser chains. Combined with wavefront correction elements and a command-and-control system in an integrated adaptive optics setup, they can help improve the laser spot quality.
Laser beam profiling plays an important role in such applications as laser welding, laser focusing and laser free-space communications. In these applications, laser profiling enables operators to capture the data needed to evaluate change in beam width and determine the details of the instantaneous beam shape, allowing manufacturers to evaluate the position of hot spots in the center of the beam and the changes in the beam’s shape.
There is a strong relationship between the performance of the laser in materials processing and the laser beam parameters in the laser material processing zone. However, the design of a laser system with optimum beam quality in the process zone is a challenge. The main tasks involved in the design of an optimized optical system are obtaining a high-quality beam, shaping the beam to the desired properties and transferring it efficiently to the process zone without distortion.
Besides beam power and polarization, the transverse beam dimensions and their change during propagation are the most important characteristics of laser beams. The transverse propagation properties of any stigmatic beam are fully determined by the beam waist, the distance from the waist and the divergence angle of the beam. The combined determination of all beam propagation parameters is usually performed by recording the free-space propagation of the beam widths at several planes transversal to the direction of the laser beam propagation. The profiles are displayed as contour maps of the beam intensity, a 3-D map or a profile. From the beam profile data at several transversal planes, the beam-propagation factor M² is derived. This parameter quantitatively compares the propagation characteristics of the real beam to those of a pure TEM00 Gaussian beam. For a given input beam width and lens focal length, this comparison allows the exact focused spot size to be predicted, as well as the irradiance of a focused spot, the Rayleigh range over which the beam is relatively collimated and the far-field divergence of the beam.
Wavefront is another characteristic of the beam yielding information about local energy flow within the beam. In a laser beam having plane wavefront, all the energy is flowing along parallel lines, so that the beam stays fully collimated irrespective of the position along the beam’s propagation direction. In contrast, focused beams feature concave wavefronts that allow the beam to concentrate the maximum energy in one place at the waist of the beam.
The wavefront displays the direction in which a given segment of a laser or optical beam is travelling. It intuitively and directly displays those components in the beam that are contributing to the beam eventually diverging from a straight-line, parallel-collimated beam. In this sense, it presents a more detailed insight than simply measuring the divergence angle itself. The picture of the wavefront provides insight into beam structure and calculations obtainable from a wavefront measurement provide quantitative insight into beam performance. Wavefront measurements provide all the aberrations in the laser beam and use this information to compute the modulation transfer function (MTF), which is used as an indication of the quality of transmission of spatial frequencies of the optical elements in the laser beam’s path.
Wavefront information is a valuable supplement to beam profile data. It provides the information necessary to predict possible future beam distribution without having to measure the beam at several transversal planes, thereby allowing better determination of the waist of the beam. It also provides more detailed information on propagation characteristics of the beam in an optical system. Wavefront data can provide more precise information on a beam nearing focus.
The wavefront analyzers currently available on the market can only provide the low-resolution wavefront data and, in the best case, low-resolution intensity distributions. Therefore, for a comprehensive laser measuring system, both a beam profiler and a wavefront sensor usually would be needed as separate instruments. In these “analog” wavefront sensors, special hardware components transform the light intensity into interferometric fringes (as in shearing interferometers) or in a series of spots (as in Shack-Hartmann sensors), so that the original high-resolution intensity data are lost and can only be captured by an independent camera.
Analog Wavefront SensorsIndustrial wavefront sensing has its roots in astronomy when in 1980 an array of micro lenses was used to improve on the transmission efficiency of wavefront sensing for low-light situations. This new Shack-Hartmann technology achieved its maturity in 1990 when wavefront sensors first became commercially available. The race for higher resolution wavefront sensing has resulted in development of wavefront sensors based on the multilateral shearing interferometry introduced in 1995 and in wavefront curvature sensors in 2000, both systems using 2-D diffraction gratings. These instruments are analog; to achieve better parameters such as dynamic range, sensitivity and resolution, they resort to a mix of more or less complex optical hardware components and electronics.
In Shack-Hartmann sensors, the surface of a wavefront is decomposed into elementary sub-wavefronts by a grid of micro lenses placed at the plane of wave front analysis. Each of the micro-lenses creates a beam focused into a spot on a focal plane where a charge-coupled device (CCD) camera is placed. The displacement of the spot with respect to a pre-calibrated position (corresponding to an undisturbed wavefront) is proportional to the local slope of the wavefront. Detecting the spots and integrating their displacements all over the focal plane in a very short time results in an instantaneous estimate of the wavefront.
A disadvantage of the Shack-Hartmann sensors is the limited resolution, particularly in detecting higher order aberrationsto obtain a measurement of a wavefront at one point in the analysis plane, several square pixels are required. First Shack-Hartmann sensors were used in closed-loop adaptive optics systems in astronomic telescopes, where the speed of the measurement and its convergence to a perfect measurement over several iterations is of prime concern. Improving the resolution by reducing the area allocated to one spot leads to reducing the dynamic range of the sensor. Moreover, reducing the size of a micro lens leads to increased crosstalk between the micro lenses as each micro lens creates several diffraction orders with elevated side lobes. This leads to difficulties with identifying the centers of each spot. Placing a high-frequency signature on each micro-lens so that each spot could be recognizable increases the manufacturing cost of the micro lenses.
To improve on resolution, the lateral shearing interferometers feature a 2-D diffraction grating, whereby the incident beam is split into several sub-beams that interfere in the plane of the camera. The interference pattern created is processed and the local slope of the wavefront at the analysis plane is measured. The resolution of the lateral shearing interferometer is several times finer than that for Shack-Hartmann sensors. Historically, the lateral shearing interferometers were first used in off-line deconvolution of images, where the quality of measurement was important. In the lateral shearing interferometers, the distance between the analysis plane and the detector plane can be modified to optimize the ratio between the dynamic range and the resolution for a given application. As a natural generalization of the Shack-Hartmann sensors, the lateral shearing interferometers share the same disadvantages as the former, however in a lesser extent at the cost of increased complexity of micro lens manufacture and processing of individual interferograms.
To further improve on resolution of the wavefront sensing, in curvature sensors, the second-order derivative of the wavefront is estimated by measuring the longitudinal variation of the wave’s intensity. Real-time sensing of the two or more intensity profiles requires introduction of a parabolic-shaped diffraction grating with spatially varying period and pitch of the diffraction grating, with images recorded on a CCD behind the grating. Instead of using a periodic 2-D grating as in lateral shearing interferometers, a specially designed diffraction grating of curvature sensors serves to spatially separate two images of the beam as it propagates along the optical axis.
The resolution of the curvature sensors is the highest among the three major analog wavefront sensors, as roughly two neighboring pixels yield one measured value of the wavefront, whereas several pixels are required to yield one measurement point on the other two sensors. This resolution, however, comes at the expense of decreased allowed bandwidth of the wavefront as the grating is designed for a specific central wavelength, increased light energy required to measure the wavefront as the division in diffraction order splits the light energy, increased complexity of the grating and therefore, higher cost of manufacturing special diffracting elements.
Today, the conventional wavefront sensors are handicapped by use of complex hardware elements. To achieve the better resolution required by advances in the industries where wavefront sensors are used as quality control tools, they need be equipped with still more complex hardware components such as special micro lenses containing high-frequency signatures or rotations for better localization of spots and for reducing the cross-talk between lenses, or complex multiple-order 2-D tri- or tetrahedral diffraction lens arrays. Despite their use in a relatively broad range of optical frequencies, the use of the sensors in a UV, IR or X-ray radiation spectra rely upon hardware components specially designed for the given application or wavelength.
Moreover, these sensors do not allow simultaneous measurement of high-resolution intensity and wavefront of a laser beam since they transform the original intensity data in intermediary data (as with interferometric fringes or spots), from which low-resolution wavefronts are computed. Thus, for a complete characterization of a laser beam, they require additional digital cameras to capture intensity information. Digital wavefront sensors enable operators to measure the high-resolution intensity and wavefront simultaneously in one plane and predict the propagation of the laser beam through the focal plane and beyond.
Digital Wavefront SensorsThe term digital associated with digital wavefront sensing technology means the minimum use of hardware components and the intensive use of specialized algorithms. As technological innovation, the digital wavefront sensing technology is based on the prevalence of software as compared to conventional use of hardware elements to achieve highest wavefront sensing performances.
The digital wavefront sensors rely upon measurements of the energy redistribution in the 3-D space. As curvature sensors, they measure the variation of the wave’s intensity in the optical axis direction, while as Shack-Hartmann and lateral shearing interferometers, digital wavefront sensors measure the redistribution of the wave’s intensity in the transversal direction. The measurement of the intensity in 3-D in real time leads to the high-resolution measurement of the wavefront with no use of the hardware diffracting elements or micro lenses at the cost of increased computational effort. The evolution of the beam through space is sensed by projecting the beam corresponding to different planes transversal to the optic axis onto a CCD camera, de-multiplexing the images and applying complex fast mathematical differential equation solvers to obtain the beam’s wavefront.
Today’s digital sensors typically have sensitivity of l/100 over the entire dynamic range of several hundreds of wavelengths. The resolution of about 250,000 measurement points per aperture diameter of 5 millimeters is achievable. With no use of hardware elements, digital wavefront sensors are suitable for measurements in a broad illumination frequency spectrum, from UV to X-ray. Although these performances come at the cost of increased computational burden, it achieves the measurement frequency of 15 hertz or higher. Digital wavefront sensors can measure tilts, divergence and convergence of the wave fronts, thereby reducing the burden onto the adaptive optics and thus the capability of measuring very rapid turbulence phenomena. Digital sensors boast considerably relaxed “resolution vs. dynamic range” trade-off.
Digital sensors open up new opportunities for laser beam characterization. When used in measuring aberrations (wavefront deformations) in laser beams, the high resolution in wavefront reconstruction coupled with straightforward measurement of light intensity allows predicting the behavior of the laser beam near focus with more accuracy. This helps to determine the exact position of the beam’s focusing point, compute the waist and divergence of the laser beam and thus beam-propagation factor M² more accurately when the current low-resolution analog wavefront sensors such as devices based on Shack-Hartmann or shearing interferometers.