We demonstrate a new Z-scan measurement technique that permits the use of non-Gaussian beams and thick, as well as thin, samples. We expect that this technique will make possible the measurement of optical nonlinearities by the use of lasers that previously would have been unsuitable for this purpose, because of either inadequate beam quality or inadequate power. Another advantage of this technique is that it does not require detailed knowledge of the temporal characteristics of the laser pulse that is used.
In the cavity of a self-mode-locked (Kerr-lens mode-locked) laser, a noncircular beam experiences a nonlinear coupling between beam parameters in the x and y planes. This coupling produces a significant change in beam radii throughout the cavity and may result in more than one TEMOO cavity mode. The dramatic nature of this effect is demonstrated with the Ti:sapphire laser as an example.
Currently work is underway to establish standards for the performance verification of 3D imaging instruments including scanners, imagers, and flash LIDAR devices. This paper discusses the figures of merit to be considered in evaluating alternative methods, and it proposes specific ranging test protocols. Experimental results are reviewed. KEYWORD LISTscanner calibration, 3D measurement, 3D imaging, E57, ranging protocol, laser tracker, laser scanner I TRODUCTIOThree-dimensional (3D) imaging instruments measure the shape and size of objects or environments in three dimensions. These instruments are increasingly important in a wide range of applications, which depends partly on the maximum range of the particular imaging instrument. Short-range 3D imaging instruments have a maximum measurement range of up to a few meters. Many of these short-range devices measure 3D position using triangulation, although other methods are used.Mid-range imaging instruments measure up to a few hundred meters, and long-range imaging instruments measure up to many kilometers. One type of imaging instrument, which may be mid-or long-range, is flash LIDAR. This type of device is similar to a digital camera except that, besides providing angular irradiance information to each pixel, it also provides each pixel with a distance value.The main type of 3D imaging system considered in this paper is the spherically based laser scanner. This type of device, which may be mid-range or long-range, emits laser light from the origin of a spherical coordinate system and projects it onto an object of interest. The light scattered by the object is picked up by an optical detection system within the instrument. The light is converted into an electrical signal that is analyzed to find the distance to the target. Angle measuring means such as angular encoders are used to measure the angle of emission of the laser beam. From the combination of angle and distance information provided by the scanner, the 3D coordinates of objects in space can be found.Currently there are no widely accepted standards for procedures to verify the performance of 3D imaging systems. The committee E57 has been formed within ASTM to develop standards for 3D imaging systems. As a first step in the development of comprehensive standards, the committee is working on the development of a ranging protocol. The ranging protocol is a test method for checking the ranging performance of a 3D imaging instrument against a manufacturer's specification. The term "ranging" in here indicates that the instrument is checked along a preferred direction, which in the case of a spherically based laser scanner is outward from the instrument origin. Ordinarily the origin of the spherically based laser scanner is the instrument gimbal point.
A beam propagating in a nonlinear, dispersive medium can experience nonlinear coupling among its parameters in the x, y, and t dimensions. We derive two new computational techniques that account for this coupling. The first technique uses the beam-propagation method to solve three coupled differential equations, and the second uses six coupled second-moment equations. Nonlinear coupling is especially important for the operation of self-mode-locked (Kerr-lens mode-locked) lasers, an example of which is considered in detail in an accompanying paper [ J. Opt. Soc. Am. 13, 560 (1996)]. The two techniques derived here can be adapted to handle most of the physical effects of importance to self-mode-locked lasers, but we concentrate on the effects of diffraction, second-and third-order dispersion, and Kerr nonlinearity.
We compare three computational techniques developed in the preceding paper [J. Opt. Soc. Am. 13, 553 (1996)] that account for the effects of nonlinear coupling on light propagating through nonlinear, dispersive media. We demonstrate that all three techniques give reasonable accuracy under conditions typical of a self-modelocked laser. We further show that these techniques are greatly superior to techniques that neglect nonlinear coupling in that they give results that are more accurate and, in some cases, qualitatively different. We demonstrate such a qualitative difference by using the example of a self-mode-locked (Kerr-lens mode-locked) Ti:sapphire laser that has only one cavity solution when nonlinear coupling is included yet two cavity solutions when nonlinear coupling is neglected.
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