Gaussian laser-beam-diameter measurement using sinusoidal and triangular rulings

Intensity influence on Gaussian beam laser based measurements using quadrant photodiodes

In many measurement applications using quadrant photodiodes, the signal is normally obtained from integrated devices incorporating current-to-voltage amplifiers that provide the necessary difference outputs with amplification. Quadrant photodiodes permit two-axis laser beam size and beam deflection determination. We show here that photodiode saturation, nonlinear characteristics of amplifying circuits, and voltage clipping features meant to prevent the output of a circuit from exceeding a predetermined voltage level to distort applied waveforms, play a significant role in measurement at low and high intensity levels, respectively. These two factors conspire to underestimate laser beam size measurement. A best-fit computation of the size versus power trend was found to permit satisfactory estimation of the beam size as well as the optimal laser power to be used. The intensity of light was also found to strongly affect the sensitivity of beam deflection measurements, in which a correction based on best-fit computation was deficient. In this case, calibration steps would be needed when light levels changed.

Diffraction of Gaussian beams by periodic and aperiodic rulings

The diffraction of Gaussian beams by periodic and aperiodic rulings is considered. The theory of diffraction is based on the Rayleigh-Sommerfeld integral equation with Dirichlet conditions. The transmitted power and the normally diffracted energy are analyzed as a function of the beam radius. Two methods to determine the Gaussian beam radius by means of periodic and aperiodic lamellar gratings are proposed. One is based on the maximum and the minimum transmitted power, and the other one considers the normally diffracted energy. Small and large Gaussian beam radii can be treated with these two methods.

Generalization of the Ronchi, sinusoidal, and triangular rulings for Gaussian-laser-beam-diameter measurements

Transmittance (or reflectance) characteristics of generalized gratings are described for Gaussian-laserbeam-diameter measurements. The generalized gratings provide for accurate measurement of both small and large Gaussian beam diameters and are superior to the Ronchi, the triangular, and the sinusoidal rulings. Also the proposed generalized gratings account for all width variations of the opaque, transparent, and transitional regions within a selected ruling.

Full-wave rectified sinusoidal ruling for measuring Gaussian beam diameters

A novel full-wave rectified sinusoidal grating is proposed for the measurement of Gaussian laser beam diameters. It is found that this new grating provides accurate measurement for both small and large Gaussian beam diameters and has proved to be superior to the Ronchi, triangular, and sinusoidal rulings.

Diffraction and beam-diameter measurement of Gaussian beams at optical and microwave frequencies

Diffraction of a one-dimensional Gaussian beam by a slit is theoretically investigated. In the visible and microwave regions a new property of the diffracted energy is presented. Analytical expressions for the transmission coefficient and the diffracted energy at normal direction are obtained in simple practical form for experimentalists. These expressions suggest a simple method for measuring Gaussian beams of 1.5-microm diameter or larger.

Ronchi ruling characterization of axially symmetric laser beams

The application of the Ronchi ruling beam characterization method to axially symmetric optical beams is analyzed. Specific results are derived for the Airy and focused annulus diffraction patterns. Plots of the ratio of minimum to maximum transmitted optical power vs the first null radius of the beam functions show that for the Airy pattern and other focused annuli with obscuration ratios smaller than ~0.30, the method should be as useful as with Gaussian beams.

Waist parameter determination from measured spot sizes

A novel simple method of determination of waist parameters of a Gaussian laser beam as a consequence of geometric treatment of the problem is introduced. The method does not require any least-squares process, ordering of experimental data, or estimates of waist parameters.

Aperiodic ruling for the measurement of Gaussian laser beam diameters

The use of an aperiodic ruling for the measurement of Gaussian laser beam diameters has been analyzed. We show that aperiodic rulings can provide spot-size measurements over a much broader range than available with Ronchi, triangular, or sinusoidal rulings used previously.