Calculation of beam diameter of He-Ne Laser
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In every laser application, whether in medical, industrial, laser printing, marking, welding and
cutting, or fiber optics, the beam profile provides valuable information for the most efficient use
of the laser. Beam profiles are very commonly the principal measurement in practical
applications found in industry. The beam profile tells all about the beam’s spatial characteristics,
which in turn describe the propagation, beam quality and utility of the beam. In addition, it can
tell how effectively optics are succeeding in modifying and shaping the laser’s output. Profiling
is particularly helpful in building optical systems for laser printers and fiber optic collimators.
What is Beam Profiling?
Spatial characteristics describe the distribution of radiant energy across the wave front of an
optical beam. The radiation can be shown as a plot of the relative intensity of points across a
plane that intersects projected path of the beam. The most basic measurement of the beam’s
irradiance is a single number defining its width or diameter. Since optical beams do not actually
have sharp physical edges, the beam width is made between two points that contain a selected
percentage of the “useful” energy. When beams are Gaussian, or at least approximately
Gaussian, the common value for this measurement is at the 1/e2 diameter. This is the point at
which the beam contains 4-sigma of the energy distribution and occurs where the beam’s power
is at 13.5% of the maximum height. Another common measurement is at the full-width-half
maximum (FWHM) level, where the power drops to one half of the maximum. The beam
diameter measurement, by either method, allows one to determine other important features of the
spatial irradiance pattern of the beam. According to wave front propagation theory, light waves
diverge, causing the beam diameter to increase as it travels along the beam path. The rate at
which the beam diverges is an angular term known as the divergence, denoted as θ (theta). The
point at which a beam width is at its minimum size is known as the beam waist (D0). By
measuring the beam diameter at various points along the axis of propagation, known as the z-
axis, the divergence and waist characteristics of the beam can be determined. Beam profiling is
the act of sampling the beam size along the z-axis and thereby determining its spatial
characteristics. The net result of profiling yields an image of the beam’s energy pattern.
Techniques to make these measurements have included mode cups, phosphors, infrared cards,
Plexiglas blocks, burn papers and film. These crude techniques do not provide numerical values
and thus require a subjective evaluation of the image. More precise instruments for measuring a
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