Design of a single-element laser-beam uniform cross projector
Amanda Bewsher and Wayne Boland
A single optical element has been designed that takes a Gaussian laser beam and expands it into a uniform diverging cross. The design and fabrication of such an element are described.
Key words: Optical design, laser-beam line projectors, structured light.
Introduction Laser-beam projection systems are widely used in the machine vision industry for precision alignment and for determining the three-dimensional shape of objects. A pattern of laser lines is projected onto the object, and the resulting beam deflections are used to determine the surface profile. Normally expanding a Gaussian laser beam into a series of lines results in a Gaussian intensity distribution along the projected lines. The resulting nonuniformity can cause major difficulties when detecting the deflected pattern. With the increasing use of silicon detectors, the problem of beam uniformity must be addressed because of the thresholding problem for the varying intensity along the length of the projected lines. For this reason there is a demand for uniform-intensity structured-light patterns. Many such projectors are now on the market, but to date there is no one single element that can produce a uniform diverging laser-beam cross, a pattern that is extremely desirable for precision alignment systems. In this Note we seek to rectify this and describe the design and fabrication of such an element.
Design Approach The design of a single-element laser-beam line expander that produces a uniform-intensity diverging line from a typical laser beam was described in a paper by Powell.1 He described a single two-dimensional optical element with two surfaces that he called
The authors are with the Optical Components Research Group, Herzberg Institute of Astrophysics, National Research Council, Ottawa, Ontario K1A 0R6, Canada.
Received 13 May 1994; revised manuscript received 8 August 1994.
the primary and the secondary. The surface shape of the primary is such as to cause the center portion of the laser beam to diverge more rapidly than that at the edges, thus producing a more uniform intensity. The surface shape that gives rise to this is a cylindrical-type lens with a small radius of curvature and a relatively large conic constant, which results in the center (most intense) portion of the laser beam seeing the small radius of curvature and thus undergoing a greater divergence than the outer edges of the beam, which are less intense because of the Gaussian profile of most laser beams. The surface shape is described by the two-dimensional equation
where c is the curvature and Q is the conic constant. For small radii of curvature the surface shape soon
reaches an asymptotic value as it moves away from the apex. This value is given by
The secondary surface merely increases the divergence of the laser line and does not affect its uniformity. It can be either planar or cylindrical. One such element with a divergence of 20° is shown (Fig. 1) along with its predicted intensity distribution at a distance of 1 m (Fig. 2).
To produce a uniform diverging cross, we used a modification to the above design method. The element is made up of four triangular quadrants, each of which is based on the cylindrical laser-beam line expander. Each quadrant produces a line of uniform intensity, and so by combining four of these cylindrical elements in the arrangement shown in Fig. 3, we
Fig. 1. (a) Side view of the laser-beam line expander. (b) Three-dimensional view of the laser-beam line expander.
can produce a diverging cross of uniform intensity. The amount of divergence depends on the radius of curvature and the conic constant of the quadrants in the same way that the divergence is determined in the laser-beam line expander. The beam is aligned with
the center of the element so that each quadrant receives a quarter of the light. When two of the cylindrical quadrants are mounted with their axes at right angles to the others, half of the light is spread into a horizontal line and the other half into a vertical
Fig. 2. Intensity distribution along the length of the projected line.
line. The intensity distribution produced by a 20° diverging cross element is shown in Fig. 4 at a distance of 1 m.
Because the system functions on axis, the only aberration present is spherical aberration, which is evident only at the extreme edges of the projected cross. This does not, however, limit the width of the projected lines that make up the cross because the only power in the segments is that which diverges the beam into lines, whereas in the other direction the beam sees only a window. The projected cross consists therefore of lines that are the width of the incident laser beam. However, because laser beams have a small natural divergence, this divergence must also be taken into account when the linewidths at a certain distance are calculated.
Fabrication To fabricate the element, a 10-cm-long cylindrical strip of BK7 is ground and polished to have the correct conic constant and radius of curvature to produce the required divergence for the laser-beam
Side view - one quadrant tilted upward Cross projected Fig. 5. Angular misalignment of the cylindrical axes in the y plane.
line-expander quadrants. The profile of this shape can be tested with a shadowgraph technique. The actual surface shape is projected with a 20× magnification, which is compared directly with the designed surface profile drawn on a transparency to a 20× scale. The strip is then cut into individual laser-beam line expanders that are ~ 1 cm long, and then they are polished to produce angles of 90° with the apex as the bisector. The four quadrants then must be cemented together to produce a single element.
Quadrant Alignment The alignment of the quadrants is critical because any angular misalignment between two opposite cylindrical axes in the x-y plane creates parallel lines (Fig. 5) instead of a cross. That is, the quadrants are not in the same plane but are inclined with respect to one another. Any angular misalignment between opposite axes in the y-z plane, that is, the axes are in the
Fig. 4. Intensity distribution along the length of the projected cross.
Fig. 6. Angular misalignment of two of the axes in the y-z plane.
Fig. 7. Displacement of the axes.
same vertical plane but instead of being a continuation of each other they have an inclination between them, causes the lines produced to diverge (Fig. 6).
A displacement between two axes in the y-z plane where there is no inclination (Fig. 7) is less critical than angular displacements. However, it causes one of the lines of the cross to appear slightly weaker in intensity than the other. The differing intensities are due to the centering of each quarter of the laser beam on the apex of each quadrant. If the axes are misaligned, it is impossible for each one to be centered properly. It is therefore extremely important that the quadrants are orientated correctly.
Concluding Remarks A single element that is capable of converting a laser beam into a uniform diverging cross has been designed. Two such elements, one with a 20° divergence and the other with a 5° divergence, have been successfully fabricated. Because of alignment difficulties it was found that the element with a greater divergence was in fact easier to fabricate because the apex was much sharper and therefore easier to locate.
A patent on this invention has been applied for and is pending certification.
The authors thank Ian Powell for useful discussions and valuable advice.
Reference 1. I. Powell, "Design of a laser beam line expander," Appl. Opt. 26,
