(Photonics Spectra - August 18, 1999)

Laser Scanning System Design:

**Choosing Elements to Fit the Nature of an Application**

Glenn E. Stutz

Lincoln Laser Company

Laser scanning is finding new applications as society moves from an industrial age to an information age. Laser scanners can be used to write information on a medium, as in machining, welding, printing and projection; or to read from a medium, as in robotic vision systems, inspection systems and densitometers.

Laser scanning can be divided into raster and vector applications. Selection of the scanning element depends on the nature of the desired scan. Galvanometers are excellent vector positioners, as are acousto-optic deflectors and peizo-driven mirrors. Raster applications requiring high speed lead one to decide between polygons and hologons. The polygon is a multifaceted spinning hologram.

This article deals primarily with polygonal deflectors and the associated beam-control optics. All of the deflectors mentioned above need similar beam-control optics. Advantages and disadvantages of each type of deflector are covered in Table 1 (The Photonics Design and Applications Handbook, 1999, pg. # H-375).

**Preobjective vs. Postobjective**

The first parameter to specify in setting up a scanning system is the number of resolvable points along a scan line. In the case of a line scanner, fewer than 10,000 points are relatively easy to accomplish. The range of 10,000 to 25,000 points requires additional complexity. If the system requires more than 25,000 points, be prepared for quite an exotic system.

The number of resolvable points together with the spot size and allowable spot size variation determines whether the system will be of a preobjective or postobjective type, figure 1. (The Photonics Design and Applications Handbook, 1999, pg. # H-374).

Postobjective scanning is the lower-cost alternative, and should be evaluated first to determine whether its drawbacks are acceptable. Postobjective scanning is used when the target plane can be curved, or when the depth of field is large and the scan angle is relatively small.

In preobjective scanning, a high-quality F-theta scan lens or mirror systems is used to produce a flat field and linear scan velocity on the target. In postobjective scanning, the final focusing element for the line-scan axis is located prior to the polygon.

The design of a polygonal scanner can include either an underfilled or overfilled facet. An overfilled facet design typically illuminates two adjacent facets with a single beam. This design approach yields high-duty cycles but at the expense of power, variations in spotsize, and beam intensity uniformity.

An underfilled design uses a beam significantly smaller than the facet length. This design approach yields higher power and beam intensity uniformity at the expense of efficiency. The duty cycle with this type of design is in the range of 40 to 80 percent. The larger the facet length for a given beam size, the greater the percent of time is spent in active scanning. The dead time with this scanner design is the time that it takes the beam to cross over the edge of the facet. The need to achieve greater duty cycles results in larger polygons.

**Polygon sizing**

After the number of resolvable points (N) has been specified, an active scan angle

(Theta) or an agular resolution must be selected. In the case of a postobjective system, an angular resolution or scan angle can be specified. The relationship between these parameters is given by:

Theta (degrees) = (angular resolution) x N

If the system is preobjective, and a scan lens has been selected as a system constraint, then the scan lens defines the active scan angle. If a scan lens has not been selected, a scan angle must be assumed. Typical scan angles range from 20 to 60°. As the scan angle is increased, the number of facets and the size of the polygon decrease: however, the polygon velocity increases. A value of 45° is a good starting point and can be altered later if the result is not optimum.

From this information, the beam size on the polygon facet can be determined by:

D = 0.00127 Lambda N / [Theta (0.01748)]

where Lambda is the wavelength (µm) and D (mm) is the (1/e²) beam diameter on the facet.

The above equation assumes that the beam incident on the polygon has been apertured at the 1.5 (1/e²) diameter. Therefore, the footprint on the facet is 1.5 x D. At this point a feed angle (a) must be chosen. This is defined as the angle between the center line of the scanned beam and the input beam. This angle should be as small as possible to reduce polygon size. Projected footprint on the facet is defined as:

D'=1.5 D/cos (a/2)

The duty cycle now needs to be selected. This defined as the ration of the active scan time over the total scan time. Duty cycles ranging from 50 greater than 90 percent are common, but the greater the duty cycle, the larger the polygon and hence the higher the cost.

Polygon facet length (L) (mm) can be given approximately by:

L @ (D' + 1) / (1 - duty cycle)

Where the value of 1 in the numerator allows for the facet rolloff at the edge. The number of facets (n) required on a polygon is found by:

n = 720*(duty cycle)/Theta.

If this turns out to be a fraction, round it off to the nearest whole number and recalculate the duty cycle and the facet length.

Polygon diameter can be determined as follows:

Facet radius = L/[2 tan (180 / n)]

**Polygon velocity**

Polygon velocity is determined by the number of scans per second and the number of scans per second and the number of facets. The vast majority of applications require rotation rates in the range of 1500 to 30,000 rpm. The material chosen for the polygon depends on speed requirements. Aluminum or glass works well at the low-to mid-range speeds, but if the tip of the polygon facet reaches a velocity where glass and aluminum deform, then beryllium is the material of choice. The general equation that can be used to determine deformation speed is:

B = Sqrt(S/(0.0000071w[(3+m)R² + (1-m)r² ]))

Where B = maximum speed (rpm), S = yield strength (lb/in.²), w = weight of material (lb/in.³),R = outer tip radius (in.), r = inner bore radius (in.), m = Poisson's ratio.'

**Jitter**

Jitter is the nonrepeatable variation in the pixel placement along the scan direction. Various systems can tolerate different levels of jitter before the artifact becomes visible. Visual systems typically can be specified with up to 1 pixel of jitter before it becomes objectionable. Output scanners that place a premium on pixel placement will typically require 0.1 pixel accuracy.

Jitter can have either a random or periodic nature. Random jitter is visually less objectionable than periodic jitter that changes sinusoidally scan to scan. The visibility will be affected by the eye response and proximity to the peak frequency. The sources of jitter include: facet flatness variations, facet radius variations, facet radius variations, start of scan triggering errors and bearings.

Variations in flatness from facet to facet will result in a periodic jitter with a frequency of once per revolution or higher. There will be no contribution to jitter if all facets are flat or have the same curvature. The curvature causes small deviations in the angle of reflection from the facet. If the curvature varies facet to facet then the time between start of scan and end of scan will vary. A facet flatness specification on the order of Lambda/8 is adequate for most applications.

If the polygon is used at high speed and is attached to the hub with three mounting holes, then a jitter problem will become apparent. We have performed a structural analysis of our standard polygons that shows a three-cycle-per-revolution asymmetrical distortion due to centrifugal loading. To compensate for this, the polygon can be mounted usin