Unified Optical Scanning Technology

Chapter 4.3.5.1 - Scanner Devices and Techniques: Architecture of the Prismatic Polygon and its Flat-Field

4.3.5.1    Architecture of the Prismatic Polygon and its Flat-Field Lens    The underfilled prismatic polygon operating preobjective with its flat-field lens is illustrated in Figure 3.7, and the critical region relating the two is detailed in Figure 4.2. This prominent configuration merits special attention for determining an imposing array of its operating parameters, such as its number of facets, diameter, orientation with respect to the optical axis, and pupil relief distance for specific input beam angle, scan angles, scan duty cycle, and size of the flat-field lens housing. These apparently unrelated major design factors can be determined to high accuracy by utilizing the design procedures represented here and in Section 4.3.5.2.

Following Figure 4.2, the distance P (pupil relief distance) is mea-sued from the scanner facet surface to the lens input surface along the principal axis of the lens. It is determined primarily by the need for the input beam to clear the edge of the lens by distance Ds (D ≡ beam diameter; s ≡ safety factor ≈ 2). A shallower input beam angle (reduced β) increases P (for the same freedom from interference) and imposes upon the lens a larger aperture-and an increase in its size and cost. However, a wider input beam angle (increased β) forces a larger facet width W because of increased off-axis landing of the beam on the facet (later determined) forming a corresponding increase in polygon diameter. Another trade-off is the scan angle Θ. Although a wider Θ also increases lens complexity for correction of aberration and flat-field operation, it relieves some demand on the precision of the scanner by allowing a greater angular (wobble) error for a given number N of resolution elements within the enlarged Θ scan. These factors must be considered for a specific design objective.

Establishment of the scanner-lens relationships requires an estimate of the polygon facet count, in light of its diameter and speed. Its speed is determined primarily by the desired bandwidth and data rates and then by other operational factors, such as inertial facet deformation, windage, and multiplexing. Diffraction-limited relationships are employed here throughout, requiring practical adjustment for anticipated aberrations in real systems.

Performance objectives that are usually predisposed for a given system are the resolution N, the full optical scan angle Θ (which relates to the format width W), and the duty cycle η.The relationships between N and Θ are the subject of Chapter 3, and duty cycle considerations appear in Section 4.3.2. The values of N and Θ must be determined as practical for the flat-field lens. Typical high values are N = 20,000 and Θ = 1 radian, achieving reasonably flat and linear scans over format widths greater than 100mm. Narrower formats generally sacrifice N

Fig. 4.2 Relationship of prismatic polygon, its input and scanning beams, and its objective lens. Undetected and limit beam conditions are shown. From L. Beiser, "Design equations for a polygon laser scanner," in Beam Deflection and Scanning Techniques, Proc SPIE, Vol. 1454 (1991). Reproduced by permission of the publisher.

and Θ because of their shortened focal lengths, striving for correspondingly lower beam f-numbers to attain the smaller spots. Following these preliminary judgments, from Equation 3-5, the beam width at the deflector is determined as

in which a is the aperture shape factor. The number of facets n is deter-mined from Table 4.1 and Equation 4-3 as

whereupon it is adjusted to an integer. This establishes the scan efficiency η for a given Θ. Because the number of facets n occurs only in integral steps, optimizing the efficiency η may warrant a minor adjustment of Θ.

 

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