Design of Extended Depth-of-Focus Laser Beams Using Orthogonal Beam Expansions
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Design of Extended Depth-of-Focus Laser Beams Using Orthogonal Beam Expansions David P. Goren Symbol Technologies Inc., One Symbol Plaza, Holtsville, NY 11742-1300, USA Email: [email protected]
Joseph Katz Symbol Technologies Inc., One Symbol Plaza, Holtsville, NY 11742-1300, USA Mitsubishi Electric Research Laboratories, 201 Broadway, Cambridge, MA 02139, USA Email: [email protected]
Leonard Bergstein Symbol Technologies Inc., One Symbol Plaza, Holtsville, NY 11742-1300, USA Email: [email protected] Received 16 April 2004; Revised 3 November 2004 Laser beams with extended depth of focus have many practical applications, such as scanning printed bar codes. Previous work has concentrated on synthesizing such beams by approximating the nondiffracting Bessel beam solution to the wave equation. In this paper, we introduce an alternate novel synthesis method that is based on maintaining a minimum MTF value (contrast) over the largest possible distance. To achieve this, the coefficients of an orthogonal beam expansion are sequentially optimized to this criterion. One of the main advantages of this method is that it can be easily generalized to noncircularly symmetrical beams by the appropriate choice of the beam expansion basis functions. This approach is found to be very useful for applications that involve scanning of the laser beam. Keywords and phrases: lasers, beam shaping, optical transfer functions, propagation, extended depth of focus, orthogonal beam expansion.
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INTRODUCTION
Laser beams are commonly used to read digital information that has been encoded as a sequence of alternating light and dark regions on a reflective media. One such application is the reading of printed bar codes [1]. In this application, the distance from the bar code reader to the bar code label is usually variable and unknown, and in many cases it is desirable to read it over the largest possible distance, a feature that greatly improves the ergonomics of the reader and reduces operator training. For such a system, the laser beam should have a large depth of focus, loosely defined as the region where the beam is “narrow enough” to resolve the fine structure of the bar code. A proper definition of the depth of focus is crucial to optimize such a system, and it must take into account that the spatially encoded information can typically withstand moderate distortions and still be properly decoded. In addition, when scanning bar codes whose aspect ratio (i.e., the ratio between the height and width of a bar code element) is high,
it is the line-spread function (LSF) of the beam, rather than its point-spread function (PSF), that determines the overall system performance. In such cases, a highly elliptical beam is desirable in order to take advantage of the vertical redundancy in the code, and to reduce printing or laser speckle noise. (In the case of two-dimensional bar codes [1], a nearly circular beam is required in order to avoid interrow interference.) Most previous work on synthesizing extended depth-offocus laser beams have been based o
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