Unified Optical Scanning Technology

Chapter 4.10.2 - Scanner Devices and Techniques: Decentered Microlens Arrays

4.10.2 Decentered Microlens Arrays

An alternate to phased array beam steering is the decentering of a group of lenses with respect to a matching lens group. Although the fundamental beam steering action of an individual pair of decentered lenses differs uniquely from the phased cellular systems described above, when lenses are assembled into mating periodic arrays, the combination exhibits some of the basic characteristics of phased arrays, including the functioning as blazed gratings [Wat1].

Consider Figure 4.30a illustrating a pair of lenses (1 and 2) oriented originally afocal and then decentered from their common axis through distance Δ (dotted axes). Whereas the input beam at the left focuses lens 1 to an initially common focal point, its diverging beam continues into lens 2 shifted off its axis, resulting in deflecting the recollimated output beam through the angle Θo.This may be confirmed with a simple ray trace. Thus a transverse shift of lens 2 with respect to lens 1 affects beam steering. The vignetting of the output beam and the related diversion of the residual output flux outside the lens are discussed below. Major constraints to using this basically simple two-lens technique are its limitation on the width of the lens aperture, consistent with the energy requirement for sufficient Δ-shift within reasonable burdens of acceleration of massive components. These limitations represent, in fact, some of the reasons for seeking agile beam steering.

However, consider miniaturizing many lenses 1 and 2 (maintaining the f-number), formatting them into arrays of microlenses, per Figure 4.30b, and illuminating the group from the left by a single broad beam. The steered waves sum into the total field in a manner similar to those of the prior phased arrays. Immediate consequences are a significant decrease in mass for a given overall aperture size (similar to Fig. 4.29b) and a decrease in shift distance Δ required to steer the beam. The effect is a dramatic reduction in array travel and in the acceleration/deceleration forces required for rapid beam steering. Although the steered wavefront is discontinuous, the periodic output components exhibit the characteristics of a blazed grating. The array of steered beams (rays) corresponds to normal wavefront segments that are tipped at the same slopes. When, at the operating wavelength, their junctions exhibit 2π phase differentials, they form the sawtooth pattern typified by a blazed grating, providing high diffraction efficiency.

The technique of Fig. 4.30b is satisfactory for small steered angles, where the 'spurious' components remain a small residue of the desired output (maintaining high fill factors at the second lens array). However, at wider steering angles, when the vignetting and the disruptive effects of the spurious components become significant, remedies are considered. A classic method for the control of vignetting is the use of a field lens [Lev], introduced into the microlens array [Wat1] and adapted to proper lens movement. Figure 4.30c illustrates this as a variation to Figure 4.30a with a field lens (FL) inserted at the focal crossover of the original lens positions 1 and 2. The bar over the output pair of lenses represents physical connection for simultaneous motion. With equal focal lengths of all lenses, the expanding light cone fills completely lens 2 through Δ-shift of the lens pair, readily confirmed with a ray trace.

Fig. 4.30 Beam steering with decentered lenses. Original afocal lenses displaced through distance Δ. [a] Macroscopic lens pair, showing Δ-shift deflecting output beam through angle Θo, while upper portion of the beam bypasses lens 2. [b] Arrays of microlenses performing as in [a], but lighter and with smaller Δ-shift. The desired components accumulate while the bypass portions are directed into a spurious angle. [c] Field lens form of [a], where (FL) provides complete filling of lens 2. When in [b], this synthesizes the output wavefront of a blazed grating. After E.A. Watson, "Analysis of beam steering with decentered microlens arrays," in Optical Engineering, Vol. 32 (1993). Reproduced by permission of the publisher.

Fig. 4.31 Increase of focal length ratio ƒ12 to eliminate spurious components over a range of operation. [a] Similar to Fig. 4-30b (Keplerian form) with ƒ12 2. [b] Analogous Galilean form with ƒ12 2.5. Although the compressed beam energy is conserved, the output wavefront represents that from a discontinuous blazed grating. After E.A. Watson, "Analysis of beam steering with decentered microlens arrays," in Optical Engineering, Vol. 32 (1993) and W. Gοltsοs and M. Hοlz, "Agile beam steering using binary optics microlens arrays," in Optical Engineering, Vol. 29 (1990). Reproduced by permission of the publisher.

This technique for sustenance of output efficiency and spectral quality is directly transferable to the microlens phased array of Figure 4.30b with an added plane of field lenses affixed to the output array. The extra inertia can be accommodated by the force of piezoelectric or electrodynamic drive transducers. Or the single element may be moved, instead. A microlens-field lens design was fabricated and measured [M&W] over a ±1.6° field, for use in optical data storage. Larger angles (±17°) have been demonstrated [Wat4], but with loss of beam quality.

Alternate considerations for suppression of the spurious beams during Δ-shift are represented in Figure 4.31. The method of Figure 4.31a is introduced [Wat1] to illustrate partial tolerance for beam displacement on lens 2 by changing the ratio of focal lengths. The initial condition of f1 = f2 is adjusted to f1/f2 > 1. This forms a modified beam compressor (see Fig. 1.7) with a compression ratio 2:1. A similar approach is indicated [G&H] using a positive-negative lens combination. The Figure 4.31a method employs the equivalent of an afocal Keplerian telescope and the Figure 4.31b method that of a Galilean telescope. Although the spurious components of Figure 4.30b may be abated over its initial range of operation, the fill factor at the second array is reduced significantly. Although the energy is conserved in this reduced but integral light cone, the ideal sawtooth pattern of the blazed grating is disrupted dramatically by the truncated sawtooth function.

This, in turn, causes its own spurious noise [Wat1, G&H] which limits operation to a small range of Δ-shift. It is proposed, therefore [G&H], that the second array be maximally filled, ideally by reducing the lens separation in Figure 4.31b to zero. This is approached with the development of thin binary optics microlens arrays.

Binary optics arrays are fabricated by utilizing high-resolution etching and transfer techniques having high finesse to form binary representations and variations of Fresnel zone patterns on substrate materials. One hundred percent fill factors of lenslet arrays are attainable with matching and abutting lens shapes (e.g., hexagonal). Imparting a multilevel relief structure approximates a continuous phase profile in a stepwise manner, allowing achievement of high diffraction efficiency. As presented above for a phased array composed of q elements per 2π phase reset (Eq. 4-46), similarly, the efficiency ηb of a multilevel binary optic [Swa] of m levels within one width of a Fresnel feature is given by

Three etching steps forms eight levels, yielding the theoretical efficiency of 95%. An experimental system [G&H] utilized such arrays of f/5 microlenses, each of 0.2-mm diameter (having focal lengths just short of 1 mm) in a hexagonal grid array. The second (negative) lenslet array was spaced from the first by 10 μm, allowing relative translation in two dimensions. Three masks were used to form the eight-level approximation of a parabolic phase profile (which allows steering without angle-dependent aberrations). This system steered a 6-mm HeNe test beam over an 11.5° field using ±0.1-mm travel at a 35-Hz sweep rate. Practical mask alignment, etch, and transfer errors during fabrication reduced the 95% maximum efficiency to measurements of 84% and 72% for the positive and negative lens arrays, respectively. Overall throughput efficiency of the unsteered beam measured ap-proximately 50%. The f/5 system exhibits low efficiency when steered. This is expected to improve with fabrication and operation at lower f-numbers. Although the accuracy of the utilized engraving system was evaluated at 0.1 μm‚ cumulative fabrication errors in the present work were estimated to limit attainable minimum feature size to 0.4μm.

A variation on the above work was conducted using "phased-array-like' binary optics [Farn].The change is effective principally during Δ-shift, when a complementary pair of lenslike elements (as in [G&H]) renders incomplete filling of the lens aperture with the desired component. This results in each lenslet pair forming only a portion of the ideal phase ramp for a proper blaze, leaving a residue from each lenslet pair ramped in the wrong direction. In the basic phased-array-like method, the continuous quadratic phase function (parabolic per [G&H]) is sampled at equal intervals of Δx‚ forming a step wise (piece-wise flat) matching of the continuous phase profile. The Δ-shifts are then conducted in integral increments of Δx, to nΔ(x) for diffraction to the nth order. Because the flat segments in the residue region maintain modulo 2π phase differentials with respect to an idealized linear continuation, this formerly disruptive region is shown analytically to render a continuous linear phase profile across the full aperture.

Experimental binary rnicrooptics were designed to compare measurements of phased-array-like and microlens arrays. They were fabricated simultaneously and adjacent on the same thin quartz substrate. Tests confirmed that the phased-array-like structure provided a significant ( 50%) increase in intensity in the steered mode and exhibited less than 1% leakage into its immediate (local) sidelobes. Although stronger distant sidelobes developed from the phased array, they were well separated from the steered mode, by ±64 mode orders in these tests.

 

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