Converting Many Diverging Sources into Collimated Beams - Analysis Summary

Converting Many Diverging Sources into Collimated Beams - Analysis Summary

Executive Summary: Converting an array of divergent sources into collimated rays is fundamentally limited by brightness (radiance) conservation and étendue. No passive optics can increase source radiance - focusing simply trades beam diameter for angle one two. In practice one must match the optical system étendue to the source. For incoherent sources (LEDs, lamps), co-illumination or imaging by a single large lens will re-create the source pattern, yielding nonuniform output three. Instead, common solutions include individual collimators per source (small lenses, reflectors or non-imaging concentrators), microlens-array homogenizers, or for coherent laser sources, phased-array (coherent) beam combining. Each method has trade-offs in alignment, efficiency, divergence, cost and complexity. For example, a large single lens covering an LED array is simple but heavy and often produces nonuniform "spotted" beams three, whereas per-LED aspheric or Fresnel lenses yield higher uniformity at cost of many components. Non-imaging CPCs (reversed) can dramatically narrow LED divergence (approximately ten times reduction) with modest efficiency loss four. Laser diodes can be collimated by cylindrical or aspheric optics but require careful alignment; coherent combining (phase-locking) can boost on-axis brightness number of channels but demands complex phase control. We compare methods in detail below - summarizing required source properties (size, NA, coherence), array layout, optical specs (focal length, f number), tolerances, efficiency, thermal issues, and cost and complexity. Recommended approach: match étendue (NA times area) at each stage two, choose optics (f number) to yield desired divergence, and test with beam profilers or M two measurements. We give design examples for one a one millimeter Lambertian LED array, two coherent laser diodes, and three an extended filament source.

Optical Principles: Collimation, Étendue and Brightness

Collimation means making rays parallel. A perfect point source at the focus of a lens or parabola yields ideally collimated light; but real sources have finite size and angular spread, so the output has residual divergence. Étendue (optical throughput) is invariant in lossless optics: roughly area times solid angle is constant. In other words, beam diameter times divergence (or NA) remains fixed (or worsens) through optics.

. Focusing an extended source (or combining many sources) thus increases angular spread: "if we one put an optical element that concentrates or focuses light, the angles of the light will increase." The second law-like rule is that étendue can only stay the same or increase. Practically, this means a collimation system cannot produce a narrower beam than allowed by the source's étendue (brightness): if the optical system's étendue is smaller than the source's, only a fraction of light can be collected. The optimum is étendue-matched optics.

High-NA (low f number) optics collect more flux but also increase output divergence: NA approximately one over two times f number. For example, a one millimeter LED under an f equals ten millimeters, ten millimeter diameter lens yields a half-angle approximately arctan zero point five over ten approximately two point nine degrees, i.e. approximately five point eight degrees full-angle divergence (neglecting lens aberrations). In general, divergence approximately D source over two f for D source less than f. Multiple sources on a plane complicate this: a single large lens will image each source to the far field. In particular, a plano-convex or Fresnel lens at focal distance will project each source's image, reproducing the array pattern. Thus a single lens often yields multiple spots rather than one uniform beam. Reflectors (parabolic) similarly collimate a point at focus, but multiple foci require multiple mirrors or a segmented dish.

Brightness and Coherent Combining: For coherent (laser) sources one can use phased-array combining. In this case the on-axis beam brightness can scale with number of channels N (brightness N for ideal phase-locking). Coherent combining requires stable phase relationships, whereas incoherent combining (simply overlaying beams) cannot exceed the brightness of the brightest input. In practice, coherent combining (e.g. fiber or cavity combining) is complex but can preserve high beam quality, while incoherent Wavelength or polarization combining yields up to N times power but same brightness as one. We address this in the "Phased-Array" section.