Recycling light back into a plasma lamp’s radiant zone can enhance its radiance. Measurements are reported for the effectiveness, spectral properties and modified plasma radiance maps that result from light recycling with a specular hemispherical mirror in commercial 150 W ultra-bright Xenon short-arc discharge lamps, motivated by projection, biomedical and high-temperature furnace applications. For certain spectral windows and plasma arc regions, radiance can be heightened by up to 70%. However, the overall light recycling efficiency is reduced to about half this value due to lamp geometry. The manner in which light-plasma interactions affect light recycling efficacy is also elucidated.
© 2007 Optical Society of America
Radiance enhancement in ultra-bright plasma short-arc discharge lamps is a prime objective for projectors [1–3], biomedical applications [4, 5] and high-temperature reactors [6, 7]. Although only visible light is pertinent for projection systems, the full lamp spectrum – in particular the prodigious near infrared (IR) emission – can be exploited in light-based fiber-optic surgery and high-flux furnaces. Recycling lamp radiation back to the mm-scale plasma arc source (Fig. 1) is an uncomplicated, effective strategy.
To our knowledge, experimental reports on the effectiveness of light recycling are sparse, limited to two recent studies of Hg short-arc discharge lamps [1,8], where a compact spherical retro-reflector was used. Corresponding raytracing studies have predicted light recycling efficiencies of 60–80%, although measurements were not reported . Commercial Xenon short-arc discharge lamps also exhibit immense radiance with broadband emission, particularly valuable in some medical applications because of the deeper optical penetration of near-IR light in biological tissue.
Light recycling should be more effective for more transparent (less emissive) plasmas, but can also be substantial for blackbodies. The emissivity of the colder denser plasma zones away from the inter-electrode axis and at axial positions closer to the anode is higher than in the hottest regions near the cathode. By adjusting the spherical mirror in Fig. 1, one can image the plasma arc to different locations, thereby mapping radiance enhancement. We present such measurements, including
- (a) spatial mapping within the plasma arc,
- (b) the contributions of the principal spectral bands,
- (c) elucidation of the thermodynamics of light recycling and
- (d) an evaluation of localized and overall light recycling efficiency in these lamps.
2. Light recycling methods
Measurements of the spectral radiance of commercial 150 W Xenon short-arc discharge lamps , including its spatial dependence within the plasma arc, were recently reported . We adopted the same radiometric methods described in , which provide the calibration for converting the relative radiance values measured with the optical system depicted in Fig. 2(a) into absolute radiance. The spectrometer’s optical fiber probe is inserted to each hole of a perforated screen [Figs. 2(a) and 3(c)] and allows a spatial and spectral mapping of lamp emission. A specular hemispherical mirror (radius 35 mm, reflectivity ~90%) was used to image plasma arc emissions back to the radiant zone (Fig. 1), and introduces negligible aberration as confirmed by both raytracing as well as the fidelity of the image of the recycled arc [e.g., Fig. 3(c)].
Moving the mirror in the plane perpendicular to the page permits translating the image off-center into colder regions, adjacent to the actual arc, as in Figs. 3(b)–3(c). At zero displacement, the axis of the image and actual arc coincide. The cathode tip of the image can be sited at the actual anode tip, referred to as full-gap recycling [Fig. 4(a)]. By translating the mirror in the plane of the page, the recycled image can also be moved along the lamp’s axis, as illustrated in Fig. 4(b) where the brightest (cathode-tip) regions of both the actual and recycled images overlap, called small-gap recycling.
Exploring how the position of the image affects recycling effectiveness is motivated by the tradeoff in optical design between attainable power density at the target and the collected étendue (collection efficiency).
- In full-gap recycling, the fraction of light reflected back into the plasma arc is greatest, but the maximum attainable radiance is limited because the brightest regions of the recycled image traverse the more emissive zones of the plasma.
- In small-gap recycling, by overlapping the brightest regions of the actual and recycled arcs one can maximize local radiance (within part of the arc), but collection efficiency is reduced because recycled light is projected beyond the plasma arc onto the cathode.
- The spectrum of the superimposed images may favor intermediate overlap strategies, e.g., for achieving the greatest near-IR intensity in biomedical applications.
3. Light recycling measurements and their interpretation
3.1 Spectral radiance enhancement
Figure 5 illustrates the spectral character of light recycling, with measurements from the brightest region near the cathode tip. The measurement for direct emission was reported previously , which we reproduced as confirmation prior to the recycling experiments. The direct emission comprises (a) narrow intense lines from the high-emissivity plasma electronic transitions and (b) a background continuum that constitutes ~80% of the emitted power and is not well described by a graybody Planck spectrum due to the non-negligible variation of plasma emissivity with both wavelength and temperature .
The radiance of the recycled image alone [as in Figs. 3(b)–3(c)] is approximately 70% that of direct emission for the continuum radiation. The surrounding optic is responsible for most of the loss in radiance, estimated as 23%: one reflection in the hemispherical mirror and Fresnel reflections off 4 additional air-glass interfaces. Because the bulb is not spherical [see Fig. 2(b)], Fresnel reflections are not fully re-imaged into the arc and hence mostly rejected.
The superimposed curve in Fig. 5 relates to overlapping the brightest cathode-tip regions of both the actual arc and the recycled image, as in Fig. 4(b). Light recycling is highly efficient over the background continuum. To wit, the radiance of the superimposed image is about the same as the sum of the direct and reflected contributions – usually the signature of a relatively transparent plasma. By assuming that the most intense line peak (at a wavelength of 824 nm in Fig. 5) has an emissivity close to 1, (a) the ratio of the continuum to the peak line intensity at that wavelength provides an emissivity estimate of ~0.2, and (b) the Planck spectral radiance function combined with the absolute spectral radiance measurement  implies a local temperature of ~9500 K for this hottest region of the plasma.
The radiance enhancement of the intense lines is noticeably lower than that of the continuum, probably because the absorbed recycled light is redistributed within the continuum spectrum. The radiance enhancement at these narrow peaks would then be lessened by a factor of the lower emissivity of the continuum. For example, the recycling boost at the most intense spectral lines is about 15–20%, which is consistent with the above observation. Furthermore, as the line spectra (in the near IR) grow less intense (i.e., of lower emissivity), the recycling efficiency at those specific wavelengths increases, as expected.
3.2 Mapping recycling efficiency
Figure 6 shows the variation of the radiance of the reflected image [Figs. 3(b)–3(c)] along the lamp’s axis. Each curve is the ratio of the radiance of the reflected image to the actual arc at the same axial position, within each of the 4 principal spectral bands, plus a curve for the integration over the spectrum. We have no explanation for the dip in the radiance of the reflected image at intermediate axial positions at the highest wavelengths or near the anode.
The spectrum-integrated radiance map measurements plotted in Fig. 7 typify the tradeoff between maximum radiance and collection efficiency as the recycled image is moved along the lamp’s axis (by adjusting the hemispherical mirror). Small-gap recycling, which superimposes the two brightest plasma regions, generates a maximal 60% radiance increase near the cathode tip, but at the expense of rejecting a large fraction of recycled light. Moving the reflected image toward the anode regenerates more radiation, but at diminished radiance enhancement. This type of exercise is particularly germane in lamp surgery [4,5] where thresholds in both power density and absolute power mandate as high a radiance as possible but subject to high collection efficiency.
3.3 Net recycling efficiency
So far, the measurements have related to light recycling effectiveness from localized regions within the plasma. It is not straightforward to translate those data into a net recycling efficiency from the entire plasma arc. We estimated the global recycling efficiency by measuring spectrum-integrated intensity over the full angular range of lamp emission (restricted to plasma arc emission by inserting an iris between the lamp and the detector). Three sets of measurements were performed: (a) direct emission only (no recycling), (b) full-gap recycling and (c) small-gap recycling, where the recycling efficiency is defined as the ratio of the intensities between the superimposed image and direct emission, integrated over the spectrum and full angular range.
The recycling efficiency for full-gap and small-gap recycling was 1.38 and 1.23, respectively – considerably less than the results reported above from localized regions within the plasma from which one might deduce a recycling efficiency closer to 1.7. The latter figure reflects the intrinsic light-plasma interactions, including the insensitivity of recycling efficiency to local plasma emissivity. We therefore posit that the lower global figure is primarily a geometric effect. In small-gap recycling, much of the recycled light is imaged beyond the inter-electrode gap. In full-gap recycling, the inverted recycled image essentially fits the inter-electrode gap, but the brightest regions reside at the anode tip. In contrast to the pointed-shape cathode, the anode is flat and wide, resulting in greater occlusion of emissions, hence a reduction in net recycling efficiency.
3.4 One-node model
A single-node model for the plasma, i.e., characterized by a single emissivity value ε, can account for several key features of light recycling. Let ηo denote the optical efficiency of the surrounding optic, in this case comprised of the mirror reflectivity and the reflective losses at 4 additional air-glass interfaces (leaving and re-entering the lamp), estimated here as ηo = 0.77. The radiance enhancement R1 due exclusively to the transmissivity 1-ε of the plasma to recycled light on its first pass through the lamp is
The remaining fraction ε of the recycled light is absorbed in the plasma and re-emitted isotropically. On the first pass through the lamp, a fraction ηoε/2 is emitted toward the detector and an equal fraction returns to the recycling optic. The repeating process results in an infinite geometric series. The supplemental radiance enhancement B2 from the absorbed light extracted in the multiple passes is then
The full recycling efficiency R is then
which represents a relatively narrow range relatively insensitive to ε
e.g, with ηo = 0.77, B ranges from 1.63 to 1.77. This is not inconsistent with our experimental findings in Section 3.2 and Fig. 6 for the weak dependence of recycling efficiency on plasma properties. In addition, the predicted values of localized recycling efficiency are commensurate with the data. This simplistic model is not intended for accurate predictions -only to capture some key trends in a physically transparent form. The one-node model does not relate to the contributions of the high-emissivity line peaks (Fig. 5) that comprise ~20% of the total intensity.
Enhancing the radiance of short-arc discharge lamps by recycling lamp emissions back to the radiant source is inherently efficient, especially when lamp emissions are dominated by a background continuum. Almost all the recycled light can be reconstituted (after deducting the optical losses of the surrounding optic) from plasma regions where emitted light is not blocked by the electrodes. For example, in our system with an optical efficiency of 77%, the radiance of some plasma regions and spectral windows can be enhanced by up to the limit of 77% (consistent with the predictions of ). Despite the strongly non-uniform spatial and spectral structure of the plasma, the recycling efficiency was found to vary only weakly over the principal spectral ranges, and was almost independent of whether recycled light traversed hotter lower-emissivity zones versus colder higher-emissivity regimes. A relatively simple one-node plasma model can account for some of the salient experimental observations.
However, the high-emissivity peaks (which constitute ~20% of full-spectrum plasma-arc emissions in Xenon lamps) display substantially lower recycling efficiency relative to that of the continuum. This can be understood in terms of the absorbed recycled light at these peaks being redistributed within the background continuum, such that its contribution at the peaks should be reduced in proportion to the lower emissivity of the continuum radiation.
More significantly, the net recycling boost – measured as ranging from 23% for small-gap recycling to 38% for full-gap recycling - is markedly lower than that deduced from localized measurements. The reason appears to be geometric. In full-gap recycling, the brightest region of the recycled image is projected at the tip of a broad anode that obstructs a sizeable fraction of the radiation. In small-gap recycling, most of the recycled light is projected outside the plasma arc. These differences sharpen the tradeoff between maximum radiance and maximum efficiency strategies in light recycling. In addition, the hotter electrode temperatures that light recycling produces may degrade the electrodes faster and hence reduce lamp lifetime  – an issue for future investigation.
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