1. Introduction

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.

 

Fig. 1. Schematic of a short-arc discharge lamp with a spherical recycling mirror, including the path of a light ray retro-reflected from the brightest zone.

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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 [9]. 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

2. Light recycling methods

Measurements of the spectral radiance of commercial 150 W Xenon short-arc discharge lamps [10], including its spatial dependence within the plasma arc, were recently reported [11]. We adopted the same radiometric methods described in [11], 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)].

 

Fig. 2. (a). Schematic of imaging lamp emissions onto a screen where the magnified plasma arc was mapped and its spectral content assessed. (b) Photograph including the lamp’s bulb and 2.0 mm inter-electrode region prior to ignition (cathode below, anode above).

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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).

 

Fig. 3. (a). Magnified image of the plasma arc (no recycling). (b) With the recycled image traversing the colder outer plasma region. (c) Adjacent images projected onto a perforated screen [see Fig. 2(a)]. The directions of axial and off-center displacement corresponding to movement of the spherical mirror are indicated. Measurements with the spectrometer’s optical fiber inserted into each hole allowed spatial and spectral mapping of the actual and recycled images which are magnified by a factor of 50. The center-to-center hole distance is 5 mm.

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Fig. 4. (a). Full-gap recycling: the recycled inverted image is superimposed upon the actual plasma arc. (b) Small-gap recycling: the hottest brightest regions of both the actual plasma and the recycled image are overlapped, but with a substantial percentage of the recycled image projected beyond the plasma arc onto the cathode.

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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 [11], 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 [11].

 

Fig. 5. Spectral radiance of the (a) direct emission, as in Fig. 3(a), (b) reflected image alongside the actual arc, as in Figs. 3(b)–3(c), and (c) reflected image superimposed on the plasma arc in small-gap recycling, as in Fig. 4(b). The inset highlights the line peaks in the near IR. The experimental uncertainty in radiance measurements here and in the graphs that follow is 10%.

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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 [11] 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.

 

Fig. 6. Ratio of the radiance of the arc recycled through the outer plasma regions [as in Figs. 3(b)–3(c)] to that of the actual arc, as a function of axial position relative to the cathode tip, for the 4 principal spectral bands and the spectrum-integrated values. The horizontal broken line indicates the estimated losses of 23% from the surrounding optic due to mirror absorptivity and Fresnel reflections at 4 additional air-glass interfaces.

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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.

 

Fig. 7. Local radiance enhancement measured along the lamp’s axis, starting from small-gap recycling (overlapping the brightest region of the inverted reflected image with the brightest region of the actual arc near the cathode tip, as in Fig. 4(b) and the inset), and translating the reflected image toward the anode. The dotted straight lines in the inset indicate the contour of the cathode’s reflected image. The photo inset overlays the circular image of the remote optical fiber tip in the lamp surgery system [4,5], toward illustrating the compromise between collection efficiency and maximum attainable radiance in such constrained applications.

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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 η_o 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 η_o = 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 η_oε/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 η_o = 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.

4. Discussion

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 [9]). 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 [9] – an issue for future investigation.