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A simple model of the wavelength dependent angular radiation characteristics of flash-lamps
15 August 1994 OPTICS COMMUNICATIONS ELSEVIER
Optics Communications 110 (1994) 321-326
A simple model of the wavelength dependent angular radiation characteristics of flash-lamps Daniele Bigazzi, Piero Mazzinghi 1, Lorenzo Ulivi Istituto di Elettronica Quantistica del Consiglio Nazionale delle Ricerche, Via Panciatichi 56/30, 1-50127 Firenze, Italy
Received 14 March 1994; revised manuscript received 30 March 1994
Abstract A new method for the measurement of the spectrally resolved angular intensity distributions (AID) of cylindrical arc or flash-lamps, in a single-shot, is presented. Use of a bidimensional CCD array and an imaging spectrograph, allows a complete determination of the emission characteristics. Typical results on a Kr flash-lamp for Nd:YAG laser pumping are shown. A simple model, permitting easier use of experimental results in ray-tracing simulations, is also presented.
1. Introduction
Still in the age of diode-pumping, all high power solid state lasers are pumped by noble gas arc or flashlamps, coupled to the active laser medium by imaging or non-imaging reflectors. With a proper optimisation of the coupling reflectors, overall efficiencies close to 5%, for Nd:YAG lasers in the kW range, were achieved [1 ]. Reflector optimisation is usually accomplished by ray-tracing optical simulation. A required input for any ray tracing operation is the spatial distribution of lamp radiation, that is, the angular intensity distribution (AID) of the radiation emitted by the lamp, considered usually as a surface emitter. In a recent paper [2] we presented a convenient method to measure, in a single shot, the angular distribution of the radiation emitted by a cylindrical flashlamp. In that work the spectral average of the lamp AID was measured, even though an extension of the procedure was suggested, to allow single-shot simultaneous spectral-angular resolution. In this work we I Corresponding author.
demonstrate the feasibility and convenience of the proposed method, presenting the results for a typical pulsed lamp. Many measurements of the lamp spectrum are available in the literature [ 3], but very few ones deal with the spatial distribution of radiation, and none, to our knowledge, is related to the wavelength dependence of the lamp radiance. A typical lamp spectrum is shown in Fig. 1. Lamp emission is produced by two different transitions: bound-bound transitions (spectral lines), and free-bound transitions (continuos background) [4]. The angular radiation distribution is expected to be sensibly wavelength dependent, since, at wavelengths close to the peak of an emission line, the plasma is optically thick [ 5 ], and the radiation should resemble more closely that of a Lambertian (surface) emitter, where the contrary is true in other spectral regions. The complication inherent to the spectral dependence of the lamp radiance distribution is usually neglected in any ray-tracing simulation, for two reasons. First, no quantitative information exists on the wavelength dependence of the flash-lamp AID.
0030-4018/94/$07.00 (~ 1994 Elsevier Science B.V. All fights reserved SSDI 0030-401 8 ( 94 ) 00327-Q
322
D. Bigazzi et al. /Optics Communications 110 (1994) 321-326
",., 811.29 nm
',,
Lamp
1.5
Power supply
,,. 800 nm "-...
Camera lens
. . . . . . . . . . . . . . . . .
~,tonochromator
r rr 0.5
Delay generator L
0 400
500
600 700 Wavelength (nm)
800
900
Fig. 1. Emission spectrum of a Kr flash-lamp (ILC mod.
L6948 150 mm arc length, 10 mm and 12 mm internal and external bore diameter) (solid line), excited with a 50/~s, 160 J pulse, at a peak current of 2.3 kA compared with the blackbody emission at a temperature of 104 K (dashed line). Secondly, even though the whole information was available, the rigorous procedure of performing a different ray-tracing simulation for any wavelength (say, 103 simulations, considering a 500 nm spectral range scanned with a 0.5 nm spectral resolution) would be prevented by the practical problem of an extremely high computing time, of the order of several days, even using very powerful computing systems. This problem is taken into account in the final part of this paper, where a simple model, describing the spectral-angular flash-lamp characteristics, is presented and discussed on a physical basis. With the use of this model the big amount of information contained in the joint spectral-angular distribution is reduced to two wavelength dependent coefficients taking into account the whole different lamp angular characteristics at all wavelengths.
2. Experimental set-up The experimental set-up is shown in Fig. 2. A lamp image is produced through a high-quality camera lens (200 mm focal length), on the entrance slit of a 250 mm imaging spectrograph (ARIES model 250 IS), equipped with toric optics to reduce spherical aberrations. Since the flash-lamp must be vertical to ensure the cylindrical symmetry of the inner discharge, an Abbe prism rotates the lamp image in
Fig. 2. Schematic diagram of the experimental set-up for the measurements of the angular intensity distribution (AID). The lamp image is formed, through a camera lens, on the entrance slit of an imaging monochromator, and acquired by a CCD detector. such a way that the vertical entrance slit of the spectrograph samples the light emitted by a horizontal semi-circumference on the lamp surface. The radiation is collected by a 512 × 512 CCD array detector (9.7 × 9.7 mm OMA IV CCD detector by EG&G PARC), located on the exit focal plane of the spectrograph. The spectral range covered in a single measurement, using a 150 lines/mm grating, is 220 nm, with a spectral resolution of 0.4 nm. The bidimensional intensity distribution on the CCD detector gives information both on the spectrum (on the x coordinate) and on the intensity distribution Iy (y) of the light on the entrance slit. The principle of the method, described in detail in Ref. [2], allows single shot measurements, with the advantage of avoiding the influence of shot to shot fluctuations, of lamp ageing during measure, and the need of averaging for different angles. The flash-lamp cylindrical symmetry permits to relate the collected radiation, emitted by different points on the lamp, to the output angle on the external surface. A ray emerging from the external surface at an angle 0' with the normal, and at a distance h = Re sin 0' from the optical axis, is focused on the image plane of the detection system in a point of coordinate y. The relationship among h and y is the lateral magnification of the optical system. In cylindrical symmetry and supposing that the collection lens is positioned at a long distance from the lamp the relation
D. Bigazzi et al. / Optics Communications 110 (1994) 321-326
y = y0sin0' leads to the simple relation, among measured distribution and lamp AID Io, ( 0 ' , 2 ) = I y ( y , 2 ) cos0',
where ly is the intensity along the direction transverse to the lamp axis, at a given wavelength 2, and Io, the AID of the radiation on the external lamp surface. The AID on the internal lamp surface can be calculated by the relationship sin 0' sin 0
Rini -
Rene'
where 0 is the angle on the internal surface, Ri, ni and Re, ne are the surface radii and refractive indexes on the internal and external surfaces, respectively. Fig. 3 shows a typical lamp spectral image, obtained using the bidimensional detector, oriented in the x y plane. On the x axis, calibrated in the usual way by using a low pressure neon lamp, wavelengths in nanometers are reported. On the y coordinate the intensity variation of the lamp image is clearly observable (analogously to what is reported in Fig. 2 of Ref. [2]. After a calibration, obtained by recording of an image of an object of known dimension, to obtain the magnification of tl~e optical system, the AID of an element of the lamp surface can be obtained and studied as a function of wavelength. 3. R e s u l t s
All experiments were performed on lamps (ILC L6948, 150 mm arc length, l0 mm and 12 mm internal and external bore diameter, K0 = 22 V/A °'5) filled with a mixture of 90% Kr and 10% Xe at a pressure of 700 Ton'. The excitation circuit is a single mesh LC network, whose capacitors, inductors and voltage are varied to obtain different pulse durations, ranging from 2 ms to 50/~s. The lamp is operated in simmer mode, with a 500 mA current and 150 V voltage discharge maintained by a separate power supply. The main discharge is controlled by an SCR, capable of peak currents up to 4 kA. Fig. 4a shows typical angular intensity distributions, obtained at a wavelength coincident with the KrI bound-bound transition 5S[1½ ]0 =~5P[1½ ] [6] at 811.29 nm for three different excitation pulse
323
durations. The solid and dashed lines represent the angular radiation distribution that would be emitted by an ideal surface and volume emitter, respectively, filling the inner lamp bore homogeneously. We immediately note from Fig. 4a that the measured angular distributions are narrower than any of the two ideal shapes. That is, apparently the plasma does not fill completely the inner lamp bore [7], even for long pulses. This effect has already been observed and interpreted as due to the time-average [2] nature of these measurements. The plasma, in fact, develops from the centre, and it takes about 300-400 lzs to fill all the space inside the lamp. This time is not negligible with respect to the duration of the whole pulse. Consequently, a considerable amount of the intensity is emitted by a plasma column considerably thinner than the lamp bore, giving an excess of intensity on the centre. An example of the wavelength dependence of the lamp angular radiance, is presented, in Fig. 4b, with the comparison among the angular distribution of the radiation emitted at 811.29 nm, corresponding to the peak of an emission line, and that emitted at 800 nm, corresponding to a less intense continuous background. The lamp was operated at an energy of 800 J, with a peak current of 1.3 kA, and a pulse duration of l ms. This example is indicative of a general result: at those wavelengths corresponding to maxima in the emission spectrum, the lamp emission is always less directive than at those wavelengths corresponding to lower spectral intensity. The reason for this difference is that, according to Kirchhoffs law, at peak emission wavelengths the plasma is more absorbing and the lamp AID resembles more closely that of surface emitters. At wavelengths where the plasma is more transparent the angular emission distribution resembles more closely that of a volume emitter. To make the huge amount of information, delivered by the joint spectral-angular intensity distribution, useful for ray tracing purposes, we have developed a simple model to describe a flash-lamp. The starting points for this model are the two observations, discussed previously, that the plasma column is thinner than the lamp bore and that the plasma emission is something between that of a surface emitter and that of a volume emitter. We have chosen, therefore, to represent the spectral AID of an element of the lamp surface, with a linear superposition of volume and sur-
324
D. Bigazzi et a L I Optics Communications 110 (1994) 321-326
Io
_=_ E
<1:
Wavelength (nm) Fig. 3. Typical spectral image recorded by the CCD detector: the spectral intensity along z-axis is plotted versus wavelength (x-axis) and position on the direction transverse to the lamp axis (y-axis), in same conditions of Fig. 1.
811.29 nm
1
501~s •
~
a)
o
0.6 o,
/
"o (1) N
0
E
1
/
•
1 ms 0 Z
b)
811.29 nm o
800 nm
•
.,,,,f/f
~
~
0.8 0.4 0. |
90
60
30
0
30
60
Angle on internal surface (degrees) Fig. 4. Typical intensity distributions ; (a), for the wavelength of 811.29 nm, for three different excitation pulse duration: 2 ms, 300 ], 500 A (open circles); 1 ms, 800 1, 1.3 kA (open squares); 50/ts, 160 J, 2.3 kA (solid circles); (b) for different wavelengths (1 ms pulse duration):spectral line at 811.29 nm (open circles) and continuous background (solid circles). Solid and dashed lines represent, respectively, ideal surface and volume emitters filling homogeneously the lamp bore.
D. Bigazzi et al. / Optics Communications 110 (1994) 321-326
325
1.2 08 "o ¢9
"E 0.8
~'0.6 ~0.6
"1o Q) N
~ 0.4
~0.4
O
z
0.2
0
0.2
400 0
30
60
90
500
600 700 Wavelength (nm)
800
900
Angle on internal surface (degrees)
Fig. 5. Lamp model in same condition of Fig. 4b. Spectral line at 811.29 nm (open circles), continuos background at 800 nm (solid circles), solid and dotted hairlines represent polynomial fit of experimental data, heavy sofid and dashed lines represent surface and volume ideal emitters i'filing homngencously a 6.5 mm diameter column, against a lamp bore of 10 mm. face ideal emitters, as I o ( 0 ) = a~cos0 + bgcos2 0. This relation was found to describe correctly the lamp AID as it was emitted by a steady, homogeneous plasma column smaller than the lamp bore, whose diameter do was also obtained from a data fitting. The plasma column of diameter do was found to emit 80% of the total lamp intensity. For the presented example, do resulted to be 6.5 m m corresponding to 65% of the lamp bore. This percentage is consistent with the plasma column time evolution described by Vitel et al. [8]. The remaining 20% of lamp emitted intensity could be better taken into account considering higher order terms in a cos 0 polynomial, but this was considered not necessary for ray tracing purposes and more difficult to be interpreted on a physical basis. Once Io (0) has been normalised imposing -Io (0) = l, the sum a~ + b~ = 1 results always very close to unity. Fig. 5 shows the results of this model when applied to the same data shown in Fig. 4b. (Confidence parameter R 2 = 0.99; as00 = 0.18, bs00 = 0.79, ash = 0.60, bsH = 0.38.) Observing Fig. 5, we can conclude that, at least in this example, the radiation emitted in correspondence of the continuum
Fig. 6. Lamp model spectrum (same conditions of Fig. 1); heavy line is the spectrum of the a~ coefficient (surface emitter), thin line is that of the b~ (volume emitter). The sum of the two coefficients, approaching 1, is also reported. spectrum exhibits an angular distribution of radiation quite similar to that of a volume emitter. Repeating this process for all wavelengths analysed in our measurements, we can study the wavelength dependence of the coefficients a~ and b~. It is very interesting to compare this "spectrum" of coefficients with the lamp spectrum represented in Fig. 6. The coefficient a~ presents its maxima exactly at those wavelengths where a spectral emission line is present. Correspondingly, b~ shows minima at the same wavelengths. This result shows in all its evidence that, for typical excitation parameters (pulse duration and energy), the lamp emission characteristics are quite complicate, since the plasma behaves as a volume or a surface emitter, depending on the wavelength. A remark can be added on the fact that the wavelength behaviour of a~ presents some differences from the spectrum shown in Fig. I. In fact, while the spectral lines at longer wavelengths correspond to pronounced maxima for a~, the same is not true for spectral lines at shorter wavelengths. This can be explained by taking into account the black-body spectrum at T = l04 K, represented, apart for an arbitrary factor, as a dashed line in Fig. I. This temperature was reported as the average temperature of the plasma in flash-lamps used in similar conditions [3]. Since the black-body intensity is lower at higher wavelengths, the emission intensity on the peaks of the red and IR
326
D. Bigazzi et al. / Optics Communications 110 (1994) 321-326
lines is much closer to that of a black-body, than that of the lines in the violet or UV.
4. Discussion The model discussed in this work allows an easy characterisation of flash-lamp emission in terms of simple functions. Moreover, this model describes the angular intensity distribution, at any wavelength, as a linear superposition of only two distributions. In this sense, this model is a new solution to the optical simulation of all systems where the lamp angular emission distribution is of some concern. In fact, it permits a complete simulation in a very fast way, performing only two different ray-tracing computations, respectively for the two angular intensity distributions, and making a linear combination of the results, using as weight factors the coefficients a~ and ba. This is particularly useful if applied to those systems that employ non-imaging optics to redirect lamp radiation. Respect to the first work that solved the problem of single shot measurements of lamp angular radiation distribution, the addition of spectral resolution permits to distinguish various contributes to lamp emission, and to measure their different angular emission distribution. Of course this model holds only if cylindrical symmetry is assumed, both for the lamp and for the discharge. All flash-lamps used in high power lasers are cylindrical, then axially symmetric. Discharge symmetry is, however, assured only if the lamp axis is vertical, as in our measurements. On the contrary, in normal laser use the lamp is held horizontally. This lead to convection currents inside the gas that shift the discharge region in the upward direction. In this case the model is not completely correct. However, since this effect is limited to less than 1 mm, otherwise the discharge will contact the lamp wall, it will affect the precision of the ray tracing simulations only marginally. In addition this is comparable with producing and mounting tolerances of flash lamps. However flash lamp pumped laser manufacturers should take into account that mounting the lamps vertically into the laser head would reduce the thermal loading of the lamp wall, and will made it radially symmetrical, resulting in a higher input power possible for the same flash lamp.
In addition, since the lamps are coupled with reflectors, a loss of cylindrical symmetry can be caused by plasma re-absorption of the reflected lamp emission. In general this is to be avoided in properly optimised reflectors, since the re-absorbed radiation reduces the overall efficiency. The model describes the time-average plasma emission over the whole pulse duration. The use of a gated CCD detector would permit the single shot study of both spectral and spatial evolution of the lamp emission [9], with time resolution up to 5 ns. Such a measure could allow the modelling of lamp, taking into account the true time evolution of radiation emission. This would be not actually necessary for quasi-steady state ray-tracing simulation of long pulse lasers, but could represent a valuable tool in plasma diagnostics. However transient simulation of short pulse lasers (< 100 ~ts) should take into account the discharge build up, requiting such a measurement.
Acknowledgements The authors are very grateful to Dr. Skowronek and Dr. Y. Vitel of Laboratoires Plasmas Denses, Universit6 Pierre et Marie Curie (Paris), for the helpful discussions about plasma properties. This work was performed in the framework of the EUREKA Project EU 226 High Power Solid State Laser. Financial support from the italian CNR Finalised Project "Tecnologie elettroottiche" is gratefully acknowledged.
References [ 1] D. Cilia, Report for 7th Intern. Meeting of Eureka Project EU226, Munich (1993). [2] L. Ulivi and P. Mazzinghi, Optics Comm. 81 ( 1991 ) 157. [3 ] O. Kahan, S. Mattews and E. Gregor, Proc SPIE 609 (1986) 138. [4] B. Smith, Proc SPIE 609 (1986) 24. [5] H. R. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964). [6] A.R. Striganov and N.S. Svetitskii, Tables of spectral lines and ionised atoms (Plenum, New York, 1968). [ 7] H. T. Powell, A.C. Edandson and K.S. Jancaititis Proc SPIE 609 (1986) 78. [8] Y. Vitel, M. Skowronek, K. Beninsty and M. M. Popovic, J. Physics D 12 (1979) 1125. [9] J. A. Antoniades and T. Peyeser, Rev. Sci. Instrum. 58 (1987) 253.
Optics Communications 110 (1994) 321-326
A simple model of the wavelength dependent angular radiation characteristics of flash-lamps Daniele Bigazzi, Piero Mazzinghi 1, Lorenzo Ulivi Istituto di Elettronica Quantistica del Consiglio Nazionale delle Ricerche, Via Panciatichi 56/30, 1-50127 Firenze, Italy
Received 14 March 1994; revised manuscript received 30 March 1994
Abstract A new method for the measurement of the spectrally resolved angular intensity distributions (AID) of cylindrical arc or flash-lamps, in a single-shot, is presented. Use of a bidimensional CCD array and an imaging spectrograph, allows a complete determination of the emission characteristics. Typical results on a Kr flash-lamp for Nd:YAG laser pumping are shown. A simple model, permitting easier use of experimental results in ray-tracing simulations, is also presented.
1. Introduction
Still in the age of diode-pumping, all high power solid state lasers are pumped by noble gas arc or flashlamps, coupled to the active laser medium by imaging or non-imaging reflectors. With a proper optimisation of the coupling reflectors, overall efficiencies close to 5%, for Nd:YAG lasers in the kW range, were achieved [1 ]. Reflector optimisation is usually accomplished by ray-tracing optical simulation. A required input for any ray tracing operation is the spatial distribution of lamp radiation, that is, the angular intensity distribution (AID) of the radiation emitted by the lamp, considered usually as a surface emitter. In a recent paper [2] we presented a convenient method to measure, in a single shot, the angular distribution of the radiation emitted by a cylindrical flashlamp. In that work the spectral average of the lamp AID was measured, even though an extension of the procedure was suggested, to allow single-shot simultaneous spectral-angular resolution. In this work we I Corresponding author.
demonstrate the feasibility and convenience of the proposed method, presenting the results for a typical pulsed lamp. Many measurements of the lamp spectrum are available in the literature [ 3], but very few ones deal with the spatial distribution of radiation, and none, to our knowledge, is related to the wavelength dependence of the lamp radiance. A typical lamp spectrum is shown in Fig. 1. Lamp emission is produced by two different transitions: bound-bound transitions (spectral lines), and free-bound transitions (continuos background) [4]. The angular radiation distribution is expected to be sensibly wavelength dependent, since, at wavelengths close to the peak of an emission line, the plasma is optically thick [ 5 ], and the radiation should resemble more closely that of a Lambertian (surface) emitter, where the contrary is true in other spectral regions. The complication inherent to the spectral dependence of the lamp radiance distribution is usually neglected in any ray-tracing simulation, for two reasons. First, no quantitative information exists on the wavelength dependence of the flash-lamp AID.
0030-4018/94/$07.00 (~ 1994 Elsevier Science B.V. All fights reserved SSDI 0030-401 8 ( 94 ) 00327-Q
322
D. Bigazzi et al. /Optics Communications 110 (1994) 321-326
",., 811.29 nm
',,
Lamp
1.5
Power supply
,,. 800 nm "-...
Camera lens
. . . . . . . . . . . . . . . . .
~,tonochromator
r rr 0.5
Delay generator L
0 400
500
600 700 Wavelength (nm)
800
900
Fig. 1. Emission spectrum of a Kr flash-lamp (ILC mod.
L6948 150 mm arc length, 10 mm and 12 mm internal and external bore diameter) (solid line), excited with a 50/~s, 160 J pulse, at a peak current of 2.3 kA compared with the blackbody emission at a temperature of 104 K (dashed line). Secondly, even though the whole information was available, the rigorous procedure of performing a different ray-tracing simulation for any wavelength (say, 103 simulations, considering a 500 nm spectral range scanned with a 0.5 nm spectral resolution) would be prevented by the practical problem of an extremely high computing time, of the order of several days, even using very powerful computing systems. This problem is taken into account in the final part of this paper, where a simple model, describing the spectral-angular flash-lamp characteristics, is presented and discussed on a physical basis. With the use of this model the big amount of information contained in the joint spectral-angular distribution is reduced to two wavelength dependent coefficients taking into account the whole different lamp angular characteristics at all wavelengths.
2. Experimental set-up The experimental set-up is shown in Fig. 2. A lamp image is produced through a high-quality camera lens (200 mm focal length), on the entrance slit of a 250 mm imaging spectrograph (ARIES model 250 IS), equipped with toric optics to reduce spherical aberrations. Since the flash-lamp must be vertical to ensure the cylindrical symmetry of the inner discharge, an Abbe prism rotates the lamp image in
Fig. 2. Schematic diagram of the experimental set-up for the measurements of the angular intensity distribution (AID). The lamp image is formed, through a camera lens, on the entrance slit of an imaging monochromator, and acquired by a CCD detector. such a way that the vertical entrance slit of the spectrograph samples the light emitted by a horizontal semi-circumference on the lamp surface. The radiation is collected by a 512 × 512 CCD array detector (9.7 × 9.7 mm OMA IV CCD detector by EG&G PARC), located on the exit focal plane of the spectrograph. The spectral range covered in a single measurement, using a 150 lines/mm grating, is 220 nm, with a spectral resolution of 0.4 nm. The bidimensional intensity distribution on the CCD detector gives information both on the spectrum (on the x coordinate) and on the intensity distribution Iy (y) of the light on the entrance slit. The principle of the method, described in detail in Ref. [2], allows single shot measurements, with the advantage of avoiding the influence of shot to shot fluctuations, of lamp ageing during measure, and the need of averaging for different angles. The flash-lamp cylindrical symmetry permits to relate the collected radiation, emitted by different points on the lamp, to the output angle on the external surface. A ray emerging from the external surface at an angle 0' with the normal, and at a distance h = Re sin 0' from the optical axis, is focused on the image plane of the detection system in a point of coordinate y. The relationship among h and y is the lateral magnification of the optical system. In cylindrical symmetry and supposing that the collection lens is positioned at a long distance from the lamp the relation
D. Bigazzi et al. / Optics Communications 110 (1994) 321-326
y = y0sin0' leads to the simple relation, among measured distribution and lamp AID Io, ( 0 ' , 2 ) = I y ( y , 2 ) cos0',
where ly is the intensity along the direction transverse to the lamp axis, at a given wavelength 2, and Io, the AID of the radiation on the external lamp surface. The AID on the internal lamp surface can be calculated by the relationship sin 0' sin 0
Rini -
Rene'
where 0 is the angle on the internal surface, Ri, ni and Re, ne are the surface radii and refractive indexes on the internal and external surfaces, respectively. Fig. 3 shows a typical lamp spectral image, obtained using the bidimensional detector, oriented in the x y plane. On the x axis, calibrated in the usual way by using a low pressure neon lamp, wavelengths in nanometers are reported. On the y coordinate the intensity variation of the lamp image is clearly observable (analogously to what is reported in Fig. 2 of Ref. [2]. After a calibration, obtained by recording of an image of an object of known dimension, to obtain the magnification of tl~e optical system, the AID of an element of the lamp surface can be obtained and studied as a function of wavelength. 3. R e s u l t s
All experiments were performed on lamps (ILC L6948, 150 mm arc length, l0 mm and 12 mm internal and external bore diameter, K0 = 22 V/A °'5) filled with a mixture of 90% Kr and 10% Xe at a pressure of 700 Ton'. The excitation circuit is a single mesh LC network, whose capacitors, inductors and voltage are varied to obtain different pulse durations, ranging from 2 ms to 50/~s. The lamp is operated in simmer mode, with a 500 mA current and 150 V voltage discharge maintained by a separate power supply. The main discharge is controlled by an SCR, capable of peak currents up to 4 kA. Fig. 4a shows typical angular intensity distributions, obtained at a wavelength coincident with the KrI bound-bound transition 5S[1½ ]0 =~5P[1½ ] [6] at 811.29 nm for three different excitation pulse
323
durations. The solid and dashed lines represent the angular radiation distribution that would be emitted by an ideal surface and volume emitter, respectively, filling the inner lamp bore homogeneously. We immediately note from Fig. 4a that the measured angular distributions are narrower than any of the two ideal shapes. That is, apparently the plasma does not fill completely the inner lamp bore [7], even for long pulses. This effect has already been observed and interpreted as due to the time-average [2] nature of these measurements. The plasma, in fact, develops from the centre, and it takes about 300-400 lzs to fill all the space inside the lamp. This time is not negligible with respect to the duration of the whole pulse. Consequently, a considerable amount of the intensity is emitted by a plasma column considerably thinner than the lamp bore, giving an excess of intensity on the centre. An example of the wavelength dependence of the lamp angular radiance, is presented, in Fig. 4b, with the comparison among the angular distribution of the radiation emitted at 811.29 nm, corresponding to the peak of an emission line, and that emitted at 800 nm, corresponding to a less intense continuous background. The lamp was operated at an energy of 800 J, with a peak current of 1.3 kA, and a pulse duration of l ms. This example is indicative of a general result: at those wavelengths corresponding to maxima in the emission spectrum, the lamp emission is always less directive than at those wavelengths corresponding to lower spectral intensity. The reason for this difference is that, according to Kirchhoffs law, at peak emission wavelengths the plasma is more absorbing and the lamp AID resembles more closely that of surface emitters. At wavelengths where the plasma is more transparent the angular emission distribution resembles more closely that of a volume emitter. To make the huge amount of information, delivered by the joint spectral-angular intensity distribution, useful for ray tracing purposes, we have developed a simple model to describe a flash-lamp. The starting points for this model are the two observations, discussed previously, that the plasma column is thinner than the lamp bore and that the plasma emission is something between that of a surface emitter and that of a volume emitter. We have chosen, therefore, to represent the spectral AID of an element of the lamp surface, with a linear superposition of volume and sur-
324
D. Bigazzi et a L I Optics Communications 110 (1994) 321-326
Io
_=_ E
<1:
Wavelength (nm) Fig. 3. Typical spectral image recorded by the CCD detector: the spectral intensity along z-axis is plotted versus wavelength (x-axis) and position on the direction transverse to the lamp axis (y-axis), in same conditions of Fig. 1.
811.29 nm
1
501~s •
~
a)
o
0.6 o,
/
"o (1) N
0
E
1
/
•
1 ms 0 Z
b)
811.29 nm o
800 nm
•
.,,,,f/f
~
~
0.8 0.4 0. |
90
60
30
0
30
60
Angle on internal surface (degrees) Fig. 4. Typical intensity distributions ; (a), for the wavelength of 811.29 nm, for three different excitation pulse duration: 2 ms, 300 ], 500 A (open circles); 1 ms, 800 1, 1.3 kA (open squares); 50/ts, 160 J, 2.3 kA (solid circles); (b) for different wavelengths (1 ms pulse duration):spectral line at 811.29 nm (open circles) and continuous background (solid circles). Solid and dashed lines represent, respectively, ideal surface and volume emitters filling homogeneously the lamp bore.
D. Bigazzi et al. / Optics Communications 110 (1994) 321-326
325
1.2 08 "o ¢9
"E 0.8
~'0.6 ~0.6
"1o Q) N
~ 0.4
~0.4
O
z
0.2
0
0.2
400 0
30
60
90
500
600 700 Wavelength (nm)
800
900
Angle on internal surface (degrees)
Fig. 5. Lamp model in same condition of Fig. 4b. Spectral line at 811.29 nm (open circles), continuos background at 800 nm (solid circles), solid and dotted hairlines represent polynomial fit of experimental data, heavy sofid and dashed lines represent surface and volume ideal emitters i'filing homngencously a 6.5 mm diameter column, against a lamp bore of 10 mm. face ideal emitters, as I o ( 0 ) = a~cos0 + bgcos2 0. This relation was found to describe correctly the lamp AID as it was emitted by a steady, homogeneous plasma column smaller than the lamp bore, whose diameter do was also obtained from a data fitting. The plasma column of diameter do was found to emit 80% of the total lamp intensity. For the presented example, do resulted to be 6.5 m m corresponding to 65% of the lamp bore. This percentage is consistent with the plasma column time evolution described by Vitel et al. [8]. The remaining 20% of lamp emitted intensity could be better taken into account considering higher order terms in a cos 0 polynomial, but this was considered not necessary for ray tracing purposes and more difficult to be interpreted on a physical basis. Once Io (0) has been normalised imposing -Io (0) = l, the sum a~ + b~ = 1 results always very close to unity. Fig. 5 shows the results of this model when applied to the same data shown in Fig. 4b. (Confidence parameter R 2 = 0.99; as00 = 0.18, bs00 = 0.79, ash = 0.60, bsH = 0.38.) Observing Fig. 5, we can conclude that, at least in this example, the radiation emitted in correspondence of the continuum
Fig. 6. Lamp model spectrum (same conditions of Fig. 1); heavy line is the spectrum of the a~ coefficient (surface emitter), thin line is that of the b~ (volume emitter). The sum of the two coefficients, approaching 1, is also reported. spectrum exhibits an angular distribution of radiation quite similar to that of a volume emitter. Repeating this process for all wavelengths analysed in our measurements, we can study the wavelength dependence of the coefficients a~ and b~. It is very interesting to compare this "spectrum" of coefficients with the lamp spectrum represented in Fig. 6. The coefficient a~ presents its maxima exactly at those wavelengths where a spectral emission line is present. Correspondingly, b~ shows minima at the same wavelengths. This result shows in all its evidence that, for typical excitation parameters (pulse duration and energy), the lamp emission characteristics are quite complicate, since the plasma behaves as a volume or a surface emitter, depending on the wavelength. A remark can be added on the fact that the wavelength behaviour of a~ presents some differences from the spectrum shown in Fig. I. In fact, while the spectral lines at longer wavelengths correspond to pronounced maxima for a~, the same is not true for spectral lines at shorter wavelengths. This can be explained by taking into account the black-body spectrum at T = l04 K, represented, apart for an arbitrary factor, as a dashed line in Fig. I. This temperature was reported as the average temperature of the plasma in flash-lamps used in similar conditions [3]. Since the black-body intensity is lower at higher wavelengths, the emission intensity on the peaks of the red and IR
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lines is much closer to that of a black-body, than that of the lines in the violet or UV.
4. Discussion The model discussed in this work allows an easy characterisation of flash-lamp emission in terms of simple functions. Moreover, this model describes the angular intensity distribution, at any wavelength, as a linear superposition of only two distributions. In this sense, this model is a new solution to the optical simulation of all systems where the lamp angular emission distribution is of some concern. In fact, it permits a complete simulation in a very fast way, performing only two different ray-tracing computations, respectively for the two angular intensity distributions, and making a linear combination of the results, using as weight factors the coefficients a~ and ba. This is particularly useful if applied to those systems that employ non-imaging optics to redirect lamp radiation. Respect to the first work that solved the problem of single shot measurements of lamp angular radiation distribution, the addition of spectral resolution permits to distinguish various contributes to lamp emission, and to measure their different angular emission distribution. Of course this model holds only if cylindrical symmetry is assumed, both for the lamp and for the discharge. All flash-lamps used in high power lasers are cylindrical, then axially symmetric. Discharge symmetry is, however, assured only if the lamp axis is vertical, as in our measurements. On the contrary, in normal laser use the lamp is held horizontally. This lead to convection currents inside the gas that shift the discharge region in the upward direction. In this case the model is not completely correct. However, since this effect is limited to less than 1 mm, otherwise the discharge will contact the lamp wall, it will affect the precision of the ray tracing simulations only marginally. In addition this is comparable with producing and mounting tolerances of flash lamps. However flash lamp pumped laser manufacturers should take into account that mounting the lamps vertically into the laser head would reduce the thermal loading of the lamp wall, and will made it radially symmetrical, resulting in a higher input power possible for the same flash lamp.
In addition, since the lamps are coupled with reflectors, a loss of cylindrical symmetry can be caused by plasma re-absorption of the reflected lamp emission. In general this is to be avoided in properly optimised reflectors, since the re-absorbed radiation reduces the overall efficiency. The model describes the time-average plasma emission over the whole pulse duration. The use of a gated CCD detector would permit the single shot study of both spectral and spatial evolution of the lamp emission [9], with time resolution up to 5 ns. Such a measure could allow the modelling of lamp, taking into account the true time evolution of radiation emission. This would be not actually necessary for quasi-steady state ray-tracing simulation of long pulse lasers, but could represent a valuable tool in plasma diagnostics. However transient simulation of short pulse lasers (< 100 ~ts) should take into account the discharge build up, requiting such a measurement.
Acknowledgements The authors are very grateful to Dr. Skowronek and Dr. Y. Vitel of Laboratoires Plasmas Denses, Universit6 Pierre et Marie Curie (Paris), for the helpful discussions about plasma properties. This work was performed in the framework of the EUREKA Project EU 226 High Power Solid State Laser. Financial support from the italian CNR Finalised Project "Tecnologie elettroottiche" is gratefully acknowledged.
References [ 1] D. Cilia, Report for 7th Intern. Meeting of Eureka Project EU226, Munich (1993). [2] L. Ulivi and P. Mazzinghi, Optics Comm. 81 ( 1991 ) 157. [3 ] O. Kahan, S. Mattews and E. Gregor, Proc SPIE 609 (1986) 138. [4] B. Smith, Proc SPIE 609 (1986) 24. [5] H. R. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964). [6] A.R. Striganov and N.S. Svetitskii, Tables of spectral lines and ionised atoms (Plenum, New York, 1968). [ 7] H. T. Powell, A.C. Edandson and K.S. Jancaititis Proc SPIE 609 (1986) 78. [8] Y. Vitel, M. Skowronek, K. Beninsty and M. M. Popovic, J. Physics D 12 (1979) 1125. [9] J. A. Antoniades and T. Peyeser, Rev. Sci. Instrum. 58 (1987) 253.