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The first application of a microlens array beam homogenizer to planar laser measurement techniques in combustion diagnostics is demonstrated. The beam homogenizing properties of two microlens arrays in combination with a Fourier lens for widespread applications are presented. An uniform line profile with very little temporal fluctuations of the spatial intensity distribution was generated resulting in a significant reduction of measurement noise and enabling an easier and faster signal processing.
©2006 Optical Society of America
1. Introduction
For more than two decades laser diagnostics are of utmost importance for the experimental investigation of reacting and non-reacting flows in fluid mechanics or combustion research. In these fields, laser based techniques offer the advantages of remote, non-intrusive measurements with high temporal and spatial resolution.
In particular, spatially resolved 2D-measurement techniques can help to understand such complex phenomena like the turbulent mixture formation in direct injection engines or the interaction of turbulence and chemistry in flames. For this purpose, widely used planar techniques are, e.g., laser-induced fluorescence (LIF) for concentration or temperature mapping [1], laser Rayleigh scattering techniques (LRS) for density or temperature field detection [2], laser-induced incandescence (LII) for soot volume concentration and particle size measurement [3] and Ramanography for two-dimensional detection of concentration fields [4]. All the mentioned techniques have in common that a laser beam is formed into a light sheet and the signal is generated from elastic or inelastic scattering, fluorescence processes or emission of Planck’s radiation in the illuminated plane. The signal is then collected by a suitable two-dimensional detection system, typically a CCD- or an intensified CCD-camera. In the commonly used linear regime of the mentioned techniques, the signal intensity is linearly dependent on the incident laser intensity.
For quantitative planar investigations, it is highly desirable to achieve a most uniform illumination of the complete region of interest since subsequent spatially dependent intensity corrections are not always possible or tend to enhance the total measurement error because of their unknown variation with time.
However, for most of the mentioned techniques, pulsed high peak-power solid-state, excimer or dye laser sources have to be used in order to achieve the high temporal resolution necessary for the characterization of turbulent, fluctuating flows or combustion processes. One of the major drawbacks of these laser systems is that they possess a rather poor beam quality compared to continuously emitting laser sources. Resulting from the actual design of the laser system, the lasers do not emit the flat top intensity profile desirable for quantitative measurements without subsequent corrections. Moreover, also the shot-to-shot fluctuations of the output energy negatively influence the spatial intensity distribution as the profile of the beam varies to a certain extent with time and thus increases the noise in single-shot measurements. This is owing to, e.g., fluctuations in the laser medium, in the pump source or the stochastic nature of the pulse generation process itself.
Therefore, the technical application of the mentioned techniques is hampered by two major problems,
- temporally stable inhomogeneities of the spatial intensity distribution and
- temporally fluctuating inhomogeneities.
a) Besides correcting the overall shot-to-shot fluctuations of the pulse energy to a reference level by logging the total output energy all over the recorded data-set, it is of common practice to normalize the instantaneous images of the scattering processes using an image recorded at defined reference conditions to get rid of optical set-up constants like the spatial distribution of the laser fluence which is in general assumed to be constant in time. However, the a-posteriori correction to reference conditions is not practicable in several fields. For instance for on-line sensor measurements or product engineering applications an in-situ interpretation of the measurement results is desirable. Moreover, the invariability of the reference conditions cannot be guaranteed for long-term investigations. In addition, temporally stable spatial inhomogeneities can be problematic, if the measurement principle is based on saturation effects, where the detectable intensities cannot be increased by further raising the laser output power [5–7]. Especially at the outer regions of the laser beam, the intensity of the laser fluence can reach values, where the condition for saturation of the signal is not fulfilled. That loss of saturation efficiency is called laser-wing effect in the literature [6, 8] and may lead to a misinterpretation of measured signals. For example in saturation LIF for minor species concentration mapping [9] or in laser-induced incandescence (LII) techniques, where the soot mass-fraction or the primary particle diameter of agglomerates is measured via the emitted Planck-radiation after laser illumination (e.g. [10–12]), signal saturation is aimed. Ni et al. [12] explicitly note that laser beam profiles with uniform intensity distribution in the context of LII techniques would ease the monitoring of the local saturation efficiency and thus simplify the modeling of the heating and cooling mechanisms of the particles which drastically reduces measurement uncertainties.
b) In contrast to the temporally stable inhomogeneities which can be corrected to a certain extend, temporal fluctuations in the spatial intensity distribution cannot be accounted for and contribute directly to the measurement uncertainty, i.e., the standard deviation of the mean value of the quantity of interest. In this context, a number of examples can be found in the literature where image corrections are applied but obviously do not fully remove the existing inhomogeneities (see, e.g., [13, 14]). Thus, the 2D interpretation of the measured signal is complicated as the measurement noise is a function of the position inside the measurement domain. One possible remedy is to detect the planar intensity distribution simultaneously to the actual measurement using an additional camera which is however connected with an increased experimental complexity.
In this work another approach to the described problem is shown which is experimentally simple to apply and comparatively inexpensive. A beam homogenizer is used to homogenize the light field in the measurement plane. Different experimental strategies for this task can be found in the literature, especially in the field of lithography and material processing (see, e.g., [15–17]). Depending on the application area, especially the homogenization by diffractive elements or microlens arrays has become accepted, mostly for homogeneously illuminating plane surfaces. Here, we have used two microlens arrays in conjunction with a Fourier lens to achieve a homogeneous illumination of the measurement plane for planar laser diagnostics. The fruitful influence of this device on the general quantification process of the measured planar signals is pointed out.
However, the reader has to be aware that for some measurement techniques the quantification is also hampered by quenching effects or temperature dependent quantum yields, which can not be influenced positively by a homogeneous illumination of the region of interest and thus are not further discussed within this paper.
2. Experimental
With the aim to demonstrate the advantages of spatially uniform beam profiles in the field of planar laser measurement techniques being generated by optical beam homogenizers, the following exemplary experiment was performed comparatively with and without the use of a beam-homogenizer in the form of microlens arrays.
2.1 Optical set-up
The laser radiation of a narrowband KrF excimer laser with a rectangular beam profile, emitted at 248 nm within 20 ns pulse width and a maximum pulse energy of 250 mJ, is formed to a light-sheet of ~100 μm thickness and 40 mm height inside the measurement area which is located inside a flow chamber. The latter is continuously purged with a homogeneous mixture of air and seeded acetone as fluorescence tracer (1.4 percent by volume). The chamber and the seeding procedure are described in Ref. [18].
Before the beam travels through the plano-convex cylindrical focusing lens with f=500 mm (see Fig. 1), it passes through two parallel fused-silica microlens arrays (LA1 and LA2), consisting of 36 plano-convex cylindrical lenses each (0.5 mm pitch, array fill factor 95%, f1=5 mm, f2=10 mm, damage threshold 2 J/cm2).
The assembly of the two microlens arrays (designed by the Bavarian Laser Centre, BLZ) which is called beam homogenizer in the following results in a separation of the incident laser beam into several segments which are formed into slightly divergent sub-beams (Fig. 2). These sub-beams are then superposed on each other in the focal plane of a planoconvex cylindrical Fourier lens (f Fourier=1000 mm), resulting in a homogeneously illuminated light-sheet. The second array LA2, which is positioned 10 mm away from LA1, is also called field array as it images the apertures of the first array into the output plane of the homogenizer [19]. Owing to interference effects the practically achievable quality of homogenization is ±5% using a narrowband laser system with a bandwidth (FWHM) of 0.2 cm-1 like in this study. The application of excimer systems without grating leads to even better homogeneity, whereas satisfying beam profiles are achievable with lens arrays consisting of more than 10 lenses each.
It shall be mentioned that this type of homogenizer, i.e., with cylindrical microlenses, does not affect the out-of-plane intensity distribution of the laser beam. Thus, for nonlinear diagnostics like two-photon laser induced fluorescence [6] where also the out-of-plane component should be uniform, a beam homogenizer either with spherical lenses or with two more lens arrays rotated by 90° has to be applied.
For the experiment without the homogenizer, the Fourier lens and the microlens arrays are removed. In our set-up the over-all intensity losses compared to the non-homogenized case sum up to around 20% and are due to reflection losses on the additional optical components, the fill-factor of 95% and the insertion of an aperture, which shall suppress intensity peaks at the edge of the laser profile, sometimes described as “dog-ears” in the context of lens arrays (see, e.g., [20]).
The laser-induced fluorescence signal of the homogeneously distributed tracer is detected under 90° viewing angle by a fiber coupled, 2nd generation ICCD-camera (quantum efficiency @ 400 nm: 12 %, electron gain of the multi-channel plate MCP: 255, 1024×1024 pixel) after passing through a filter combination of a Schott WG335 and a WG375 long-pass filter to suppress elastically scattered light. The signal of the image plane is collected via a Soligor 90 mm f/2.5 objective on the CCD chip. In order to reduce the read-out noise, a 2×2 square binning of the pixels is applied which results in an effective size of 512×512 pixels.
2.2 Statistics
For a statistical evaluation of the detectable signal, 512 single-shot measurements Ii(x,y) were taken. The shot-to-shot fluctuations of the laser pulse energy were recorded by a whole-field energy meter and normalized to the maximum detected pulse energy. Each individual image was background-subtracted, corrected pixelwise for vignetting effects and then multiplied by a normalizing factor accounting for the time-dependent incident total laser pulse energy. Subsequent to this pre-treatment, a temporal average over the ensemble of taken images Ii(x,y) was generated
with the aim to compare the resulting temporally averaged intensity distributions with and without homogenization.
In order to assess the property of the beam homogenizer, which is not only to accomplish homogeneous illumination of the image plane, but also to reduce the temporal fluctuations of the intensity profile significantly, the single-shot images are divided by the average image. From that normalized images, the root mean square (RMS) fluctuation is calculated by
The RMS-fluctuation is expressed in a normalized way, as partly different intensity levels within the non-homogenized data-series are to be compared with uniform intensity profiles for the homogenized case.
3. Results
3.1 Comparison of averaged images
In Figs. 3 and 4 the ensemble averaged images of both measurement series are illustrated in false colors. Fig. 3 shows the result of the non-homogenized PLIF-experiment. The inhomogeneous spatial distribution is clearly visible. That strong inhomogeneity cannot be corrected sufficiently in the single exposures by correlating the instantaneous images with that of the averaged image as the temporal fluctuations of the spatial intensity distribution is significant, as will be shown later. The averaged image of the series including the beam homogenizer (Fig. 4) shows almost uniform intensity distribution. The absolute intensity variation in the field is less than 5%. The residual inhomogeneities in the image in form of faint strips result from interference of the superposed sub-beams inside the measurement area and can be minimized by the adjustment of the homogenizer and the Fourier lens.
Obviously real-time engineering investigations are facilitated by the application of the homogenizer since image corrections are now dispensable and the measurement can be evaluated directly.
As perspective, an exemplary single-shot result, obtained from a planar Tracer-LIF experiment for the concentration mapping of two different turbulent flows in the context of validation of sub-scale transport models in Large-eddy simulation [21] is shown in Fig. 5. Here the shear layer of both flows is illustrated, whereas the tracer is seeded to the flow on the left-hand side. The flow on the right side of the picture is unseeded. The false color image indicates high concentration of the left flow in bright colors, the pure flow on the right is presented in black. It is emphasized, that the image in Fig. 5 has not been processed.
Fig. 5. Exemplary non-processed image with applied homogenizer (shown is the single shot result of a tracer-LIF measurement of the mixing field of two different turbulent flows.
3.2 Comparison of the statistical fluctuations of the spatial intensity distribution
As deduced in Eq. (2), the improvements to planar laser measurement techniques with respect to the statistical fluctuations of the spatial intensity fluctuation of the illuminating laser beam, which can lead to high statistical errors, are displayed comparatively in Figs. 6 and 7 without and with the application of a beam homogenizer.
Fig. 6. RMS image of the normalized fluorescence signal, without the application of the beam-homogenizer.
Fig. 7. RMS image of the normalized fluorescence signal, with the application of the beam-homogenizer.
A noticeable spatial distribution of the fluctuations is obvious for the non-homogenized case (Fig. 6). The image shows clearly the stripes observed in many investigations, even where corrections for the inhomogeneous laser beam profile were performed (e.g. in Refs. [9, 13, and 14]). In regions, where the mean intensities are relatively large (Fig. 3), the RMS-fluctuations of the normalized intensities are lower compared to regions with lower signal intensity.
By contrast, the application of the beam homogenizer smoothes drastically the spatial distribution of the averaged fluctuations (Fig. 7). Within the complete region of interest the statistical noise, especially evoked by temporal fluctuations of the incoming laser beam is almost uniform. Moreover it is worth to mention, that the absolute noise level has decreased noticeably.
The observed improvements when using homogenized illumination of the image plane are illustrated in Fig. 8. The effect of beam homogenization is a clear reduction in statistical fluctuations of measured signals as a function of incident laser energy.
Fig. 8. RMS fluctuation of the normalized intensity as a function of the averaged intensity - with and without the application of the homogenizer (the black curves indicate the relationship I′¯~(I¯)-1/2).
Whereas the normalized intensity fluctuation I′¯, which can be regarded as the overall noise of the measurement, is scattered over a broad range for the non-homogenized case, following the camera related noise via the relation I′¯~(I¯)-1/2) (see, e.g., [6]), the intensity distribution for the homogenized case is distributed much narrower. The total amount of these fluctuations has reduced by 26 % from an average value of 0.172 in the non-homogenized case to 0.127 in the homogenized study.
In order to evaluate this remaining fluctuation which forms the overall measurement noise in this case, the signal-to noise ratio SNR of the detector system is analyzed in more detail. Following the formulation of Paul [22], according to Roy et al. [23], the SNR for a single pixel on an array detector with a multi-channel plate intensifier is
where Np is the number of photons incident on the pixel, η is the quantum efficiency of the photocathode, G e,MCP is the electron gain of the MCP, κ is the noise factor associated with the MCP intensification, G e,MCP is the conversion efficiency of electrons at the output of the MCP to electrons in the array pixel, and N x is the sum of noise electrons that are due to the read out process, dark noise, charge-transfer efficiency, etc.
The SNR for the presented experiment according to that estimation is 9.9, taking into account the binning of 2×2 pixels. With a average signal of 40000 counts the uncertainty is 4057 counts which corresponds to a relative fluctuation of 0.1. Obviously the beam homogenization reduces the total measurement error close to the minimum practical achievable uncertainty, which is the overall-noise of the applied ICCD camera.
Thus, the reduced uncertainty achieved by the here presented beam homogenizing method reveals a direct improvement in the planar measurement of temperature, species concentration and fuel-air ratio measurement for the investigation of fluid dynamic phenomena.
4. Conclusion
In summary, we have demonstrated, for the first time to the best of our knowledge, the application of microlens arrays as beam-homogenizers for planar laser techniques. It is shown, that the principle of beam-homogenizing for the illumination of plane surfaces can be established also for homogenizing high peak-power pulsed laser beams with the aim to gain a homogeneous spatial distribution on a line profile.
By the application of the microlens arrays to the inhomogeneous laser profile, an almost uniform beam profile with a remaining non-uniformity of less than 5 % could be achieved. From this fact two major implications for planar laser measurement techniques can be formulated:
- The homogeneous illumination of the image plane enables the direct evaluation of the measured data in terms of quantitative results without necessary and often not satisfying corrections for non-uniform profiles. This is of special interest for a further development of planar laser techniques towards engineering practice, where results from instantaneous, single-shot measurements have to be judged quickly.
- The recombination of the sub-beams passing the second microlens array, which is the actual principle of the homogenization here, significantly reduces the spatial fluctuations of the beam profile. The remaining fluctuations are uniformly distributed all over the measurement area. As a result, it could be shown, that the measurement uncertainty can be reduced to a level, which is close to the actual noise level of the used detector.
However it must be mentioned here that one aspect in the discussion of image improvements in planar laser diagnostics has been neglected so far. Beam non-uniformities must not necessarily originate from the laser source like discussed in this work. They may be introduced also from the investigated object in case of a strongly inhomogeneous density field that introduces beam non-uniformities by beam steering from refractive index variations. This problem is discussed, e.g., in [24] and cannot be solved with the beam homogenizer. A possible solution is suggested in [25] by the application of Rayleigh scattering in combination with a ray tracing based correction algorithm. The approach gives promising results for a turbulent non-premixed flame and is assumed to give also reasonable results in combination with other imaging techniques.
In future applications, the use of the homogenizer will prove even more valuable for nonlinear optical techniques (see, e.g., [26]). Here, the dependence of the signal on the spatial laser intensity distribution is much stronger than in the linear techniques discussed in this work.
Acknowledgments
The authors gratefully acknowledge financial support of parts of this work by the German National Science Foundation DFG and by the Bavarian government within the framework of the Bavarian research cooperation FORTVER.
Furthermore the authors would like to express their gratitude to the involved staff of the Bavarian Laser Centre (BLZ, Erlangen/Germany), who performed the design of the beam homogenizer.
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