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A measurement technique capable of recording three-dimensional laser induced images with a spatial resolution of 610x512x20 voxels over a volume of 29x24x15 mm3 and at a frame rate of 1 kHz is presented. A novel approach for sweeping the illuminating laser sheet across the investigated volume is introduced as a key feature. The technique is applied to imaging nebulized water droplets with a nitrogen-jet central feature.
©2011 Optical Society of America
1. Introduction
The ability to characterize turbulent flows is of importance in areas such as combustion, fluid dynamics, chemistry, etc. Laser based measurement techniques, capable of probing non-intrusively with high spatial and temporal resolution, are now well established for diagnostics in these areas. Many measurement techniques that are applied to turbulent flows, such as flow tagging, planar laser induced fluorescence (PLIF), and particle image velocimetry (PIV) [1,2], are based on illuminating a two-dimensional section of the flow with a thin laser sheet. However, turbulent and reacting flows are intrinsically three dimensional phenomena; therefore, two-dimensional measurements do not always lead to an accurate understanding of flow processes. One approach which extends planar measurements into the third dimension is to rapidly scan the sample with the laser sheet. During the scan, several images are recorded at different depths and used to reconstruct a three-dimensional image of the sample. To obtain a sufficiently short exposure time to freeze the motion and/or chemical reactions of the flow, either a high frequency pulsed laser [3], or long pulses in combination with a framing camera can be used [4, 5]. Increased signal to noise and the ability to frequency convert the laser radiation into a broader wavelength region are obtained by increasing the laser fluence. A high laser fluence can be achieved by using a cluster of several Nd:Yag lasers in combination with a framing camera containing a cluster of intensified CCD’s. Three dimensional images made from 8 2D images with recording times down to 44 µs have been obtained in this way [6–8]. The recent development of megahertz-rate pulse burst laser systems also enables 3D images with higher resolution, i.e., more images, to be recorded within a time period on the order of ~100 µs [9–11].
The scanning techniques discussed so far produce a single 3D image where the flow and/or reactions are frozen in time. However, turbulent flows are stochastic in nature and time resolved measurements are required in order to fully capture their intrinsic behavior. Fortunately, the recent improvements in high speed CMOS camera technology and high frequency solid state pumped lasers approaches the point where three dimensional image sequences can be recorded with a temporal and spatial resolution that can resolv, at minimum, processes with moderate flow and reaction rates. In addition, the post triggering ability of CMOS cameras enables the capture of rare events such as flame extinction or miss-fire.
In this paper a diode pumped Nd:Yag laser is continuously operated at 20 kHz. A laser sheet is scanned through a plume of nebulized water droplets with a central nitrogen-jet and 3D images are recorded at a frame rate of ~1 kHz.
2. Experimental setup
Figure 1 illustrates the optical arrangement used in this investigation. An Edgewave HD40I-OE laser is operated at 532 nm, emitting 12 ns laser pulses with a pulse energy of 5 mJ at 20 kHz. A telescope lens arrangement, L1 and L2, is used to contract the rectangular laser profile onto oscillating mirrors, which are placed at either side of a 4f-setup. A cylindrical negative lens, L5, is located at its focal distance (−50 mm) from the last oscillating mirror (OM2) to expand the laser beam in the vertical direction.
Fig. 1 The experimental setup seen from above. All lenses (L1-L5) are cylindrical lenses except L6 which is spherical. L:s focal length (f), Mirror (M), Oscillating Mirror (OM), Glass Plate (GP), Dye Cuvette (DC).
A spherical positive lens, L6, also positioned at its focal distance (500 mm) from OM2, forms a horizontally focused and vertically collimated laser sheet above the nebulizer nozzle. To obtain information regarding the spatial energy distribution of the laser sheet and pulse to pulse fluctuations, a fraction of the laser sheet irradiance is reflected by a glass plate into a dye cuvette. Dye solution is pumped through the cuvette to avoid bleaching and convection as would occur with a closed dye cuvette. The illuminated flow of water droplets above the nebulizer and the laser induced fluorescence from the dye cuvette are simultaneously imaged onto a high speed CMOS camera (Photron Fastcam SA5) by a f = 135 mm F/22 objective with a magnification of m ~0.4. This yields an imaging focal depth of 18 mm wherein the two dimensional spatial resolution is still limited by the pixel size [12]. The laser intensity profiles cover a narrow strip ~30 pixels wide at the edge of the CMOS while the Mie-scattered light from the nebulized water droplets covers the rest. The maximum resolution of the camera is 1064x1064 pixels. However, to reach a frame rate of 20 kHz it is limited to a region of interest of 640x512 pixels. At these settings, the 8 gigabyte internal memory of the camera can store up to 17463 images (corresponding to 873 3D stacks with 20 images in each stack).
3. Scanning
In most cases, the displacement of the laser sheet is achieved by combining a collimating lens with an angular deflector such as a rotating, galvano or resonant oscillating mirror. To achieve equidistant spacing between the illuminated planes, the deflector needs to be operated at a constant angular velocity from the first to the last section of the 3D image. For slowly propagating flows, where only moderate scanning speeds are required, this can be easily achieved by galvano mirrors [12]. However, for scanning speeds in the kHz range, the acceleration and deceleration time of the deflector becomes comparable to the total sweep time, i.e. a fast oscillating mirror cannot achieve a constant angular velocity during the entire scan. Therefore, in most scanning based 3D imaging techniques, a long scanning period is used in comparison to the recording time of the 3D image. In that way only the linear part of the scan is used.
For time resolved 3D measurements with the laser operated continuously at a constant frequency, restriction to only the central part of the mirror oscillation, would reduce the temporal resolution, i.e. increase the time between successive 3D images. Alternatively if the entire mirror oscillation is used it would result in a varying sheet separation, i.e. varying spatial resolution. If the laser sheet deflection instead could follow a triangle wave, the entire oscillation could be used without alternating the spatial resolution during the scan. Acousto optical deflectors (AOD) can perform triangle wave deflections at high frequencies (>kHz) and would be a suitable choice if it was not for the low damage threshold and efficiency. Another possible candidate would be rotating polygonal mirrors (PM) which can provide scanning speeds above 100 kHz [13], well above what is required for the present setup. Unlike resonant oscillating mirrors, the scanning frequency of PM can be varied continuously. However, the angular deflection in one scan is set by the number of facets in the polygon and cannot be adjusted. Also, the axis of rotation is in the center of the polygon and not in the center of the mirrors surfaces. This, together with the laser beam width limits the part of the scan that can be used. It also introduces errors in the linearity of the scan as the laser beam would not be reflected from the same position for every deviation [13]. Here resonant oscillating mirrors are used to scan the laser sheet. Such mirrors oscillate in a sinusoidal manner, and in order to generate a more linear displacement of the laser sheet, i.e. angular deflections following the shape of a triangle wave, the angular deflections from more than one oscillating mirror are added together.
As indicated in Eq. (1), a triangle wave, can be created by summing up an infinite amount of sine waves,
Thus, adding odd overtones with decreasing amplitude, step by step converts the initial sine wave into a triangle wave. The adding up of sinusoidal deflections can in reality be achieved by placing oscillating mirrors in each end of a 4f setup as illustrated in Fig. 2 .
Fig. 2 Schematic drawing of a 4f-setup. The wave front exiting the first (left) oscillating mirror is identical to the wave front at the second oscillating mirror. There is no magnification in this 4f-setup, i.e. f1 = f2.
The wave front at the second mirror is an identical reconstruction of the wave front immediately after the first mirror. Thus the angular deflections induced by the two mirrors are added together. Additional 4f setups can be added in order to include higher frequencies. However, as the frequency increases, the size of the mirror must decrease in order to match its eigenfrequency. Eventually the mirror is too small to withstand the power density of a laser pulse train with small enough beam profile to fit the size of the mirror. In addition, the experimental complexity increases as more oscillating mirrors are added. Fortunately, the benefit of adding higher overtones decreases rapidly as a function of number of overtones already used. In this demonstration, two scanning mirrors were used, one at a base frequency of ~1 kHz and one at the first odd overtone at ~3 kHz.
In the given configuration, each sweep of the laser sheet produces ten images. The timing could be set for the laser sheet to illuminate the same sections regardless direction of the sweep. However, to increase the spatial resolution, the timing of the laser pulses are instead adjusted so that their positions are shifted half the inter sheet distance in between each sweep (see Fig. 3(a) ). To form a triangular oscillation from an infinite amount of overtones added to the base frequency, as in Eq. (1), the amplitude of the first odd overtone should be one ninth the amplitude of the base frequency. With only the first odd overtone added, an amplitude corresponding to one tenth of the fundamental frequency's amplitude is found to produce more evenly spaced laser sheets and is thus used in this demonstration. To visualize the position of the laser sheet during a scan, the nebulizer is replaced with a white diffusive paper, oriented perpendicular to the laser light propagation. The camera is positioned behind the paper to record the different positions of the laser sheet. In Fig. 3(a), the recorded position is plotted as a function of time. A simulated curve constructed from the two sine waves corresponding to the mirrors oscillations is plotted on top of the measured laser sheet positions. A pure sine wave and a triangle wave are also plotted for comparison. In Fig. 3(b) simulated normalized laser sheet positions from the sine wave, the triangular wave and the measured laser sheet positions are shown. Closer to the turning point for the pure sinusoidal scanning the distances are smaller than in the center of the scan. By adding the first odd overtone, a more homogeneous distance distribution is achieved.
Fig. 3 (a) Example of a sine wave, a triangle wave and the sum of the sine wave and −10% of its first odd overtone. The measured depth position of the laser sheet is also plotted. In (b) the measured positions of the laser sheet is plotted together with the positions as it would be for a sine wave and a pure triangle wave.
The width of the laser sheet in the measurement volume approximately corresponds to the distance between the laser sheets.
4. 3D image visualization of nebulizer water droplet/nitrogen flow
The measurement technique is demonstrated on a nebulizer water droplet nitrogen flow. As the nitrogen propagates through the nebulizer, small droplets of water are pulled along the flow and through the 21.5 mm diameter nozzle. The bulk flow velocity is estimated using cross correlation between images of the same sections recorded within consecutive 3D images, to approximately 0.4 m/s. To increase the complexity of the flow, an inner flow of pure nitrogen is added with a circular exit diameter of 4 mm.
The volume illuminated during one scan (29x24x15 mm3) covers the entire width and half the depth of the nebulizer. To merge the recorded two-dimensional images of the Mie-scattered laser light into three dimensional visualizations of the flow, some post processing of the data is required. In addition to background correction, the images are also corrected for non uniformities and pulse to pulse fluctuations in the laser sheet by dividing with the imaged dye cell fluorescence intensity.
Each 2D image is thereafter plotted at its corresponding position in a 3D volume with transparency values inversely proportional to the intensity values in the data set. A surface is also plotted to better visualize the boundaries of the flow. Normally an isosurface of constant concentration or scattering intensity would provide a good indication of the flow boundaries; however, since the Mie-scattering from droplets is highly localized with intensity variations ranging from maximum to minimum between adjacent pixels, this is not possible. Instead, the 2D images are first low-pass filtered using a Gaussian filter (40 pixels wide) in the frequency domain. The intensity values in the filtered images are now smooth enough to form an isosurface of constant intensity marking the boundaries of the flow. In Fig. 4 the 2D images used to create the first 3D image in the recorded series (Media 1) are displayed together with the resulting 3D image.
Fig. 4 (a) - (q) 17 of the 20 images used to create one 3D image covering approximately half of the spray. The droplet free part of the spray seen in images (l) – (r) is created by a stream of nitrogen gas entering the flow at the nebulizer nozzle. The three omitted images show no signal, as the laser sheet was outside the flow region. (r) The resulting 3D image.
During the recording time of one 3D image (1 ms) the flow has moved approximately 9 pixels corresponding to 0.4 mm (measured by PIV). Since the sampling of the images in one 3D image is interleaved (sampling order b,d,e,g,i,k,m,o,q,p,n,l,j,h,e,c,a in Fig. 4 the relative distortion between two adjacent images varies, with smallest distortion (~0.5 pixel) between Fig. 4(p) and Fig. 4(q) and largest distortion (~7 pixels) between Fig. 4(a) and Fig. 4(b). For higher flow rates, where the distortions cannot be assumed to be negligible, the time resolution could be increased by a factor of two by scanning the same sections in both directions. In addition, if the velocity field is measured, it can be used to correct for the droplets movement during the scan [12].
In Fig. 5 four of the recorded 3D images are plotted. To better visualize the dynamics of the flow, the time separation has been increased from 1 ms to 3 ms by selecting every third image. The images shown are part of the movie available online (Media 1). From studying this image sequence, it is clear that a part of the flow in the upper right corner is detached from the main flow. From only two dimensional images, including recordings with high frame rate, it would not be possible to judge whether a structure is in fact detached, or merely folding in from a region outside the probe volume.
Fig. 5 From the 3D image sequence (Media 1 and Media 2), four images (a)-(c) have been selected. Although consecutive images are not identical, two images between each image pair, (a)-(b) (b)-(c) and (c)-(d) has been discarded. This results in a time separation of 3 ms which better visualizes the dynamical processes of the flow. The two dimensional images are plotted at the corresponding position of the laser sheet with transparency proportional to their intensity values. A semi transparent surface helps to judge the boundaries of the nebulizer flow. All values are given in mm. Approximately half of the spray is scanned and the droplet free nitrogen flow can be seen as a pillar in the center of the spray. The spray propagates in the upward direction with the lowest part just above the nozzle tip.
5. Conclusion and outlook
A technique has been demonstrated that utilizes a high frequency Nd:YAG laser in combination with oscillating mirrors and a high speed CMOS camera to record sequences of up to 873 3D images at a frame rate of 1 kHz and with a resolution of 610x512x20 voxels covering a volume of 29x24x15 mm3. The scanning of the laser sheet is achieved by adding the deflections from two oscillating mirrors in order to create more equidistant positions between the laser sheets. The frame rate is limited by the maximum repetition rate of the laser (20 kHz) as well as the desired number of images recorded for one 3D image. The technique is not, however, constrained to Mie-scattering. The kHz laser system presented here can be used to extend other planar laser measurements into three dimensions, e.g., PIV [14], flow tagging [2], fuel PLIF [15] and OH PLIF [14], providing there is sufficient signal, and that the flow is slow in comparison to the image acquisition time. From LIF measurements, 3D- isosurfaces of concentrations can be mapped, and if the measurements are performed quantitatively with adequate signal to noise and spatial resolution, scalar dissipation rates could be calculated.
Acknowledgments
The authors wish to thank the Competence Centre for combustion processes as well as the CECOST through SSF and STEM for financial support. Also the ERC Advanced grant DALDECS is acknowledged.
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