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					Single-shot, two-dimensional ballistic imaging through scattering media
Megan Paciaroni and Mark Linne

Imaging through scattering materials is an important research area that is generally limited to medical diagnostic applications. Published techniques typically use a method of time- or coherence-gating of ballistic photons that separates these early photons in order to acquire an image without the large background created by the later-arriving diffuse light. Because of the limited number of ballistic photons and the typically low signal-to-noise ratios of these schemes, a large number of averages or scans is necessary. If the desired image is changing rapidly, however, single images of this transient are required. We have therefore evaluated a two-dimensional, single-shot method that can be used for imaging rapid transients in scattering environments. © 2004 Optical Society of America OCIS codes: 190.3270, 280.1740, 280.2470, 280.2490, 290.7050.

1. Background

Sprays have been studied for a significant period of time see, e.g., Ref. 1 . They are extremely complex structures that have not been fully described, especially in the case of a combusting transient fuel spray. Liquid jet fuel sprays have a series of fluidmechanical zones, including the liquid core that intrudes into the gas phase, the primary breakup region where the liquid core breaks into droplets, the secondary breakup region where primary droplets break into smaller droplets, and the vaporization region where the small droplets are evaporated before burning. Spray behavior is controlled by a large number of processes.1–3 Internal flow effects in the nozzle before the spray exits including turbulence and cavitation, are important. The physical and thermodynamic states of the liquid e.g., density, viscosity, and surface tension and the gas are also critical. The initial breakup of the liquid core is thought by many to be driven by the growth of harmonic disturbances, originating most likely within these internal flows. When the density of the surrounding gas is high,

M. Paciaroni is with the Division of Engineering, Colorado School of Mines, 1500 Illinois Street, Golden, Colorado 80401. M. Linne is with the Department of Combustion Physics, Lund Institute of Technology, 221 00 Lund, Sweden. Received 4 December 2003; revised manuscript received 16 June 2004; accepted 17 June 2004. 0003-6935 04 265100-10$15.00 0 © 2004 Optical Society of America 5100 APPLIED OPTICS Vol. 43, No. 26 10 September 2004

aerodynamic effects may contribute to the coherent growth of these waves. Conversely, when the gas has a low density and the jet is turbulent, the interior forces in the jet may induce turbulent primary breakup. There is, in fact, a debate regarding the existence of a liquid core in the atomization regime, and, if there is one, what its length and characteristics might be. This is the case because, in the atomization regime, it has not been possible to observe the very near field of the spray because the surrounding droplet field is quite turbid. Smallwood and Gulder4 ¨ have suggested that ballistic imaging could be used to mitigate this problem, making this technique useful for determining the structure of the dense core region of diesel sprays.4 Ballistic imaging5 offers an opportunity to investigate this region of the spray because it provides a shadowgraph- or schlieren-style image of structures that are embedded inside a turbid field. Indeed, one example of a ballistic image of the very near field of a water jet in a liquid-oxygen injector has been provided by Galland et al;6 this work was combined with image processing techniques to generate images through turbid media with attenuation on the order of 10 10.7 In the research described here, we evaluate various approaches to ballistic imaging to find the optimal configuration for single-shot imaging of rapid transients through the near field of transient diesel fuel sprays. The small amount of light that is transmitted through turbid material is separated into three components: ballistic, snake, and diffuse.8 Although it is possible to use a continuous wave source for bal-

listic imaging, we discuss the use of short pulses 150 fs because, in this case, these three components can be temporally separated from one another. Upon exiting the medium, a resultant pulse is typically orders of magnitude longer in time and much weaker in strength than the input pulse. A small group of photons, called ballistic photons, propagate directly through the material with no scattering. These photons traverse the shortest path and are the first to exit the material. The second group of photons, called snake photons, are forward scattered minimally and remain within a small forwarddirected solid angle. These photons traverse a slightly longer path and exit the material just after the ballistic photons. The remaining diffuse photons are scattered quite severely into a large solid angle, take the longest path, and are the last group of photons to exit the material. Because of their straight path, ballistic photons retain an undistorted image of structures within the material. If used in a shadowgram arrangement, the ballistic photons can provide diffraction-limited imaging of these structures. Unfortunately, in most highly scattering and absorbing environments, the number of transmitted ballistic photons is insufficient to provide the signal-to-noise ratio necessary for forming an image. In this case, the snake photons retain slightly distorted information and can be used in imaging, together with the ballistic photons, with little degradation of resolution. In contrast, diffuse photons retain no memory of the structure within the material. If allowed to participate in the formation of an image, the various paths that these multiply scattered photons take through the material will cause any image point they form to appear as if it came from an entirely different part of the object; this will seriously degrade image resolution. Unfortunately, diffuse photons are more numerous in light transmitted through highly scattering media. Thus the problem of obtaining a high-resolution image through highly scattering materials is a matter of separating and eliminating the diffuse light from the ballistic and snake light. This can be achieved with discrimination methods that make use of the properties retained by the early light and those lost in multiple scattering events: timing, coherence, direction, and polarization. Discrimination can be achieved in one of four ways: time gating a pulse of light, coherence gating a pulse of light, direction gating via spatial filtering, polarization gating, or by using a combination of two or more of these. Typically, ballistic imaging methods described in the literature use either raster-scanned single-point imaging techniques or two-dimensional systems that require a significant amount of averaging. However, scanning and averaging methods are unsuitable for imaging rapid transients. We describe a system that implements a 2-ps time gate by using the optical Kerr effect OKE in conjunction with a CCD camera that has on-chip multiplication gain. This system is capable of acquiring a high-resolution, single-shot

image in a highly scattering environment, which is appropriate for our spray research. In the following paragraphs we describe the development of this single-shot ballistic imaging system. We present results from initial experiments, along with their implications, including the resolution capabilities of our OKE time-gating system minimum spatial resolution as well as the modulation transfer function MTF and the point-spread function PSF of the system , the sensitivity i.e., the minimum intensity of ballistic light necessary for a signal , the dynamic range, and the acquisition time. Finally, we briefly present some proof-of-concept results for a water jet.
A. Ultrafast Optical Kerr Effect Time Gate

The OKE time gate works in the following manner. The intense electric field of the gating beam causes the molecular dipoles in a Kerr active liquid to align along the polarization vector of the electric field, creating a temporary OKE birefringence in the liquid. The most commonly used Kerr active liquid is carbon disulfide CS2 owing to its fast molecular relaxation time and large nonlinear refractive index.9 The induced birefringence is limited in time by either the duration of the laser pulse or the molecular reorientation time of the Kerr medium, whichever is longer. In our case the incident laser pulse is of much shorter duration than the molecular relaxation time of 2 ps Ref. 10 for CS2; therefore the CS2 molecular reorientation time determines the gate time. The approximate birefringence, n, is given by11 n n 2e E 2 t exp n 2oE 102
2 L L L o

erf ,









2 o


where n2e is the electronic contribution and n2o is the molecular reorientation contribution to the induced birefringence, E t is the electric field of the laserpulse envelope, L is the laser-pulse duration, and o is the molecular reorientation time of CS2. We assume a Gaussian laser-pulse envelope in both time and space. The values of n2e and n2o have been measured experimentally for several materials; for CS2, n2e 1.9 10 12 cm statvolt 2 and n2o 1.8 11 10 cm statvolt 2 .9 The total phase shift experienced by an imaging beam is then t 2 L n. (2)

If the Kerr active liquid is located between a pair of crossed polarizers, the transmitted intensity is I I 0 sin2 2 sin2 2 , (3)

where L is the path length of the Kerr active medium, I is the transmitted intensity, I0 is the incident intensity, and is the angle between the polarization vector of the gating and the imaging beams.12 For
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maximum transmission, is set to 45°. Equation 3 assumes zero delay between the gating and the imaging beam arrival at the OKE gate, infinite extinction ratio of the crossed polarizers, and colinear gating and imaging beams; experimental results see Fig. 2 in Section 3 validate these assumptions. Typically, when an OKE shutter is used in imaging applications, the first harmonic of an Nd:YAG laser is used for the imaging beam, and the second harmonic is used for the gating beam. The output pulse of our Ti:sapphire laser is centered at 790 nm. Consequently, the second-harmonic wavelength is 395 nm. This wavelength falls just within the absorption band of CS2. The second harmonic can be used, but absorption results in photodissociation in CS2. Over time, the nonlinear refractive index of the liquid is decreased, and OKE gate transmission is substantially reduced. Because of the difficulties associated with this problem, we evaluate two separate OKE gating cases. In the first case the OKE shutter is gated with the second harmonic of the laser system. In the second case the OKE shutter is gated with the first harmonic of the laser. For the first-harmonic gating case, the gating pulse with 0.7 W of average power and a 1-kHz repetition rate has a peak power of 1013 W; the electric field is 3100 statvolt cm. In our research this pulse traverses a 10-mm vial of CS2. Neglecting the molecular reorientation contribution, this field rotates the phase of an imaging pulse 2.4 rad; the theoretical gate transmission is 88%. For the second-harmonic gating case, the pulse average power is reduced by our secondharmonic-generation crystal conversion efficiency. Therefore the average power at the shutter is 80 mW, and the resulting electric field is 1615 statvolt cm. This field rotates the phase of an imaging pulse 0.65 rad; the theoretical gate transmission is 12%.
B. Scattering

distilled water and the PS sphere solution was negligible compared with the scattering cross section and was neglected. Based on single-scatterer Mie calculations, we expect ext in a diesel spray to fall in the range of 5–15 cm 1. Parker et al.13 have measured ext 8 cm 1 in a diesel spray by using a HeNe laser. For this reason, we initially chose experimental PS scattering values for ext of 5, 10, and 15 cm 1. We were unable to obtain a single-shot image, however, through an extinction coefficient as high as 15 cm 1. Therefore our actual extinction coefficients were 5, 10, 13, and 14 cm 1. In comparison, human tissue has an extinction coefficient of ext 11 cm 1 at 785 nm.14
C. Modulation Transfer Function and Point-Spread Function

To compare techniques, we measured the MTF, together with the other system benchmarks mentioned in Section 1, for each experimental configuration. Images were acquired through the resolution test chart immersed in varying concentrations of PS spheres; these images were used to calculate the MTF and the PSF of each experimental configuration. Minimum spatial resolution of an optical system can be determined by looking at the fringe visibility when the system is imaging a square-wave grating. Fringe visibility is directly related to the contrast, or modulation, of the image. Modulation, or contrast, is given by M I max I max I min , I min (6)

where Imax is the maximum intensity and Imin is the minimum in the square-wave grating. The MTF is given by MTF u Mi u , Mo u (7)

To evaluate the effectiveness of this technique, we placed a high-resolution test chart that consists of lines of varying spatial frequencies inside a 10-mm path-length cell containing scattering media: a solution of distilled water containing various concentrations of 0.7- m-diameter polystyrene PS spheres. The attenuation of the scattering solutions was calculated by use of a Beer’s-law approach as follows: I I0 exp

L ,


where I is the intensity transmitted through the medium, I0 is the incident intensity, I I0 is the relative intensity transmitted through the system, ext is the extinction coefficient, and L is the path length through the scatterers. The extinction coefficient is given by






where N is the number density of scatterers, abs is the absorption cross section, and scatt is the scattering cross section. The absorption cross section of the
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where Mi u is the modulation of the image, Mo u is the modulation of the object, and u is the spatial frequency. The MTF, which is analogous to the frequency response or transfer function in an electrical system, is a method of determining the best resolution a system can achieve. In reality, the MTF of a typical system begins at one for a spatial frequency equal to zero e.g., at dc and decreases with increasing spatial frequency. The maximum resolvable spatial frequency is determined by the point at which the MTF is effectively zero. Aberrations in the system create ripples in the MTF; thus a system with an MTF that approaches zero at lower spatial frequencies and then exhibits a ripple at a higher spatial frequency may appear to outperform a system with a higher maximum resolvable spatial frequency. The Fourier transform of the MTF yields the PSF. The PSF is useful for determining the size of the image blur spot15; a best-case MTF yields a diffractionlimited PSF.

Fig. 1. OKE high-speed shutter experimental configuration.

2. Experimental Methods

The experimental configuration is shown in Fig. 1. The 80-fs, 1-mJ pulse centered at 800 nm originates from a 1-kHz repetition rate Spectra-Physics Spitfire Ti:sapphire regenerative amplifier seeded with a Spectra-Physics Tsunami Ti:sapphire mode-locked laser. The linearly polarized beam is split into gating and imaging beams; 30% of the optical power is used as the imaging beam, and the remaining power is used to create the OKE time gate. Because of the extremely high peak power of the amplified gating pulse 1013 W , the gating beam is not focused. The polarization state of the imaging beam is first cleaned up with a polarizer because the OKE gate relies on polarization gating. The beam is then rotated 45° for maximum gate efficiency and is time delayed by use of an adjustable-length delay arm. The time delay allows one to control the temporal overlap between the gating and the imaging pulses at the OKE gate. Maximum gate efficiency occurs with zero delay between the two pulses. The imaging beam then passes through a telescope formed by two achromatic doublets; the first achromat is a 100-mm focal-length f 2 lens, whereas the second achromat is a 50-mm focal-length f 2 lens. The telescope reduces the imaging-beam diameter from a spot size of 4 to 2 mm; the smaller spot size increases irradiance at the image plane. The imaging beam then passes through a calcite polarizer oriented 45° with respect to the polarization vector of the gating beam; the 45° angle between the imaging and the gating beam polarization vectors creates maximum transmission of the imaging beam through the OKE time gate. The beam is then transmitted through the scattering material, into the OKE gate, and is blocked after exiting CS2. The extinction ratio of the polarizers used in the OKE gate was greater than 105; without the electric field of the laser pulse present, there was less than 10 5 transmission of the imaging beam through the second polarizer or analyzer . Adjustment of the imaging-beam time delay allows maximum signal transmission through the OKE shutter. After the first polarizer, the imaging beam is focused into the CS2 cell with a f 5 achromat and is then upcollimated with a second f 5 achromat. The birefringence created in CS2 by the gating beam rotates the plane of polarization of the imaging beam. This polarization rotation allows transmission through the analyzer for

2 ps, effectively creating a high-speed shutter that transmits early light and rejects later light. The collimated signal is then bandpass filtered with a 50-nm-bandwidth optical filter centered at 800 nm, passed through a spatial filter, and imaged onto a display screen. The spatial filter is composed of two f 2 achromats with a pinhole at the focal plane, and it is included to provide some spatial discrimination of the ballistic light. Because the gating and imaging pulses are degenerate in the first-harmonic gating case, the signal includes some light from the gating beam that is forward scattered into the imaging optical train. This scattered light is included in the detected signal. Spatial filtering reduces this undesired background; unfortunately, spatial filters also remove high-spatial-frequency components the small features, including sharp edges of the image itself. This is because the pinhole is placed at the focus of the first lens. This focal plane is also the Fourier plane where high-frequency components of the image can be found off axis. The pinhole can block these high-frequency components, resulting in a blurred image. For comparison, two sizes of pinholes were evaluated: 200 and 400 m. The smaller pinhole is more efficient at eliminating the background signal but reduces image quality. The larger pinhole passes higher spatial frequencies but is less efficient at removing the background signal. When an image is relayed in a laser beam, there can be a problem with identifying an object plane for the camera. An alternative, but equivalent, explanation is that the phase fronts of the imaging beam are somewhat mixed, and this makes it difficult to construct a high-fidelity image at the camera imaging plane owing to the coherence of the beam. For this reason, we use a display screen as shown in Fig. 1. The image screen creates an object plane for the camera while reducing the damage potential from the extremely high-power laser pulse. Unfortunately, scattering at the screen plane reduces the signal by 30%. A Roper Scientific Cascade CCD camera equipped with on-chip multiplication gain is used to acquire the image on the screen. The laser-beam imaging optics were designed for maximum spatial resolution by use of Optics Software for Layout and Optimization OSLO , a commercial ray-trace code. The design was based on readily available optics; however, by careful choice of these optics, we have ensured that the optical train itself is diffraction limited. There are no spurious aberrations or distortions introduced by the imaging optics in this system.
3. Experimental Results

OKE shutter efficiency was determined by examining the transmitted signal with the optical axes of both polarizers parallel, as well as the transmitted signal with the polarizers crossed with and without the gating beam. The transmission efficiency through the Kerr gate with the second harmonic was 20%, whereas the extinction of the polarizers was below the noise floor. The frequency conversion efficiency
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Fig. 3. Image of a 6.3-lp mm section of the resolution test chart through an aqueous solution of polystyrene spheres 10 cm 1 , with degenerext ate OKE switching and a 400m-pinhole spatial filter.

Fig. 2. OKE time gate is limited by the molecular relaxation time of the CS2 molecule to 1.8 ps. This measurement was performed with the first harmonic of the laser system.

of the second-harmonic-generation system was approximately 10%. The signal transmission efficiency through the Kerr gate with the first harmonic was much higher, 70%. The time gate was then characterized by varying the time delay; these results, along with model calculations, are shown in Fig. 2. Six different experimental setups were used: no OKE gating with and without spatial filtering, second-harmonic OKE gating with and without spatial filtering, and first-harmonic OKE gating with and without spatial filtering. First, we investigated system performance with no OKE gating. Signal transmission of the imaging beam through the scattering solutions was measured with the polarizers removed from the setup and the gating beam blocked. The no-gating case was then repeated with a spatial filter added just before the display screen; two pinhole sizes were evaluated. Second, these experiments were repeated with an OKE time gate by use of the second harmonic of the laser pulse as the gating beam. Again, the sequence of experiments was performed both with and without spatial filtering. In the second-harmonic-gating case, spatial filtering does not provide the same benefit as it does with the first-harmonic-gating case. In addition, signal levels are substantially lowered owing to the reduced efficiency of the OKE gate. For these reasons, only the larger pinhole size was evaluated. Finally, the time-gate experiments were repeated with the OKE shutter and the first harmonic of the laser pulse as the gating beam. Again, this was performed both with and without spatial filtering after the scattering medium. In this case two pinhole sizes were used in the spatial filter. It is important to mention that had we not used these measures and then attempted to obtain an image by simply passing a beam through the scatterers, it would not have been possible to observe the test chart except under extremely transmissive conditions. An example image of the resolution test chart is shown in Fig. 3; this image was obtained at a high 10 cm 1 , using an OKE scattering density ext time gate with the first harmonic of the laser and a 400- m spatial filter. One can readily observe that,
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under highly scattering conditions, clean resolution of the image is not trivial. As mentioned in Subsection 2.C, the MTF and PSF for each case are used to compare the various configurations. The MTF and PSF of each configuration are shown in Figs. 4 –11. The top line in each MTF and PSF plot, composed of black triangles labeled 0 cm 1 in the no-OKE switching case and ext composed of black circles labelled system in the OKE switching cases is the MTF–PSF measurement of the optical system. In the OKE switching cases, the system MTF and PSF are measured without OKE gating. This measurement provides a reference for comparison and shows that the maximum resolvable spatial frequency for the optical system without OKE switching is 50 line pairs per millimeter lp mm . This corresponds to a resolved object size of 10 m.

Fig. 4. MTF and PSF of the system measured with no OKE gating, no spatial filtering, and various volume fractions of PS spheres.

Fig. 5. MTF and PSF of the system measured with no OKE gating, spatial filtering with a 200- m pinhole, and various volume fractions of PS spheres.

Fig. 6. MTF and PSF of the system measured with no OKE gating, spatial filtering with a 400- m pinhole, and various volume fractions of PS spheres.

When a scattering medium is added to the optical train, the MTF narrows and the PSF broadens. For the first sequence of experiments no OKE gating , three cases were evaluated: no spatial filter, a 400- m spatial filter, and a 200- m spatial filter. These measurements were performed with the crossed polarizers removed and no OKE gating and at various concentrations of scattering solution. In this case, although there is no active high-speed optical gating, there is some spatial separation of the early and later light owing to the optical design of the system. The finite aperture of the optical system can block the transfer of some of the multiply scattered photons while the on-axis ballistic and paraxial snake photons are transferred through the optical train with the highest efficiency. The plots for the first sequence are shown in Figs. 4 – 6. In this sequence the ext 0 cm 1 line is the same as the system measurement. For this reason, a system line is not included in these figures. As the loading of the PS spheres is increased, the MTF degrades. Obviously, as sphere number densities increase, more scattering events occur; therefore the MTF narrows and the PSF broadens. At lowernumber sphere densities, the no-spatial-filtering case produced good results; however, as sphere loading increased, spatial filtering improved system performance. This is because the spatial filter eliminated some of the diffuse photons, thereby preventing them

from adding to the background signal. In fact, spatial filtering by itself has been shown to be an effective ballistic imaging technique for imaging through materials with low extinction coefficients.16 For the highest extinction coefficient in this sequence ext 13 cm 1 , the 200- m pinhole provided the best image fidelity, with a maximum resolvable spatial frequency of 2 lp mm corresponding to a resolved object size of 250 m. Although this first sequence of experiments no OKE switching was the simplest of the three sequences and provided good results at low extinction coefficients, the system was unable to resolve the lowest spatial frequency above extinction values of 13 cm 1. For the second sequence of experiments, OKE time gating with the second harmonic of the laser was used. Two cases were evaluated: no spatial filter and a 400- m spatial filter. These measurements were performed with the crossed polarizers replaced as shown in Fig. 1, and various concentrations of the scattering solution were evaluated. The results can be seen in Figs. 7 and 8. Again, the top line in each figure is the MTF measurement of the optical system with no scatterers present. These graphs show that OKE gating slightly degraded the MTF, with the maximum spatial resolution reduced to 31.6 lp mm with a resolved object size of 15.8 m in the absence of a spatial filter. This is possibly caused by the spatial-filtering effect created by the OKE gate itself.
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Fig. 7. MTF and PSF of the system measured with secondharmonic OKE gating, no spatial filtering, and various volume fractions of PS spheres.

Fig. 8. MTF and PSF of the system measured with secondharmonic OKE gating, spatial filtering with a 400- m pinhole, and various volume fractions of PS spheres.

Because the OKE birefringence is due to the electric field of the gating pulse, any imaging-beam spatial frequencies located outside the gating beam diameter are not rotated and are blocked at the analyzer, thereby degrading the spatial resolution. As sphere loading increased, however, OKE gating exhibited superior performance despite the spatial-filtering effect of the OKE gate. The poor efficiency of the OKE time gate with the second harmonic limits image acquisition to an extinction coefficient of 5 cm 1 or less. For the third sequence of experiments, when OKE time gating with the fundamental of the laser was used as the gating pulse, three cases were evaluated: no spatial filter, a 400- m spatial filter, and a 200- m spatial filter. These results are shown in Figs. 9 –11. It can be seen that, although the addition of a spatial filter results in the degradation of the spatial resolution of the optical system, the spatial resolution is actually improved for the degenerate OKE switching case. This is because spatial filtering removes the large background signal created by the scattered switching beam; the system spatial resolution was best for the 400- m pinhole, with a maximum spatial frequency of 31.6 lp mm corresponding to a resolved object size of 15.8 m. The system spatial resolution was the worst for the no-filtering case, with a maximum spatial frequency of 25.1 lp mm or a resolved object size of 19.9 m, and large ripples in the MTF indicate severe aberrations in the
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optical system. The system spatial resolution for the 200- m pinhole was comparable with that of the 400- m-pinhole case; the maximum spatial frequency of 31.6 lp mm was the same, but ripples in the MTF indicate aberrations in the system. However, the cutoff spatial frequency increased at higher sphere loading with the 200- m pinhole. At the highest extinction coefficient of 14 cm 1, the maximum spatial frequency for the 200- m pinhole was 3.2 lp mm, corresponding to a resolved object size of 158 m, whereas the maximum spatial frequency for the 400- m pinhole was 1.3 lp mm or 400 m. Overall, spatial resolution is better for the larger pinhole, but the smaller pinhole is more efficient at removing the background signal with increased sphere loading. Overall, the first-harmonic, spatial-filtered OKE gating case is the most efficient for imaging through higher extinction coefficients such as those we expect to see in a diesel spray. This is the only configuration that was able to resolve greater than 1 lp mm through ext 14 cm 1. Although the smaller pinhole increases the maximum resolvable spatial frequency at higher extinction coefficients, the larger pinhole provides improved resolution at lower extinction coefficients. The reduced gate transmission in the second-harmonic case limits the capacity of this configuration to image the test chart through extinction coefficients greater than 5 cm 1. The case of

Fig. 9. MTF and PSF of the system measured with first-harmonic OKE gating, no spatial filtering, and various volume fractions of PS spheres.

Fig. 10. MTF and PSF of the system measured with firstharmonic OKE gating, spatial filtering with a 200- m pinhole, and various volume fractions of PS spheres.

the no-OKE gate provides superior performance for very low extinction coefficients, because the resolution capability of this configuration is the highest. This system was able to resolve an object size of 158 m through an extinction coefficient of 14 cm 1, although the resolution was 50 m for extinction coefficients of 10 cm 1. The expected extinction coefficients in a diesel spray are estimated to be in the range of 10 to 15 cm 1.13 Image-acquisition time is approximately 20 ms limited by the camera . The sensitivity of this system is on the order of 80 dB, and the dynamic range is approximately 120 dB. It should be noted that this sensitivity level was achieved with no signal averaging. Signal averaging and other data-acquisition techniques can be used in conjunction with this method to acquire images through even higher extinction coefficients. We did not try these techniques; the goal of this research was to create a single-shot imaging technique. A possible concern regarding the imaging capabilities of this system is the characteristic of the resolution test chart. The test chart consists of a series of square-wave gratings of varying spatial frequencies composed of transparent and opaque bar patterns; the opacity is created by means of an aluminum substrate on glass. This created a question regarding the capacity of the imaging systems to resolve a refracting object with the same spatial res-

olution as that demonstrated with the nonrefracting test chart. To evaluate this, we imaged a series of soap bubbles with this system. Two of these images are shown in Fig. 12; the bubbles originate from a metal syringe with a 0.5-mm tip immersed in a cuvette of soapy solution with no additional obscuration. The syringe can be seen in these images as a diagonal line. It is evident from this image that the spatial resolution of the system is comparable in the refracting and nonrefracting object cases.
4. Sprays

Using the results of this comparison study, we applied this technology to acquire an image of a water jet, as shown in Fig. 13.17 The water-jet system used a piston accumulator to provide high pressure 13.6 MPa over 1 min of spray time. A stock spray nozzle was modified to omit internal components that destroy the solid core. Thus the jet approaches the simplicity of the diesel nozzle, which is typically a short-length 1 d of 2 to 6 hole, submillimeter in diameter 100 –300 m . The pressure control available in this system provides access to a range of Reynolds and Weber numbers along with the associated range of liquid core lengths. The jet reaches the atomization regime for a single-hole atomizer spray. In the ballistic image, structures of the spray are clearly visible. This image contains the first conclu10 September 2004 Vol. 43, No. 26 APPLIED OPTICS 5107

Fig. 13. Image of a water jet taken 25 mm from the jet nozzle with first-harmonic OKE gating and a 400- m spatial filter. The approximate extinction coefficient of the spray at this location is 5. Fig. 11. MTF and PSF of the system measured with firstharmonic OKE gating, spatial filtering with a 400- m pinhole, and various volume fractions of PS spheres.

sive demonstration of turbulent primary breakup in an atomizing spray.18 These raw images still require some processing. Xiang et al.7 performed some initial research on image processing of their raw ballistic spray images. As an example, they applied a computational spatial filter to smooth the image data. This method preserves larger structures but eliminates the small droplet images and other smaller structures. However, there are questions about aerodynamic strip-

ping, and these structures are on the order of 5 to 10 m.4 For structures below this size, we indeed want to eliminate any noise in the image. Therefore we continue to explore the optimal trade-off between spatial resolution and imaging capability. The spray results will be discussed in more detail in a future paper.
5. Conclusion

Fig. 12. Ballistic image of soap bubbles emanating from a metal syringe with its 0.5-mm tip immersed in a cuvette of soapy solution. 5108 APPLIED OPTICS Vol. 43, No. 26 10 September 2004

In conclusion, there is a need for transient highresolution images through liquid sprays, especially at high pressures and temperatures. We have proved the ability of the OKE shutter to acquire highresolution, two-dimensional, single-shot ballistic images through dense, scattering media. Our results showed superior spatial resolution in a single-shot acquisition format, resolving 50- m bars through an attenuation of 10 5. The minimum spatial resolution achieved previously with single-shot techniques was greater than 1 mm.4,7 Optimum spatial resolution through scattering materials with extinction coefficients greater than 5 was obtained with degenerate OKE switching combined with spatial filtering. Expected extinction coefficients above 10 are best imaged by use of a 200m-pinhole spatial filter, whereas the larger pinhole size of 400 m provided superior resolution for extinction coefficients below 10. This technology was applied to image sprays, and we will eventually apply this technology to acquire an image of a diesel spray. Financial support for this research was provided in part by the Department of Education Graduate As-

sistance in Areas of National Need grant P200A000447, the National Science Foundation Community Technology Fund Major Research Instrumentation Grant CTS-9711889, and the Army Research Office Project DAAD19-02-1-0221. We thank Lambda Research for free use of the OSLO software through the University Gratis program.
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Vol. 43, No. 26



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