Quantitative Rayleigh thermometry for high background scattering applications with structured laser illumination planar imaging Nathan J. Kempema* and Marshall B. Long Department of Mechanical Engineering and Materials Science, Yale University, 15 Prospect St., New Haven, Connecticut 06511, USA *Corresponding author: [email protected] Received 9 May 2014; revised 6 August 2014; accepted 2 September 2014; posted 4 September 2014 (Doc. ID 211816); published 2 October 2014
This work demonstrates structured laser illumination planar imaging (SLIPI) for Rayleigh thermometry with high background scattering. Two coherent laser beams were crossed to produce an interference pattern, from which the modulated Rayleigh signal was collected. The modulated signal serves as a signature that identifies information about Rayleigh scattering from the probe volume against additional contributions in the image from background scattering. This work shows that the structured nature of the illumination allows for a simplified background correction. The experimental approach is validated in a non-premixed methane/air flame, and the temperature is found to be in excellent agreement with previous experimental and computational results. Rayleigh SLIPI is then applied to a high background scattering application as part of the full-field temperature measurement of sooting non-premixed ethylene/air flames. For these flames, standard Rayleigh background corrections are impossible since scattering from soot just outside the field of view is the main source of the background. Good agreement is found between SLIPI and intensity-ratio thin-filament pyrometry-derived temperature along their adjoining interface in the flame. © 2014 Optical Society of America OCIS codes: (280.1740) Combustion diagnostics; (290.5870) Scattering, Rayleigh; (110.4280) Noise in imaging systems. http://dx.doi.org/10.1364/AO.53.006688
1. Introduction
Laser Rayleigh scattering, a simple, non-invasive diagnostic with relatively strong signal strength among molecular scattering techniques, has been used for spatially and temporally resolved measurement of temperature and, under certain conditions, species in reacting and non-reacting gas flows [1–4]. The Rayleigh signal intensity from an illuminated volume, V, can be written as:
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I Rayleigh CI 0 NV
m X
X iσi;
(1)
i1
where C is an experimental constant accounting for the collection solid angle and subsequent throughput of the optics, I 0 is the incident laser intensity, and N is the local number density. The summation is over the product of a total of m species’ mole fractions, X i , with their respective Rayleigh scattering cross sections, σ i . At constant pressure, temperature can be recovered from the number density, N, through the ideal gas law. However, since Rayleigh scattering is an elastic process, the signal is susceptible to
contamination by additional scattering from the surroundings (optical components, windows, containment vessels, or scatterers outside the measurement region) and must be corrected. For temperature measurements in systems in which species concentrations and cross sections vary significantly, some means is required to account for variations in the summation term in Eq. (1). In the limit where background noise and molecular composition can be corrected, Rayleigh thermometry is an accurate diagnostic tool [5]. As a result, Rayleigh thermometry is most readily applied to open atmosphere flames containing no particulate matter and with low flame luminosity. Improved methods to deal with high levels of background scattering would greatly extend the use of Rayleigh thermometry. Structured illumination was originally developed as a means to enhance the image contrast of threedimensional (3D) structures in a conventional wide field microscope [6]. Samples are illuminated with a grid pattern of known frequency, ensuring that only regions where the light is focused on the sample image efficiently. The illumination grid is then phase shifted and multiple images are acquired to reconstruct an image free of the original pattern. In a similar way, structured laser illumination planar imaging (SLIPI) relies on an intensity-modulated laser sheet to impart a known pattern into the collected signal [7]. This technique has been used for imaging in situations where multiple scattering becomes important, such as in dense sprays. In SLIPI, photons from the probe volume that retain the original pattern are considered to have undergone one scattering event and are thus representative of the sample. Multiscattered photons generally lose the pattern and are considered as a source of noise in the measurement. Kristensson et al. have done extensive work characterizing the technique and demonstrating its applicability to turbid media such as sprays in 2D and 3D [8–16]. In previous SLIPI applications, a structured light sheet is achieved by projecting odd harmonics of an illuminated Ronchi grating onto a frequency cutter. The cutter acts as a physical barrier by blocking all harmonics except the 1 modes. The two remaining beams cross and produce an interference pattern that can be phase shifted via rotation of a glass plate located after the Ronchi grating. Blocking the fundamental and higher order modes results in a loss of ∼50% of the incident energy [14]. This is in addition to the physical limitations of a Ronchi grating, which is not designed for high-energy laser applications. One experiment was able to achieve 30 mJ per pulse for single-phase measurement without the rotating glass plate [15]. This energy is sufficient for the strong signals associated with Mie scattering or resonant processes such as laser-induced fluorescence. However, increased laser energy is desirable for improved signal-to-noise in nonresonant measurements, such as those made with Rayleigh scattering. Recently, Kristensson et al.
demonstrated Rayleigh thermometry in a premixed flame with SLIPI via a two-faceted optical component [17], which allows for increased laser energy over use of a Ronchi grating. Their work demonstrated that SLIPI could extend the accuracy of Rayleigh thermometry over conventional planar Rayleigh scattering when the source of the background was external to the measured flame. This paper demonstrates SLIPI for Rayleigh thermometry via a split-beam approach that also allows for increased laser energy over use of a Ronchi grating. Comparisons are made between SLIPI-derived temperature and previous experimental and computational results in a non-sooting non-premixed methane/air flame. Rayleigh SLIPI thermometry is then applied as part of the measurement of the full temperature field in sooting ethylene coflow diffusion flames. In this case, scattering from soot just outside the field of view is the main source of the background and standard Rayleigh background corrections are not possible. 2. Experiment
In SLIPI, information is applied to the laser sheet in the form of modulated intensity. The laser sheet intensity at location x; y has the form Lx; y Cx; y ·
m · cos2πνy φ 1 ; 2
(2)
where Cx; y is the conventional planar laser intensity, m is the modulation depth, ν is the spatial frequency, and φ is the phase. The coordinate system is as in the top view of the experimental configuration shown in Fig. 1. For perfect modulation (m 1), the sheet intensity goes to zero with spatial frequency ν, resulting in regular intervals of no Rayleigh scattering. However, due to multiple scattering effects and collection of light originating outside the probe volume, locations of zero Rayleigh scattering in the probe volume are recorded as non-zero values at the detector. As a result, the signal incident on the detector can be thought of as the summation of a dc offset I C i; j and a local amplitude I S i; j modulated at frequency ω with phase shift φ, as shown in Eq. (3) [14]. The new i; j coordinate system
Fig. 1. Experimental configuration for slit-beam Rayleigh SLIPI. 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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is located on the detector surface, representing the ith row and jth column. The functional dependence between the x; y and i; j coordinate systems depends on the magnification and resolution of the imaging system. For the practical case with m < 1, the nonzero modulation offset is included in the I C i; j term: Ii; j I C i; j I S i; j · cos2πωi φ:
(3)
Post-processing is used to keep the local modulation envelope while excluding the dc offset that results from collection of spurious photons. A series of (n ≥ 3) spatially phase-shifted images is acquired where each new image has a relative phase shift of 2π∕n with respect to the previous. This allows for the modulation envelope to be extracted as in Eq. (4), where the subtraction of different phases acts to keep features that are unique (local modulation amplitude) and remove those that are common (dc offset). Here, I l i; j and I k i; j are expressions of Eq. (3) with phase shifts φl and φk , respectively. Three phaseshifted images are the minimum required to extract the local modulation amplitude without loss of spatial resolution [17]: p n−1 n 1∕2 2 X X 2 I S i; j I i; j − I k i; j : n l1 kl1 l
(4)
The period of the interference pattern produced by crossing two laser beams is proportional to the wavelength of the light and inversely proportional to the sine of the half-angle separating the beams. Therefore, for application to macroscopic imaging, the half-angle must be small to produce a sufficiently large period. In this experiment, the output of a laser is split into two beams and propagated over several meters before crossing in the region of interest above the burner. This split-beam experimental configuration allows for laser energies that surpass those in a Ronchi grating system. The second harmonic output of an Nd:YAG laser (Continuum PL-8010, 10 Hz rep rate) is clipped by a circular aperture to a diameter of 5 mm. The laser produces 205 mJ per pulse and its polarization is oriented vertically. The beam is directed through a 50/50 beam splitter so that one beam passes parallel to the optical table and the other is reflected in a direction normal to the table surface. A 532 nm dichroic mirror reflects the beam traveling normal to the table back down the optical path and is fixed above the beam splitter so that the two beams have an initial separation of 10 mm. A neutral density filter (0.2) is placed in the path of the beam traveling parallel to the table surface to balance intensity between the beams to within 1%. The two beams are propagated for 6.9 m from the location of the beam splitter to the center of the burner via a sequence of dichroic mirrors. A cylindrical plano-convex lens (focal length 300 mm) focuses 6690
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the two beams into a sheet centered on the burner fuel tube, where the modulation period is measured to be in the range 370–450 μm, depending on the finetuning of the two beams. The combined laser energy from both beams is measured just before the focusing lens to be 103 mJ per pulse. Beam width at the focal point of the lens and at a location 5 mm closer to the focusing lens is 144 and 170 μm, respectively. The dichroic mirror fixed above the beam splitter is mounted on a rotating stage so the relative spatial position of the top beam with respect to the bottom beam can be fine-tuned. The signal is collected at an angle of 90 deg to the laser path. A 50 mm f/1.4 Nikon camera lens with an achromatic macro filter for close-up imaging collects light through a 532 nm interference filter and forms an image at its back focal plane. A 45-degree mirror in the image plane is used to reflect the signal from one side of the flame to a relay lens that refocuses the image from the hot gas adjacent to the flame onto the camera. This relay-imaging configuration was used to exclude scattering from the sooty region of the flames, which will be discussed in Section 6. This configuration allows the orders of magnitude stronger and unwanted signal from incandescence and elastic soot particle scattering to pass. The mirror must be thin to minimize additional scattering due to its location in the image plane. Therefore, a piece of cover glass (22 × 22 × 0.14 mm) coated with 100 nm of aluminum is used. The Rayleigh signal is recorded by an interline transfer EMCCD camera (Andor Luca S, 14 bit A/D) with a Navitar 35 mm f ∕1.4 lens and 20 mm extension tube. The thermoelectrically cooled camera has 658 × 496 pixels (10 μm∕pixel) and is electronically gated to its minimum exposure of 470 μs. An area of 27 × 27 μm2 from the plane of the laser sheet is projected onto each pixel and 2 mm image segments are tiled together from 2 mm to 10 cm above the burner. Open source software OMA is used for data acquisition [18]. 3. SLIPI Data Acquisition and Processing
Spatial phase shifting of the structured light sheet can be accomplished by rotating a glass plate in the yz-plane as shown in Fig. 1. However, a significant shot-to-shot phase jitter was observed in the scattering from the interfering beams above the burner, presumably due to small vibrations in the beam splitter arrangement, where differences in spacing between the mirrors on the order of one wavelength cause a significant phase change. The jitter was characterized by acquiring two 1000 image sequences. One sequence imaged planar Rayleigh scattering in air as in the above experimental configuration to assess fluctuations in the y-direction while the other sequence imaged the cross section of the beam at the focal point of the cylindrical lens to address z-direction fluctuations. The power spectrum of each image was derived from its Fourier transform and used to monitor the energy contained in each frequency component.
Fig. 2. Rayleigh SLIPI scattering in air (left) and the application of Eq. (5) for phase identification (right).
No change in the modulation frequency was observed, indicating that the angle between the beams is stable on a shot-to-shot basis. A reference image is selected with a phase equal to the mean phase of each 1000 image sequence to within one pixel in the i; j coordinate system. The phase shift of each image with respect to the reference image is determined by minimizing the norm of the difference between a sub-rectangle of each new image and a sub-rectangle in the reference image over a sequence of integer values δ. The rectangles have the same coordinates within each image except that the rectangle in the new image is shifted in the i-direction by an integer number of pixels δ, which is varied by one from minus two to plus two spatial periods in the reference image. The shift of the new image is determined from the minimum in the sequence as stated in Eq. (5) and illustrated in Fig. 2. The left side of Fig. 2 shows the relative position of the sub-rectangles in the reference image and the right side shows the output of Eq. (5), where the new image is shifted five pixels with respect to the reference image. The range of δ was chosen to differentiate between images possessing an integer multiple of 2π phase shift with respect to the reference image, since the sheet intensity has a periodic character: Shift mini ‖recti δ; jnew − recti; jref ‖2 :
(5)
This method was validated against a crosscorrelation algorithm to determine pixel-level shifting of the same object in two images. Approximately 90% of the images in the two 1000 image sets were distributed equally between maximum spatial shifts of plus or minus one period in the y-direction, and no detectable z-direction fluctuation was observed. Thus, while the jitter does not allow for direct integration of the signal due to changes in phase, it does not affect the focus of the imaging system in the zdirection. The glass plate is used to center the distribution on a given phase in the y-direction, but Eq. (5) is needed to identify the phase of each image relative to the reference. Because of the shot-to-shot phase jitter, it is impossible to continuously integrate at a given phase.
Therefore, during data acquisition, images are kept only if the shift determined by Eq. (5) is equal to one of n 3 predetermined values of δ that are chosen to have a phase shift of approximately 0 and 2π∕3 with respect to the reference image. The reference image is selected at the mean phase shift of a 100image sequence acquired in air with the glass plate rotated zero degrees. This is done to center the reference image within the jitter-induced phase shift distribution and therefore speed data acquisition. At a given measurement location, 250 images are sampled and the phase shift is determined from Eq. (5) to within one pixel at a rate of 3 Hz. Approximately 20% of the images correspond to one of the three predetermined phase shifts and are saved. The magnification and resolution of the imaging system limits the phase resolution for image identification when using Eq. (5). It is estimated that determination of the phase shift to within one pixel in the i-direction limits the resolution for phase detection to 10–12 degrees in the y-direction. This is based on observed spatial periods ranging from 370 to 450 μm in x; y projecting onto 15–18 pixels in the i; j system. The range of values results from changes made to the initial separation of the beams between data sets. All saved images are corrected for variations in total intensity and normalized to an average fundamental mode to account for spatial and temporal variations in the laser output as discussed in [14]. After corrections, the set of 5–25 acquired images for each of the three predetermined values of δ is averaged to create the corresponding I 1, I 2 , or I 3. This operation averages the phases of the individual images, resulting in a new phase at the modulation frequency, ν, equal to φi for image I i where i 1, 2, or 3. Because of the system’s phase-resolution limits, averaging images at slightly different phases can lead to loss of modulation depth. Numerical simulations estimate that less than 2% of the modulation signal was lost in this experiment. After averaging the images from each collection bin, the phase of I 1 , I 2 , or I 3 is precisely determined within a particular quadrant of the complex plane using Eq. (6). The numerator and denominator of Eq. (6) are the 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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imaginary and real components of the Fourier transform of the image at the modulation frequency ν. The phases (φ1 , φ2 , and φ3 ) are determined by adjusting all the phases so that φ2 0 and calculating the phase difference between (φ2 , φ1 ) and (φ2 , φ3 ). The magnitude of the phase shifts for φ1 and φ3 ranged from 105 to 120 deg. The modulation signal was recovered using Eq. (7), which is a general form of Eq. (4) for n 3 that allows for phase shifts between images other than 2π∕3 [14,19]: Imfˆ Iyjν φ tan Refˆ Iyj −1
and 1 I S φ1 −φ3 2 · sin 2 8 9 < I −I = I − I 1 2 2 3 − : (7) ·I 3 − I 1 i φ2 −φ3 ; :tan φ1 −φ2 tan 2 2
4. Background Correction Conventional Rayleigh Background Correction
The elastic nature of Rayleigh scattering poses a problem for quantitative measurements since the signal is at the same wavelength as the incoming laser. It can make it difficult to distinguish between the signal of interest (generated within the illumination sheet) and light scattered from other sources. The experimental signal at pixel location i; j on the detector from a Rayleigh image of a flame has the form: SignalF i; j Rdet i; jI F i; j B0 i; j FPi; j; (8) where Rdet i; j is the overall response of the imaging optics and detector, I F i; j is the Rayleigh-scattered intensity of interest, B0 i; j is background, and FPi; j is fixed pattern noise due to A/D offset and small pixel-to-pixel variations. The background term, B0 i; j, results from collection of spurious laser scattering in the experiment, Bi; j, and flame luminosity, Li; j. A background correction can be made by imaging a uniform distribution of a gas with a different Rayleigh cross section than that of air, under the same experimental conditions [20]. Helium is often used due to its small Rayleigh cross section. A background image can be constructed from a linear combination of helium and air scattering images with their respective cross sections (σ He , σ Air ), as in Eq. (9): 6692
− SignalHe i; j Rdet i; jBi; j FPi; j.
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(9)
Assuming that Bi; j and Rdet i; j are the same in all images, a full correction for background, response, and laser sheet non-uniformities is done as in Eq. (10):
(6)
ν
A.
Backgroundi; j SignalHe i; j σ He SignalAir i; j − σ Air − σ He
Ratio
SignalF − Background − Luminosity − Dark ; Response − Background (10)
where the numerator consists of the flame signal [Eq. (8)], Background [Eq. (9)], a Luminosity image obtained with the flame on and no laser, and a Dark image where the camera lens is capped. The Luminosity shot accounts for flame emission [Li; j] and the Dark shot accounts for the fixed pattern noise in the Luminosity image. The denominator contains a response image, which is typically Rayleigh scattering from air at ambient conditions in the same experimental configuration, and the same Background image as in the numerator. Equation (10) produces a scalar field that is inversely proportional to temperature (assuming constant Rayleigh cross section, see discussion in Section 5). Thus, a full correction of the experimental signal requires five different images in the same experimental configuration. If any part of the configuration is changed (e.g., to measure different heights above the burner), a new set of correction images usually must be recorded. For many experiments, obtaining good images with the imaged region uniformly filled with particle-free helium represents a significant problem, particularly at larger downstream locations. It should be noted that the assumption that Bi; j is the same in all images may be quite good in cases where the main source of background scattering is from outside the flame (e.g., from optical components, windows, or vessel walls). However, in cases where there is significant scattering from the flame just outside the field of view (as will be the case in the sooting flames to be discussed in Section 6), the conventional background correction breaks down entirely. B. SLIPI Background Correction
For SLIPI, where the Rayleigh intensity incident on the detector has the form of Eq. (3), the application of Eq. (8) gives an expression for the collected signal shown in Eq. (11): SignalF i; j Rdet i; jfI C i; j I F i; j · cos2πωi φg B0 i; j FPi; j: (11)
If three spatially modulated flame images are collected with the flame/laser on and processed with Eq. (7), the result is Rdet i; j · I F i; j. Taking the difference of pairs of phase-shifted images, as in Eq. (7), acts to subtract the background, fixed pattern, and I C i; j components. Thus, if these terms are constant between phase-shifted images, then only a response image is needed to make a full correction of the Rayleigh data. This assumption is valid as the Background is generally diffuse light that does not depend on small spatial changes in the laser intensity. The modulation offset, I C i; j, does not change significantly and can be corrected for small variations [14]. For SLIPI, a response image is derived from Rayleigh scattering in air at three different phases processed with Eq. (7). A ratio of the flame and response images is then used to divide out the Rdet i; j term, again yielding an image inversely proportional to temperature. Thus, SLIPI allows for a simplification of the conventional Rayleigh correction by not requiring a new reference image at each measurement location [e.g., SignalHe in Eq. (9)]. It also relaxes the assumption that the Background must be the same in the response and flame data to the case where it need only be the same among the phase-shifted images used to calculate I A i; j or I F i; j. These two benefits are obtained through the added complexity of a SLIPI experiment and, as will be shown, extend the application of Rayleigh thermometry to cases that could not otherwise be measured. A concrete metric to determine if SLIPI-based Rayleigh thermometry is advantageous over the method outlined in Section A, is whether or not Bi; j is constant between signal and response images. If Bi; j is constant, then both conventional and SLIPI methods apply. However, if Bi; j is not the same between the signal and response images, then conventional Rayleigh images cannot be quantitatively corrected for background. 5. Temperature Measurement in a Non-Sooting Flame
To validate the use of SLIPI for quantitative temperature measurements, a previously characterized nonsooting, non-premixed methane/air flame is used as a benchmark [21,22]. The coflow burner has a 4 mm I.D. fuel tube concentric with a 74 mm I.D. coflow. The average fuel-tube exit velocity (parabolic velocity profile) and coflow exit velocity (flat velocity profile) are fixed at a constant 35 cm∕s. The coflow is fitted with a honeycomb mesh containing 0.8 mm perforations to provide a consistent and stable flow. Methane is diluted with nitrogen to 65% by volume. This results in soot-free conditions except for a faint incandescence that can be observed at the flame tip. An initial approximation to temperature is calculated by assuming a constant scattering cross section in all regions of the flow as in Eq. (12), where s is a known scalar associated with the response image [20]. The subscripts F and A refer to I S x; y obtained from the flame and from only coflow air, respectively:
Temperaturex; y s
I A x; y . I F x; y
(12)
The assumption of a constant Rayleigh cross section is not correct for this flame, as the collected signal is proportional to the mole fraction weighted cross sections of all species present as seen in Eq. (1). A system of two equations is developed to account for this fact, where the first is given by a ratio of the flame and response signals, allowing the effective Rayleigh cross section to vary with temperature [23]. The second equation is derived from computational results and relates cross section to temperature, since computational and experimental results for temperature and major species concentrations in this flame are in good agreement [21,24]. A map of relative scattering cross section is derived from a summation of the computational mole fraction profiles of the major species multiplied by their respective scattering cross section. A scatterplot is then produced from the relative cross section and temperature at each grid point. The result has a two-branch structure where the lower curve relates to the oxidizer side of the flame and the upper curve relates to the fuel side of the flame. Both curves are fitted with second-order polynomials and serve as a second equation relating temperature and cross section on their respective side of the flame front [23]. Iterating on this system produces a self-consistent result in three or four iterations and a temperature corrected for variation in local species concentrations. At each downstream location, between 5 and 25 images were acquired for each of three phases and processed as discussed previously. No smoothing was done until the final temperature was calculated, at which point the data were smoothed once with a Gaussian kernel (171 × 171 μm, σ x σ y 41 μm). The same procedure was used for the sooting ethylene flames, which will be discussed in Section 6. Figure 3 shows results from a previously measured simultaneous Rayleigh/Raman temperature measurement [24], next to the Rayleigh SLIPI measurement, in addition to computational results [22]. The Rayleigh/Raman data were corrected as in Section A and the Rayleigh scattering cross-section was corrected with species concentrations obtained from a spontaneous Raman measurement. The two leftmost plots in Fig. 3 provide a comparison between the methods outlined in Section A and Section B. Overall agreement between the temperature maps is seen to be very good. For a more detailed comparison, Fig. 4 shows line plots at different flame locations. On the upper left, the centerline temperature for the two experimental approaches is seen to be in excellent agreement from the burner to the location of peak temperature. In the post flame region, the SLIPI data are ∼50 K lower than the Rayleigh/Raman measurement on average but displays a linear nature that is more consistent with the computational results. 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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Fig. 3. Rayleigh/Raman (left), Rayleigh SLIPI (center), and computational (right) temperatures for the 65% methane/air flame. Temperature scale is shown in Kelvin.
The remaining plots in Fig. 4 display radial temperature profiles at three downstream locations. At 1.50 cm height above burner (HAB), the SLIPI results are in excellent agreement with computational results in terms of shape and peak temperature. Rayleigh/Raman results at this location show a wider profile and a lower peak temperature, which is consistent with observation through the rest of the flame. At 3.0 cm HAB, the experimental and computational results compare well except for the centerline temperature in the Rayleigh/Raman data, which may be attributed to noise in the measurement, as seen in the centerline plot. In the post flame region (4.5 cm HAB), no major discrepancies are observed except for the lower centerline SLIPI temperature as noted above. 6. Temperature Measurement in a Sooting Flame
With the good agreement demonstrated in the relatively low background case of the non-sooting flame,
Rayleigh SLIPI was used to measure temperature in a high background noise application as part of the full-field temperature measurement in two sooting, non-premixed ethylene coflow flames. The goal is not to measure the entire temperature field of the sooting flame with Rayleigh SLIPI, but rather to measure temperature in a case where conventional Rayleigh background corrections (see Section A) fail. The fuel was diluted with nitrogen to 60% and 80% by volume in the same burner used for the nonsooting methane/air flame. Maximum soot volume fractions for the two flames were measured previously to be 1.6 ppm and 4 ppm, respectively [25]. To map the full temperature field of the ethylene flames, three diagnostic techniques were combined to measure specific regions of the flow. Temperature in sooting regions of the flame was measured with a two-color ratio pyrometry technique [25,26]. Hot gases adjacent to the flame and above ∼1150 K were measured with intensity-ratio thin-filament pyrometry (TFP) as discussed in [27] and Rayleigh SLIPI was used to measure temperature below ∼1150 K outside the flame. Since TFP and two-color soot pyrometry are not scattering techniques, their data correction is simplified compared to the Rayleigh scattering measurement. For TFP, an image of the flame was subtracted from the TFP signal and used to correct for flame luminosity and fixed pattern noise. For two-color soot pyrometry, only a dark shot with the camera lens capped is needed to correct for fixed pattern noise and A/D offset. For the TFP measurement, the flame was translated via a stepper motor at a constant rate of 2 mm∕s through a 15 μm silicon carbide (SiC) fiber fixed horizontally above the burner and centered on the fuel tube. Fiber incandescence was imaged at a rate of 2 Hz through a narrowband interference filter (700, 10 nm FWHM). The Rayleigh SLIPI data from the ethylene flame were acquired as detailed above and demonstrates the capability of the technique with high background
Fig. 4. Centerline and radial plots of temperature for computational results, Rayleigh/Raman, and Rayleigh SLIPI. 6694
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Fig. 5. Column plot from three SLIPI images (dashed lines) along with the signal from conventional planar laser imaging (solid line).
noise levels. To avoid direct detection of the scattering from soot, only that portion of the real image to one side of the flame’s sooting region was directed to the camera by the thin 45-deg mirror. Figure 5 illustrates the signature left in the collected signal via structured illumination as compared to conventional planar imaging. An approximation to planar imaging with a non-modulated sheet was derived from the average of the three phase-shifted SLIPI images. Some residual frequencies are apparent in the conventional signal since the three phase-shifted images are not equally separated by one third of a period. However, Fig. 5 shows how the modulation is a unique feature that can be extracted verses conventional imaging where it is not clear how to discern the signal of interest from background noise. Figure 5 shows a case where the modulation offset due to the sum of I C i; j, Bi; j, and FPi; j is approximately 1.2 times greater than the peak modulation signal; this factor was as high as 20 for portions of the data set along the adjoining interface between TFP and Rayleigh SLIPI measurements near the flame. In addition, the background due to spurious light scattering, Bi; j, was estimated at up to 75% of the detector dynamic range. In contrast, Bi; j in the non-sooting flame and in the response image for the sooting flame was less than 1% of the detector dynamic range. Despite the relay-imaging configuration meant to capture only Rayleigh signal from nonsooting regions of the flame, some elastic scattering from soot also was collected and contributed the main source of background to the measurement. The magnitude of background scattering from soot varied for the two flames and depended on the proximity of the thin relay mirror to the real image of the sooting portion of the flame. The reason for the difference in Bi; j between the signal and response images in this sooting flame is the fact that scattering from soot contributes to Bi; j in the signal image but not in the response image, which is precisely the situation where conventional background corrections fail. It should be noted that Rayleigh SLIPI fails when the background becomes so large that the modulated signal cannot be reliably extracted within the finite dynamic range of the detector. Thus, in a
Fig. 6. Flame temperature profiles for 60% and 80% ethylene flames where white lines indicate the interface of two adjoining thermometry techniques. Temperature color bar is shown in Kelvin.
SLIPI experiment, the detector’s dynamic range should be maximized. Figure 6 shows the full-field temperature maps for the 60% and 80% ethylene flames, where the data are spatially overlaid from Rayleigh SLIPI, TFP, and soot pyrometry. The figure shows a region of no data from the fuel tube to approximately 3 cm above the burner in both flames. This is a location where measurement with the three diagnostic techniques was impossible. The soot volume fraction is too low for two-color ratio soot pyrometry, temperature is too low for TFP, and there is too much soot for Rayleigh SLIPI. Figure 7 provides a closer evaluation of the agreement between the techniques, where the temperature of each technique is plotted as a function of HAB at the spatial interface of two adjoining thermometry techniques in the 80% flame. The interfaces are shown as white lines in Fig. 6, with the Rayleigh SLIPI/TFP interface outside the TFP/soot pyrometry interface. Since the Rayleigh SLIPI data were only measured on one side of the flame, the images from all techniques are mirrored about the centerline. The dominant source of uncertainty in the soot pyrometry measurement is the assumption that
Fig. 7. Temperature at the interface of TFP/Rayleigh SLIPI (left) and TFP/soot pyrometry (right). 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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the soot optical properties are constant throughout the flame [25]. The optical properties are of course not a constant, thus resulting in an uncertainty of approximately 60 K [26]. The TFP measurement is limited by the thermocouple used to calibrate the fiber incandescence signal. As detailed in [27], the uncertainty associated with TFP at 1700 K is estimated to be 33 K. The primary source of uncertainty in the Rayleigh SLIPI measurement is from reconstruction errors in I F x; y and I A x; y, which lead to noise in the temperature field. The accuracy of Rayleigh SLIPI is determined in comparison to the detailed Rayleigh/ Raman measurement present in Fig. 3. Aside from small differences in flame structure, the two measurements are found to differ by less than 3%. As a measure of precision, the signal-to-noise ratio (SNR) in the methane flame was ∼28 while the SNR for the highest background scattering case in the 80% ethylene flame was ∼11. The left plot in Fig. 7 compares TFP and Rayleigh SLIPI temperature at their adjoining interface. The agreement is good and does not differ by more than 40 K above 2 cm HAB in the flame. Note that these temperatures are not expected to be exactly the same since the interface of the two techniques sits at a radial temperature gradient, where the SLIPI Rayleigh data should be cooler due to the proximity to the co-flow. As expected, the discrepancy between the two techniques is largest below 2 cm in the flame where the temperature gradient is steepest. The curves are not smooth due to small fluctuations in the flame position during acquisition of the TFP data. A smaller radial temperature gradient exists between TFP and soot pyrometry data, indicating that only minor differences should be observed between values at the interface. This is seen on the right in Fig. 7, where the difference along the length of the flame is less than 15 K. Similar results are observed for the 60% ethylene flame. 7. Conclusion
This work has demonstrated the application of SLIPI to quantitative Rayleigh thermometry. A split-beam approach was used to allow laser energies that would otherwise damage a Ronchi grating. The output of an Nd:YAG laser was split into two beams and interfered in the region of interest above a coflow burner. The two beams were propagated over several meters to achieve a sufficiently large period. Given a loss of approximately 50% of the laser energy prior to the focusing lens, the system is limited primarily by the laser output in terms of energy through the probe volume. Thus, split-beam SLIPI is benefited by increased energy for application to Rayleigh scattering. A primary concern for the accuracy of Rayleigh thermometry is a proper background correction for spurious elastically scattered light. The use of a structured light sheet was shown to simplify the correction by not requiring a reference image with the same background as the signal image. 6696
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In conventional Rayleigh thermometry, it is typically assumed that the observed background is the same in the flame and response images. Using SLIPI, the background must only be the same among phaseshifted images used to construct I F x; y or I A x; y and not for both. This is advantageous for measurements in environments with high background scattering that changes significantly at different measurement locations or, as in the sooting flame measured here, where the main source of background scattering originates from the flame in regions just outside the imaged area. Thus, SLIPI simplifies and extends the capacity of Rayleigh thermometry to handle spurious light scattering. A quantitative comparison of Rayleigh SLIPIderived temperature is made against a previously studied non-sooting, non-premixed methane/air flame. The experimental results are consistent with regard to the location of peak temperature and agree with computational results in terms of the magnitude of peak temperature. Radial consideration of SLIPI derived temperature is in excellent agreement with computational results throughout the flame. In the post-flame region, SLIPI temperatures are lower than the computational results but exhibit the same linear behavior with increasing HAB. The average difference between experimental and computational results is less than 10 and 90 K within the flame and post flame regions, respectively. SLIPI Rayleigh thermometry is then demonstrated in a high background noise application in conjunction with the full-field temperature measurement of 60% and 80% ethylene coflow diffusion flames. The collected Rayleigh SLIPI signal is relay imaged to the camera via a mirror placed in the image plane of the collection lens. The mirror is positioned to reflect the Rayleigh scattering from gases adjacent to the flame’s sooting region to the camera while allowing the stronger signal due to soot scattering and incandescence to pass. Despite relay imaging, significant background signal due to elastic scattering from soot is collected and is the main source of background noise in the measurement. However, Rayleigh scattering from the gases adjacent to the sooting regions could be extracted due to its known pattern. Good agreement was observed at the interface between intensity-ratio TFP and SLIPI Rayleigh-derived temperatures. This research was supported by the U.S. Department of Energy Office of Basic Energy Sciences (Dr. Wade Sisk, contract monitor) under contract DE-FG02-88ER13966. References 1. F. Q. Zhao and H. Hiroyasu, “The applications of laser Rayleigh-scattering to combustion diagnostics,” Prog. Energy Combust. Sci. 19, 447–485 (1993). 2. G. H. Wang, N. T. Clemens, P. L. Varghese, and R. S. Barlow, “Turbulent time scales in a nonpremixed turbulent jet flame by using high-repetition rate thermometry,” Combust. Flame 152, 317–335 (2008).
3. R. W. Dibble and M. B. Long, “Investigation of differential diffusion in turbulent jet flows using planar laser Rayleigh scattering,” Combust. Flame 143, 644–649 (2005). 4. J. Fielding, J. H. Frank, S. A. Kaiser, M. D. Smooke, and M. B. Long, “Polarized/depolarized Rayleigh scattering for determining fuel concentrations in flames,” Proc. Combust. Inst. 29, 2703–2709 (2002). 5. G. Sutton, A. Levick, G. Edwards, and D. Greenhalgh, “A combustion temperature and species standard for the calibration of laser diagnostic techniques,” Combust. Flame 147, 39–48 (2006). 6. M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22, 1905–1907 (1997). 7. E. Berrocal, E. Kristensson, M. Richter, M. Linne, and M. Alden, “Application of structured illumination for multiple scattering suppression in planar laser imaging of dense sprays,” Opt. Express 16, 17870–17881 (2008). 8. E. Kristensson, E. Berrocal, and M. Alden, “Quantitative 3D imaging of scattering media using structured illumination and computed tomography,” Opt. Express 20, 14437–14450 (2012). 9. E. Kristensson, E. Berrocal, and M. Alden, “Extinction coefficient imaging of turbid media using dual structured laser illumination planar imaging,” Opt. Lett. 36, 1656–1658 (2011). 10. E. B. Rikard Wellander, E. Kristensson, M. Richter, and M. Aldén, “Three-dimensional measurement of the local extinction coefficient in a dense spray,” Meas. Sci. Technol. 22, 1–15 (2011). 11. E. Kristensson, E. Berrocal, R. Wellander, M. Ritcher, M. Alden, and M. Linne, “Structured illumination for 3D Mie imaging and 2D attenuation measurements in optically dense sprays,” Proc. Combust. Inst. 33, 855–861 (2011). 12. E. Kristensson, M. Richter, S. G. Pettersson, M. Alden, and S. Andersson-Engels, “Spatially resolved, single-ended twodimensional visualization of gas flow phenomena using structured illumination,” Appl. Opt. 47, 3927–3931 (2008). 13. E. Kristensson, E. Berrocal, M. Richter, S. G. Pettersson, and M. Alden, “High-speed structured planar laser illumination for contrast improvement of two-phase flow images,” Opt. Lett. 33, 2752–2754 (2008). 14. E. Kristensson, Structured Laser Illumination Planar Imaging (SLIPI) Applications for Spray Diagnostics (Lund University, 2012). 15. E. Berrocal, J. Johnsson, E. Kristensson, and M. Alden, “Single scattering detection in turbid media using single-phase
16.
17. 18. 19.
20.
21.
22.
23. 24. 25. 26.
27.
structured illumination filtering,” J. Eur. Opt. Soc. 7, 12015 (2012). E. Kristensson, L. Araneo, E. Berrocal, J. Manin, M. Richter, M. Alden, and M. Linne, “Analysis of multiple scattering suppression using structured laser illumination planar imaging in scattering and fluorescing media,” Opt. Express 19, 13647–13663 (2011). E. Kristensson, A. Ehn, J. Bood, and M. Alden, “Advancements in Rayleigh scattering thermometry by means of structured illumination,” Proc. Combust. Inst. (2014). P. A. M. Kalt and M. B. Long, “OMA—Image processing for Mac OS X,” http://www.oma‑x.org. M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Lever, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001). M. B. Long, “Multi-dimensional imaging in combusting flows by Lorenz-Mie, Rayleigh, and Raman scattering,” in Instrumentation for Flows with Combustion, A. M. K. P. Taylor, ed. (Academic, 1993), pp. 467–508. K. T. Walsh, J. Fielding, M. D. Smooke, and M. B. Long, “Experimental and computational study of temperature, species, and soot in buoyant and non-buoyant coflow laminar diffusion flames,” Proc. Combust. Inst. 28, 1973–1979 (2000). M. D. Smooke, A. Ern, M. A. Tanoff, B. A. Valdati, R. K. Mohammed, D. F. Marran, and M. B. Long, “Computational and experimental study of NO in an axisymmetric laminar diffusion flame,” Symposium (International) on Combustion 1–2, 2161–2170 (1996). K. T. Walsh, Quantitative Characterizations of Coflow Laminar Diffusion Flames in a Normal Gravity and Microgravity Environment (Yale University, 2000). D. F. Marran, Quantitative Two-Dimensional Laser Diagnostics in Idealized and Practical Combustion System (Yale University, 1997). P. B. Kuhn, B. Ma, B. C. Connelly, M. D. Smooke, and M. B. Long, “Soot and thin-filament pyrometry using a color digital camera,” Proc. Combust. Inst. 33, 743–750 (2011). B. Ma and M. B. Long, “Combined soot optical characterization using 2D multi-angle light scattering and spectrally resolved line-of-sight attenuation and its implication on soot color-ratio pyrometry,” Appl. Phys. B, 1–17 (2014). B. Ma, G. Wang, G. Magnotti, R. S. Barlow, and M. B. Long, “Intensity-ratio and color-ratio thin-filament pyrometry: uncertainties and accuracy,” Combust. Flame 161, 908–916 (2014).
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This work demonstrates structured laser illumination planar imaging (SLIPI) for Rayleigh thermometry with high background scattering. Two coherent laser beams were crossed to produce an interference pattern, from which the modulated Rayleigh signal was collected. The modulated signal serves as a signature that identifies information about Rayleigh scattering from the probe volume against additional contributions in the image from background scattering. This work shows that the structured nature of the illumination allows for a simplified background correction. The experimental approach is validated in a non-premixed methane/air flame, and the temperature is found to be in excellent agreement with previous experimental and computational results. Rayleigh SLIPI is then applied to a high background scattering application as part of the full-field temperature measurement of sooting non-premixed ethylene/air flames. For these flames, standard Rayleigh background corrections are impossible since scattering from soot just outside the field of view is the main source of the background. Good agreement is found between SLIPI and intensity-ratio thin-filament pyrometry-derived temperature along their adjoining interface in the flame. © 2014 Optical Society of America OCIS codes: (280.1740) Combustion diagnostics; (290.5870) Scattering, Rayleigh; (110.4280) Noise in imaging systems. http://dx.doi.org/10.1364/AO.53.006688
1. Introduction
Laser Rayleigh scattering, a simple, non-invasive diagnostic with relatively strong signal strength among molecular scattering techniques, has been used for spatially and temporally resolved measurement of temperature and, under certain conditions, species in reacting and non-reacting gas flows [1–4]. The Rayleigh signal intensity from an illuminated volume, V, can be written as:
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I Rayleigh CI 0 NV
m X
X iσi;
(1)
i1
where C is an experimental constant accounting for the collection solid angle and subsequent throughput of the optics, I 0 is the incident laser intensity, and N is the local number density. The summation is over the product of a total of m species’ mole fractions, X i , with their respective Rayleigh scattering cross sections, σ i . At constant pressure, temperature can be recovered from the number density, N, through the ideal gas law. However, since Rayleigh scattering is an elastic process, the signal is susceptible to
contamination by additional scattering from the surroundings (optical components, windows, containment vessels, or scatterers outside the measurement region) and must be corrected. For temperature measurements in systems in which species concentrations and cross sections vary significantly, some means is required to account for variations in the summation term in Eq. (1). In the limit where background noise and molecular composition can be corrected, Rayleigh thermometry is an accurate diagnostic tool [5]. As a result, Rayleigh thermometry is most readily applied to open atmosphere flames containing no particulate matter and with low flame luminosity. Improved methods to deal with high levels of background scattering would greatly extend the use of Rayleigh thermometry. Structured illumination was originally developed as a means to enhance the image contrast of threedimensional (3D) structures in a conventional wide field microscope [6]. Samples are illuminated with a grid pattern of known frequency, ensuring that only regions where the light is focused on the sample image efficiently. The illumination grid is then phase shifted and multiple images are acquired to reconstruct an image free of the original pattern. In a similar way, structured laser illumination planar imaging (SLIPI) relies on an intensity-modulated laser sheet to impart a known pattern into the collected signal [7]. This technique has been used for imaging in situations where multiple scattering becomes important, such as in dense sprays. In SLIPI, photons from the probe volume that retain the original pattern are considered to have undergone one scattering event and are thus representative of the sample. Multiscattered photons generally lose the pattern and are considered as a source of noise in the measurement. Kristensson et al. have done extensive work characterizing the technique and demonstrating its applicability to turbid media such as sprays in 2D and 3D [8–16]. In previous SLIPI applications, a structured light sheet is achieved by projecting odd harmonics of an illuminated Ronchi grating onto a frequency cutter. The cutter acts as a physical barrier by blocking all harmonics except the 1 modes. The two remaining beams cross and produce an interference pattern that can be phase shifted via rotation of a glass plate located after the Ronchi grating. Blocking the fundamental and higher order modes results in a loss of ∼50% of the incident energy [14]. This is in addition to the physical limitations of a Ronchi grating, which is not designed for high-energy laser applications. One experiment was able to achieve 30 mJ per pulse for single-phase measurement without the rotating glass plate [15]. This energy is sufficient for the strong signals associated with Mie scattering or resonant processes such as laser-induced fluorescence. However, increased laser energy is desirable for improved signal-to-noise in nonresonant measurements, such as those made with Rayleigh scattering. Recently, Kristensson et al.
demonstrated Rayleigh thermometry in a premixed flame with SLIPI via a two-faceted optical component [17], which allows for increased laser energy over use of a Ronchi grating. Their work demonstrated that SLIPI could extend the accuracy of Rayleigh thermometry over conventional planar Rayleigh scattering when the source of the background was external to the measured flame. This paper demonstrates SLIPI for Rayleigh thermometry via a split-beam approach that also allows for increased laser energy over use of a Ronchi grating. Comparisons are made between SLIPI-derived temperature and previous experimental and computational results in a non-sooting non-premixed methane/air flame. Rayleigh SLIPI thermometry is then applied as part of the measurement of the full temperature field in sooting ethylene coflow diffusion flames. In this case, scattering from soot just outside the field of view is the main source of the background and standard Rayleigh background corrections are not possible. 2. Experiment
In SLIPI, information is applied to the laser sheet in the form of modulated intensity. The laser sheet intensity at location x; y has the form Lx; y Cx; y ·
m · cos2πνy φ 1 ; 2
(2)
where Cx; y is the conventional planar laser intensity, m is the modulation depth, ν is the spatial frequency, and φ is the phase. The coordinate system is as in the top view of the experimental configuration shown in Fig. 1. For perfect modulation (m 1), the sheet intensity goes to zero with spatial frequency ν, resulting in regular intervals of no Rayleigh scattering. However, due to multiple scattering effects and collection of light originating outside the probe volume, locations of zero Rayleigh scattering in the probe volume are recorded as non-zero values at the detector. As a result, the signal incident on the detector can be thought of as the summation of a dc offset I C i; j and a local amplitude I S i; j modulated at frequency ω with phase shift φ, as shown in Eq. (3) [14]. The new i; j coordinate system
Fig. 1. Experimental configuration for slit-beam Rayleigh SLIPI. 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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is located on the detector surface, representing the ith row and jth column. The functional dependence between the x; y and i; j coordinate systems depends on the magnification and resolution of the imaging system. For the practical case with m < 1, the nonzero modulation offset is included in the I C i; j term: Ii; j I C i; j I S i; j · cos2πωi φ:
(3)
Post-processing is used to keep the local modulation envelope while excluding the dc offset that results from collection of spurious photons. A series of (n ≥ 3) spatially phase-shifted images is acquired where each new image has a relative phase shift of 2π∕n with respect to the previous. This allows for the modulation envelope to be extracted as in Eq. (4), where the subtraction of different phases acts to keep features that are unique (local modulation amplitude) and remove those that are common (dc offset). Here, I l i; j and I k i; j are expressions of Eq. (3) with phase shifts φl and φk , respectively. Three phaseshifted images are the minimum required to extract the local modulation amplitude without loss of spatial resolution [17]: p n−1 n 1∕2 2 X X 2 I S i; j I i; j − I k i; j : n l1 kl1 l
(4)
The period of the interference pattern produced by crossing two laser beams is proportional to the wavelength of the light and inversely proportional to the sine of the half-angle separating the beams. Therefore, for application to macroscopic imaging, the half-angle must be small to produce a sufficiently large period. In this experiment, the output of a laser is split into two beams and propagated over several meters before crossing in the region of interest above the burner. This split-beam experimental configuration allows for laser energies that surpass those in a Ronchi grating system. The second harmonic output of an Nd:YAG laser (Continuum PL-8010, 10 Hz rep rate) is clipped by a circular aperture to a diameter of 5 mm. The laser produces 205 mJ per pulse and its polarization is oriented vertically. The beam is directed through a 50/50 beam splitter so that one beam passes parallel to the optical table and the other is reflected in a direction normal to the table surface. A 532 nm dichroic mirror reflects the beam traveling normal to the table back down the optical path and is fixed above the beam splitter so that the two beams have an initial separation of 10 mm. A neutral density filter (0.2) is placed in the path of the beam traveling parallel to the table surface to balance intensity between the beams to within 1%. The two beams are propagated for 6.9 m from the location of the beam splitter to the center of the burner via a sequence of dichroic mirrors. A cylindrical plano-convex lens (focal length 300 mm) focuses 6690
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the two beams into a sheet centered on the burner fuel tube, where the modulation period is measured to be in the range 370–450 μm, depending on the finetuning of the two beams. The combined laser energy from both beams is measured just before the focusing lens to be 103 mJ per pulse. Beam width at the focal point of the lens and at a location 5 mm closer to the focusing lens is 144 and 170 μm, respectively. The dichroic mirror fixed above the beam splitter is mounted on a rotating stage so the relative spatial position of the top beam with respect to the bottom beam can be fine-tuned. The signal is collected at an angle of 90 deg to the laser path. A 50 mm f/1.4 Nikon camera lens with an achromatic macro filter for close-up imaging collects light through a 532 nm interference filter and forms an image at its back focal plane. A 45-degree mirror in the image plane is used to reflect the signal from one side of the flame to a relay lens that refocuses the image from the hot gas adjacent to the flame onto the camera. This relay-imaging configuration was used to exclude scattering from the sooty region of the flames, which will be discussed in Section 6. This configuration allows the orders of magnitude stronger and unwanted signal from incandescence and elastic soot particle scattering to pass. The mirror must be thin to minimize additional scattering due to its location in the image plane. Therefore, a piece of cover glass (22 × 22 × 0.14 mm) coated with 100 nm of aluminum is used. The Rayleigh signal is recorded by an interline transfer EMCCD camera (Andor Luca S, 14 bit A/D) with a Navitar 35 mm f ∕1.4 lens and 20 mm extension tube. The thermoelectrically cooled camera has 658 × 496 pixels (10 μm∕pixel) and is electronically gated to its minimum exposure of 470 μs. An area of 27 × 27 μm2 from the plane of the laser sheet is projected onto each pixel and 2 mm image segments are tiled together from 2 mm to 10 cm above the burner. Open source software OMA is used for data acquisition [18]. 3. SLIPI Data Acquisition and Processing
Spatial phase shifting of the structured light sheet can be accomplished by rotating a glass plate in the yz-plane as shown in Fig. 1. However, a significant shot-to-shot phase jitter was observed in the scattering from the interfering beams above the burner, presumably due to small vibrations in the beam splitter arrangement, where differences in spacing between the mirrors on the order of one wavelength cause a significant phase change. The jitter was characterized by acquiring two 1000 image sequences. One sequence imaged planar Rayleigh scattering in air as in the above experimental configuration to assess fluctuations in the y-direction while the other sequence imaged the cross section of the beam at the focal point of the cylindrical lens to address z-direction fluctuations. The power spectrum of each image was derived from its Fourier transform and used to monitor the energy contained in each frequency component.
Fig. 2. Rayleigh SLIPI scattering in air (left) and the application of Eq. (5) for phase identification (right).
No change in the modulation frequency was observed, indicating that the angle between the beams is stable on a shot-to-shot basis. A reference image is selected with a phase equal to the mean phase of each 1000 image sequence to within one pixel in the i; j coordinate system. The phase shift of each image with respect to the reference image is determined by minimizing the norm of the difference between a sub-rectangle of each new image and a sub-rectangle in the reference image over a sequence of integer values δ. The rectangles have the same coordinates within each image except that the rectangle in the new image is shifted in the i-direction by an integer number of pixels δ, which is varied by one from minus two to plus two spatial periods in the reference image. The shift of the new image is determined from the minimum in the sequence as stated in Eq. (5) and illustrated in Fig. 2. The left side of Fig. 2 shows the relative position of the sub-rectangles in the reference image and the right side shows the output of Eq. (5), where the new image is shifted five pixels with respect to the reference image. The range of δ was chosen to differentiate between images possessing an integer multiple of 2π phase shift with respect to the reference image, since the sheet intensity has a periodic character: Shift mini ‖recti δ; jnew − recti; jref ‖2 :
(5)
This method was validated against a crosscorrelation algorithm to determine pixel-level shifting of the same object in two images. Approximately 90% of the images in the two 1000 image sets were distributed equally between maximum spatial shifts of plus or minus one period in the y-direction, and no detectable z-direction fluctuation was observed. Thus, while the jitter does not allow for direct integration of the signal due to changes in phase, it does not affect the focus of the imaging system in the zdirection. The glass plate is used to center the distribution on a given phase in the y-direction, but Eq. (5) is needed to identify the phase of each image relative to the reference. Because of the shot-to-shot phase jitter, it is impossible to continuously integrate at a given phase.
Therefore, during data acquisition, images are kept only if the shift determined by Eq. (5) is equal to one of n 3 predetermined values of δ that are chosen to have a phase shift of approximately 0 and 2π∕3 with respect to the reference image. The reference image is selected at the mean phase shift of a 100image sequence acquired in air with the glass plate rotated zero degrees. This is done to center the reference image within the jitter-induced phase shift distribution and therefore speed data acquisition. At a given measurement location, 250 images are sampled and the phase shift is determined from Eq. (5) to within one pixel at a rate of 3 Hz. Approximately 20% of the images correspond to one of the three predetermined phase shifts and are saved. The magnification and resolution of the imaging system limits the phase resolution for image identification when using Eq. (5). It is estimated that determination of the phase shift to within one pixel in the i-direction limits the resolution for phase detection to 10–12 degrees in the y-direction. This is based on observed spatial periods ranging from 370 to 450 μm in x; y projecting onto 15–18 pixels in the i; j system. The range of values results from changes made to the initial separation of the beams between data sets. All saved images are corrected for variations in total intensity and normalized to an average fundamental mode to account for spatial and temporal variations in the laser output as discussed in [14]. After corrections, the set of 5–25 acquired images for each of the three predetermined values of δ is averaged to create the corresponding I 1, I 2 , or I 3. This operation averages the phases of the individual images, resulting in a new phase at the modulation frequency, ν, equal to φi for image I i where i 1, 2, or 3. Because of the system’s phase-resolution limits, averaging images at slightly different phases can lead to loss of modulation depth. Numerical simulations estimate that less than 2% of the modulation signal was lost in this experiment. After averaging the images from each collection bin, the phase of I 1 , I 2 , or I 3 is precisely determined within a particular quadrant of the complex plane using Eq. (6). The numerator and denominator of Eq. (6) are the 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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imaginary and real components of the Fourier transform of the image at the modulation frequency ν. The phases (φ1 , φ2 , and φ3 ) are determined by adjusting all the phases so that φ2 0 and calculating the phase difference between (φ2 , φ1 ) and (φ2 , φ3 ). The magnitude of the phase shifts for φ1 and φ3 ranged from 105 to 120 deg. The modulation signal was recovered using Eq. (7), which is a general form of Eq. (4) for n 3 that allows for phase shifts between images other than 2π∕3 [14,19]: Imfˆ Iyjν φ tan Refˆ Iyj −1
and 1 I S φ1 −φ3 2 · sin 2 8 9 < I −I = I − I 1 2 2 3 − : (7) ·I 3 − I 1 i φ2 −φ3 ; :tan φ1 −φ2 tan 2 2
4. Background Correction Conventional Rayleigh Background Correction
The elastic nature of Rayleigh scattering poses a problem for quantitative measurements since the signal is at the same wavelength as the incoming laser. It can make it difficult to distinguish between the signal of interest (generated within the illumination sheet) and light scattered from other sources. The experimental signal at pixel location i; j on the detector from a Rayleigh image of a flame has the form: SignalF i; j Rdet i; jI F i; j B0 i; j FPi; j; (8) where Rdet i; j is the overall response of the imaging optics and detector, I F i; j is the Rayleigh-scattered intensity of interest, B0 i; j is background, and FPi; j is fixed pattern noise due to A/D offset and small pixel-to-pixel variations. The background term, B0 i; j, results from collection of spurious laser scattering in the experiment, Bi; j, and flame luminosity, Li; j. A background correction can be made by imaging a uniform distribution of a gas with a different Rayleigh cross section than that of air, under the same experimental conditions [20]. Helium is often used due to its small Rayleigh cross section. A background image can be constructed from a linear combination of helium and air scattering images with their respective cross sections (σ He , σ Air ), as in Eq. (9): 6692
− SignalHe i; j Rdet i; jBi; j FPi; j.
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(9)
Assuming that Bi; j and Rdet i; j are the same in all images, a full correction for background, response, and laser sheet non-uniformities is done as in Eq. (10):
(6)
ν
A.
Backgroundi; j SignalHe i; j σ He SignalAir i; j − σ Air − σ He
Ratio
SignalF − Background − Luminosity − Dark ; Response − Background (10)
where the numerator consists of the flame signal [Eq. (8)], Background [Eq. (9)], a Luminosity image obtained with the flame on and no laser, and a Dark image where the camera lens is capped. The Luminosity shot accounts for flame emission [Li; j] and the Dark shot accounts for the fixed pattern noise in the Luminosity image. The denominator contains a response image, which is typically Rayleigh scattering from air at ambient conditions in the same experimental configuration, and the same Background image as in the numerator. Equation (10) produces a scalar field that is inversely proportional to temperature (assuming constant Rayleigh cross section, see discussion in Section 5). Thus, a full correction of the experimental signal requires five different images in the same experimental configuration. If any part of the configuration is changed (e.g., to measure different heights above the burner), a new set of correction images usually must be recorded. For many experiments, obtaining good images with the imaged region uniformly filled with particle-free helium represents a significant problem, particularly at larger downstream locations. It should be noted that the assumption that Bi; j is the same in all images may be quite good in cases where the main source of background scattering is from outside the flame (e.g., from optical components, windows, or vessel walls). However, in cases where there is significant scattering from the flame just outside the field of view (as will be the case in the sooting flames to be discussed in Section 6), the conventional background correction breaks down entirely. B. SLIPI Background Correction
For SLIPI, where the Rayleigh intensity incident on the detector has the form of Eq. (3), the application of Eq. (8) gives an expression for the collected signal shown in Eq. (11): SignalF i; j Rdet i; jfI C i; j I F i; j · cos2πωi φg B0 i; j FPi; j: (11)
If three spatially modulated flame images are collected with the flame/laser on and processed with Eq. (7), the result is Rdet i; j · I F i; j. Taking the difference of pairs of phase-shifted images, as in Eq. (7), acts to subtract the background, fixed pattern, and I C i; j components. Thus, if these terms are constant between phase-shifted images, then only a response image is needed to make a full correction of the Rayleigh data. This assumption is valid as the Background is generally diffuse light that does not depend on small spatial changes in the laser intensity. The modulation offset, I C i; j, does not change significantly and can be corrected for small variations [14]. For SLIPI, a response image is derived from Rayleigh scattering in air at three different phases processed with Eq. (7). A ratio of the flame and response images is then used to divide out the Rdet i; j term, again yielding an image inversely proportional to temperature. Thus, SLIPI allows for a simplification of the conventional Rayleigh correction by not requiring a new reference image at each measurement location [e.g., SignalHe in Eq. (9)]. It also relaxes the assumption that the Background must be the same in the response and flame data to the case where it need only be the same among the phase-shifted images used to calculate I A i; j or I F i; j. These two benefits are obtained through the added complexity of a SLIPI experiment and, as will be shown, extend the application of Rayleigh thermometry to cases that could not otherwise be measured. A concrete metric to determine if SLIPI-based Rayleigh thermometry is advantageous over the method outlined in Section A, is whether or not Bi; j is constant between signal and response images. If Bi; j is constant, then both conventional and SLIPI methods apply. However, if Bi; j is not the same between the signal and response images, then conventional Rayleigh images cannot be quantitatively corrected for background. 5. Temperature Measurement in a Non-Sooting Flame
To validate the use of SLIPI for quantitative temperature measurements, a previously characterized nonsooting, non-premixed methane/air flame is used as a benchmark [21,22]. The coflow burner has a 4 mm I.D. fuel tube concentric with a 74 mm I.D. coflow. The average fuel-tube exit velocity (parabolic velocity profile) and coflow exit velocity (flat velocity profile) are fixed at a constant 35 cm∕s. The coflow is fitted with a honeycomb mesh containing 0.8 mm perforations to provide a consistent and stable flow. Methane is diluted with nitrogen to 65% by volume. This results in soot-free conditions except for a faint incandescence that can be observed at the flame tip. An initial approximation to temperature is calculated by assuming a constant scattering cross section in all regions of the flow as in Eq. (12), where s is a known scalar associated with the response image [20]. The subscripts F and A refer to I S x; y obtained from the flame and from only coflow air, respectively:
Temperaturex; y s
I A x; y . I F x; y
(12)
The assumption of a constant Rayleigh cross section is not correct for this flame, as the collected signal is proportional to the mole fraction weighted cross sections of all species present as seen in Eq. (1). A system of two equations is developed to account for this fact, where the first is given by a ratio of the flame and response signals, allowing the effective Rayleigh cross section to vary with temperature [23]. The second equation is derived from computational results and relates cross section to temperature, since computational and experimental results for temperature and major species concentrations in this flame are in good agreement [21,24]. A map of relative scattering cross section is derived from a summation of the computational mole fraction profiles of the major species multiplied by their respective scattering cross section. A scatterplot is then produced from the relative cross section and temperature at each grid point. The result has a two-branch structure where the lower curve relates to the oxidizer side of the flame and the upper curve relates to the fuel side of the flame. Both curves are fitted with second-order polynomials and serve as a second equation relating temperature and cross section on their respective side of the flame front [23]. Iterating on this system produces a self-consistent result in three or four iterations and a temperature corrected for variation in local species concentrations. At each downstream location, between 5 and 25 images were acquired for each of three phases and processed as discussed previously. No smoothing was done until the final temperature was calculated, at which point the data were smoothed once with a Gaussian kernel (171 × 171 μm, σ x σ y 41 μm). The same procedure was used for the sooting ethylene flames, which will be discussed in Section 6. Figure 3 shows results from a previously measured simultaneous Rayleigh/Raman temperature measurement [24], next to the Rayleigh SLIPI measurement, in addition to computational results [22]. The Rayleigh/Raman data were corrected as in Section A and the Rayleigh scattering cross-section was corrected with species concentrations obtained from a spontaneous Raman measurement. The two leftmost plots in Fig. 3 provide a comparison between the methods outlined in Section A and Section B. Overall agreement between the temperature maps is seen to be very good. For a more detailed comparison, Fig. 4 shows line plots at different flame locations. On the upper left, the centerline temperature for the two experimental approaches is seen to be in excellent agreement from the burner to the location of peak temperature. In the post flame region, the SLIPI data are ∼50 K lower than the Rayleigh/Raman measurement on average but displays a linear nature that is more consistent with the computational results. 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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Fig. 3. Rayleigh/Raman (left), Rayleigh SLIPI (center), and computational (right) temperatures for the 65% methane/air flame. Temperature scale is shown in Kelvin.
The remaining plots in Fig. 4 display radial temperature profiles at three downstream locations. At 1.50 cm height above burner (HAB), the SLIPI results are in excellent agreement with computational results in terms of shape and peak temperature. Rayleigh/Raman results at this location show a wider profile and a lower peak temperature, which is consistent with observation through the rest of the flame. At 3.0 cm HAB, the experimental and computational results compare well except for the centerline temperature in the Rayleigh/Raman data, which may be attributed to noise in the measurement, as seen in the centerline plot. In the post flame region (4.5 cm HAB), no major discrepancies are observed except for the lower centerline SLIPI temperature as noted above. 6. Temperature Measurement in a Sooting Flame
With the good agreement demonstrated in the relatively low background case of the non-sooting flame,
Rayleigh SLIPI was used to measure temperature in a high background noise application as part of the full-field temperature measurement in two sooting, non-premixed ethylene coflow flames. The goal is not to measure the entire temperature field of the sooting flame with Rayleigh SLIPI, but rather to measure temperature in a case where conventional Rayleigh background corrections (see Section A) fail. The fuel was diluted with nitrogen to 60% and 80% by volume in the same burner used for the nonsooting methane/air flame. Maximum soot volume fractions for the two flames were measured previously to be 1.6 ppm and 4 ppm, respectively [25]. To map the full temperature field of the ethylene flames, three diagnostic techniques were combined to measure specific regions of the flow. Temperature in sooting regions of the flame was measured with a two-color ratio pyrometry technique [25,26]. Hot gases adjacent to the flame and above ∼1150 K were measured with intensity-ratio thin-filament pyrometry (TFP) as discussed in [27] and Rayleigh SLIPI was used to measure temperature below ∼1150 K outside the flame. Since TFP and two-color soot pyrometry are not scattering techniques, their data correction is simplified compared to the Rayleigh scattering measurement. For TFP, an image of the flame was subtracted from the TFP signal and used to correct for flame luminosity and fixed pattern noise. For two-color soot pyrometry, only a dark shot with the camera lens capped is needed to correct for fixed pattern noise and A/D offset. For the TFP measurement, the flame was translated via a stepper motor at a constant rate of 2 mm∕s through a 15 μm silicon carbide (SiC) fiber fixed horizontally above the burner and centered on the fuel tube. Fiber incandescence was imaged at a rate of 2 Hz through a narrowband interference filter (700, 10 nm FWHM). The Rayleigh SLIPI data from the ethylene flame were acquired as detailed above and demonstrates the capability of the technique with high background
Fig. 4. Centerline and radial plots of temperature for computational results, Rayleigh/Raman, and Rayleigh SLIPI. 6694
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Fig. 5. Column plot from three SLIPI images (dashed lines) along with the signal from conventional planar laser imaging (solid line).
noise levels. To avoid direct detection of the scattering from soot, only that portion of the real image to one side of the flame’s sooting region was directed to the camera by the thin 45-deg mirror. Figure 5 illustrates the signature left in the collected signal via structured illumination as compared to conventional planar imaging. An approximation to planar imaging with a non-modulated sheet was derived from the average of the three phase-shifted SLIPI images. Some residual frequencies are apparent in the conventional signal since the three phase-shifted images are not equally separated by one third of a period. However, Fig. 5 shows how the modulation is a unique feature that can be extracted verses conventional imaging where it is not clear how to discern the signal of interest from background noise. Figure 5 shows a case where the modulation offset due to the sum of I C i; j, Bi; j, and FPi; j is approximately 1.2 times greater than the peak modulation signal; this factor was as high as 20 for portions of the data set along the adjoining interface between TFP and Rayleigh SLIPI measurements near the flame. In addition, the background due to spurious light scattering, Bi; j, was estimated at up to 75% of the detector dynamic range. In contrast, Bi; j in the non-sooting flame and in the response image for the sooting flame was less than 1% of the detector dynamic range. Despite the relay-imaging configuration meant to capture only Rayleigh signal from nonsooting regions of the flame, some elastic scattering from soot also was collected and contributed the main source of background to the measurement. The magnitude of background scattering from soot varied for the two flames and depended on the proximity of the thin relay mirror to the real image of the sooting portion of the flame. The reason for the difference in Bi; j between the signal and response images in this sooting flame is the fact that scattering from soot contributes to Bi; j in the signal image but not in the response image, which is precisely the situation where conventional background corrections fail. It should be noted that Rayleigh SLIPI fails when the background becomes so large that the modulated signal cannot be reliably extracted within the finite dynamic range of the detector. Thus, in a
Fig. 6. Flame temperature profiles for 60% and 80% ethylene flames where white lines indicate the interface of two adjoining thermometry techniques. Temperature color bar is shown in Kelvin.
SLIPI experiment, the detector’s dynamic range should be maximized. Figure 6 shows the full-field temperature maps for the 60% and 80% ethylene flames, where the data are spatially overlaid from Rayleigh SLIPI, TFP, and soot pyrometry. The figure shows a region of no data from the fuel tube to approximately 3 cm above the burner in both flames. This is a location where measurement with the three diagnostic techniques was impossible. The soot volume fraction is too low for two-color ratio soot pyrometry, temperature is too low for TFP, and there is too much soot for Rayleigh SLIPI. Figure 7 provides a closer evaluation of the agreement between the techniques, where the temperature of each technique is plotted as a function of HAB at the spatial interface of two adjoining thermometry techniques in the 80% flame. The interfaces are shown as white lines in Fig. 6, with the Rayleigh SLIPI/TFP interface outside the TFP/soot pyrometry interface. Since the Rayleigh SLIPI data were only measured on one side of the flame, the images from all techniques are mirrored about the centerline. The dominant source of uncertainty in the soot pyrometry measurement is the assumption that
Fig. 7. Temperature at the interface of TFP/Rayleigh SLIPI (left) and TFP/soot pyrometry (right). 10 October 2014 / Vol. 53, No. 29 / APPLIED OPTICS
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the soot optical properties are constant throughout the flame [25]. The optical properties are of course not a constant, thus resulting in an uncertainty of approximately 60 K [26]. The TFP measurement is limited by the thermocouple used to calibrate the fiber incandescence signal. As detailed in [27], the uncertainty associated with TFP at 1700 K is estimated to be 33 K. The primary source of uncertainty in the Rayleigh SLIPI measurement is from reconstruction errors in I F x; y and I A x; y, which lead to noise in the temperature field. The accuracy of Rayleigh SLIPI is determined in comparison to the detailed Rayleigh/ Raman measurement present in Fig. 3. Aside from small differences in flame structure, the two measurements are found to differ by less than 3%. As a measure of precision, the signal-to-noise ratio (SNR) in the methane flame was ∼28 while the SNR for the highest background scattering case in the 80% ethylene flame was ∼11. The left plot in Fig. 7 compares TFP and Rayleigh SLIPI temperature at their adjoining interface. The agreement is good and does not differ by more than 40 K above 2 cm HAB in the flame. Note that these temperatures are not expected to be exactly the same since the interface of the two techniques sits at a radial temperature gradient, where the SLIPI Rayleigh data should be cooler due to the proximity to the co-flow. As expected, the discrepancy between the two techniques is largest below 2 cm in the flame where the temperature gradient is steepest. The curves are not smooth due to small fluctuations in the flame position during acquisition of the TFP data. A smaller radial temperature gradient exists between TFP and soot pyrometry data, indicating that only minor differences should be observed between values at the interface. This is seen on the right in Fig. 7, where the difference along the length of the flame is less than 15 K. Similar results are observed for the 60% ethylene flame. 7. Conclusion
This work has demonstrated the application of SLIPI to quantitative Rayleigh thermometry. A split-beam approach was used to allow laser energies that would otherwise damage a Ronchi grating. The output of an Nd:YAG laser was split into two beams and interfered in the region of interest above a coflow burner. The two beams were propagated over several meters to achieve a sufficiently large period. Given a loss of approximately 50% of the laser energy prior to the focusing lens, the system is limited primarily by the laser output in terms of energy through the probe volume. Thus, split-beam SLIPI is benefited by increased energy for application to Rayleigh scattering. A primary concern for the accuracy of Rayleigh thermometry is a proper background correction for spurious elastically scattered light. The use of a structured light sheet was shown to simplify the correction by not requiring a reference image with the same background as the signal image. 6696
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In conventional Rayleigh thermometry, it is typically assumed that the observed background is the same in the flame and response images. Using SLIPI, the background must only be the same among phaseshifted images used to construct I F x; y or I A x; y and not for both. This is advantageous for measurements in environments with high background scattering that changes significantly at different measurement locations or, as in the sooting flame measured here, where the main source of background scattering originates from the flame in regions just outside the imaged area. Thus, SLIPI simplifies and extends the capacity of Rayleigh thermometry to handle spurious light scattering. A quantitative comparison of Rayleigh SLIPIderived temperature is made against a previously studied non-sooting, non-premixed methane/air flame. The experimental results are consistent with regard to the location of peak temperature and agree with computational results in terms of the magnitude of peak temperature. Radial consideration of SLIPI derived temperature is in excellent agreement with computational results throughout the flame. In the post-flame region, SLIPI temperatures are lower than the computational results but exhibit the same linear behavior with increasing HAB. The average difference between experimental and computational results is less than 10 and 90 K within the flame and post flame regions, respectively. SLIPI Rayleigh thermometry is then demonstrated in a high background noise application in conjunction with the full-field temperature measurement of 60% and 80% ethylene coflow diffusion flames. The collected Rayleigh SLIPI signal is relay imaged to the camera via a mirror placed in the image plane of the collection lens. The mirror is positioned to reflect the Rayleigh scattering from gases adjacent to the flame’s sooting region to the camera while allowing the stronger signal due to soot scattering and incandescence to pass. Despite relay imaging, significant background signal due to elastic scattering from soot is collected and is the main source of background noise in the measurement. However, Rayleigh scattering from the gases adjacent to the sooting regions could be extracted due to its known pattern. Good agreement was observed at the interface between intensity-ratio TFP and SLIPI Rayleigh-derived temperatures. This research was supported by the U.S. Department of Energy Office of Basic Energy Sciences (Dr. Wade Sisk, contract monitor) under contract DE-FG02-88ER13966. References 1. F. Q. Zhao and H. Hiroyasu, “The applications of laser Rayleigh-scattering to combustion diagnostics,” Prog. Energy Combust. Sci. 19, 447–485 (1993). 2. G. H. Wang, N. T. Clemens, P. L. Varghese, and R. S. Barlow, “Turbulent time scales in a nonpremixed turbulent jet flame by using high-repetition rate thermometry,” Combust. Flame 152, 317–335 (2008).
3. R. W. Dibble and M. B. Long, “Investigation of differential diffusion in turbulent jet flows using planar laser Rayleigh scattering,” Combust. Flame 143, 644–649 (2005). 4. J. Fielding, J. H. Frank, S. A. Kaiser, M. D. Smooke, and M. B. Long, “Polarized/depolarized Rayleigh scattering for determining fuel concentrations in flames,” Proc. Combust. Inst. 29, 2703–2709 (2002). 5. G. Sutton, A. Levick, G. Edwards, and D. Greenhalgh, “A combustion temperature and species standard for the calibration of laser diagnostic techniques,” Combust. Flame 147, 39–48 (2006). 6. M. A. A. Neil, R. Juskaitis, and T. Wilson, “Method of obtaining optical sectioning by using structured light in a conventional microscope,” Opt. Lett. 22, 1905–1907 (1997). 7. E. Berrocal, E. Kristensson, M. Richter, M. Linne, and M. Alden, “Application of structured illumination for multiple scattering suppression in planar laser imaging of dense sprays,” Opt. Express 16, 17870–17881 (2008). 8. E. Kristensson, E. Berrocal, and M. Alden, “Quantitative 3D imaging of scattering media using structured illumination and computed tomography,” Opt. Express 20, 14437–14450 (2012). 9. E. Kristensson, E. Berrocal, and M. Alden, “Extinction coefficient imaging of turbid media using dual structured laser illumination planar imaging,” Opt. Lett. 36, 1656–1658 (2011). 10. E. B. Rikard Wellander, E. Kristensson, M. Richter, and M. Aldén, “Three-dimensional measurement of the local extinction coefficient in a dense spray,” Meas. Sci. Technol. 22, 1–15 (2011). 11. E. Kristensson, E. Berrocal, R. Wellander, M. Ritcher, M. Alden, and M. Linne, “Structured illumination for 3D Mie imaging and 2D attenuation measurements in optically dense sprays,” Proc. Combust. Inst. 33, 855–861 (2011). 12. E. Kristensson, M. Richter, S. G. Pettersson, M. Alden, and S. Andersson-Engels, “Spatially resolved, single-ended twodimensional visualization of gas flow phenomena using structured illumination,” Appl. Opt. 47, 3927–3931 (2008). 13. E. Kristensson, E. Berrocal, M. Richter, S. G. Pettersson, and M. Alden, “High-speed structured planar laser illumination for contrast improvement of two-phase flow images,” Opt. Lett. 33, 2752–2754 (2008). 14. E. Kristensson, Structured Laser Illumination Planar Imaging (SLIPI) Applications for Spray Diagnostics (Lund University, 2012). 15. E. Berrocal, J. Johnsson, E. Kristensson, and M. Alden, “Single scattering detection in turbid media using single-phase
16.
17. 18. 19.
20.
21.
22.
23. 24. 25. 26.
27.
structured illumination filtering,” J. Eur. Opt. Soc. 7, 12015 (2012). E. Kristensson, L. Araneo, E. Berrocal, J. Manin, M. Richter, M. Alden, and M. Linne, “Analysis of multiple scattering suppression using structured laser illumination planar imaging in scattering and fluorescing media,” Opt. Express 19, 13647–13663 (2011). E. Kristensson, A. Ehn, J. Bood, and M. Alden, “Advancements in Rayleigh scattering thermometry by means of structured illumination,” Proc. Combust. Inst. (2014). P. A. M. Kalt and M. B. Long, “OMA—Image processing for Mac OS X,” http://www.oma‑x.org. M. J. Cole, J. Siegel, S. E. D. Webb, R. Jones, K. Dowling, M. J. Dayel, D. Parsons-Karavassilis, P. M. W. French, M. J. Lever, L. O. D. Sucharov, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Time-domain whole-field fluorescence lifetime imaging with optical sectioning,” J. Microsc. 203, 246–257 (2001). M. B. Long, “Multi-dimensional imaging in combusting flows by Lorenz-Mie, Rayleigh, and Raman scattering,” in Instrumentation for Flows with Combustion, A. M. K. P. Taylor, ed. (Academic, 1993), pp. 467–508. K. T. Walsh, J. Fielding, M. D. Smooke, and M. B. Long, “Experimental and computational study of temperature, species, and soot in buoyant and non-buoyant coflow laminar diffusion flames,” Proc. Combust. Inst. 28, 1973–1979 (2000). M. D. Smooke, A. Ern, M. A. Tanoff, B. A. Valdati, R. K. Mohammed, D. F. Marran, and M. B. Long, “Computational and experimental study of NO in an axisymmetric laminar diffusion flame,” Symposium (International) on Combustion 1–2, 2161–2170 (1996). K. T. Walsh, Quantitative Characterizations of Coflow Laminar Diffusion Flames in a Normal Gravity and Microgravity Environment (Yale University, 2000). D. F. Marran, Quantitative Two-Dimensional Laser Diagnostics in Idealized and Practical Combustion System (Yale University, 1997). P. B. Kuhn, B. Ma, B. C. Connelly, M. D. Smooke, and M. B. Long, “Soot and thin-filament pyrometry using a color digital camera,” Proc. Combust. Inst. 33, 743–750 (2011). B. Ma and M. B. Long, “Combined soot optical characterization using 2D multi-angle light scattering and spectrally resolved line-of-sight attenuation and its implication on soot color-ratio pyrometry,” Appl. Phys. B, 1–17 (2014). B. Ma, G. Wang, G. Magnotti, R. S. Barlow, and M. B. Long, “Intensity-ratio and color-ratio thin-filament pyrometry: uncertainties and accuracy,” Combust. Flame 161, 908–916 (2014).
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