High-speed light field camera and frequency division multiplexing for fast multi-plane velocity measurements 1 and Jurgen ¨ ¨ Andreas Fischer,1,∗ Christian Kupsch,1 Johannes Gurtler, 1 Czarske 1

Technische Universit¨at Dresden, Laboratory for Measurement and Sensor System Techniques, 01062 Dresden, Germany ∗ [email protected]

Abstract: Non-intrusive fast 3d measurements of volumetric velocity fields are necessary for understanding complex flows. Using high-speed cameras and spectroscopic measurement principles, where the Doppler frequency of scattered light is evaluated within the illuminated plane, each pixel allows one measurement and, thus, planar measurements with high data rates are possible. While scanning is one standard technique to add the third dimension, the volumetric data is not acquired simultaneously. In order to overcome this drawback, a high-speed light field camera is proposed for obtaining volumetric data with each single frame. The high-speed light field camera approach is applied to a Doppler global velocimeter with sinusoidal laser frequency modulation. As a result, a frequency multiplexing technique is required in addition to the plenoptic refocusing for eliminating the crosstalk between the measurement planes. However, the plenoptic refocusing is still necessary in order to achieve a large refocusing range for a high numerical aperture that minimizes the measurement uncertainty. Finally, two spatially separated measurement planes with 25×25 pixels each are simultaneously acquired with a measurement rate of 0.5 kHz with a single high-speed camera. © 2015 Optical Society of America OCIS codes: (110.6880) Three-dimensional image acquisition; (120.6200) Spectrometers and spectroscopic instrumentation; (140.3518) Lasers, frequency modulated; (280.7250) Velocimetry.

References and links 1. R. Wellander, M. Richter, and M. Ald´en, “Time resolved, 3D imaging (4D) of two phase flow at a repetition rate of 1 kHz,” Opt. Express 19, 21508–21514 (2011). 2. B. Thurow, N. Jiang, and W. Lempert, “Review of ultra-high repetition rate laser diagnostics for fluid dynamic measurements,” Meas. Sci. Technol. 24(1), 012002 (2013). 3. X. Li and L. Ma, “Volumetric imaging of turbulent reactive flows at kHz based on computed tomography,” Opt. Express 22, 4768–4778 (2014). 4. K. Lynch, T. Fahringer, and B. Thurow, “Three-dimensional particle image velocimetry using a plenoptic camera,” in 50th AIAA Aerospace Sciences Meeting, AIAA 2012-1056 (2012). 5. M. A. F. Kendall, N. J. Quinlan, S. J. Thorpe, R. W. Ainsworth, and B. J. Bellhouse, “Measurements of the gas and particle flow within a converging-diverging nozzle for high speed powdered vaccine and drug delivery,” Exp. Fluids 37, 128–136 (2004). 6. C. Willert, G. Stockhausen, M. Beversdorff, J. Klinner, C. Lempereur, P. Barricau, J. Quest, and U. Jansen, “Application of doppler global velocimetry in cryogenic wind tunnels,” Exp. Fluids 39, 420–430 (2005).

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Received 9 Jul 2015; revised 1 Sep 2015; accepted 6 Sep 2015; published 14 Sep 2015 21 Sep 2015 | Vol. 23, No. 19 | DOI:10.1364/OE.23.024910 | OPTICS EXPRESS 24910

7. R. A. Patton, K. N. Gabet, N. Jiang, W. R. Lempert, and J. A. Sutton, “Multi-kHz mixture fraction imaging in turbulent jets using planar Rayleigh scattering,” Appl. Phys. B 106, 457–471 (2012). 8. A. Fischer, U. Wilke, R. Schl¨ußler, D. Haufe, T. Sandner, and J. Czarske, “Extension of frequency modulated Doppler global velocimetry for the investigation of unsteady spray flows,” Opt. Lasers Eng. 63, 1–10 (2014). 9. A. Fischer, R. Schl¨ußler, D. Haufe, and J. Czarske, “Lock-in spectroscopy employing a high-speed camera and a micro-scanner for volumetric investigations of unsteady flows,” Opt. Lett. 39(18), 5082–5085 (2014). 10. A. Fischer, L. B¨uttner, J. Czarske, M. Eggert, and H. M¨uller, “Measurement uncertainty and temporal resolution of Doppler global velocimetry using laser frequency modulation,” Appl. Opt. 47, 3941–3953 (2008). 11. H. M¨uller, M. Eggert, J. Czarske, L. B¨uttner, and A. Fischer, “Single-camera Doppler global velocimetry based on frequency modulation techniques,” Exp. Fluids 43, 223–232 (2007). 12. E. H. Adelson and J. Y. A. Wang, “Single Lens Stereo with a Plenoptic Camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 99–106 (1992). 13. R. Ng, M. Levoy, M. Br´edif, G. Duval, M. Horowitz, and P. Hanrahan, “Light Field Photography with a Handheld Plenoptic Camera,” Stanford Computer Science Technical Report, CSTR 2005-02 (2005). 14. M. Levoy, “Light Fields and Computational Imaging,” Computer 39, 46–55 (2006). 15. C. Perwaß and L. Wietzke, “Single lens 3D-camera with extended depth-of-field,” Proc. SPIE 8291, 829108 (2012). 16. A. Fischer, D. Haufe, L. B¨uttner, and J. Czarske, “Scattering effects at near-wall flow measurements using Doppler global velocimetry,” Appl. Opt. 50(21), 4068–4082 (2011). 17. A. Fischer, J. K¨onig, D. Haufe, R. Schl¨ußler, L. B¨uttner, and J. Czarske, “Optical multi-point measurements of the acoustic particle velocity with frequency modulated Doppler global velocimetry,” J. Acoust. Soc. Am. 134, 1102–1111 (2013). 18. A. Fischer, L. B¨uttner, and J. Czarske, “Simultaneous measurements of multiple flow velocity components using frequency modulated lasers and a single molecular absorption cell,” Opt. Commun. 284, 3060–3064 (2011). 19. T. O. H. Charrett, H. D. Ford, D. S. Nobes, and R. P. Tatam, “Two-frequency planar Doppler velocimetry (2-ν PDV),” Rev. Sci. Instrum. 75(11), 4487–4496 (2004). 20. T. O. H. Charrett, I. A. Bledowski, S. W. James, and R. P. Tatam, “Frequency division multiplexing for interferometric planar Doppler velocimetry,” Appl. Opt. 53(20), 4363–4374 (2014).

1.

Introduction

The rapid progress in CMOS camera technology regarding speed and data rate drives metrology for three dimensional (3d) investigations. As a result, 3d imaging of complex unsteady flows with kHz rates was achieved, for instance by combining a pulsed laser light sheet illumination with a single high-speed camera and a scanner [1, 2] or by using volumetric illumination and multiple high-speed cameras with different views and a tomographic reconstruction [3]. For measuring the flow velocity, one common principle is to image and to track the motion of tracer particles. This principle works with scanning, tomographic or holographic approaches to yield volumetric flow velocity measurements. As the most recent development, a light field camera was shown to be applicable for tracking the three-dimensional motion of particles in a volumetric flow region of interest [4]. However, all these techniques require the optical resolution of particles or particle structures, which becomes difficult in dense sprays without additional tracers. In contrast to this, spectroscopic measurement principles allow to measure, e. g., the droplet velocity distribution in dense sprays without an optical resolution of single droplets and without additional tracer particles [5]. Thereby a high data to pixel ratio is achieved, because each pixel signal yields one measurement point [6]. By introducing high-speed cameras, spectroscopic principles based on Rayleigh and Mie scattering were accelerated, yielding planar measurements of, e. g., mixture fractions with 10 kHz [7] and spray velocities with 25 kHz [8], respectively. However, the investigation of fast unsteady flow phenomena requires 3d measurements with similar speeds. Obtaining 3d results with kHz rate is possible by scanning [9], but then the volumetric dataset is not acquired simultaneously. Furthermore, the scanning principle requires multiple frames for the reconstruction of the measurement volume, which lowers the achievable measurement rate. In order to yield simultaneous spectroscopic measurements in the 3d region of interest with a measurement rate that is in principle only limited by the camera frame rate, a novel approach is

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Received 9 Jul 2015; revised 1 Sep 2015; accepted 6 Sep 2015; published 14 Sep 2015 21 Sep 2015 | Vol. 23, No. 19 | DOI:10.1364/OE.23.024910 | OPTICS EXPRESS 24911

presented by introducing a high-speed light field camera. The used principle for flow velocity measurements is described at first. Then the setup of the developed high-speed light field camera (HS-LFC) is explained and validated. For eliminating the crosstalk between the different measurement planes, an additional multiplexing technique is found to be necessary. The HSLFC and the multiplexing technique are applied to enhance the measurement capability from 2d to 3d, which is proven by simultaneous measurements at two spatially separated planes in a steady nozzle flow. The high-speed capability is finally demonstrated by measurements in an unsteady spray. 2.

Measurement principle and setup

The considered measurement principle is the frequency modulation Doppler global velocimetry (FM-DGV) [10], which is depicted in Fig. 1. The measurement plane is illuminated by a laser light sheet (direction i, laser wavelength λ ) and the scattered light is observed through a molecular filter with a camera (direction o). In a spray, the light is scattered on the spray droplets, whereas tracer particles are used in single phase flows. The scattered light is shifted in frequency according to the Doppler effect, cf. Fig. 1. The Doppler frequency fD is directly proportional to the droplet velocity component along the sensitivity vector (o −i). For the chosen perpendicular arrangement o ⊥i and the laser wavelength λ = 895 nm, the relation between the o−i) Doppler frequency and the measured velocity component voi = ( v reads |o−i| fD =

|o −i| · voi = 1.58 MHz/(m/s) · voi . λ

(1)

In order to measure the Doppler frequency with a camera, a narrow band laser is used for illumination and is operated near the resonance of the molecular filter. As a result, the molecular filter serves as frequency to intensity converter. For eliminating the cross-sensitivity with respect to the scattering intensity with a single camera, a sinusoidal laser frequency modulation is applied and the non-linearity of the transmission curve of the molecular filter is used. Evaluating the amplitude ratio A1 /A2 of the first and second order harmonic of the camera signal yields a measure of the desired velocity field at the illuminated plane, that is independent of the mean scattering intensity. The relation between the amplitude ratio and the Doppler frequency, which is directly proportional to the desired velocity according to Eq. (1), is shown in Fig. 2. resulting intensity signal

transmission

1

laser light sheet

i velocity v

scattering particles

o

(o - i). v Doppler fD = l frequency

molecular filter high-speed camera

0.5

0 frequency

laser frequency modulation

fc

fc + fD

Fig. 1. FM-DGV principle for planar (2d) measurements: Arrangement of the measurement setup (left) and transmission of the molecular filter (right) illustrating the applied sinusoidal laser frequency modulation and the resulting intensity signal with/without Doppler shift. The symbol fc denotes the laser center frequency without Doppler shift.

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Received 9 Jul 2015; revised 1 Sep 2015; accepted 6 Sep 2015; published 14 Sep 2015 21 Sep 2015 | Vol. 23, No. 19 | DOI:10.1364/OE.23.024910 | OPTICS EXPRESS 24912

ratio A1 / A2

4 3 2 1 0

0

50

100

150

Doppler frequency [MHz]

Fig. 2. FM-DGV calibration curve, where the relation between the measured velocity component voi =

(o−i) v |o−i|

and the Doppler frequency fD is voi /(m/s) = 0.633 · fD /(MHz), cf.

Eq. (1).

Note that the FM-DGV principle requires multiple frames in order to detect the amplitudes A1 , A2 . Hence, FM-DGV is no single-shot measurement technique, which reduces the maximum achievable measurement rate. However, the number of required frames per modulation period can be minimized, e. g., by using a frequency shift keying technique [11]. FM-DGV is mainly applied here as a representative for the combination of spectroscopic measurement principles with high-speed light field evaluation. The key idea for obtaining simultaneous 3d measurements is to apply multiple light sheets at different z-positions and to separate these measurement planes after image acquisition by refocusing using light field technology [12–14]. As a proof-of-principle, the case of two parallel measurement planes P1, P2 with a spacing of d = 12 mm is investigated subsequently. For this purpose, a HS-LFC is realized, see Fig. 3, whose depth of field is smaller and whose refocusing range is larger than the distance of the measurement planes. The HS-LFC consists of a main lens to adjust the working distance, a micro lens array according to the light field principle, a relay lens to adjust the number of pixels per micro lens and a commercial high-speed camera as fast sensing unit. With the main lens, the plane P1 is imaged at the position of the micro lens array with magnification 1.4. The micro lenses have a pitch of 0.25 mm and 25×25 micro lenses are used. Since the resolution of the refocused images is determined by the pitch and the number of the micro lenses [13], the setup yields a lateral resolution of 0.2 mm and 25×25 points per measurement plane. 133.6 mm 171 mm

P1

ML

162 mm

Focal plane MLA

49.7 mm

P2

73.18 mm

molecular filter

121.6 mm

MLA

RL

HSC

Fig. 3. Setup of the high-speed light-field camera (HS-LFC): Main Lens ML ( fML = 75 mm), Micro Lens Array MLA ( fMLA = 0.86 mm), Relay Lens RL ( fRL = 50 mm), HighSpeed Camera HSC.

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Received 9 Jul 2015; revised 1 Sep 2015; accepted 6 Sep 2015; published 14 Sep 2015 21 Sep 2015 | Vol. 23, No. 19 | DOI:10.1364/OE.23.024910 | OPTICS EXPRESS 24913

An image of the camera sensor is placed in the focal plane of the micro lens array to obtain a light field camera type 1.0, and the refocusing algorithm is adopted from [13]. In order to adjust the number of pixel per micro lens, the focal plane of the lens array is imaged onto the camera sensor with the relay lens. Due to the magnification of 2.24 and the camera pixel pitch of 28 µm, 20×20 pixel are available for each micro lens. This means further a required frame size of 500×500 pixel, which limits the frame rate to max. 49 kfps. The used camera type Phantom v1610 can provide up to 1 Mfps, but only with a smaller frame size. This illustrates the trade-off between the maximal measurement rate and the number of pixels per micro lens, which influences the depth of field and the refocusing range. In order to reach the design aims regarding a small depth of field and a large refocusing range, the design of the HS-LFC was supported by optical simulations. Here, geometric optics was applied and diffraction phenomena and aberrations were neglected. The image sharpness was evaluated by calculating of the effective resolution ratio ERR [15]. The ERR is the resolution of the imaged object normalised by the maximum resolution of the refocused image. The maximum achievable image resolution is the number of available image pixels along the considered axis, which gives an ERR of one. Here, the maximum image resolution is 25 according to the number of the micro lenses. The resulting ERR is shown in Fig. 4(a) for both cases, a refocusing at the measurement plane P1 and a refocusing at the measurement plane P2. As a result and as expected, the highest resolution is achieved when refocusing at the position of the measurement plane. The depth of field defined as the width of more than half of the maximum resolution amounts to 1 mm and 2 mm, respectively, while the refocusing range is 21 mm. According to [13], the refocusing range of the HS-LFC is calculated by the square root of the number of pixel per micro lens multiplied by the depth of field of a camera with equal configuration but without micro lens array. Consequently, the depth range to obtain sharp images (refocusing range) of a light field camera is directly proportional to the square root of the number of pixel per micro lens and is higher than the depth of field of a conventional camera with equal configuration. For the HS-LFC, the depths of field are smaller and the refocusing range is larger than the distance between both measurement planes. As a result, objects at measurement plane P1 occur blurred and, thus, with a 90 % reduced intensity when it is refocused on plane P2 and vice versa. For validation, an illuminated pinhole with a diameter of 300 µm is placed in the plane P1 and P2, respectively. The refocused images shown in Fig. 4(b) left and right, respectively, finally prove that design of the HS-LFC allows to separate the measurement planes after image acquisition by refocusing. The intensity reduction of the out-of-focus measurement plane is essential, because the light from the out-of-focus plane is detected together with the light from the in-focus measurement plane, and the resulting velocity value is a weighted average of the velocity value from both planes with the scattered light intensity as weighting factor [16]. Note that the intensity reduction is even more essential in the case of more than two measurement planes, because then the unwanted light from each defocused plane accumulates. However, the intensity reduction of the out-of-focus measurement plane (intensity multiplex) was found to be based on two prerequisites. The first prerequisite is that the size of the particles imaged onto the micro lens array have to be smaller than the size of one micro lens. In order to illustrate and explain this finding, a simplified simulation is performed. The image of one scattering particle is assumed to have a Gaussian intensity distribution with the standard deviation σp , and the in- and out-of-focus image is calculated, cf. Fig. 5(a). For the simulation, the defocused image is obtained by a two-dimensional convolution of the focused image with a Gaussian filter. In agreement with the setup of the HS-LFC, the width of the Gaussian filter is adjusted to achieve an intensity reduction by defocusing to 10 % of the original level. Note that intensity means the intensity of

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Received 9 Jul 2015; revised 1 Sep 2015; accepted 6 Sep 2015; published 14 Sep 2015 21 Sep 2015 | Vol. 23, No. 19 | DOI:10.1364/OE.23.024910 | OPTICS EXPRESS 24914

P1

ERR

1

P2

ERR P1 ERR P2

0.8 0.6 0.4 0.2 0 110

120

130

140

150

Distance to ML in mm

a)

pinhole at P1

b)

refocused at P1

pinhole at P2

refocused at P2

refocused at P1

refocused at P2

Fig. 4. a) Calculated effective resolution ratio (ERR) and b) experimental refocusing results.

one image pixel, which corresponds to one element of the micro lens array and not a camera pixel according to the light-field technique. The region of the considered image pixel is marked in Fig. 5(a) by a red rectangle. The desired attenuation of the pixel signal thus can be evaluated by calculating the pixel intensity ratio between the defocused and the focused image. This intensity ratio is shown in Fig. 5(b) over the size of the particle image. The particle image size is defined by 4σp and normalized by the edge length of the pixel. For a normalized particle image size of one, the intensity ratio is about 10 % as expected. For larger particle sizes, the intensity ratio increases and converges towards 100 %, which means no intensity reduction occurs. As a result, the intensity reduction by defocusing requires a particle image size that is smaller than the pixel width, i. e. smaller than the diameter of one micro lens. pixel intensity ratio

focused image 1 0.5 0

defocused image 0.02 0.01

0.6 0.4 0.2 0

0

a)

1 0.8

b)

0

5

10

15

particle size (4σp ) / pixel width

Fig. 5. a) Example of a simulated focused and defocused particle image, where the red rectangle marks the area of a single pixel that is evaluated, and b) the calculated pixel intensity ratio between the defocused and focused image (i. e. the signal attenuation by defocusing) for different particle sizes.

The second prerequisite is that the number of imaged particles per pixel has to be sufficiently

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Received 9 Jul 2015; revised 1 Sep 2015; accepted 6 Sep 2015; published 14 Sep 2015 21 Sep 2015 | Vol. 23, No. 19 | DOI:10.1364/OE.23.024910 | OPTICS EXPRESS 24915

small. In order to prove this finding, the simulation is enhanced to consider multiple particles. For the sake of convenience, the particles are arranged with equidistant spacings, cf. Fig. 6(a). In order to eliminate artifacts due to the specific particle position within the pixel area, the average intensity ratio for random particle positions within the pixel area is calculated. A fix particle size is assumed, which fulfills the first prerequisite. The resulting pixel intensity ratio between the defocused and the focused image is shown in Fig. 6(b) over the number of particles per pixel. The minimal intensity ratio of 10 % is asymptotically attained for a number of particles per pixel near zero. The intensity ratio monotonously increases with an increasing particle concentration and converges towards 100 %. The maximum of the intensity ratio is already achieved for one particle per pixel. As a result, the intensity reduction by defocusing requires a number of particles per pixel (micro lens) that is significantly smaller than one. pixel intensity ratio

focused image 1 0.5 0

defocused image 0.05

1 0.8 0.6 0.4 0.2 0

0

a)

b)

0

0.5

1

1.5

2

number of particles / pixel

Fig. 6. a) Example of a simulated focused and defocused image with multiple particles, where the red rectangle marks the area of a single pixel that is evaluated, and b) the calculated pixel intensity ratio between the defocused and focused image (i. e. the signal attenuation by defocusing) for different particle concentrations.

At least one of both requirements is not fulfilled for the subsequently described experiments. For the nozzle flow experiment, seeding particles with a diameter of 1 µm are applied [17]. As a result, the particle images are about two orders of magnitude smaller than one micro lens and, thus, sufficiently small. However, the particle concentration too high. A seeding particle concentration of 1 × 1011 m−3 is typical for the DGV technique [16], which means about nine particles within the depth of field range of one micro lens. For the nozzle flow experiment, the seeding particle concentration can be reduced in principle, but this will decrease the signal to noise ratio and, thus, will increase the measurement uncertainty. Regarding the spray experiment, no seeding particles are added. The spray droplets are used as scattering objects. The imaged spray droplets are expected to vary in size, but according to the spray nozzle exit of 0.4 mm the imaged droplets are probably either too large or too dense with respect to the dimension of one micro lens. This hinders the required intensity reduction for the out-of-focus measurement plane. Under these circumstances, the intensity signals from the two measurement planes cannot be separated by refocusing only. In order to eliminate the crosstalk between both planes, a different multiplexing technique must be added. This means that the design requirement of the HS-LFC with respect to the sufficiently large refocusing range maintains, while the demand for a small depth of field can be released. However, a large numerical aperture of the imaging system is important for achieving a high signal to noise ratio, which is crucial for the uncertainty of the FM-DGV measurement. Since the desired numerical aperture leads a small depth of field, the light field refocusing technique remains an essential part of the measurement system despite the additional multiplexing. It is a key feature of the light field technology, that sharp images are

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Received 9 Jul 2015; revised 1 Sep 2015; accepted 6 Sep 2015; published 14 Sep 2015 21 Sep 2015 | Vol. 23, No. 19 | DOI:10.1364/OE.23.024910 | OPTICS EXPRESS 24916

obtained by refocusing within a comparably large depth range (refocusing range) for a given numerical aperture. Without refocusing, the measured out-of-focus velocity field is blurred for the present configuration, because the depth of field is smaller than the distance of the two measurement planes. With refocusing, both velocity fields in the two measurement planes are simultaneously measured with maximal resolution. For multiplexing the intensity signals of both measurement planes, a frequency division multiplexing is performed, i. e. two lasers with a different modulation frequency are used [18]. The resulting measurement setup of the light-field-FM-DGV is depicted in Fig. 7. Laser 1 modulated with 1 kHz illuminates measurement plane P1, and Laser 2 modulated with 1.5 kHz illuminates measurement plane P2. In comparison with the non-camera FM-DGV system described in [18], the modulation frequencies are decreased due to the lower frame rate of the camera. Note also that the different laser wavelengths (895 nm, 852 nm) are not necessarily required, but are due to laser availability reasons. The emitted power of each laser is about 300 mW. The light sheets are 5 mm high and 0.3 mm thick. The thickness determines the axial spatial resolution. The lasers are power amplified diode lasers with linewidths in the order of 1 MHz that is about three orders of magnitude smaller than the linewidth of the molecular filter curve. The laser wavelengths coincide with resonances of cesium gas that is used as molecular filter, and each laser center frequency is stabilized at the respective resonance with a separate control circle. Further details of the filter transmission curve and the laser stabilization can be found, e. g., in [10, 17]. Here, the molecular filter is included in the HS-LFC setup, cf. Fig. 3. In order to minimize the amount of data to be processed, the high-speed camera is operated with 12 kfps, which is sufficiently high to resolve the first and second order harmonics of the intensity signals from both measurement planes. The signals are separated implicitly when performing the FM-DGV signal analysis in frequency domain and selecting the appropriate Fourier coefficients for laser 1 (1 kHz, 2 kHz) and laser 2 (1.5 kHz, 3 kHz), respectively. Consequently, the measurement setup enables simultaneous velocity measurements at both planes with 25×25 pixel and kHz measurement rate.

nozzle

illumination

i

Laser 2 (852 nm)

light sheet P2

Laser 1

light sheet P1

(895 nm)

z

v

signal generator modulation

DAQ

computer

10 GigE

data acquisition & signal processing

HS-LFC

1.5 kHz 1 kHz

o

y

x

high-speed light-field camera*

*incl. molecular filter

observation

Fig. 7. Setup of the Light-Field-FM-DGV system with frequency division multiplexing (HS-LFC according to Fig. 3).

3.

Validation

In order to validate the measurement system, mean velocity fields are measured at a steady nozzle flow. The measurement results are shown in Fig. 8. The averaging time amounts to 4.8 s. By applying a threshold, invalid values with a signal to noise ratio below one were discarded.

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The nozzle exit has a diameter of 1 cm and the distance along the nozzle axis from the center of the nozzle exit to the measurement plane P2 is 1.4 cm. The flow center in the measurement plane P2 is at x = 6.5 mm, y = 2.5 mm. As intended, the measurement plane P1 is located at the right side of the nozzle flow indicated by the decreasing velocity over x, whereas the measurement plane P2 is located at the left side of the flow indicated by the increasing velocity over x, cf. Fig. 7. Both edges of the nozzle flow are clearly resolved. Comparing the case of both lasers switched on (top) and only a single laser running (bottom), only a slight crosstalk between the measurement planes is visible in the upper left region of plane P1. In order to illustrate the crosstalk reduction by the frequency multiplexing technique, the measurement results are compared with the very first measurement results without frequency multiplexing, which are shown in Fig. 9 (modulation frequency 1 kHz). Note that these early results can only be used for a qualitative comparison with Fig. 8, because the system setups and the location of the nozzle exit are different. However, the measurement results where both measurement planes are illuminated (top) are entirely different from the results where only a single measurement plane is illuminated (bottom). The reason is the crosstalk between both measurement planes, which hinders simultaneous measurements at both planes. The crosstalk is significantly reduced with the frequency multiplexing technique, cf. Fig. 8. As a result, the necessity and the effect of the applied multiplexing technique is demonstrated.

1 2 3 4 5

y in mm

1 2 3 4 5

refocused on P2

1 2 3 4 5 x in mm y in mm

y in mm y in mm

Laser on for refocused plane

Laser 1 & 2 on

refocused on P1

1 2 3 4 5 x in mm

1 2 3 4 5

1 2 3 4 5

m/s 1 2 3 4 5 x in mm

20 10 0

1 2 3 4 5 x in mm

Fig. 8. Measurement result for the steady jet flow with frequency multiplexing.

For the purpose of validation, a measured velocity profile (from plane P2) is compared with a reference measurement using a laser Doppler anemometer, see Fig. 10. Both measurements agree within the 95 % confidence interval. Hence, systematic errors are negligible. The velocity standard deviation is directly proportional to the square root of the measurement rate and amounts to 10 m/s in the flow core region for a measurement rate of 0.5 kHz. Note that the value of the standard deviation is a mean value of several measurement points attributed to the flow core region. Note further that the measured standard deviation is valid for a fixed camera frame rate and laser modulation frequency and can be different for other system parameters. Since the measured standard deviation is significantly higher than the turbulence intensity of the nozzle flow of 2 %, the uncertainty can be mainly attributed to the measurement system. However, the random error is about two orders of magnitude larger than what can be achieved with the FM-DGV principle [17]. The two main reasons for the increased random error are

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Received 9 Jul 2015; revised 1 Sep 2015; accepted 6 Sep 2015; published 14 Sep 2015 21 Sep 2015 | Vol. 23, No. 19 | DOI:10.1364/OE.23.024910 | OPTICS EXPRESS 24918

y in mm

y in mm

1 2 3 4

refocused on P2

1 2 3 4

y in mm

1 2 3 4 x in mm y in mm

Laser on for refocused plane

Laser 1 & 2 on

refocused on P1

1 2 3 4 x in mm

1 2 3 4

1 2 3 4

m/s 20

1 2 3 4 x in mm

10 0

1 2 3 4 x in mm

Fig. 9. Measurement result for the steady jet flow without frequency multiplexing.

the increased spatial resolution and the larger region of interest due to the usage of the camera instead of a linear detector array and the light sheet (2d) illumination instead of a beam (1d) illumination. The increased spatial resolution, which means less spatial averaging and less particles per pixel in the mean, leads to an increase of the scattered light intensity fluctuations. Such fluctuations of the scattered light intensity are a known error source for FM-DGV, but can be improved by increasing the laser modulation frequency. For a given camera frame rate, this can be achieved in future studies by minimizing the required number of frames per modulation period [11]. Using a camera and a planar illumination also means a lower available light power per measurement point and, thus, a decreased signal-to-noise ratio. Hence, an increase of the laser power, an increased scattering cross-section of the scattering particles and a higher number of observed scattering particles are desired in future setups in order to increase the signal-tonoise ratio. Actually, a higher scattering light intensity by a factor of four was observed for the subsequently described spray experiments, either due to larger scattering particles or a higher concentration of the droplets near the nozzle exit. As a result, the random error is then expected to be by a factor of four (for dominant read-out noise) or by a factor of two (for dominant shot noise) smaller than for the validation experiment. 25

v in m/s

20 15 10 Light-Field-FM -DG V LDA

5 0

0

2

4

6

8

10

12

x in mm Fig. 10. Comparison of Light-Field-FM-DGV with laser Doppler anemometry (LDA) reference measurements (confidence level of 95 % is illustrated as filled region).

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4.

Application

The Light-Field-FM-DGV is finally applied to an unsteady spray to demonstrate the spatiotemporal resolution. In contrast to the nozzle flow experiment, no seeding particles are used. The spray droplets are used as scattering particles and, thus, the desired droplet velocity is measured without slip. The spray nozzle exit with an estimated diameter of 0.4 mm is directed towards observation direction o with an angle of 7 , see Fig. 11. Here, the main spray direction is not the measured velocity component along the sensitivity vector (o −i), and is obtained by a coordinate transform neglecting others than the main velocity component. The distance along the nozzle axis from the center of the spray nozzle exit to the measurement plane P2 is 1 cm, and the spray flow center in the measurement plane P2 is at x = 2 mm, y = 2.5 mm.

spray nozzle

i light sheet P2 light sheet P1

z

v

o

y

x

HS-LFC Fig. 11. Measurement arrangement for the spray experiment.

The spray was actuated two times as is visible in Fig. 12(a), which shows the velocity time series at the position (x = 2 mm, y = 2.5 mm) from the simultaneously measured planes P1, P2. In P2 the measurement position is near the spray center, while it is more towards the spray boundary region in plane P1. Each spray cycle is different and not reproducible, which illustrates the necessity of simultaneous measurements in the 3d spray region. The measurement rate of 0.5 kHz allows to resolve the transient behavior during the beginning and the ending of each spray cycle. Especially an overshoot is resolved at the beginning of the first spray cycle, whereas the velocity is monotonically decreasing during the endings. An image sequence from the ending of the first spray cycle is shown in Fig. 12(b) as an example. Note that the maximum velocity occurs not at the spray flow center position, because not the mean velocity field but a time series sample is shown. In agreement with the spray orientation, the spray occurs more left in the plane P1 than in P2. Note that the core region of the spray cross-section is actually outside the observed P1 region, which explains the lower velocities there. Between the transient beginning and ending of the spray cycle, the spray behavior appears to be almost steady. A Fourier analysis over a duration of 0.6 s reveals a characteristic velocity oscillation at 200 Hz in plane P2, see Fig. 12(c). However, no such oscillation occurs in the observed region in plane P1, which is plausible due to increasing turbulence downstream. The velocity spectrum further allows to estimate the maximum random error. The white noise level of 0.2 m/s corresponds to a standard deviation of 3.5 m/s for a measurement rate of 0.5 kHz. This value includes flow turbulence and uncertainty contributions from the measurement system. As expected, the random error is smaller than for the validation experiment at the seeded nozzle flow, because the scattered light intensity is larger. The random error reduction is at least by a factor of three while the increase of the scattered light intensity is by a factor of four. Hence, the reduction of the random error can be explained by the camera read-out noise and the shot noise as dominant error sources, which is an important finding for minimizing the random error in future applications of the presented Light-Field-FM-DGV measurement technique. #245655 © 2015 OSA

Received 9 Jul 2015; revised 1 Sep 2015; accepted 6 Sep 2015; published 14 Sep 2015 21 Sep 2015 | Vol. 23, No. 19 | DOI:10.1364/OE.23.024910 | OPTICS EXPRESS 24920

FFT eval.

v in m/s

60

P1 P2

40 20

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cycle 2

0 0

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y in mm

1.298 s

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1.306 s

1.314 s

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c)

3

t in s

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P1

P1

P2

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0 40

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1.5

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1 0.5 0 50

100

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f in Hz

Fig. 12. a), b) Time domain and c) frequency domain analysis of the investigated unsteady spray. The ’x’ in b) marks the measurement position (x = 2 mm, y = 2.5 mm) of the data shown in a) and c).

#245655 © 2015 OSA

Received 9 Jul 2015; revised 1 Sep 2015; accepted 6 Sep 2015; published 14 Sep 2015 21 Sep 2015 | Vol. 23, No. 19 | DOI:10.1364/OE.23.024910 | OPTICS EXPRESS 24921

5.

Conclusion and outlook

In conclusion, the concept of using a high-speed light field camera to yield fast spectroscopic measurements in a 3d flow region of interest was proven. However, when using light field refocusing only, a crosstalk between the measurement planes occurred mainly due to the high concentration of the scattering particles. In order to eliminate the crosstalk, a frequency multiplexing technique was applied in addition to the light field technology. The light field imaging allowed to maintain a high numerical aperture, which is important to minimize the measurement uncertainty, while the depth range for which sharp images are obtained (refocusing range) is increased in comparison with conventional imaging with equal numerical aperture. However, the wider depth range is at the cost of lateral resolution. A unique advantage of the light field measurement approach is that multiple measurement planes at different depths can be acquired simultaneously, which is an important feature for investigating fast varying transient flow phenomena. In addition, the approach allows to achieve high measurement rates near the kHz range. Note that the measurement rate is lower than the camera frame rate, because the applied FM-DGV principle requires multiple frames per measurement. As outlook the measurement rate can be increased, e. g., by minimizing the number of frames per modulation period using frequency shift keying [11] or frequency switching [19]. Then the maximum achievable measurement rate with the light field approach is ultimately limited by the camera performance, where the trade-off between a high frame rate (maximal measurement rate) and a large frame size (maximal resolution of the measurement volume) remains. With the FM-DGV principle, simultaneous velocity measurements at two spatially separated planes with 25×25 pixels each were achieved in an unsteady spray with a measurement rate of 0.5 kHz. More measurement planes can be obtained in future setups by adding multiple laser sources. As an alternative, a code multiplexing can be used [20], which requires only a single laser source, but increases the number of required frames per measurement. Finally, the presented approach of using a high-speed light field camera is promising to be also applicable for other spectroscopic measurement principles. Acknowledgments The contribution from Andr´e D¨ohring is gratefully acknowledged as well as the financial support of the German Research Foundation (DFG) for the high-speed camera and the project (INST 269/536-1 FUGG, Cz55-25-3).

#245655 © 2015 OSA

Received 9 Jul 2015; revised 1 Sep 2015; accepted 6 Sep 2015; published 14 Sep 2015 21 Sep 2015 | Vol. 23, No. 19 | DOI:10.1364/OE.23.024910 | OPTICS EXPRESS 24922