EVALUATION OF THE SHADING METHOD FOR REDUCING IMAGE BLOOMING IN THE PIV MEASUREMENT OF OPEN CHANNEL FLOWS*

ZHONG Qiang, LI Dan-xun, CHEN Qi-gang, WANG Xing-kui

State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China,

E-mail:zhongq08@mails.tsinghua.edu.cn

EVALUATION OF THE SHADING METHOD FOR REDUCING IMAGE BLOOMING IN THE PIV MEASUREMENT OF OPEN CHANNEL FLOWS*

ZHONG Qiang, LI Dan-xun, CHEN Qi-gang, WANG Xing-kui

State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China,

E-mail:zhongq08@mails.tsinghua.edu.cn

The shading method is a simple but effective way of reducing image blooming in the measurement of open channel flows with the Particle Image Velocimetry (PIV). The current paper proposes a simplified analytical model for light attenuation using this method. The model is verified against experimental data, and the influence of several parameters is illustrated numerically. The possible adverse effect due to the light attenuation is shown to be limited when the parameters in the shading method are in an adequate range, as shown by processing standard images of Case B in PIV Challenge 03. A simple criterion for setting the shade in experiment is given for controlling the errors caused by the shading technique within an acceptable range.

Particle Image Velocimetry (PIV), blooming, shade, open channel flows

Introduction

The Particle Image Velocimetry (PIV) is a measurement technique widely used in fluid mechanics study. Because it is a 2-D (or 3-D) and undisturbed optical method, it is especially used in water flow researches in recent years, for example, the gas-liquid or solid-liquid two-phase flow[1,2], and the open channel flow with submerged rigid vegetation[3]. Because the PIV is a technique based on the information from images of the flow, the image blooming, which frequently occurs in PIV experiments, becomes an issue.

The image blooming refers to a situation in which the neighboring pixels are saturated with excess charges, which would lead to streaking, flare, or even complete “whiteout” of the recorded images, ruining the cross-correlation analysis in the PIV measurement[4]. Basically, the output of a pixel in a Charge-Coupled Device (CCD) is related with the amount of electrons and is therefore proportional to the amount of light falling onto it. Each pixel cell can store a maximum number of electrons, as its full well capacity[5], which depends on the CCD type. When this number is exceeded during exposure, the additional electrons migrate to the neighboring pixels, leading to image blooming. In many PIV measurement cases, the objects in the test section always have highly reflective surfaces, so the blooming would frequently occur in places close to these surfaces. Examples are aluminum or steel surfaces in wind tunnels and fluid machineries, glass surfaces in the channel, and solid particles or bubbles in multiphase flows, among others. Information of the blooming area is missing, so the vectors calculated from these areas must be interpreted carefully because with the blooming, their values can significantlydistorted[5], and sometimes the blooming may cause measurement failures near the surface[6]. In addition, the blooming may also damage the sensors of cameras[7]. So the light reflection and the blooming control are the key factors of the PIV measurement[8].

Several methods are used commonly in experiments to prevent blooming. First is that the PIV recording techniques might be improved. In modern CCD sensors, the blooming can be reduced significantly through incorporating specialized anti-blooming architectures[4], an example is the prevention of the electrons of saturated pixels from polluting adjacent cells by the anti-blooming gate between pixels[9]. However, the use of such devices may limit the pixel size and possibly the resulting pixel sensitivity. Another option is the use of Complementary Metal Oxide Semiconductor (CMOS) cameras[10,11]. One of the main advantages of most CMOS sensors is their capability to record images with high contrast without blooming. However, the image quality and signal-to-noise ratios of CMOS cameras are generally lower than those of CCD cameras[10]. The second method is the limited use of reflective surfaces. Arnott et al.[12]used a matt black, self-adhesive plastic foil to cover the reflective surface for eliminating the area for blooming. In the work of Yu et al.[8], Di et al.[13], Wu et al.[14]and Mula et al.[15], the surfaces in the model were painted with coating to reduce laser blooming effects. The last and a commonly used method is the adjustment of various parameters such as intensity of laser, aperture value, shutter time, ISO, and gain, among others. This method reduces the blooming probability by finding an appropriate combination of parameters. It is more like an art, and the image quality is generally affected because fewer photons hit the pixel and the sensitivity of CCD is also affected.

In open channel flow experiments, all aforementioned “anti-blooming” methods have serious limitations. The first method requires an increased investment in hardware. The second one fails completely as the channel bed, usually made of glass, must remain clear and transparent in the test section to allow passage of laser light for the bottom-to-top illuminetion. The third method is difficult to apply in practice, as the optimization of illumination parameters requires tremendous experience and patience. Other approaches are not commonly used. For example, highly reflective objects could be placed outside the measurement windows to avoid camera blooming[16]. However, this method is unsuitable because the PIV test section is usually determined by the problems to be studied.

Another commonly used method, termed as the“shading method” in the current study, proves to be a simple but effective way of reducing the image blooming. The idea of the shading method is not really new. In fact, it is also a widely used approach, mostly as one of the last resorts when all other options have failed. For example, Voges et al.[17]used this method in studying the rotor blade tip interaction with a casing treatment in a transonic compression stage by PIV. The reflected light from the moving blades led to image blooming, and they shaded the blade with a piece of sheet metal immediately in front of the observation window, resulting in the drastic reduction of blooming. Therefore, the shading method is more convenient than many other methods.

However, the influence of the shading method in the PIV experiment and its evaluation are lack in literature. Therefore, the current study aims to examine the effectiveness of the shading method and to discuss its possible adverse effects on image quality and PIV calculation, and to provide some guidance in setting the shade in experiment.

Fig.1 Sketch of the shading method

1. Light attenuation by the shading method

1.1 Sketch of the shading method

In an open channel flow measurement with PIV, the image blooming often occurs in the vicinity of the channel bed because of the intensive light reflections caused by the glass bed or by the clumping of particles on the bed, as illustrated in Fig.1, where the plane AC is the target and is illuminated by a laser sheet. In this article, the streamwise direction is defined as x, and the wall-normal direction is defined as y, and the coordinate origin point is set on the bed and at the middle of the channel. The lens is reduced to a single convex lens; its diameter is designated by Φ, and the distance from the lower edge to the plane of the channel bed is designated byH. By attaching a small shade to the flume wall, the high-intensity light coming from the near-bed region is blocked from entering a part of the CCD lens, i.e., the DE part of the lens is prevented from “seeing” the channel bed (point A). Before the shade is set, the reflective light from point A can go into the camera through the dotted line AD and the solid line AF. All parts of the lens can receive light from A. When the shade is set, the light can only go through the solid line AE and AF, so the shaded part of the lens cannot receive light from A anymore. Therefore, the gray value of point A in the images will be reduced, so will the risk of blooming. In addition, the effect of shade is limited. Figure 1 clearly shows that B is the demarcation point. The height of DE is reduced to zero as A goes up to point B, beyond which the influence of the shade vanishes. Therefore, the shading method is a local influence method, it only reduces the amount of light near the bed but not other parts falling into the camera, and the near-bed band is the only area where the blooming takes place frequently. The risk of blooming will be reduced near the bed, and at the same time, the image quality will be kept as good as before.

The distance of point B above the channel bed iswhere h is the height of the shade, d1is the distance of the shade to the target plane AC, d2is the distance between the shade and the lens, andν= 1/1.3333 is the refractive index. Note that for simplicity, the influence ofν is not shown in Fig.1.

When y＜LAB, the height of the “blocked” part of the lens is

When y＞LAB, the entire lens is free from the blocking effect, i.e., m=0 and whenν2d2+1(h-y)2(ν2-1)＜0, m=Φ. Formula (2) shows that mincreases with h and decreases with H. A combination of h and H should be determined carefully to ensure thatm ＜Φ, otherwise, the entire CCD lens will be blocked.

1.2 Analysis of the light-attenuation factor

Let OV(y) represent the original image gray value at point y, which changes to CV(y) when the shading is in effect, i.e.,

where α(y) is the light intensity attenuation factor of the shading method. α(y) is assumed to be proportional to the area of the CCD lens that receives light, i.e.,

where θ=arccos(1-2m/Φ). Expanding the second term of the numerator in the right part of formula (4),

As 1/2Φmsinθ＞0,θ＞sinθ when 0≤θ≤π, therefore, 1/4Φ2sinθ-Φ/2msinθ＞0. According to formula (4),α≤1. Formula (4) can be simplified to the following form

Based on Formula (4), the effect of the light attenuation can be estimated approximately. Therefore, the value of α at every point is

Fig.2 Influence of hon the light attenuation factor

1.3 Numerical illustration of the light attenuation factor

The light attenuation factor, as quantified in Formula(5), involves some complexity. The following shows the numerical variations of α(y) with d1/d2and h. Under the condition of Φ=0.02m, H= 0.003m, d1+d2=0.4m , d1/d2=1 and with the water level is 0.03 m, the characteristics ofα are shown inFig .2(a). α=1 ata very small h, which indicates that the shade has no effect in blocking thelight when it is small. Ash increases,α decreases, whereas L, the size of the influence area, increases. The variation in a gray value gradient factor (1-α)/LABwith h is shown in Fig.2(b). The gray value gradient at h=0.01m is about five times as great asthatat h=0.0015m.

Fig.3 Influence of d1/d2on the light attenuation factor

The variation in α with d1is shown in Fig.3 for the caseof Φ=0.02m, H=0.003m,h= 0.006m, d1+d2=0.4m, and with the water level is 0.03 m. The value of αincreases ac cordingly as d1increases as shown inFig.3(a). As expected, the influence area also increases. Figure 3(b) shows a dramatic decrease in (1-α)/LABwith d1.

In practical PIV experiments, parameters h and d1/d2can be determined ba s ed on Formula (5) with the above illustrations in mind.

Fig.4 Schematic diagram of the experimental setup

1.4 Experimental illustration of the light attenuation factor

Formula (5) is checked against experimental data fromPIV measurements conducted in a 10.8 m long, 0.25m wide hydraulic flume with a glass bed and glass side walls. A 2W Nd-YAG laser provides the illumination. Two identical CCD cameras (AVT Pike F032B ASG16 with lens of EF 0.05 m f/1.2L USM) were placed symmetrically on both sides of the flume (Fig.4). Their heights and other parameters were kept the same for capturing the same series of images from the same illuminated sheet. The difference is that the shading method was used only on the left side.

Images were captured under different sizes of the shade, e.g., h=0, 0.003 m, 0.005 m, 0.008 m, and 0.01m, and the gray level of each pixel in an image was obtained.Based on the linear relationship between the photon hits and the pixel saturation, the effect of light attenuation is quantified by comparing the gray values to the benchmark values at h=0. To ensure the statistical significance, a total of 8 000 images were averaged for each case (frame rate is 50 Hz and sampling time is 160 s).

Table 1 Parameters of the experiment

The parameters of the CCD, as well as those of the flow, are listed in Table 1. Note that the gain and thegamma value of the CCD were set to zero to ensure the linear relationship between the photon hits and the pixel saturation. The shutter time was 10 000 μs. To prevent the seeding particles from becoming streamwise bands, or the existence of dagger-like stripes in the images at high velocity flows, the experiments were conducted under a very small flow velocity.

Figure 5(a) shows the average gray value of the imagescaptured without the shading effect (h=0m). The gray value reaches its maximum on the be d an d decre ases dramatica lly as the dista nce abovethechannelbedincreases,indicatingthattheimage blooming occurs most likely in the near-bed region. Figure 5(b) shows the experimental results of the light attenuation factor for each case. The experimental results agree well with Formula (5).

Fig.5Experimental results of light attenuation

Table 2 Experiment parameters

2. Effect of the shading method

The effect of the shading method is investigated in the experiments. The flow parameters, the aperture value, the shutter time, the ISO value, and the gain in the experiment are all set within the normal range and are listed in Table 2. Figure 6 shows the comparison of the sampled images and the corresponding vector fields calculated with the same PIV algorithm. The image pair consists of two images taken simultaneously using two cameras (see Fig.4). Due to the lasersheet thickness, the shape, the size, and the brightness of the corresponding particles shown in Figs.6(a) and 6(b) are not exactly the same. Figure 6(a) shows that the blooming image is contaminated by several bright vertical streaks and a flaring bright layer in the vicinity of the channel bed, which affects greatly the velocity calculation. In contrast, the image quality shown in Fig.6(b) (with shading, h=0.003m) is enhanced substantially, and the corresponding vector field appears faultless. Figure 6 shows that the shading method can reduce the risk of blooming and improve the quality of PIV data near the bed.

Fig.6 Comparison of images and calculated velocity vectors. The field of view is 0.0225 m×0.0181 m

To quantify the effect of the shadingmethod, the risk of blooming is defined as a parameter in the presentstudy. When the image blooming occurs, the gray level of a pixel reaches its maximum value of 255 in an eight-bit BMP image. Therefore, counting the number of points whose gray value is equal to 255 is an accurate way of showing the blooming influence. The risk of blooming at a certain pixel can be defined as the ratio of N/NT, where N is the number of images in which the gray level of the pixel is equal to 255, and NTis the total number of images in a series, and NT=8000 in this article.

The size of the shade h is an important parameter in the shading method. An increase of h leads to adecrease of the risk of blooming. The effects of the shading method under four different sizes of h are compared. The other parameters of the experiments are listed in Table 2. The image capturing rate is 50 Hz, and a total of 8 000 images are gathered for each experimental run.

Figure 7(a) shows the percentage R of blooming along the y-axis.For clarity, the axes are set inlogarithmic scales. When there is no shade (solid line, h=0m), about 10% of the points at the bed are suffered with blooming, and this ratio decreases rapidly to ab out 0.04% at y=0.0005m. The risk of blooming drops rapidly when the shading method is used, e.g., from 10% to 0.5%, 0.002%, and nearly zero at h= 0.003 m, 0.005 m, and 0.008 m, respectively. At a higher flow area (y＞0.01m), however, the shading method has no effect at all. This finding is further confirmed by the risk ratio at various h values over that without shading h=0m (Fig.7(b)). Figure 7 shows that the shading method can reduce the risk of blooming near the bed and does not affect the upper part as expected.

Fig.7 Risk of image blooming at various shading sizes

3. Influence of shading method on PIV calculation and a rule for setting the shade

3.1 Influence of shading method on PIV calculation

The shading method is effective inreducing the risk of image blooming. However, there remains one major question to be anwered: Does the light attenuation have an adverse effect on the PIV correlation and calculation? This question is answered by applying thefrom a Direct Numerical Simulation (DNS) simulation of a turbulent open channel flow with the following variables: the flow depth is 0.3 m, the maximum velocity Umax=1.19m/s, the shear velocity uτ= 0.0341m/s, the viscosity ν= 0.01616m2/s, and the Reynolds number Reτ= huτ/ν=640.Theimage diameter is 1.3 pixels for a unit standard deviation and 2.6 pixels for two standard deviations (the standard deviation is 0.65 pixels).

Table 3 Various parameters (units: m)

Fig.8Variation in the light attenuation factor imposed on the original images

The shading effect is simulated by transformingthe o riginal images through mu ltiplying them with the light attenuation factor, as in Formula (5). The parameters are listed in Table 3, and the attenuation factors are shown in Fig.8. The original and transformed images are analyzed by the window displacement iterative multigrid algorithm[19-21], which uses an iterative multi-grid approach for cross-correlation and a three-point Gaussian peak fit for the determination of displacement with a sub-pixel accuracy. The grid size is 16×4. The iteration number is 2, and the IW sizes are 64×16, 32×8 and 16×4.

Figure 9(a) shows the comparison of the mean velocity profile with the original data for the five cases. The agreement between the different terms is very good. Figure 9(b) shows the difference ε between the shading values and the original value for the mean streamwise velocity. For y＞100 pixels, the agreement among the results of all cases is very good. In fact, good results are also obtainednear the bed, with deviations all within ±0.015 pixels except for the first case (No. 1). The result of the first case

Fig.9 Mean velocity profile obtained from the five cases compared with the original data

Fig.10 Streamwise and wall-normal turbulence intensities obtained from the five cases compared withthe originnal data

has a more significant deviation near the bed. Figures 10(a) and 10(b) show the profiles of the results for streamwise and wall-normal turbulence intensities, Urmsand Vrms. The agreement is particularly good except for the points near the bed, where one sees some deviations due to the gray level gradient and the reduction of the particles, and due to the low value of α.

Fig11 Cumulative histogram of the error on the streamwise and wall-normal velocities near the bed

Another way of assessing the accuracy is to plothe cumulative histogram of the velocity differences near the bed. From Fig.8, the shortest influence area is about 60 pixels for No. 1, therefore, the velocity differences of 14 points near the bed for all five cases are taken into account. The results are shown in Fig.11, which shows significant differences among the different cases. The results of No. 5, 4, 3 and 2 are particularly good, where more than 80% errors are less than 0.01 pixels for both streamwise and wall-normal velocities. The result of No.1 is relatively poor, and only about 60% errors are less than 0.01 pixels for both streamwise and wall-normal velocities. A few large errors reaching dozen pixels appear in No.1 because the gray value is very low near the bed due to the low value of α (see Fig.8), with a limited amount of information. Figure 12 shows the profiles of the root mean square (rms) errors ε for the five groups. The conclusion is similar to that of the other figures. The rms errors are all within about 0.08 pixelfor streamwise velocities and 0.035 pixel for wallnormal velocities except No. 1.

Fig.12 RMS errors on the streamwise and wall-normal velocity

3.2 A ru le for setting the shade

The above discussion shows that the shading will introduce some small errors in the PIV calculation.of the pixel size (see Fig.11), which is smaller than that in the experimental system. For example, the errors of many PIV processing methods are in the order of 1 of the pixel size[16]. Therefore, this error is acceptable in actual experiments. When the parameters are not adequate, errors will increase, for example, as in the case of No.1.

The error in the shading method is due to the gray level gradient in the interrogation window and the reduction in the number of particles, and more accurately, is due to the valueofαat the bed, as shown in Fig.8. The value of α at the bed is a most important parameter that affects the characteristics of errors. From foregoing discussions and Fig.8, we may give a simple criterian for determining α at the bed, to control the error characteristics in the PIV calculation

Based on Formula (5), this criterion can be written as

In this criterion, all parameters can be obtained easily except forΦ. Φis the diameter of the single convex lens, which isdetermined by the real lens used inthe experiment. It may be estimated roughly through the diameter of the lens aperture, or can be obtained by fitting the experimental data with Formula (5). After all the parameters in the Formula (7) are known, one may determine whether the experiment conditions meet this criterion. If this criterion is satisfied, the errors caused by the shading technique will be controlled within an acceptable range; if not, it would be best to adjust the test parameters to meet this simple criterion.

4. Conclusion

The present article has evaluated the shading method for reduc ing the image blooming in the PIV measurement. The effect of the method on the light attenuation isquantified by a simplified analytical model and is tested by experimental data. The results show that the risk of blooming near the channel bed is reduced substantially when the shading is implemented. To facilitate its practical use, the influence of parameters on the image gray level is discussed. The standard images of Case B in PIV Challenge 03 are used for evaluating the adverse effects of the conversion of the light attenuation on the PIV calculation. The result shows that when the parameters in the shading method are adequate, the shading method causes negligible errors on the PIV calculations. Based on the discussion, a simple criterion for setting the shade in the experiment is given, and when the criterion is satisfied, the errors coming from the shading technique will be controlled within an acceptable range. Generally speaking, the shading method is a convenient and efficient method for the reduction of image blooming in the PIV measurement of open channel flows. The proposed model of the light attenuation can be used when applying the shading method in practice.

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September 24, 2011, Revised January 5, 2012)

* Project supported by the National Natural Science Foundation of China (Grant No. 50779023).

Biography: ZHONG Qiang (1985-), Male. Ph. D. Candidate

LI Dan-xun,

E-mail: lidx@mail.tsinghua.edu.cn