JP2012145430A - Method and apparatus for visualizing density gradient - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for visualizing a density gradient of an air current by simple image operation without requiring a concave mirror and a convex lens.SOLUTION: In the method for visualizing the density gradient, a background image is arranged on the back of a measurement area, a digital camera is arranged on the front side, and result image obtained by calculating a difference in each pixel and a density gradient from two images, i.e. a reference image obtained by photographing the measurement area in a state of no density distribution and a measurement image obtained by imaging the measurement area in a state of generating density distribution is used.

Description

  The present invention relates to a method for visualizing a density gradient of an air flow and an apparatus for implementing the method.

  In airflow measurement and wind tunnel testing, flow visualization is an extremely effective technique for grasping phenomena, and is now an indispensable technique. Conventionally, the Schlieren method has been used to visualize the density gradient. (For example, see page 174 of Non-Patent Document 1.) As a related method, as a method of visualizing the density disturbance state, not the density gradient itself, the moire interferometry is a method of visualizing the density contour line. The Mach-Zehnder method is known. In recent years, as a method for quantitatively measuring a density gradient using a digital image, for example, the Background oriented schlieren method (hereinafter referred to as BOS method) as shown in Non-Patent Document 2 has been studied.

The conventional schlieren method requires a complicated optical device as shown in FIG. 8 in order to visualize the phenomenon of the flow field of a target having a density gradient. In other words, since it is necessary to irradiate the measurement unit with uniform parallel light, a light source, a condenser lens, a pinhole, and a concave mirror or convex lens of a size that matches the dimensions of the measurement unit are required. There are restrictions on the direction. In addition, there is a problem that a technique is required for adjusting the optical axis.
In addition, the conventional moire interferometry method and the Mach-Zehnder method require a reference optical path. For example, as can be seen in Non-Patent Document 3, this places restrictions on the installation location and shooting direction more than the conventional Schlieren method. Furthermore, there is a problem that the spatial resolution is limited to the interval between density contour lines, and interpolation between the contour lines must be relied upon.
In the BOS method, the density gradient can be quantified using the cross-correlation method. However, as seen in Non-Patent Document 4, the cross-correlation processing has a large calculation load and is not suitable for use as a qualitative visualization. In addition, there is a problem that processing for removing errors (false vectors) is indispensable.

"Mechanics of Compressible Fluids" Takefumi Ikui, Kazuyasu Matsuo, Science and Engineering Company, April 2001 "Principle and applications of the background of riented schlieren (BOS) method" H. Richard and M. Raffel Measurement Science and Technology Vol.12, p.l576-1585, (2001) "Measurement of natural convection temperature field by moire interferometry" Isao Ishihara et al. Theory B63-614 (1997) “PIV Handbook” edited by Visualization Information Society Morikita Publishing July 2002

  An object of the present invention is to provide a technique that does not require a concave mirror or a convex lens and makes it possible to visualize the density gradient of airflow by simple image calculation.

The method of visualizing the density gradient according to the present invention includes a background image behind the measurement region, a digital camera placed in front, a reference image obtained by photographing the measurement region without the density distribution, and a state in which the density distribution has occurred. The result image obtained by calculating the difference and density gradient for each pixel from the two images of the measurement image photographed in FIG.
And the said calculation which obtains a result image shall be obtained by following Formula.
R_result (i, j) = {R_run (i, j) −R_ref (i, j)} × ∠R_run (i, j) + Offset
Here, R (i, j) represents the luminance value of the pixel at i and j, the subscript ref represents the reference image, run represents the measurement image, and result represents the resulting image. ∠R_run (i, j) in the above equation is a term that gives the direction of density change, and uses a first-order differential value around the pixel (i, j) point.
Further, for example, to visualize the density gradient in the i direction now, if the stripe is in the i direction, the term ∠R_run (i, j) that gives the direction of density change is It was obtained by the formula.
∠R_run (i, j) = [{R_run (i + 1, j) −R_run (i−1, j)} / 2
+ {R_ref (i + 1, j) -R_ref (i-1, j)} / 2] / 2
Furthermore, smoothing is performed on the obtained result image by moving average processing.

An apparatus for visualizing a density gradient according to the present invention includes a background image arranged behind a measurement area, a digital camera arranged in front of the measurement area, a reference image obtained by photographing the measurement area without a density distribution, and a density It is assumed that it comprises means for calculating a difference and a density gradient for each pixel from two images of the measurement image in a state where the distribution is generated.
The background image uses a striped pattern with a continuous luminance distribution.
As one form, the calculation means is installed in the body of a digital camera.
The apparatus for visualizing the density gradient of the present invention employs a configuration in which the measurement area is in the wind tunnel, and the area is a rear window on the background image side and a transparent window on the front camera side.

The present invention can be implemented with a simple apparatus configuration that does not require a large-scale optical system such as a concave mirror for producing a collimated beam indispensable in the conventional Schlieren method. As a result, there is no restriction on the photographing direction depending on the installation of an optical system such as a concave mirror, and visualization from any direction is possible. This facilitates visualization of a portion that has conventionally become a shadow of the subject and could not be visualized. Furthermore, it is a measurement method having portability regardless of the application place such as indoors and outdoors.
In addition, it does not require complicated operations such as the direct cross-correlation method used in the conventional BOS method and cross spectrum calculation by Fourier transform, and the removal of errors that occur statistically.
Since the calculation method is simple image processing based on Equation (1), an imaging device that can be incorporated into the imaging device and visualized alone can be commercialized. In addition, there is an effect that the installation adjustment of the optical device can be simplified as compared with the prior art.

It is a figure which shows one Example of this invention. It is a figure which shows an example of the background image used by this invention. It is an example of A reference image in one Example of this invention, and B measurement image obtained. It is the visualization image of A density gradient obtained by the method of the present invention, and an image obtained by subjecting it to B moving average processing. It is a figure which shows the form (Example 2) which applied the method of this invention to the wind tunnel apparatus. A is an image obtained by taking a background image in Example 2 of the present invention, B is a measurement image in the ultrasonic wind tunnel test, and C is a visualized image of the calculation result. It is the figure which contrasted the image of this invention and the conventional schlieren method image. It is a figure explaining the structure of the conventional schlieren apparatus.

Hereinafter, embodiments of the present invention will be described in detail.
A background image having a distribution in the direction of the density gradient to be visualized is prepared. For example, when a density gradient in the vertical direction is to be visualized using a monochrome camera, a screen on which an image having a luminance value distribution in stripes as shown in FIG. 2 is prepared. Flow field (measurement region) 1 of a target having a density gradient, in the example shown in FIG. 1, a digital camera or digital camera for photographing on the opposite side of the background image (screen) 2 with a high-temperature atmosphere region caused by a banner flame A video camera 3 is installed. In the present invention, the above-described configuration is sufficient for an apparatus for acquiring image information. As for the positional relationship between the camera 3, the object, and the background 2, the optimum value is determined by the same positional relationship as in the conventional BOS method. At this time, the distance between the stripes of the background 2 is set larger than the assumed stripe movement amount. Prior to generating the flow field, the background image 2 is acquired in advance as a reference image. Next, the flow field 1 is generated, and the measurement image is acquired in the same manner as the acquisition of the reference image 2. In this measurement image, light is refracted by the generated density gradient and is captured by the camera 3 as a distorted fringe image.
Next, the following calculation is performed on the obtained measurement image and reference image. This calculation can be performed by a general-purpose personal computer without requiring a special device, and can be incorporated in the body of the digital camera. The following equation (1) shows the difference between the measurement image of the pixel at i and j and the reference image and the direction of density change.
R_result (i, j) = {R_run (i, j) −R_ref (i, j)} × ∠R_run (i, j) + Offset (1)
Here, R (i, j) represents the luminance value of the pixel at i and j, the subscript ref represents the reference image, run represents the measurement image, and result represents the resulting image. ∠R_run (i, j) in equation (1) is a term that gives the direction of density change, and uses a first-order differential value around point (i, j). For example, to visualize the density gradient in the i direction, assuming that the fringes are in the i direction, the average of the spatial differences around the (i, j) points of the measurement image and the reference image is the following simplest calculation method: (2)
∠R_run (i, j) = [{R_run (i + 1, j) −R_run (i−1, j)} / 2
+ {R_ref (i + 1, j) −R_ref (i-1, j)} / 2] / 2 ………… (2)
Can be used.

  Due to the action of the expression (2), the first term of the expression (1) gives the luminance value according to the direction and the change amount for the place where the density has changed. The offset term at the end is an addition term used to give a luminance value at a point where there is no change. In the case of monochrome 8-bit, if the value of the grant term is 128, which is the intermediate value of gray scale, an image that changes to gray or white or black according to the direction of change is obtained as in the conventional Schlieren method. be able to. When a color image is used, the same calculation may be performed for each RGB value.

  An example of visualization of the warmed airflow 1 will be described. As shown in FIG. 1, a digital camera 3, a background image 2, and a gas burner 4 are installed. The background image 2 is attached to an acrylic frame. In order to obtain the density gradient in the vertical direction, the background image used a striped pattern of continuous luminance distribution shown in FIG. As described above, the conventional schlieren method requires a complicated optical device as shown in FIG. 8 to visualize this phenomenon. However, in the present invention, such a complicated optical system is not required at all, and the measurement area is measured by the digital camera 3 from the desired front angle only by placing the background image 2 behind the measurement area (warmed airflow field) 1. Can be taken. First, when the gas burner 4 is not ignited, the reference image shown in FIG. 3A is acquired. After the gas burner is ignited, the measurement image shown in FIG. 3B is acquired. Image processing is performed from the acquired two pieces of image information according to Expression (1), R_result (i, j) is calculated for each (i, j) point, and FIG. 4A is obtained as a composite image of the calculation results. This calculation is executed using a personal computer (not shown). In FIG. 4A, a place where there is a positive density gradient upward in the image is grayed and visualized in the black direction, and if there is a negative density gradient, the gradation is visualized in the white direction. It can be seen that when a high-resolution imaging device is used, a smooth natural image can be obtained as a schlieren photograph with sufficient resolution when the moving average processing is performed for interpolation as shown in FIG. 4B.

  Next, an embodiment in which the method of the present invention is applied to visualization of density gradient in a supersonic wind tunnel test will be described. As shown in FIG. 5, the specimen 5 is installed in the measurement region 1 in the wind tunnel 6, the background image 2 is placed behind it, and the digital camera 3 is placed in the wind tunnel ahead. The airflow flowing in the wind tunnel 6 is a supersonic flow of M = 3.0, and in the flow, a compression region due to a shock wave and an expansion region due to an expansion wave are generated around the conical specimen 5. The background image used the striped pattern shown in FIG. 6A. A reference image is acquired before the airflow is generated, and the measurement image shown in FIG. 6B is acquired after the airflow is generated. As in the previous embodiment, R_result (i, j) is calculated for each (i, j) point, and image processing is performed according to Equation (1) as a composite image of the calculation result, and FIG. 6C is obtained as a result image. It was. In the image, the compression area is visualized as black and the expansion area is visualized as white.

  FIG. 7 shows a visualized image according to the present invention in comparison with a conventional schlieren image. The upper image is an image according to the present invention, and the lower image is a conventional schlieren image. As can be seen from FIG. 5, the present invention is easy to install and easy to calculate, and can obtain an image equivalent to the conventional Schlieren method. In FIG. 7, the imaging sensitivity of the image according to the present invention on the upper side is better than that of the conventional schlieren image on the lower side, and as a result, the compression region due to the shock wave and the expansion region due to the expansion wave are clearly obtained.

DESCRIPTION OF SYMBOLS 1 Measurement area (density gradient field) 2 Background image 3 Digital camera 4 Gas burner 5 Specimen 6 Wind tunnel 7 Window part 8 Light source

Claims (8)

  A background image is placed behind the measurement area, a digital camera is placed on the front side, and a reference image obtained by photographing the measurement area without a density distribution and a measurement image with the density distribution generated are displayed for each pixel. To visualize the density gradient from the result image obtained by calculating the difference and the density gradient. The method for visualizing a density gradient according to claim 1, wherein the result image is obtained by the following equation.
R_result (i, j) = {R_run (i, j) −R_ref (i, j)} × ∠R_run (i, j) + Offset
Here, R (i, j) represents the luminance value of the pixel at i and j, the subscript ref represents the reference image, run represents the measurement image, and result represents the resulting image. ∠R_run (i, j) in the above equation is a term that gives the direction of density change, and uses a first-order differential value around the pixel (i, j) point. The method for visualizing a density gradient according to claim 2, wherein the term ∠R_run (i, j) giving the direction of density change is obtained by the following equation.
∠R_run (i, j) = [{R_run (i + 1, j) −R_run (i−1, j)} / 2
+ {R_ref (i + 1, j) -R_ref (i-1, j)} / 2] / 2   The method for visualizing a density gradient according to claim 3, wherein the obtained result image is smoothed by a moving average process.   2 of a background image arranged behind the measurement region, a digital camera arranged in front of the measurement region, a reference image obtained by photographing the measurement region without a density distribution, and a measurement image with a density distribution generated An apparatus for visualizing a density gradient comprising a pixel-by-pixel difference and a means for calculating the density gradient from one image.   The apparatus for visualizing a density gradient according to claim 5, wherein the background image uses a stripe pattern having a continuous luminance distribution.   The apparatus for visualizing a density gradient according to claim 5 or 6, wherein the calculation means is installed in a body of a digital camera.   The device for visualizing a density gradient according to any one of claims 5 to 7, wherein the measurement region is in a wind tunnel, and the region is a transparent window on the rear side of the background image side and on the front camera side.