AU2016308995B2

AU2016308995B2 - Method, device, and program for measuring displacement and vibration of object by single camera

Info

Publication number: AU2016308995B2
Application number: AU2016308995A
Authority: AU
Inventors: Shien RI; Hiroshi Tsuda
Original assignee: National Institute of Advanced Industrial Science and Technology AIST
Current assignee: National Institute of Advanced Industrial Science and Technology AIST
Priority date: 2015-08-19
Filing date: 2016-07-11
Publication date: 2019-02-14
Anticipated expiration: 2036-07-11
Also published as: AU2016308995A1; WO2017029905A1; JPWO2017029905A1; JP6534147B2

Abstract

With regards to methods that use a plurality of cameras to measure out-of-plane displacement or three-dimensional displacement of an object, there are various practical problems such as accurate synchronization between cameras, the cost incurred by a plurality of camera devices, an increase in analysis time, and the inability to analyze outside the range that can be simultaneously imaged in images captured by two or more cameras. The present invention captures with a single digital (video) camera a grating marker that is attached or transferred to an object surface, and using the sampling moire method quantitatively finds by image processing the out-of-plane displacement amount from a minute change in the phase of the grating pitch in an image due to out-of-plane displacement. Also, the present invention similarly uses the sampling moire method to quantitatively find the out-of-plane/in-plane displacement amount from a minute change in the phase of the same grating due to in-plane/out-of-plane displacement, and finds the three-dimensional displacement amount by excluding the effect of the apparent in-plane displacement.

Description

(57) Abstract: With regards to methods that use a plurality of cameras to measure out-of-plane displacement or three-dimensional displacement of an object, there are various practical problems such as accurate synchronization between cameras, the cost incurred by a plurality of camera devices, an increase in analysis time, and the inability to analyze outside the range that can be simultaneously imaged in images captured by two or more cameras. The present invention captures with a single digital (video) camera a grating marker that is attached or transferred to an object surface, and using the sampling moire method quantitatively finds by image processing the out-of-plane displacement amount from a minute change in the phase of the grating pitch in an image due to out-ofplane displacement. Also, the present invention similarly uses the sampling moire method to quantitatively find the out-of-plane/inplane displacement amount from a minute change in the phase of the same grating due to in-plane/out-of-plane displacement, and finds the three-dimensional displacement amount by excluding the effect of the apparent in-plane displacement.

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2016308995 04 Oct 2018

METHOD, DEVICE, AND PROGRAM FOR MEASURING DISPLACEMENT AND VIBRATION OF OBJECT BY SINGLE CAMERA

Technical Field [0001] The present invention relates to an analysis technique, an apparatus, and a program for simply measuring, with high accuracy, out-of-plane displacement distribution or threedimensional displacement distribution including in-plane and out-of-plane displacements, of an object, and a vibrational distribution obtained from time-series measurement results.

Background [0002] Conventional contact displacement and non- contact laser displacement meters, ultrasonic displacement meters, etc., can provide measurement results with high reliability and often have high time resolutions.

However, since only displacement information in one direction at one point can be obtained by one measurement, sensors are preferably placed at multiple points in order to determine the displacement vibration behavior of an entire structure. Therefore, the wiring is complicated, and results in increased costs and analysis.

In particular, in small objects or very large structures, sensors may be prevented from being simultaneously placed due to the limited sizes of the sensors or limitation on installation of scaffolding for the attachment of the sensors.

[0003] On the other hand, displacement distribution information of an entire photographing area can be acquired by a full-field measurement method by image measurement.

21387082 (IRN: P299684)

The full-field measurement method include a speckle interferometric technique, a digital holography method, a digital image correlation method, and a sampling moire method.

[0004] When an object is deformed, in-plane displacement, which is the amount of displacement in x and y (longitudinal and lateral) directions parallel to the plane of the imaging element of a camera, and out-ofplane displacement, which is the amount of displacement in a z (depth) direction perpendicular to the plane of the imaging element of the camera, occur as illustrated in FIG. 1.

[0005] According to the principles of a current measurement method, using a single camera, in-plane displacement can be measured, but out-of-plane displacement cannot be measured, as described in Patent literature 1.

In addition, a method for measuring out-of-plane displacement or three-dimensional displacement including in-plane and out-of-plane displacements, of an object using two cameras has been developed as described in Patent literature 2. However, neither a method nor a measurement apparatus capable of measuring threedimensional displacement with only a single camera has been developed.

Citations List

Patent Literature [0006] Patent literature 1: Japanese Patent No. 2015527141

Patent literature 2: Japanese Unexamined Patent Publication (Kokai) No. 2013-221801

Non Patent Literature [0007] Non-Patent literature 1: Ri, S., Fujigaki, M., Morimoto, Y., Sampling Moire Method for Accurate Small Deformation Distribution Measurement, Experimental Mechanics, Vol. 50, No. 4, pp. 501-508 (2010).

2016308995 04 Oct 2018 [0008] In a method in which multiple cameras are used in order to measure the out-of-plane or three-dimensional displacement of an object, there are many restrictions for the measurement, such as correct synchronization between the cameras, increased cost for preparing the multiple cameras, increased analysis time for using multiple images, and possible analysis of only an area that can be simultaneously photographed in images captured with the two or more cameras.

[0009] In particular, when multiple cameras are used, not only analysis of an image captured with each camera but also a search for the same point is needed, and a long calculation time is needed before a result is obtained.

In outdoor experiments or the like, images are captured in locations in which vibrations are always occurred, as a photographing environment. Although the two or more cameras are fixed, different micro vibrations are slightly occurred in respective cameras themselves and often cause measurement errors.

Summary [0009a] It is an object of the present invention to substantially overcome or ameliorate one or more of the disadvantages of the prior art, or at least provide a useful alternative.

[0009b] According to an aspect of the present invention, there is provided a method for measuring out-of-plane displacement distribution using a single digital camera, wherein the digital camera comprises: an objective lens having a focal length f; and imaging elements arranged in a grating pattern in horizontal and vertical directions, in a state in which a periodic pattern having a pitch p is affixed, in a same direction as a horizontal or vertical direction of the imaging elements, to a surface of an object to be measured, the method comprising: photographing, when an out-of-plane load is applied to the object to be measured, the periodic pattern before and after out-of-plane displacement caused by the out-of-plane load by the digital camera; determining pitches Q, Q' at a coordinate (i, j ) of the periodic pattern on images corresponding to the pitch p before and after the out-of-plane displacement; and determining an amount of the out-of-plane displacement Az of the periodic pattern in accordance with the following Equation 16 to obtain an out-of-plane displacement distribution in a full-field, wherein the periodic pattern has the pitch p in a horizontal direction; a in Equation 16 is a constant; the pitches Q, Q' are determined in accordance with Equation 17 and Equation 18; T in

21387082 (IRN: P299684)

Equation 17 and Equation 18 represents a pixel spacing at which reduction processing is carried out by a sampling moire method; <j)_m represents a phase of a moire fringe; and 4>_m and φ' _m represent phase gradients determined using a value of the phase before and after the out-of-plane displacement:

2016308995 04 Oct 2018

(16) (17) (18) [0010] In certain aspects, arithmetic processing of an image obtained from a single digital (video) camera, as illustrated in FIG. 2, is performed in an operation unit of an informationprocessing apparatus with a display apparatus as another housing, such as, for example, a personal computer, to easily measure and display out-of- plane displacement or threedimensional displacement including in-plane and out-of-plane displacements, of an object, as well as the vibrations of the object.

When the camera has such a display unit, arithmetic processing can be performed in an operation unit in the camera to appropriately display a measurement result on the display unit.

[0011] (1) Measurement Method 1: Out-of-Plane Displacement Measurement (Principle of Outof-Plane Displacement Measurement with Single Camera)

The present disclosure focuses on slight changes in a grating pitch on an image, caused by an out-of-plane displacement generated when a grating marker (with an optional repeated pattern, such as a sine wave, a cosine wave, a square wave, or a triangular wave, as a grating pattern) affixed to or transferred onto the surface of an object is photographed with a digital (video) camera.

[0012] The grating pitch on the image is larger as the grating physically approaches the camera,

21387082 (IRN: P299684)

4a

2016308995 04 Oct 2018 whereas the grating pitch is smaller as the distance of the grating from the camera is increased.

A method capable of quantitatively determining the amount of out-of-plane displacement on the basis of a slight change in the grating pitch on an image due to the out-of-plane displacement by combining such characteristics and the principle of the magnification of a lens will be described below.

[0013] With reference to FIG. 2, it is assumed that the size of the grating pitch recorded on an image sensor including imaging elements arranged in a grating pattern in horizontal and vertical directions is Q [pixels], the sensor size (actual size of one pixel) is a [mm/pixel], and the grating pitch of the grating affixed to the object in advance is p [mm], the ratio between the sizes of the pitches is proportional to the distance d between the image surface (image sensor surface) and the lens, as well as the distance z between the surface of the object and the lens. In other words, the following equation is derived from the similarity relationship of a triangle,

Qa: p = d: z.

[0014]

21387082 (IRN: P299684)

(1) [0015] It is impossible to correctly measure the distance d between the image surface and the lens in Equation (1) because the distance changes slightly due to focusing of the lens.

Thus, d is represented using a focal length f on the basis of the lens imaging formula.

[0016]

1-1 1 (2) [0017] In Equation (2), the focal length f of the lens and d can be approximated as f = d (z >> d) when the distance z between the lens and the grating is sufficiently greater than the distance d between the image sensor and the lens.

The distance Z between the lens and the grating can be represented by Equation (3) using f on the basis of this approximate equation and Equation (1).

[0018]

(3) [0019] Likewise, z' can be determined from the grating pitch Q' on the image after out-of-plane displacement and can be represented by Equation (4).

[0020]

(4) [0021] Thus, the amount of out-of-plane displacement

Δζ = z' - z is calculated to derive Equation (5), and can be quantitatively determined from the change in grating pitch before and after deformation.

[0022] a\Q QJ [0023] The grating pitches before and after deformation can be determined with high accuracy from the respective phase gradients (phase inclinations) of the phases of moire fringes before and after the deformation, determined by an existing sampling moire method (Non Patent literature 1), by Equation (8) and Equation (9), respectively. The phases of moire fringes are as follows: [0024]

ΦΑΒ ΦΆΪ) (6) [0025] The respective phase gradients (phase inclinations) of the phases are as follows:

[0026]

Φ'&ί) (7) [0027] (8) [0028]

2πΤ

2π + φ_η(ί,ί)Τ <2Ό = (9) [0029] There are various methods for determining the phase gradients (Equation (7)) of the phases (Equation (6)) of moire fringes. As an example thereof, the phase gradients of moire fringes in a lateral direction can be determined from a second-order central difference, which is a differentiation method commonly used in image processing, i.e., the average value of the differences between the phase values of adjacent two pixels.

The phase gradients are represented by the following Equations .

[0030] =U) -^(«-1 .J)} / 2 (io)

Φ'„(ίΡ={Φ'^+^)-Φ'^-υ)}/2 (11) [0031] Equation (5) reveals that the amount of out-ofplane displacement depends on the pitch p [mm] of the grating marker used in the experiment, the pixel size a [mm/pixel] of the image sensor, and the focal length f [mm] of the camera lens.

[0032] These parameters are determined depending on the specifications of the measurement apparatus used when the measurement experiment is performed. Therefore, the amount of out-of-plane displacement can be directly

2016308995 04 Oct 2018 calculated from the change in grating pitch before and after the out-of-plane displacement on the basis of Equation (5) if the pitch p of the grating affixed to the object, the size a of the CCD of the camera, and the focal length f of the lens can be precisely known in advance.

[0033] On the other hand, even when it is difficult to precisely know any one of the parameters, the parameter can be correctly determined in advance by calibrating the constant k = p (f/a) on the basis of the change in grating pitch on the image before and after out-of-plane displacement as well as the amount of the out-of-plane displacement by using a moving stage the amount of movement of which is known in advance.

[0034] (2) Measurement Method 2: Principle of Simultaneous Measurement of In-Plane and Out-of-Plane Displacements with Single Camera

In optical imaging measurement, in-plane displacement originally intended to be measured and apparent in-plane displacement caused by out-of-plane displacement are generated on an image when in-plane displacement and out-of-plane displacement simultaneously occurs.

Therefore, it is impossible to correctly measure the in-plane displacement.

[0035] In certain aspects, the amounts of in- plane and out-of-plane displacements of an object can be simultaneously determined in consideration of the amount of apparent in-plane displacement caused by an out-of-plane displacement.

[0036] FIG. 3 is a conceptual diagram of the principle of a technique of simultaneously measuring in-plane and out-of-plane displacements with a single camera.

When in-plane and out-of-plane displacements occur in an object to which a grating is affixed, the amount of in-plane displacement Δχ in the X-direction, which is measured by a sampling moire method, is represented by

21387082 (IRN: P299684)

Equation (11).

[0037] (12) χ=Δχ+δ [0038] In Equation (12), Δχ represents the in-plane displacement in the X-direction, and δ represents apparent in-plane displacement caused by out-of-plane displacement in the Z-direction.

The apparent in-plane displacement δ caused by the out-of-plane displacement is represented by Equation (14) .

In small deformation, it is assumed that the following approximate equation is established.

[0039]

Θ = θ' (13) [0040] It is assumed that Θ represents the horizontal or vertical component of the angle between the optical axis of the lens and a line connecting the center of the lens and the grating affixed to the object before deformation, and θ' represents the horizontal or vertical component of the angle between the optical axis of the lens after the deformation and the line connecting the center of the lens and the grating after the deformation. [0041]

S= Aztan Θ = Δζ tan θ' (θ = θ') (14) [0042] Accordingly, on the basis of Equation (12) and Equation (14), the amount of in-plane displacement from which the influence of an apparent amount of in-plane displacement caused by an out-of-plane displacement is excluded, is represented by Equation (15).

[0043]

2016308995 04 Oct 2018 ίο

Δχ = χ- Δζ tan# (15) [0044] With regard to an apparent in-plane displacement, Δζ tan 0, caused by an angle of view, 0 tan can be determined in advance by determining an apparent in-plane displacement δ occur by generating only an out-of-plane displacement in an object under constant experimental conditions.

[0045] In a simple method, tan 0 can be determined from the angle of view depending on the specifications of a camera lens when the focal length of the lens is known.

[0046] The correct amount of in-plane displacement can be determined by determining the amount of out-of-plane displacement Δζ from determined tan 0 and a change in grating pitch on an image, caused by an out-of-plane displacement, determining the amount d of apparent inplane displacement caused by the out-of-plane displacement on the basis of Equation (13), and subtracting the amount of the apparent in-plane displacement from the amount of the in-plane displacement, which is determined based on Equation (14).

[0047] The three-dimensional displacement of an object can be finally determined by determining the amount of in-plane displacement in the y-direction, Ay, in a similar manner.

[0048] Aspects enable a three- dimensional displacement to be measured using only a single camera and therefore has the advantages of a wider photographing area than a photographing area when using two cameras, a low cost, synchronization between cameras is not necessary, and a small calculation time.

[0049] According to the disclosure, highly-accurate out-of-plane displacement and threedimensional displacement distributions, and the vibrational distributions thereof can be easily measured by merely affixing or transferring a marker with a regular pattern onto the surface of the object to be measured and continuously photographing the marker with a digital camera.

[0050] Therefore, measurement of displacements and vibrations in a wide range from a nanoscale to a mega scale is enabled by selecting an optical element used for photographing according to the size of an object to be observed with various microscopes (such as, for example, electron scanning microscopes, laser scanning microscopes, and optical microscopes)

21387082 (IRN: P299684)

2016308995 04 Oct 2018 and single-lens reflex cameras (such as, for example, CCD cameras, CMOS cameras, and video cameras).

[0051] Specifically, one or more aspects of the present disclosure have the following effects.

Out-of-plane displacement, and in addition, three-dimensional displacement can be measured using only one camera. Therefore, aspects can be easily applied to dynamic measurement and enables vibration measurement.

In comparison with a method in which multiple displacement sensors are attached, wiring is not necessary, and information on the displacements and vibrations of multiple points can be simultaneously obtained.

Remote measurement can be performed from a distant place.

Brief Description of Drawings [0051a] Example embodiments should become apparent from the following description which is given by way of example only, of at least one preferred but non-limiting embodiments described in connection with the accompanying figures.

[0052] FIG. 1 is a schematic view illustrating an optical system for measuring in-plane and outof-plane displacements of an object with a single camera.

FIG. 2 is a schematic view illustrating the relationship between the distance between a digital camera and a grating, and the size of the grating on a

21387082 (IRN: P299684)

CCD sensor.

FIG. 3 is a conceptual diagram of the principle of simultaneous measurement of in-plane and out-of-plane displacements of an object using a single camera.

FIG. 4 illustrates photographic images of optical systems for measuring an out-of-plane displacement: (a) the entire optical system (left side); (b) the optical system with a camera lens having a focal length of 8 mm (upper right); and (c) the optical system with a camera lens having a focal length of 25 mm (lower right).

FIG. 5 is a graph representing experimental results (actual displacement and measurement displacement) of the amount of out-of-plane displacement (small deformation).

FIG. 6 is a graph representing experimental results (actual displacement and measurement displacement) of the amount of out-of-plane displacement (large deformation).

FIG. 7 is a photographic image of an experimental optical system for simultaneously measuring in-plane and out-of-plane displacements.

FIG. 8 is a comparative view of the measurement results of in-plane displacements obtained with a single camera and two cameras (left bar corresponds to single camera, and right bar corresponds to two cameras). (Accuracy similar to the accuracy when using a conventional two-camera system is obtained.)

FIG. 9 is a comparative view of the measurement results of out-of-plane displacements obtained with a single camera and two cameras (left bar corresponds to single camera, and right bar corresponds to two cameras). (Accuracy similar to the accuracy when using a conventional two-camera system is obtained.)

FIG. 10 is a photographic image of an optical system for a cantilever vibration analysis experiment.

FIG. 11 illustrates graphs representing the results of out-of-plane displacement (deflection) distributions obtained from image data captured using a single camera. FIG. 11(a) represents the results of a state without deflection, FIG. 11(b) represents the results in deflection in a depth direction, and FIG. 11(c) represents the results in deflection in a frontward direction .

FIG. 12 is a graph representing vibration measurement results obtained with a laser Doppler vibration meter.

FIG. 13 is a graph representing vibration measurement results obtained in the present invention.

FIG. 14 is a graph representing vibration frequency analysis results obtained in a laser Doppler vibration meter and the present invention.

Description of Embodiments

Example 1 [0053] (1) Example 1: Measurement of Out-of-Plane

Displacement with Single Camera

The following experiment was conducted in order to confirm the measurement accuracy of out-of-plane displacement according to the present invention.

[0054] An optical system for the experiment is illustrated in FIG. 4.

Apparatuses used includes a two-axis moving stage (having a movement resolution of 1 gm) , a grating marker, and a CCD camera (1280 x 960 pixels, monochrome, pixel size of 4.65 gm x 4.65 gm) .

[0055] A square wave pattern having a grating pitch of 1 mm was affixed to a moving stage fixed on a vibrationisolated table.

The moving stage was moved in an out-of-plane (depth) direction, for each movement amount, the grating was photographed, and each image was analyzed to thereby determine the amount of out-of-plane displacement.

[0056] Three types of camera lenses having focal lengths of 8 mm, 16 mm, and 25 mm were used in the accuracy confirmation experiment. Optical systems with camera lenses having focal lengths of 8 mm and 25 mm are illustrated in FIG. 4(b) and FIG. 4(c), respectively. [0057] The amounts of out-of-plane displacement were measured in the case of moving the moving stage up to 1 mm by 0.01 mm step in an out-of-plane direction (zdirection) (small deformation) and the case of moving the moving stage up to 10 mm by 0.1 mm step(large deformation), respectively.

[0058] Phase analysis was carried out under the analysis conditions of the accuracy investigation experiment in that a low-pass filter (having a kernel half-width of 40 pixels and a cut-off frequency of 0.01 Hz) was applied to each captured image in a Y-direction, a one-dimensional grating pattern in only a lateral direction was extracted from the two-dimensional grating pattern, and the sampling pitch was 20 pixels in a sampling moire method.

[0059] Smoothing processing of the phase distribution of obtained moire fringes was repeatedly performed three times with a sin/cos filter (kernel half-width of 3 pixels, kernel height of 3 pixels) in order to enhance stability calculating a phase gradient.

The average amount of displacement in 100 x 100 pixels in the vicinity of the center of an image was used in an evaluation method.

[0060] The experimental results of the amount of outof-plane displacement in the case of small deformation are illustrated in FIG. 5.

When the camera lenses with the three different focal lengths were used, all the obtained results were satisfactorily consistent with the given amounts of outof-plane displacement.

[0061] Likewise, the experimental results of the amount of out-of-plane displacement in the case of large deformation are illustrated in FIG. 6.

Likewise, when the camera lenses with the three different focal lengths were used, all the obtained results were satisfactorily consistent with the given amounts of out-of-plane displacement.

[0062] It is confirmed that out-of-plane displacement can be correctly measured on the whole measurement area, independent of an analysis point, from analysis results at different analysis points on the image (for example, the center of the image, a side end of the image, and the end of a corner of an image).

[0063] Accordingly, highly-accurate measurement of out-of-plane displacement in a wide dynamic range from small deformation to large deformation can be performed in the present invention.

In arithmetic processing of an image in the present invention, a C/C⁺⁺ program on a personal computer was executed to determine measurement results. However, the type of program can be appropriately changed depending on a measurement execution environment in which the present invention is carried out.

Example 2 [0064] (2) Example 2: Experimental Results of Accuracy

Confirmation of Measurement of In-Plane and Out-of-Plane Displacements with Single Camera

An optical system for an experiment for investigation of the accuracy of simultaneous measurement of in-plane and out-of-plane displacements, including two cameras, is illustrated in FIG. 7.

[0065] The apparatuses used includes a two-axis moving stage (having a movement resolution of 1 gm), a grating marker (having a two-dimensional square wave pattern having a grating pitch cycle of 1 mm), and two CCD cameras (1280 x 960 pixels, monochromatic, pixel size of 4.65 gm x 4.65 gm).

[0066] The focal lengths of the two camera lenses are both 16 mm.

The distance between the two cameras is 55 mm, and the distance between the surface of the CCDs and the grating of the object is 365 mm.

[0067] A specific experimental procedure will be described below.

(1) The positions of camera 1 and camera 2 were adjusted so that the grating pitch on each image was 10 pixels .

(2) A displacement of 0.1 mm was applied in an outof-plane direction, photographing was performed with each camera, and the angles of view, tan 0, of camera 1 and camera 2 were calculated based on the apparent in-plane displacement.

(3) Image data obtained by photographing the grating affixed to the moving stage with each camera was stored.

(4) Ten in-plane displacements in total were applied by 0.001 mm in an X-direction, and 11 images in total from 0 to 0.01 mm were captured with each camera.

(5) The movement amount of the moving stage in the X-direction was restored to 0 mm.

(6) An out-of-plane displacement of 0.01 mm was applied in the Z-direction, and an image thereof was captured with each camera.

(7) The operations (4) to (5) were performed in the state that the movement in the Z-direction has been performed.

(8) The operations (4) to (7) were performed 11 times in total in a range of the amount of out-of-plane displacement between 0 mm and 0.1 mm.

(9) The operations (3) and (4) to (8) were performed, and analysis of the amounts of in-plane and out-of-plane displacements was carried out using the image obtained with the single camera, and the images obtained from the two cameras.

[0068] In the analysis, a low-pass filter (having a kernel half-width of 20 pixels and a cut-off frequency of 0.01) was applied, a sin/cos filter was applied to a phase distribution (kernel size half-width of 10 pixels in a longitudinal direction and 10 pixels in a lateral direction, the application was repeated three times), and the in-plane and out-of-plane displacements were determined. An average value in an evaluation area of 200 x 200 pixels was calculated.

[0069] In this experiment, displacements in in-plane and out-of-plane directions were applied to the grating affixed onto the moving stage and image capture was performed in synchronization with camera 1 and camera 2.

The results of the calculation of in-plane and outof-plane displacements from the images captured with the two conventional cameras, and the results of the calculation of in-plane and out-of-plane displacements from the image acquired using the single camera (camera 1) according to the present invention were compared. [0070] The measurement results of the in-plane and out-of-plane displacements obtained by the single camera according to the present invention and the two conventional cameras are illustrated in FIG. 8 and FIG.

9.

[0071] Each of the in-plane and out-of-plane displacements in the figure represents the average value of ten measured values when the displacement in each direction was applied (the average value of ten measured values in the case of an amount of out-of-plane displacement of 0.01 to 0.1 mm in the case of an amount of in-plane displacement of 0.001 mm) .

[0072] The error bar in the graph represents the standard deviation of the ten items of data.

On the basis of FIG. 8 and FIG. 9, according to the average value of a predetermined evaluation area in an experiment for measurement of small displacement, it is confirmed that the accuracy of measurement when using the single camera is similar to the accuracy of measurement when using two cameras.

Example 3 [0073] (3) Example 3: Cantilever Vibration Measurement

Vibrations having a frequency equal to one-half a frame rate or less in video shooting can be measured according to the present invention.

FIG. 10 illustrates an optical system for a cantilever vibration analysis experiment as an example of the vibration measurement according to the invention. [0074] In the experiment, the left edge of the cantilever to which a grating was affixed was fixed, and free vibrations after application of deflection to the right edge were simultaneously measured with a singlelens reflex camera and a laser Doppler vibration meter. [0075] A 30cm straight ruler made of stainless steel, the tip of which was equipped with a weight, was used as the cantilever.

A grating having a pitch period of 2.3 mm was affixed to the surface of the straight ruler.

[0076] The Doppler laser vibration meter (hereinafter referred to as LDV) has a resolution of 1.5 μιη and was set in a measurement range of ±5.2 mm in the experiment.

The sampling period is 52.08 Hz. The frame rate of the single-lens reflex digital video camera used is 24 fps .

[0077] The distance between each camera and the grating was set so that one cycle of the grating on the image was about 20 pixels.

The distance between each camera and the grating was 350 mm.

[0078] Video shooting of a state in which free vibrations were applied to the cantilever was performed with the single-lens reflex camera, and vibrations were measured with the LDV from the backside.

Moving images obtained by the cameras were converted into JPEG images on a time-series basis, and the vibrations of the cantilever were measured from the obtained images.

[0079] The results of measurement of out-of-plane displacement (deflection) distributions obtained from image data captured using the single camera are illustrated in FIG. 11.

[0080] FIG. 11(a) represents the results of a state without deflection, FIG. 11(b) represents the results in deflection in a depth direction, and FIG. 11(c) represents the results in deflection in a frontward direction .

[0081] The experimental results reveal the state of the deflection of the entire cantilever on a time-series basis .

[0082] The vibration waveforms obtained in the laser Doppler vibration meter and the present invention (analysis area of 40 x 40 pixels in the center of an image) are illustrated in FIG. 12 and FIG. 13, respectively.

Based on the experimental results, it is confirmed that the accuracy of vibration measurement in the present invention is the same as the accuracy in the LDV.

[0083] As illustrated in FIG. 13, a free decay coefficient can be determined from the vibration waveforms of the cantilever, obtained in the present invention .

[0084] FIG. 14 illustrates a graph in which the frequency histograms of the vibration waveforms in the LDV and the present invention overlap one another.

The peaks of the first and second vibrations were measured to be 3.70 Hz and 7.38 Hz, respectively in a sampling moire method, and measured to be 3.71 Hz and 7.40 Hz, respectively, in the LDV.

As a result, it is understood that vibration frequency analysis can be performed in the method of the present invention with high accuracy that is the same as the accuracy in the conventional LDV.

[0085] The camera having a frame rate of 24 fps was used in this vibration measurement experiment. According to Nyquist-Shannon's sampling theorem, vibrations of up to 12 Hz, which are one-half the frame rate can be measured.

In order to measure vibrations of a higher frequency, a camera capable of capturing at a high frame rate may be used.

[0086] In the present invention, the deflection and frequency distributions of the entire cantilever during vibration can be obtained as compared to the conventional LDV.

Industrial Applicability [0087] This measurement technique can used in threedimensional displacement measurement and vibration measurement in wide fields including nanostructures (such as, for example, photovoltaic cells, thin-film solar cell devices, optical sensors, biosensors, and gas sensors) and infrastructure (such as, for example, bridges, tunnels, high-rise buildings, and plant pipes).

Reference Signs List [0088] 1 digital camera, digital video camera objective lens image sensor (imaging elements arranged in grating pattern in horizontal and vertical directions) grating object to be measured (object) z plane with grating pitch p before deformation z plane with grating pitch p after deformation optical axis plane of image sensor

2016308995 31 Jan 2019

Claims

1. A method for measuring out-of-plane displacement distribution using a single digital camera, wherein the digital camera comprises: an objective lens having a focal length f; and imaging elements arranged in a grating pattern in horizontal and vertical directions, in a state in which a periodic pattern having a pitch p is affixed, in a same direction as a horizontal or vertical direction of the imaging elements, to a surface of an object to be measured, the method comprising:

photographing, when an out-of-plane load is applied to the object to be measured, the periodic pattern before and after out-of-plane displacement caused by the out-of-plane load by the digital camera;

determining pitches Q, Q' at a coordinate (i, j) of the periodic pattern on images corresponding to the pitch p before and after the out-of-plane displacement; and determining an amount of the out-of-plane displacement Δζ of the periodic pattern in accordance with the following Equation 16 to obtain an out-of-plane displacement distribution in a full-field, wherein the periodic pattern has the pitch p in a horizontal direction; a in Equation 16 is a constant; the pitches Q, Q' are determined in accordance with Equation 17 and Equation 18; T in Equation 17 and Equation 18 represents a pixel spacing at which reduction processing is carried out by a sampling moire method; φηι represents a phase of a moire fringe; and (p_m and Misrepresent phase gradients determined using a value of the phase before and after the out-ofplane displacement:

8z=p (16) (17)

2πΓ

2π+Ο./)Γ (18)

21969461 (IRN: P299684)

2016308995 31 Jan 2019

2. A method for simultaneously measuring in-plane and out-of-plane displacements using a single digital camera, comprising:

measuring, simultaneously with the measurement of Az according to claim 1, respective in-plane displacements Ax and Ay in the horizontal and vertical directions by subtracting an amount of an apparent in-plane displacement from respective in-plane displacements x, y in the horizontal and vertical directions which are determined by a sampling moire method at the pitch p of the object to be measured, wherein Ax and Ay are determined in accordance with the following Equations; and θχ and 0y are components in the horizontal and vertical directions of an angle between the optical axis of the objective lens and a line connecting a center of the objective lens and the pitch p affixed to the object before deformation:

Ax = x-Aztan&

(19) (20)

3. A method for dynamically measuring an out-of-plane displacement distribution using a single digital video camera, wherein the single digital camera according to claim 1 further comprises a video shooting mechanism having a predetermined time resolution (frame rate, fps);

the method comprising:

applying the out-of-plane load to the object to be measured;

photographing the periodic pattern before and after an out-of-plane displacement caused by the out-of-plane load by the digital video camera at the frame rate; and consecutively determining an out-of-plane displacement distribution in the full-field in a predetermined time period from consecutive frame images captured before and after the out-ofplane load.

4. The method for measuring out-of-plane displacement distribution according to claim 1, wherein the single digital camera further is configured to comprise a video shooting mechanism having a time resolution (frame rate, fps) that is more than 2 times greater than a period of measured vibrations; and the method further comprises:

21969461 (IRN: P299684)

2016308995 31 Jan 2019 applying the out-of-plane load to the object to be measured by vibrations;

photographing the periodic pattern before and after an out-of-plane displacement caused by the out-of-plane load at a predetermined position at the frame rate using the single digital video camera; and determining a vibration waveform of the object to be measured based on the out-of-plane displacement at the predetermined position, consecutively obtained in a predetermined time period from consecutive frame images captured before and after the vibrations, to analyze a vibration frequency.

5. A program which carries out the processing of an image captured by the method for measuring an out-of-plane displacement distribution using the single digital camera according to claim 1; and a recording medium which stores the program.

6. A program which carries out the processing of an image captured by the method for simultaneously measuring in-plane and out-of-plane displacements using the single digital camera according to claim 2; and a recording medium which stores the program.

7. A program which carries out the processing of an image captured by the method for dynamically measuring an out-of-plane displacement distribution using the single digital video camera according to claim 3; and a recording medium which stores the program.

8. A program which carries out the processing of an image captured by the method for measuring out-of-plane displacement distribution according to claim 4; and a recording medium which stores the program.

9. A device for measuring an out-of-plane displacement distribution using a single digital camera, the apparatus comprising:

at least a single digital camera;

an operation unit that processes an image captured by the single digital camera; and a display unit that displays a result of the operation, wherein the method for measuring an out-of-plane displacement distribution using the single digital camera according to claim 1 is performed.

10. A device for simultaneously measuring in-plane and out-of-plane displacements using a single digital camera, the apparatus comprising:

21969461 (IRN: P299684)

2016308995 31 Jan 2019 at least a single digital camera;

an operation unit that processes an image captured by the single digital camera; and a display unit that displays a result of the operation, wherein the method for simultaneously measuring in-plane and out-of-plane displacements using the single digital camera according to claim 2 is performed.

11. A device for dynamically measuring an out-of-plane displacement distribution with a single digital video camera, the apparatus comprising:

at least a single digital video camera;

an operation unit that processes an image captured by the single digital video camera; and a display unit that displays a result of the operation, wherein the method for dynamically measuring an out-of-plane displacement distribution using the single digital video camera according to claim 3 is performed.

12. A device for analyzing a vibration frequency with a single digital video camera, the apparatus comprising:

at least a single digital video camera;

an operation unit that processes an image captured by the single digital video camera; and a display unit that displays a result of the operation, wherein the method for measuring out-of-plane displacement distribution according to claim 4 is performed.

National Institute of Advanced Industrial Science and Technology

Patent Attorneys for the Applicant/Nominated Person

SPRUSON & FERGUSON

21969461 (IRN: P299684)

P180004W0

Z

FIG. 1

FIG. 2

4 Grating marker ²/s

FIG. 3 (a)

FIG. 4 %

FIG. 5

Actual, z [mm]

FIG. 6

0.0 2.0 4.0 6.0 8.0 10.0

Actual, z [mm] ⁴/s

FIG. 7

FIG. 8