Shulou(Shulou.com)11/24 Report--

The sound of firecrackers during the Spring Festival has thinned out

The strong feeling of hometown is not reduced at all

The Spring Festival holiday is coming to an end

People are starting to leave their homes.

Before you board a train or an airplane

Security check is an essential link

No matter what's in your suitcase, it doesn't matter if it's a local specialty.

Or heavy knowledge?

They're moving through security

will be seen by staff.

source| How does pixabay security work? This article attempts to explain how existing X-ray security equipment works, providing readers with an opportunity to pass time while increasing their knowledge on the road.

01. Single energy X-ray imaging First of all, what is X-ray?

X-ray is a kind of high-energy electromagnetic wave, which is usually called X-ray when the frequency is in the range of 3×10 µ Hz~3×10 µ Hz (single photon energy is about 100eV~100keV, and the higher the frequency, the higher the single photon energy).

X-rays were discovered by German physicist Wilhelm Conrad Röntgen in 1895, hence the name Roentgen rays.

Roentgen| WikipediaWhat happens when X-rays hit an object?

X-rays have a strong penetrating ability. When they penetrate matter, they interact with atoms in matter, especially electrons, and lose energy. The intensity decreases exponentially with the depth of transmission.

For the moment, let us not consider how X-rays interact with atoms in matter, but focus on the exponential decay of ray intensity, where the ray intensity refers to the energy of the ray passing through the unit cross-sectional area per unit time (colloquially, the density of photons contained in the ray).

Where I represents the intensity of incident X-rays, I represents the intensity of X-rays emitted after penetrating the substance, x is the distance traveled by X-rays in the object, μ is the linear attenuation coefficient, and the above formula indicates that X-rays exhibit exponential attenuation when penetrating the substance.

How do we use this principle to peer into our suitcases?

X-ray intensity attenuation can be used for imaging. X-ray intensity attenuation occurs when passing through the detected luggage, considering that the contents of the luggage are not evenly distributed, so the intensity of X-ray passing through the luggage from different positions will be different, detect the intensity distribution of transmitted X-ray and convert it into gray image, and then an image reflecting the internal structure of the detected object can be obtained.

X-rays decay exponentially as they pass through matter and can be imaged using transmission intensity to reveal the internal structure of matter.| Figure source [2] Considering that the detected object is not uniform, so the linear attenuation coefficient μ is also a function of spatial position, we can use μ=μ(s) to express, then

Take the logarithm of the above equation and define the logarithmic transmission signal t (d) as

The intensity image of transmitted X-rays actually reflects the relative size of t (d) at different positions.

02. Dual-energy X-ray imaging seems to be perfect up to this point. We can image it based on the attenuation of the radiation intensity, so we get an outline of the internal structure of the baggage.

The problem is, we have no way of knowing the elemental composition of the object being examined.

Why do you need to know the composition of the elements? Why is it not enough to just see the shape of an object?

We know that the purpose of security inspection is to protect the safety of trains or aircraft and their passengers, so security inspection hopes to focus on some dangerous goods, such as explosives, etc. Obtaining the elemental composition of the detected object can help the detection of explosives.

So what techniques can help us get information about the elemental composition of matter?

Dual-energy X-ray imaging simultaneously detects the intensity of X-rays with one high energy and one low energy after passing through the object, and further obtains the information of the element composition of the object.

So how does it work?

Single-energy X-ray imaging depends on the product of the linear attenuation coefficient μ and the thickness x. Generally, μ is large for substances with large atomic numbers. Thin sheets with large atomic numbers may produce the same effect as thick materials with smaller atomic numbers, so single-energy imaging is difficult to resolve the elemental composition of substances, as shown in the figure.

The linear attenuation coefficient μ of a substance is related to the atomic number of the material and the photon energy of the X-ray. In order to simplify the analysis, we temporarily consider a uniform substance A. The linear attenuation coefficient of A can be expressed as a linear combination of α and β reference substances.

For a selected reference material, μα(E) and μβ(E) are known, and multiplying both sides of the above equation by L gives the logarithmic transmission signal t (E), which is also a function of energy.

where Lα and Lβ are the product of the linear combination coefficient and L, t (E) is measured for high and low energy rays respectively, and Lα and Lβ are solved, the effective atomic number of a point on the image can be determined from the ratio Lβ/Lα.

The effective atomic number can reflect the true atomic number of the substance to some extent, and we know that each element and the atomic number of the element atom are one-to-one corresponding, so we can determine the information of the composition of the substance elements. Color the image according to the effective atomic number value, and you get a false color security image, as shown below.

Dual-energy X-ray imaging gives a false color image in which metals, alloys, and hard plastics are shown in blue and less dense materials are shown in green or orange.| Source [4] The figure below shows the layout of a dual-energy X-ray security device. X-ray tubes emit a continuum of X-rays (containing multiple frequencies, i.e., containing multiple energies). After passing through the object, the radiation is first received by the low-energy detector, and then passes through a thin copper sheet, which absorbs the lower-energy radiation, so that only the higher-energy part passes through the copper sheet to reach the high-energy detector. In this way one obtains signals of high and low energy rays separately.

Layout of dual-energy X-ray security inspection equipment| Source [3]03. Multi-view X-ray security technology Usually our luggage is very full, there is more than one object in the path of the ray, and the above method projects objects in only one direction, making it difficult to distinguish overlapping objects.

So how do you solve the overlap problem?

Just as human eyes can view an object from different perspectives, multi-view imaging techniques have been developed. The 3D information of the object can be obtained partially from the 2D images of different viewing angles, and the overlapping problem can be solved effectively. In addition, multi-view imaging technology can also improve the accuracy of atomic number discrimination by dual-energy security equipment.

The existing multi-view X-ray security inspection equipment includes single-ray source multi-view model and vertical multi-view model. The diagram below shows the structure of both models.

Multi-view model of single ray source| Source [5] The layout above divides the rays emitted by the same ray source into two parallel beams, which are irradiated on different positions of the conveyor belt respectively. When the detected object passes through the areas irradiated by the two beams in turn on the conveyor belt, people will obtain X-ray transmission images observed from two directions.

vertical multi-view model| In the layout of Figure Source [6], the ray source is placed in two mutually perpendicular directions, and the transmission images of the detected object are obtained from the two perpendicular directions. According to the images of the two vertical viewing angles, the three-dimensional information of the detected object can be reconstructed accurately.

04.CT security technology Multi-view X-ray imaging technology can only obtain images of several views, and the ability to reconstruct three-dimensional information of objects is still limited. Is there a better way?

Computed tomography, that is, CT security inspection technology, obtains two-dimensional images of objects from multiple perspectives, can reconstruct three-dimensional information of objects, can solve the problem of object overlap and occlusion, and improve the accuracy of material discrimination. Let's look at its principle below.

CT technology irradiates X-rays from multiple viewing angles and obtains projections of the object under inspection in various directions. To simplify the problem, we only consider the case where the object under inspection is a two-dimensional object with a linear attenuation coefficient μ(x,y). If we shine X-rays in only one direction, denoted by θ, then we can get a projection along this direction, as shown in the figure below.

The logarithmic transmission signal along theta direction is expressed as follows

If we rotate the X-ray, as in the animation above, we obtain projections of the object under examination in all directions, that is, t (θ,r) is a function of the projection direction θ of the ray and the position r of the ray through the object.

After a certain deduction, we can get that t (θ,r) makes a one-dimensional Fourier transform of r, which is actually the same as μ(x,y) makes a two-dimensional Fourier transform of x,y and then "slices" along the θ direction.

The following figure illustrates the above formula vividly. From left to right, t (θ, r) is obtained by X-ray imaging along the theta direction, and t (θ,r) is placed along the theta direction to obtain a two-dimensional image. This two-dimensional image is the two-dimensional Fourier transform of μ(x,y) to x,y.

Source [7] Introduction to Fourier Transform

Fourier transform is a mathematical transformation that decomposes a function into its frequency components (also understood as expanding a function with plane waves as basis functions), each frequency component representing an overall structural characteristic of the function. The Fourier transform F (k) of a function f (x) takes frequency k as an argument and represents the weight of the frequency component in f (x). A function and its Fourier transform contain the same information.

The upper and lower lines of the above formula are Fourier forward transform and inverse transform respectively

plane wave concept diagram| At this point in pixabay, we have a way to reconstruct three-dimensional information about the object being examined, but for simplicity, we will still only discuss two-dimensional objects. The reconstruction of object information can be expressed by t (θ,r) as much as possible.

If expressed by formula, the process of reconstructing object information from projections in various directions is

In the above formula, the bottom row represents the two-dimensional inverse Fourier transform of T (θ,ω) in polar coordinates (where polar coordinates v=-ωsinθ, unlike convention), and the top two rows represent the two-dimensional inverse Fourier transform of F (u,v).

Using the symmetry of Fourier transform function in polar coordinates, T (θ,ω)=T (θ+π,-ω), the above formula can be changed into

This method can be shown in the following flowchart.

We have obtained projections t (θ,r) along various directions, noting that for a two-dimensional object every projection of fixed θ is a one-dimensional function of r.

We Fourier transform these functions on r, and then arrange them in a circular way to get the two-dimensional Fourier transform of the object. We then perform an inverse Fourier transform to obtain the original information of the object.

Reconstruction of CT image by Fourier transform| Of course, this is a very ideal situation, in practical applications, the designers of the security inspection machine also need to consider a lot of engineering problems, such as signal noise reduction, blur correction and so on.

This paper introduces the single-energy X-ray imaging technique, which uses the exponential attenuation characteristic of X-ray passing through matter to obtain images reflecting the internal structure of the object to be detected.

Dual-energy X-ray imaging has been developed to facilitate identification of the elemental composition of matter; multi-view X-ray security technology has been developed to solve the overlap problem; and CT technology has been applied to security inspections to help people accurately reconstruct three-dimensional information of objects.

Technological progress is to ensure the safety of the journey, I wish you a happy journey, in the new year all your wishes come true!

References:

[1]https://en.wikipedia.org/w/index.php? title=Wilhelm_R%C3%B6ntgen&oldid=1134755758

[2]Mery D. X-ray testing: The state of the art[J]. The e-Journal of Nondestructive Testing (NDT), 2013, 18(09): 01.

[3]Macdonald R D R. Design and implementation of a dual-energy X-ray imaging system for organic material detection in an airport security application[C]//Machine Vision Applications in Industrial Inspection IX. SPIE, 2001, 4301: 31-41.

[4]Bhowmik N, Wang Q, Gaus Y F A, et al. The good, the bad and the ugly: Evaluating convolutional neural networks for prohibited item detection using real and synthetically composited X-ray imagery[J]. arXiv preprint arXiv:1909.11508, 2019.

[5]Evans P. Three-dimensional X-ray imaging for security screening[J]. Security Journal, 2005, 18(1): 19-28.

[6]Chen Bing. Automatic recognition of prohibited articles based on multi-energy X-ray imaging [D]. Beijing Institute of Technology, 2018. DOI:10.26948 / d.cnki.gbjlu.2018.001633.

[7]https://campus.tum.de/tumonline/LV_TX.wbDisplaySemplanDoc? pStpSplDsNr=22390

This article comes from Weixin Official Accounts: Institute of Physics, Chinese Academy of Sciences (ID: cas-iop), author: Li Youyou

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