A High-Resolution Magnetic Field Imaging System Based on the Unpackaged Hall Element Array

Abstract

We have designed a high-resolution magnetic field imaging system using 256 unpackaged Hall elements. These unpackaged Hall elements are arranged in a Hall linear array, and the distance between adjacent elements reaches 255 µm. The sensitivity of the unpackaged Hall element array can be adjusted using a computer to measure magnetic environments with different magnetic field strengths. High-resolution magnetic field images of 256 × 256 pixels can be generated by moving the array using the X–Y axis motorized rail. This spatial resolution can reach 99.61 pixels per inch (ppi). This rail allows for the spatial resolution of the system to be further increased to 199.22 ppi by using a special movement route. In the experiments, we employ this system to image magnetized metal scissors, and the result displays the structural features of the scissor surface. We also detected the magnetic suction wireless charging coil inside an Apple phone. The image obtained shows the shape of the coil and the gap between the magnets. The high-resolution magnetic imaging system displays the magnetic characteristics of the sample very well and easily obtains information about small-shaped structures and defects on the sample surface. This provides the system with potential in several fields such as quality inspection, security, biomedicine, and detection imaging.

1. Introduction

Magnetic field imaging is widely used in many fields such as non-destructive testing (NDT), metal detection, biomedicine, and circuit diagnostics [1,2,3,4], etc. Also associated with magnetic field imaging is eddy current imaging, which has promising applications in several areas [5,6]. Magnetic field imaging can visualize the distribution of magnetic fields in magnetic materials or magnetized metals, which can help study their properties. Misron et al. [2] designed a removable magnetic detection system using the Hall linear array, which was used to image the shape of ferromagnetic objects within floors or walls. Suksmono et al. [7,8] developed a subsurface magnetic imaging system using a magnetometer inside a smartphone to probe the geometry of buried objects. They then also assembled a magnetic camera using several AMR triaxial magnetometers to detect the effect of hidden objects on the ambient magnetic field and imaged the magnetic field of cables loaded with 50 Hz alternating current. Benitez et al. [9,10,11,12] used solid-state magnetic induction probes and arrays to develop a magnetic scanning system that detected and imaged rebars within concrete. The experimental results demonstrated the ability of the system to image embedded metal objects, as well as its potential applications in biomedical, surveillance, and security fields.

Magnetic field imaging also maps the leakage magnetic field at defects on the surface of magnetized metal samples to obtain defect information, which has been the subject of much research in NDT of metallic materials. Jakubas et al. [13] employed the magnetic camera to image surface defects in soft magnetic composites (SMCs) and investigated the effect of defect size and material permeability on the magnetic field through numerical analysis. Le et al. [14] proposed a moisture separator reheater (MSR) piping system for nondestructive testing, which used the Hall sensors array to detect artificial defects on the piping. Gong et al. [15] employed a gradient Hall sensors array to predict the shape of cracks on the rail surface and assessed the depth of the cracks by a BP neural network algorithm. In addition, magnetic imaging can detect the magnetic field radiation of electronic devices and household appliances to determine whether they meet electromagnetic compatibility standards [16], and it is also used to measure and analyze the magnetic field of rock samples [17].

The key sensing unit to realize the magnetic imaging technique is the magnetic sensor. Currently, there are many types of magnetic sensors, such as AMR, GMR, induction coils, and Hall sensors [18,19,20,21]. Hall sensors are characterized by high accuracy and good linearity, small size and low power consumption, thermal stability, and low price, which makes them very suitable for measuring magnetic fields. A single Hall sensor can spend much time scanning and detecting magnetic fields, so using a Hall sensor array to detect magnetic fields can significantly speed up the process. Several packaged Hall sensors are currently used to form linear or faceted arrays [2,22]. However, the packaged Hall sensors have low detection resolution due to the presence of package housing that results in a larger sensor volume, making the spacing between neighboring Hall sensors larger. Using unpackaged Hall elements avoids the increased volume and packaging costs associated with packaged housings and effectively improves detection resolution. However, the research on unpackaged Hall element arrays is still relatively small.

This paper describes a high-resolution magnetic field imaging system in which the magnetic sensing probe consists of a linear array of 256 unpackaged Hall elements, which are fabricated in GaAs material and have a spacing of 255 µm between the centers of adjacent elements. The detection distance between the magnetic sensing probe and the samples can be less than 1 mm. The total size of the double-layer printed circuit board (PCB) containing the magnetic sensing probe and the main processing module is 140 mm × 109 mm × 17 mm. We develop a software interface to adjust the sensitivity of unpackaged Hall elements to change the array’s magnetic field measurement range. The X–Y axis motorized rail is capable of moving the magnetic sensing probe to detect and image a 15 cm × 15 cm magnetic field area. The spatial resolution of this magnetic imaging system reaches 99.61 ppi. In addition, the special movement of this rail enables a further resolution of 199.22 ppi.

2. Materials and Methods

2.1. Fabrication of Unpackaged Hall Element Array

Currently, the vast majority of magnetic field imaging systems are designed using arrays of packaged Hall sensors, but the enclosures of these sensors limit the spacing of neighboring sensors and also result in the presence of positional offsets of the Hall elements, as shown in Figure 1. The distance h₁ between the sensors is limited by the enclosure size to millimeters, making it difficult to further improve the spatial resolution of the system. In addition, the presence of the enclosure interferes with the soldering process, causing the sensors to shift their position, as shown in Figure 1b. Assuming no offset error for the first sensor, the ideal spacing of the sensors is y₀. For the second and third sensors, their offsets in the x-direction are x₁ and x₂, and in the y-direction, they are y₁ − y₀ and y₂ − y₀, respectively. Figure 1c illustrates the positional offset caused by the placement of the Hall elements inside the package enclosure. The limited alignment accuracy of the die bonder makes it difficult for two Hall elements to be located at the same position inside the enclosure. In order to overcome the above problems, we designed the magnetic sensing probe of the system using unpackaged Hall elements.

Figure 2 demonstrates the alignment design of the unpackaged Hall elements. These elements all come from the same wafer, which is diced in segments by the wafer dicing to form multiple segments of unseparated Hall elements. Since the wafers are fabricated using a photolithography process, which has micron-level manufacturing accuracy, the offset error of the unseparated Hall elements is effectively reduced. In addition, the width of the dicing channel between the Hall elements is only retained, which is typically a few tens of micrometers, significantly reducing the pixel center distance between the elements and improving the spatial resolution of the system.

In this study, the unpackaged Hall linear array using 256 Hall elements is designed to extend the detection area of the system. These Hall elements are made of GaAs, model MG1A01, which provide more than eight times the sensitivity of silicon-based elements and have good linearity. The performance parameters of the GaAs Hall element are shown in

Table 1. Performance parameters of MG1A01 Hall element.

Offset Voltage	Input Resistance	Output Resistance	Sensitivity	Linearity
<2 mV	750 Ω	750 Ω	1.4 mV/mT@5 V	0.5% (<500 mT)

.

Since the performance of Hall elements on different wafers varies slightly, the 256 Hall elements used in this paper all come from the same wafer to eliminate this effect. Figure 3 presents a designed unpackaged Hall linear array board. The electrode sections of each Hall element attach to the output pads via metal leads, requiring a total of 512 pads, which are aligned on both sides of the array. In addition, arranging the VCC and GND pads provides voltage bias to the array. Each Hall element has dimensions of 200 µm × 200 µm × 200 µm and the spacing between the centers of adjacent elements is 255 µm. There is an absence of gaps between the adjacent Hall elements, retaining a dicing channel width of only 55 µm. The unpackaged Hall linear array is 6.53 cm in length and the entire PCB measures 7.95 cm × 7.59 cm.

2.2. Design of the Magnetic Field Imaging System

Figure 4 illustrates the system block diagram of the magnetic field imaging system. This system consists of 256 Hall elements, 32 channel multiplexers, switch modules, programmable amplifiers, a data acquisition card, an X–Y axis motorized rail, etc. The 256 Hall elements grouped into 16 subarrays, each 1 × 16, with the switching modules controlling one or two subarrays of supplies simultaneously. The output signals of each subarray are transmitted to 32 channel multiplexers with a 23 ns transition time. The amplifiers are designed as programmable linear amplifiers convert differential Hall signals to single-ended signals, allowing for repetitive gain adjustments to ensure suitability for different magnetic field environments. The microcontroller controls the switching modules activating the power terminals of the subarrays sequentially to reduce signal interference, while the selected and amplified Hall signals are captured by the DAQ system.

The analog input resolution of the DAQ system is 16-bit, introducing 50 µV_RMS of random noise, allowing for continuous signal acquisition. The Hall voltage values captured by the DAQ system are displayed in real-time as waveforms on the computer. The pulse-type controller with a 32-bit ARM processor is connected to the computer using an RJ45 network cable. The controller has an output frequency of 200 KHz for each axis and an integrated pulse counting function, which enables precise control of the position and speed of drive motors. This allows the X–Y axis motorized rail with a 10 µm movement accuracy, the route of which is determined by the program written. According to the movement route of the X–Y axis motorized rail, the interactive interface is designed using MATLAB R2023a, which arranges the data into a corresponding 2D matrix and maps it into a high-resolution image.

2.3. Construction of the Magnetic Field Imaging System

The core component that makes up the magnetic field imaging system is the magnetic sensing probe module, as shown in Figure 5. This module consists of an unpackaged Hall linear array and a main processing module that includes a microcontroller, 32 channel multiplexers, switch modules, flexible flat cables (FFC) connectors, etc. In order to prevent the magnetic field from interfering with the operation of the chips in the main processing module, the sensor probe and this module were placed on separate PCBs. Power and signals were transferred between PCBs through FFC. Voltage limiting and anti-reverse connection functions have been added to the power supply interface of the circuit module to enhance system reliability and stability.

Figure 6 presents the magnetic field imaging system. The Hall linear array board is fixed underneath the slide, which is driven by the slide through the ball screw. A limit switch is fitted on each side of the ball screw for determining the position of the slide table and protecting the device. In this system, the moving trajectory of the slide table is controlled by the written software program and the maximum moving range of this slide is 15 cm × 15 cm. The X–Y axis motorized rail with ±10 µm repeated positioning accuracy, effectively reduces the movement error of the slide table, allowing the Hall linear array to accurately measure each point to be detected in a magnetic field area. The distance between the Hall elements without packaging enclosures and the samples can be less than 1 mm, which can better show the magnetic field distribution on the sample surface.

2.4. Coil Calibration and Resolution Enhancement

The different sensitivity of each Hall element affects the measurement of the magnetic field. A Helmholtz coil is utilized to calibrate the sensitivity of Hall elements, and the equation for sensitivity calibration is as follows:

$$S_1=\frac{V_1}{B},$$

(1)

$${\alpha }_n{S}_n=\frac{{\alpha }_n{V}_n}{B}=S_1,$$

(2)

where B is the value of the magnetic field generated by the Helmholtz coil, and V₁ and S₁ are the Hall voltage and sensitivity of the first Hall element in the array. V_n, S_n, and α_n are the Hall voltage, sensitivity, and scaling factor of the n th Hall element, respectively. A software algorithm is used to calculate these scaling factors to achieve the sensitivity of the other Hall elements to be consistent with the sensitivity of the first Hall element.

The special moving route of the X–Y axis motorized rail further improves the detection resolution of the system. Figure 7 describes the movement of the X–Y axis motorized rail. Unpackaged Hall linear array in the initial position indicated by solid black lines. The slide table drives the array in the way shown in Figure 7 to increase the number of points to be measured. The data are then rearranged and processed to plot higher-resolution images. This movement makes the spacing between adjacent points to be detected about 127.5 µm. The spatial resolution is increased from 99.61 ppi to 199.22 ppi.

The interpolation algorithm is used to increase the number of pixels and colors in these images, enabling a resolution of 398.43 ppi. The software flowchart and settings page are shown in Figure 8. The auto-zero function is included in the software to cancel out the zero voltage of each Hall element. As the unpackaged Hall linear array is driven by the slide to disrupt the data arrangement order, we have written a function to restore the order of data arrangement using MATLAB 2023a, which automatically arranges the data into a 2D matrix according to the number of movements of the array in different directions. This function also handles the data generated after the above special moves to draw higher-resolution images. Based on the magnetic field range to be measured, the interface provides a choice of the number of scanning elements whose detected data are processed.

3. Experiments and Analysis

For testing the performance of the magnetic field imaging system, circular magnets, a magnet array, defective steel plates, magnetic suction wireless charging coils, and a metal sample were used in the study cases. This system measures the magnetic field perpendicular to the sample surface. The distance between the unpackaged Hall linear array and the object under test is 1 mm in each study case. The step size of each movement of the X–Y axis motorized rail is set to 255 µm, which is the same size as the spacing between adjacent Hall elements. To facilitate research and analysis, we converted the test results of the magnetic field imaging system into 2D/3D magnetic field images.

3.1. Imaging Samples of Magnetic Materials

3.1.1. Imaging Ring-Shaped Magnets

In the first experiment, we imaged a pattern of four ring-shaped magnets. The material of the ring-shaped magnet is NdFeB. As shown in Figure 9a, each ring-shaped magnet has an outer diameter of 10 mm, an inner diameter of 5 mm, and a height of 10 mm. Four ring-shaped magnets are placed on the right side of the unpackaged Hall linear array, which is detected by the array scanning. The magnetic field distribution of the four ring-shaped magnets is shown in Figure 9b. The colors in the figure indicate the magnetic flux density in Tesla (T). The image shows well the magnetic field polarity and shape of the four ring-shaped magnets. In order to compare with the experimental results measured by this magnetic field imaging system, the magnetic field of four ring-shaped magnets was simulated with Maxwell software. The simulation result is shown in Figure 9c. According to the image comparison, the results of the measured and simulated plots are very similar in terms of magnet shape, magnetic field polarity, and magnetic field values. This indicates that the magnetic field imaging system is capable of detecting and visualizing magnetic fields in two dimensions.

3.1.2. Imaging an Array of Cylindrical Magnets

In the second experiment, an array of cylindrical magnets was imaged with the magnetic field imaging system. For comparison with the test results of this system, we designed a linear array of Hall sensors, as shown in Figure 10. The array contains 12 Hall sensors with 2 mm spacing between adjacent sensors and the sensitivity has been adjusted to be consistent with the Hall elements. The detected sample consists of 16 small cylindrical magnets. The material of each small cylindrical magnet is also NdFeB, which has a diameter of 5 mm and a height of 5 mm.

The 3D magnetic field images of the sample measured by the two Hall arrays are displayed in Figure 11a,b. The Hall sensor array loses a significant amount of magnetic field information in the detection process, resulting in a relatively ambiguous field distribution of the magnet array. In contrast, the unpackaged Hall element array with high spatial resolution captures more magnetic field details and maps a sharper and more complete magnetic field image. Then, we extracted the values of the magnetic field at the dashed position in Figure 10b for analysis, as shown in Figure 11c,d. In Figure 11c, two Hall arrays measured the magnetic field of the first row of magnets. The Hall sensor array captured only 12 points, with the magnet peaking at the poles to about 160.5 mT and −151.9 mT. However, the unpackaged Hall element array is capable of capturing 96 points, with peak magnetic fields at the poles of approximately 176.2 mT and −180.2 mT. The peak magnetic field of the magnet at the two poles differs less in absolute value and the resulting field distribution is relatively symmetrical, but the Hall sensor array has difficulty in detecting this. Furthermore, the low spatial resolution of this array challenges the capture of real magnetic field peak points. Ditto for Figure 11d, which illustrates a similar phenomenon. This experiment demonstrates that a high-spatial-resolution system will capture more magnetic field information and display the magnetic field characteristics of the sample more comprehensively and completely.

3.2. Detecting Defective Stainless Steel Plate

In this experiment, magnetic flux leakage detection (MFL) was performed on a stainless steel plate of type 2Cr13 with dimensions of 120 mm × 30 mm × 5 mm, as shown in Figure 12. To simulate the defect on the stainless steel plate, a circular groove with diameters of 4 mm was manufactured on the surface of the plate, with a depth of 3 mm. Two cylindrical magnets with a magnetic strength of 350 mT were used to provide magnetic flux. The stainless steel plate on the bottom was used as a sinking plate to form the magnetic circuit.

The detection results for the defective steel plate are presented utilizing two Hall arrays in Figure 13a,b. A comparison of the images indicates the result measured by the unpackaged Hall element array provides the shape of the MFL signal more completely, allowing for easier observation of the direction of the magnetic circuit in the steel plate. In Figure 13c,d, the MFL signal flowing through the center of the groove was measured. The Hall sensor array failed to detect the actual peak point of the MFL signal, which measured only about 3.82 mT, yet the unpackaged Hall element array captured a peak point of 4.79 mT. In addition, from analyzing Figure 13c, the distance between the two peaks of the MFL signal in the horizontal direction can only be roughly evaluated as 4 mm. However, according to Figure 13d, this distance is relatively accurately evaluated as 3.32 mm, less than 4 mm. The experiment demonstrates that the magnetic field imaging system with high spatial resolution better restores the defect-induced MFL signals, which assists us in analyzing and researching the property characteristics of different defects.

3.3. Measuring the Wireless Charging Coils inside the Apple Phone

Apple has developed a magnetic wireless charging technology. The phone and charger are drawn together by magnets inside the phone and charger for fast and stable charging. If one of the magnets on the coil provides a smaller magnetic force, the weak suction between the phone and the charger at that position tends to shift the phone in the direction of that magnet, affecting the charging efficiency of the phone. Therefore, there is a requirement to measure and screen the magnets.

The magnetic field distribution arising from the array of magnets inside the Apple phone appears in Figure 14a. For measuring the wireless charging coil sample, we reacquired a coil from the interior of an Apple phone, as shown in Figure 14b. Figure 14c,d plots the measurements of the unpackaged Hall element array for this sample. The high-resolution system provides a very clear visualization of the magnetic field distribution of the coil. The magnetic field peak values from each magnet range from 43 mT to 51 mT in absolute terms. From the imaging results, no magnet with magnetic anomalies is detected; the entire magnet array exhibits a symmetrical field distribution and provides a tight suction to the other coils.

In addition, we also obtained the magnet array on a non-genuine wireless charging coil, as shown in Figure 15a. The gap between two adjacent magnets is 470 µm. Figure 15b presents the images measured by an unpackaged Hall element array. From the test results, the array successfully detected and visualized these gaps. Meanwhile, the magnetic field peaks produced by these magnets range from 51 mT to 72 mT in absolute value, with a relatively asymmetric distribution of the magnetic field. As to further improving the spatial resolution of the system using a special movement of the X–Y axis motorized rail, the results are shown in Figure 15c. The spacing between adjacent Hall elements reduces to approximately 127.5 µm, increasing the resolution of the system to 199.22 ppi. These gaps become easier for the system to recognize, and the magnet gaps in the black dashed area appear more distinctly. This indicates that the system with high spatial resolution captures more detailed information about the magnetic field and visualizes the magnetic characteristics of the sample more realistically.

3.4. Metal Identification

To validate the ability of this magnetic field imaging system to identify metal objects, a pair of metal scissors was used as the sample. Figure 16a exhibits the experimental environment for magnetizing the scissors by generating an excitation magnetic field with a Helmholtz coil. The identification of the metal scissors after removing the background magnetic field using the software algorithm is shown in Figure 16b. Due to the tilting of the metal scissors during the measurement process, the bottom of the scissors is farther away from the magnetic sensing probe, which makes it harder to detect. The image displays the outline of the metal scissors clearly, and the detailed features of the scissors within the red dashed circle in Figure 16a are also presented. This system identified a hole and several bumps on the surface of the metal scissors. It demonstrates the capability of this system to image detailed features of samples and its potential in the field of sample identification.

4. Discussions

In recent years, arrays of packaged magnetic sensing sensors have been commonly used to image magnetic fields. However, the package enclosure increases the size of the sensor, which makes it difficult to reduce the spacing between adjacent sensors, resulting in low spatial resolution. The minimum detection distance between the packaged magnetic sensing sensor and the sample surface is also affected by the thickness of the packaged enclosure, making it more difficult to detect the magnetic field on the sample surface at close range. In addition, the position of the packaged sensor may be shifted during soldering to the PCB, resulting in a positional error between the actual and ideal detection points for the magnetic field. In order to overcome the above problems, this paper utilizes the unpackaged Hall element array to design a magnetic field imaging system. The Hall elements are not limited by the package enclosure, which enables the spacing of adjacent Hall elements up to 255 µm. The size of the Hall elements can be further decreased by the photolithography process, allowing for smaller spacing between adjacent Hall elements.

The magnetic field imaging system designed in this paper is capable of imaging samples of magnetic materials, which helps us to study the magnetic characteristics of the samples. This system also has the ability to measure the wireless charging coils inside an Apple phone, which makes it potentially valuable for quality inspection applications. In addition, the magnetic field imaging system also provides non-destructive testing and identification of metallic materials, which has potential value in several fields such as metal identification, biomedicine, mark detection, and security.

5. Conclusions

The magnetic field imaging system designed in this paper has a spacing of 255 µm between adjacent Hall elements and can generate high-resolution magnetic field images. The X–Y motorized rail moves the array to detect and image a wide range of magnetic field areas. A Helmholtz coil and software algorithms keep the sensitivity of each Hall element consistent and adjust the sensitivity of the Hall element array with programmable amplifiers. The results of the above experiments demonstrate that a high-spatial-resolution system captures more magnetic field information, allowing us to display the magnetic field characteristics of the samples more comprehensively, which benefits our analytical study of the samples.