PHASE CODING WITH FREQUENCY SWEEP PULSES FOR MAGNETIC RESONANCE IMAGING IN INHOMOGENEOUS MAGNETIC FIELDS.

Abstract

Single-sided MRI devices, systems, and methods are described. One method may include transmitting a frequency-sweep excitation pulse comprising a low-to-high frequency sweep; phase encoding during the frequency-sweep excitation pulse; and adjusting the amount of phase accumulated during the frequency-sweep excitation pulse of adjacent slices on the slab. The frequency-sweep excitation pulse may be a chirping pulse. Encoding in this way can prevent spin echoes from being swerved and avoid k-space truncation in certain cases. In addition, the resulting images can be combined more efficiently.

Description

Phase coding with frequency sweep pulses for magnetic resonance imaging in inhomogeneous magnetic fields CROSS REFERENCE TO RELATED APPLICATION This application claims the benefit of priority under § 119(e) of title 35 of the United States Code with respect to United States Provisional Patent Application No. 62 / 987,292, entitled SYSTEMS AND METHODS FOR LIMITING A--SPACE TRUNCATION IN A SINGLE-SIDED MRI SCANNER, filed on March 9, 2020, the full description of which is incorporated herein by reference. BACKGROUND OF THE INVENTION Single-sided or open magnetic resonance imaging (MRI) scanners typically have a permanent or inherent gradient magnetic field along a longitudinal axis extending from the single-sided MRI machine into a field of view. The permanent gradient magnetic field can be produced by rare-earth magnets and two sets of gradient coils on the face of the permanent magnets. This orientation allows imaging within a field of view above the magnet face. By designing a system with this form factor, it is possible to obtain images without enclosing the region to be scanned. Therefore, imaging can be acquired without the patient entering a hole, allowing the scanner to be used with other medical devices, such as a biopsy robot.It is also more comfortable for claustrophobic patients to have images taken outside of an imaging port than in a conventional, enclosed MRI scanner. Single-sided MRI scanners can also be portable and can image any object within the field of view. The use of a surface gradient coil with a single-sided scanner, although generally necessary for single-sided scanning, can result in a change in the field of view along the Z-axis, a drift echo, and / or ultimately, truncation of k-space, which can cause blurring and effectively limit the image quality obtained by the single-sided MRI scanner. BRIEF DESCRIPTION OF THE INVENTION In one aspect of the present description, a method for imaging a slab having at least two cuts with a single-sided magnetic imaging apparatus defining an inherent gradient magnetic field extending from the magnetic imaging apparatus into a field of view, comprises transmitting a frequency sweep excitation pulse comprising a low-to-high frequency sweep; phase encoding during the frequency sweep excitation pulse; and adjusting the amount of phase accumulated during the frequency sweep excitation pulse of adjacent cuts in the slab. In another aspect of the present description, a magnetic imaging apparatus comprises a permanent magnet, a set of gradient coils, an electromagnet, a radio frequency coil, wherein an inherent gradient magnetic field extends from the magnetic imaging apparatus relative to a first axis into the field of view, wherein the first axis is perpendicular to the permanent magnet, and a control circuit configured to image a slab having at least two cuts, wherein the imaging comprises: transmitting a frequency sweep excitation pulse comprising a low-to-high frequency sweep; phase encoding during the frequency sweep excitation pulse; and adjusting the amount of phase accumulated during the frequency sweep excitation pulse of adjacent cuts in the slab. BRIEF DESCRIPTION OF THE DRAWINGS The novel features of the various aspects are set out in detail in the appended claims. However, the aspects described, both in terms of organization and methods of operation, can be better understood by reference to the following description, taken in conjunction with the accompanying drawings. Figure 1 is a perspective view of an MRI scanner, in accordance with several aspects of the present description. Figure 2 is an exploded perspective view of the MRI scanner of Figure 1, in which the permanent magnet assembly and gradient coil assemblies within the housing are exposed, in accordance with various aspects of the present description. Figure 3 is an elevation view of the MRI scanner in Figure 1, in accordance with several aspects of the present description. Figure 4 is an elevation view of the MRI scanner in Figure 1, in accordance with several aspects of the present description. Figure 5 is a perspective view of the permanent magnet assembly of the MRI scanner in Figure 1, in accordance with various aspects of the present description. Figure 6 is an elevation view of the gradient coil assembly and permanent magnet assembly of the MRI system shown in Figure 1, in accordance with various aspects of the present description. Figure 7 illustrates the illustrative positioning of a patient for imaging using a single-sided MRI scanner for certain surgical procedures and interventions, in accordance with various aspects of the present description. Figure 8 is a control scheme for a single-sided MRI system, in accordance with several aspects of the present description. Figure 9 is a schematic of the magnetic gradient along the Z axis, in accordance with several aspects of the present description. Figure 10 is a graphical representation of the gradient X along the X-axis, in accordance with several aspects of the present description. Figure 11 is a collection of MRI images comparing image slices that represent the changing field of vision along the Z-axis and image slices that do not represent the changing field of vision along the Z-axis, according to various aspects of the present description. Figure 12 is a graphical representation of the location of the echoes in time as one moves through the phase table, according to various aspects of the present description. Figure 13 is a diagram of a pulse sequence that compensates for the variable field of view in cuts along the Z axis, according to several aspects of the present description. Figure 14 is a representative graph of a sweep frequency pulse, according to several aspects of the present description. Figure 15 is a flow diagram of steps in a sequence of impulses that represents the changing field of view in the cuts along the Z axis, according to various aspects of the present description. Figures 16A to 16F are a collection of MRI image slices, in accordance with various aspects of the present description. Figure 17 is a collection of MRI image slices, in accordance with various aspects of the present description. The accompanying drawings are not intended to be drawn to scale. The corresponding reference characters indicate the relevant parts in the various views. For clarity, not all components can be labeled in every drawing. The examples provided herein illustrate certain embodiments of the invention, and such examples should not be construed as limiting the scope of the invention in any way. DETAILED DESCRIPTION OF THE INVENTION The Applicant is also the owner of the International Patent Application entitled PULSE SEQUENCES AND FREQUENCY SWEEP PULSES FOR SINGLE-SIDED MAGNETIC RESONANCE IMAGING, filed on March 9, 2021, which claims priority to the United States Provisional Patent Application No. 62 / 987,286, entitled SYSTEMS AND METHODS FOR ADAPTING DRIVEN EQUILIBRIUM FOURIER TRANSFORM FOR SINGLE-SIDED MRI, filed on March 9, 2020, both of which are incorporated by reference in their respective entireties herein. The following international patent applications are incorporated herein by reference in their entirety: • International Application No. PCT / US2020 / 018352, entitled SYSTEMS AND METHODS FOR ULTRALOW FIELD RELAXATION DISPERSION, filed on February 14, 2020, now International Publication No. WO2020 / 168233; • International Application No. PCT / US2020 / 019530, entitled SYSTEMS AND METHODS FOR PERFORMING MAGNETIC RESONANCE IMAGING, filed on February 24, 2020, now International Publication No. WO2020 / 172673; • International Application No. PCT / US2020 / 019524, entitled PSEUDOBIRDCAGE COIL WITH VARIABLE TUNING AND APPLICATIONS THEREFOF, filed on February 24, 2020, now International Publication No. WO2020 / 172672; • International Application No. PCT / US2020 / 024776, entitled SINGLE-SIDED FAST MRI GRADIENT FIELD COILS AND APPLICATIONS THEREOF, filed on March 25, 2020, now International Publication No. WO2020 / 198395; • International Application No. PCT / US2020 / 024778, entitled SYSTEMS AND METHODS FOR VOLUMETRIC ACQUISITION IN A SINGLE-SIDED MRI SYSTEM, filed on March 25, 2020, now International Publication No. WO2020 / 198396; • International Application No. PCT / US2020 / 039667, entitled SYSTEMS AND METHODS FOR IMAGE RECONSTRUCTIONS IN MAGNETIC RESONANCE IMAGING, filed on June 25, 2020, now International Publication No. WO2020 / 264194; • International Application No. PCT / US2021 / 014628, entitled MRI-GUIDED ROBOTIC SYSTEMS AND METHODS FOR BIOPSY, filed on January 22, 2021; and • International Application No. PCT / US2021 / 018834, entitled RADIO FREQUENCY RECEPTION COIL NETWORKS FOR SINGLE-SIDED MAGNETIC RESONANCE IMAGING, filed on February 19, 2021. The United States Patent Application Publication No. 2018 / 0356480, entitled UNILATERAL MAGNETIC RESONANCE IMAGING SYSTEM WITH APERTURE FOR INTERVENTIONS AND METHODOLOGIES FOR OPERATING SAME, published on December 13, 2018, is incorporated into this description by reference in its entirety. Before explaining various aspects of an IRM system and methods in detail, it should be noted that the illustrative examples are not limited in their application or use to the construction details and arrangement of the parts illustrated in the accompanying drawings and description. The illustrative examples can be implemented or incorporated into other aspects, variations, and modifications, and can be practiced or carried out in various ways. Furthermore, unless otherwise indicated, the terms and expressions used herein have been chosen for the purpose of describing the illustrative examples for the reader's convenience and are not intended to limit them. It will also be appreciated that one or more of the aspects, aspect expressions, and / or examples described below may be combined with any one of the other aspects, aspect expressions, and / or examples. Depending on several factors, an MRI system is provided that may include a single imaging region that can be moved from the face of a magnet. Such offset and single-sided MRI systems are less restrictive compared to traditional MRI scanners. Furthermore, this form factor may have a built-in or inherent magnetic field gradient that creates a range of magnetic field values ​​over the region of interest. In other words, the inherent magnetic field may be inhomogeneous. The inhomogeneity of the magnetic field intensity in the region of interest for the single-sided MRI system can be greater than 200 parts per million (ppm). For example, the inhomogeneity of the magnetic field intensity in the region of interest for the single-sided MRI system may range from 200 ppm to 200,000 ppm.In several aspects of this description, the inhomogeneity in the region of interest can be greater than 1,000 ppm and can be greater than 10,000 ppm. In one example, the inhomogeneity in the region of interest can be 81,000 ppm. The inherent magnetic field gradient can be generated by a permanent magnet within the MRI scanner. The magnetic field strength in the region of interest for the single-sided MRI system can be less than 1 Tesla (T), for example. For instance, the magnetic field strength in the region of interest for the single-sided MRI system can be less than 0.5 T. In other cases, the magnetic field strength can be greater than 1 T and can be 1.5 T, for example. This system can operate at a lower magnetic field strength compared to typical MRI systems, allowing for a relaxation of the design constraints of the X-ray coil and / or the use of additional mechanisms, such as robotics, with the MRI scanner. Illustrative MRI-guided robotic systems are further described in International Application No.PCT / US2021 / 014628, entitled MRI-GUIDED ROBOTIC SYSTEMS AND METHODS FOR BIOPSY, filed on January 22, 2021, for example. Figures 1-6 illustrate an MRI scanner 100 and its components. As shown in Figures 1 and 2, the MRI scanner 100 includes a housing 120 having a front face or surface 125, which is concave and recessed. Alternatively, the face of the housing 120 may be flat. The front surface 125 can be oriented toward the object being imaged by the MRI scanner. As shown in Figures 1 and 2, the housing 120 includes a permanent magnet unit 130, a radio frequency (TX) transmitting coil 140, a gradient coil assembly 150, an electromagnet 160, and a radio frequency (RX) receiving coil 170. In other cases, the housing 120 may not include the electromagnet 160. In addition, in certain cases, the RF receiving coil 170 and the RF transmitting coil 140 may be incorporated into a series of combined Tx / Rx coils. With reference primarily to Figures 3-5, the permanent magnet assembly 130 includes a series of magnets. The series of magnets forming the permanent magnet assembly 130 are configured to cover the front surface 125, or patient-facing surface, of the MRI scanner 100 (see Figure 3) and are shown as horizontal bars in Figure 4. The permanent magnet assembly 130 includes a plurality of cylindrical permanent magnets in a parallel configuration. With reference primarily to Figure 5, the permanent magnet assembly 130 comprises parallel plates 132 held together by brackets 134. The system can be attached to the housing 120 of the MRI scanner 100 on a bracket 136. There may be a plurality of holes 138 in the parallel plates 132.The permanent magnet assembly 130 can include any suitable magnetic material, including but not limited to rare earth-based magnetic materials, such as, for example, neodymium-based magnetic materials. The permanent magnet assembly 130 defines an access opening or hole 135, which can provide patient access through the housing 120 from the opposite side. In other aspects of this description, the series of permanent magnets forming a permanent magnet assembly in the housing 120 may be holeless and define an uninterrupted or contiguous arrangement of permanent magnets without a defined hole through it. Still in other cases, the series of permanent magnets in the housing 120 may form more than one access / piercing opening through it. According to several aspects of the present description, the permanent magnet assembly 130 provides a magnetic field B0 in a region of interest 190 that lies along the Z-axis, as shown in Figure 1. The Z-axis is perpendicular to the permanent magnet assembly 130. In other words, the Z-axis extends from the center of the permanent magnet assembly 130 and defines a direction of the magnetic field B0 away from the face of the permanent magnet assembly 130. The Z-axis can define the direction B0 of the primary magnetic field. The primary magnetic field B0 can decrease along the Z-axis, i.e., by an inherent gradient, further from the face of the permanent magnet assembly 130 and in the direction indicated by the arrow in Figure 1. In one respect, the magnetic field inhomogeneity in the region of interest 190 for the permanent magnet assembly 130 can be approximately 81,000 ppm. In another respect, the magnetic field strength inhomogeneity in the region of interest 190 for the permanent magnet assembly 130 can range from 200 ppm to 200,000 ppm and can be greater than 1,000 ppm in certain cases, and greater than 10,000 ppm in several cases. In one aspect, the magnetic field strength of the permanent magnet assembly 130 may be less than 1 T. In another aspect, the magnetic field strength of the permanent magnet assembly 130 may be less than 0.5 T. In other cases, the magnetic field strength of the permanent magnet assembly 130 may be greater than 1 T and may be 1.5 T, for example. With reference primarily to Figure 1, the Y-axis extends upward and downward from the Z-axis, and the X-axis extends left and right from the Z-axis. The X-axis, Y-axis, and Z-axis are all orthogonal to each other, and the positive direction of each axis is indicated by the corresponding arrow in Figure 1. The RF transmission coils 140 are configured to transmit RF waveforms and associated electromagnetic fields. The RF pulses from the RF transmission coils 140 are configured to rotate the magnetization produced by the permanent magnet 130 by generating an effective magnetic field, denoted Bl, which is orthogonal to the direction of the permanent magnetic field (e.g., an orthogonal plane). With reference primarily to Figure 3, the gradient coil assembly 150 comprises two gradient coil assemblies 152 and 154. The gradient coil assemblies 152 and 154 are positioned on the front face or surface 125 of the intermediate permanent magnet assembly 130 between the permanent magnet assembly 130 and the region of interest 190. Each gradient coil assembly 152 and 154 includes a coil portion on opposite sides of the hole 135. With reference to the axes in Figure 1, the gradient coil assembly 154 can be the gradient coil assembly corresponding to the X-axis, for example, and the gradient coil assembly 152 can be the gradient coil assembly corresponding to the Y-axis, for example. The gradient coils 152 and 154 enable encoding along the X-axis and the Y-axis, as further described herein. According to several aspects, by using the MRI scanner 100 illustrated in Figures 1-6, a patient can be placed in any number of different positions depending on the type of anatomical scan. Figure 7 shows an example where the pelvis is scanned with the MRI scanner 100. To perform the scan, the patient can be placed on a surface in the lithotomy position. As illustrated in Figure 7, for pelvic scanning, the patient 210 can be positioned with their back resting on a table and the radiofrequency transmitting coils 310. The precession of the object generates an induced electrical current, or MR current, which is detected by the RF receiving coils 314. The RF receiving coils 314 can send the excitation data to an RF preamplifier 316. The RF preamplifier 316 can boost or amplify the excitation data signals and send them to the spectrometer 304.Spectrometer 304 can send excitation data to computer 302 for storage, analysis, and image construction. Computer 302 can combine multiple stored excitation data signals to create an image, for example. From the spectrometer 304, signals can also be transmitted to the radio frequency transmitting coils 310 via an RF power amplifier 306, and to the gradient coils 320 via a gradient power amplifier 318. The RF power amplifier 306 amplifies the signal and sends it to the RF transmitting coils 310. The gradient power amplifier 318 amplifies the signal from the gradient coil and sends it to the gradient coils 320. Systems and methods for effectively collecting nuclear magnetic resonance spectra and magnetic resonance images in inhomogeneous fields, such as with the 100 single-sided MRI scanner and the 300 system, for example, are described herein. Acquiring images with an open or single-sided MRI presents many challenges. Typically, two sets of gradient coils (see Figure 6) are placed on the face of the permanent magnet assembly in single-sided systems. As a result, the gradient amplitude decreases as one moves away from the face of the permanent magnet assembly. Therefore, for a given phase code signal, the field of view will change as one moves along the axis of the permanent magnetic field B0. In other words, the pulsed gradient coils in a single-sided scanner have a small component along the direction of the permanent gradient. Figure 9 is a schematic of the magnetic field gradient along the Z-axis for the MRI scanner. The permanent magnet has an inherent gradient along the Z-axis. The strength of the Z-gradient decreases as one moves away from the permanent magnet. The Z-gradient can be seen in the schematic bending as one moves away from the permanent magnet, causing the gradient intensity to decrease. The MRI scanner takes multiple slices to create a slab. Each slice is excited for imaging at a different frequency. Lower frequencies excite the tissue for slices farther from the permanent magnet, and higher frequencies excite the tissue in slices closer to the magnet. In the electrical plane, the axial or slab image is composed of several slices ranging from slice 0 to slice n. Each slice has a corresponding frequency from f0 to fn, where f0 is a frequency lower than fn. iviA / a / zuzz / ui 11 yo Due to the way the gradient changes along the Z-axis, each slice has a different field of view. This changing field of view makes the same object appear to shrink and grow along the Z-dimension in different slices because the magnitude of the gradient also varies along the Z-axis. This causes the images to appear bluer when converted to axial images because they are composed of several images of different sizes collapsing onto each other. Therefore, the slab slices must have the same field of view and the same scale to produce a high-quality axial image. Additionally, there are magnetic gradients along the Y-axis and X-axis created by the gradient coils, and these gradients have a similar shape and a similar effect along the X and Y axes. With reference to Figure 10, a 600 graph provides an example of how the X gradient changes as you move along the X-axis. The changes in the X gradient due to movement along the axis are shown as the different types of lines, which vary from a distance of 3 cm to 8.6 cm along the Z-axis. In other words, the slope of the gradient will change depending on the distance from the face of the magnet. The magnitude of the change can be significant. In other words, the size of the object in the image can change by as much as a factor of 2 over only 2.54 cm (1 inch) of movement along the Z-axis. Zero on the X-axis is at the center of the magnet along the Z-axis. As you move away from the Z-axis along the X-axis, the value of the gradient can change significantly. The further you move along the X-axis, the greater the magnitude of the gradient. To reiterate, the implications of gradient magnetic fields in single-sided MRI scanners are remarkable. For example, exciting a thick slice of an object (e.g., tissue) along the longitudinal axis of the permanent gradient (i.e., the Z-axis) will result in the scale, or image size, of the object changing as one moves along the Z-axis. A 3D image with any thickness along the Z-axis will be scaled down—that is, appear to shrink—to lower-frequency slices, which are slices positioned farther from the permanent magnet. This results in significant image blurring when adjacent slices are combined, as features of different sizes overlap. As a result of the changing gradients as you move away from the magnet, the field of view will change as you move away from the magnet's face. Combining slices with different fields of view on a single slab causes features to become blurred. Figure 11 shows MRI image slices, where one set represents the changing field of view along the Z-axis, and not a set. In other words, Diagram 700 shows how the scale of a scanned object can change if the changing field of view along the Z-axis is not taken into account. The slices in column A (left) show the structure changing size as you move along the Z-axis. Column B (right) shows the structure remaining close to the same size because the changing field of view has been accounted for. The size of the object in column A increases as one moves away from the permanent magnet along the Z-axis due to the Z-gradient. Combining these slices into an axial image or block results in a blurred image, as the size of the object in adjacent slices has changed due to the change in the field of view. In other words, objects will appear to shrink and grow along the Z-dimension because the magnitude of the gradient also varies along z. This makes the images appear bluer when converted into axial images or slabs because they are composed of several images of different sizes that collapse together. By taking into account the changing field of view, the object remains close to the image, and a much clearer image is obtained when combined into a slab. An additional implication of the permanent gradient magnetic field in single-sided MRI systems, beyond the variable field of view, is the changing location of the spin echo during image encoding with a surface gradient coil. In a single-sided MRI system, image encoding is performed using phase encoding; frequency encoding is performed only with the permanent gradient. The signals collected with a single-sided MRI system are variations of a spin echo, with the acquisition window of the MRI scanner array positioning the echo in the center. In order to form an echo, the phase that accumulates after excitation must be refocused at the moment acquisition begins. Referring now to Figure 12, the location of the echoes also changes as one moves through the phase table, because each X or Y gradient pulse will also add some phase along Z, which must then be refocused with the permanent gradient. As the image resolution increases, the echoes will begin to move closer to the edge of the acquisition window. Graphic 800 shows how the spin echo moves in time relative to the number of phase codes. The black line 810 shows the center of the acquisition window. If time and phase are not accounted for correctly, then the spin echo could be outside the acquisition window and overlooked, effectively truncating the image space and quality. When no pulsed gradient is applied, the spin echo occurs after the refocus pulse, with the time after which it occurs determined by the duration of the excitation pulse and the delay between the excitation and refocus pulses. If a phase code is applied during this period, the phase it imparts to the system must not be refocused. The X and Y components of a phase encode performed with a surface gradient coil will not be refocused during a spin echo sequence, ensuring that the signal is spatially encoded. However, the phase code will also impart the Z phase to the signal. This Z phase lies along the same axis as the permanent gradient, meaning its presence will change when the echo forms. If the phase along the Z-axis must be refocused before the echo forms, then adding the Z-phase with a pulsed gradient will change when the echo forms. For example, if a gradient is applied after excitation, the phase that accumulates between the excitation pulse and the refocusing pulse will be equal to the sum of the phase accumulated due to the permanent gradient and the phase accumulated due to the pulsed gradient. If the pulsed gradient has the same sign as the permanent gradient, the two will add together. Therefore, after the refocusing pulse, it will take longer for the echo to occur because both the phase of the permanent gradient and the phase of the pulsed gradient will be refocused by the permanent gradient. This will cause the echo to appear later than it would otherwise. The stronger the pulsed gradient, the later the echo will appear.Changing the sign of the pulsed gradient can also have the opposite effect, causing the echo to appear sooner than expected. This can have catastrophic effects on the imaging sequence. In an imaging sequence, the acquisition period is defined as a fixed time interval. The duration of the acquisition period cannot be arbitrarily changed without altering the pulse sequence in many other ways. For example, most single-sided scanners work by collecting a train of spin echoes, with the time between refocusing pulses kept as short as possible. This means that the acquisition period between refocusing pulses is also kept as short as possible. Therefore, if the echo location changes as one progresses through the imaging sequence, the echo may occur before or after the acquisition period begins. This means that the signal for that phase encoding will be lost. As a result of the Z-phase added to the signal by the pulsed X and Y gradients, there is effectively a maximum resolution that can be achieved without increasing the echo separation of the pulse sequence. Echoes produced at the edges of k-space, when the pulsed gradients are strong, can be lost, resulting in k-space where the signal amplitude drops off sooner than in any other way. k-space is effectively truncated, which generally leads to the need for a wider acquisition, requiring a sacrifice of signal-to-noise ratio (SNR) to obtain a longer echo time. In summary, using a surface gradient coil with a single-sided MRI scanner—a necessary feature for the scanner to be single-sided—results in a shifting field of view along the Z-axis, drift echoes, and ultimately, truncation of k-space. This effectively limits the image quality of a single-sided MRI scanner. According to several aspects of this description, it is possible to compensate for added phase by applying a phase code during a frequency sweep or chirp excitation pulse. A frequency sweep pulse can affect turns at different frequencies at different times during a pulse. This means that it is also possible to impart different amounts of phase at different frequencies by applying a phase code during an excitation pulse. Turns excited at the beginning of the pulse can accumulate more phase than turns excited at the end of the pulse, which may accumulate little phase. Depending on several factors, if the turns farthest from the permanent magnet are excited first, and if a phase code is applied during the frequency sweep excitation pulse, then those farther turns can accumulate more phase than the turns closest to the permanent magnet, which can be excited last. This can reverse the usual way in which the turns accumulate phase in a surface gradient coil, allowing the normal variation in gradient strength along the Z-axis to be counteracted. By precisely adjusting the amount of phase accumulated during the frequency sweep excitation and during subsequent phase coding, it is possible to apply an even amount of phase to the XY plane along the Z-axis of the permanent magnet. Figure 13 shows a 900 pulse sequence configured to compensate for the variable field of view in slices along the Z-axis produced by surface gradient coils (see, for example, gradient coils 152, 154 in Figure 6). This compensation is achieved with phase coding applied during a frequency sweep excitation pulse. In several cases, the frequency sweep pulses described herein are chirps or chirp pulses that have a linear frequency sweep. A chirp excitation pulse can define a linear frequency sweep from low to high. Other monotonic low-to-high frequency increases are also contemplated.Low frequencies excite tissue farther from the permanent magnet assembly (see, for example, permanent magnet assembly 130 in Figure 2), and high frequencies excite tissue closer to the permanent magnet assembly. Therefore, at the end of the pulse, the slices farther from the magnet will have been phase-encoded for a longer time, compensating for the weaker gradient. The first pulse 902 in the pulse sequence is a sweep excitation pulse of frequency 902, with the chirping frequency sweep direction set from low to high. The gradients in the X and Y directions begin to phase-shift at 918 and 922, respectively, and are refocused by the second pulse 904 in the pulse sequence. The gradient in Z is constant throughout the pulse sequence. The second pulse 904 is a refocusing pulse that refocuses the X and Y gradients.After the second pulse 904, a spectral echo 906 is produced in which the X and Y gradients are phase-shifted 920 and 924, respectively. After the spectral echo 906, the signal is read with a chirping echo train 908. The chirping echo train 908 comprises a third pulse 910, a rotating echo 912, a fourth pulse 914, and a spectral echo 916. In one respect, the third pulse 910 may be a second refocusing pulse and the fourth pulse 914 may be a second excitation pulse. In this implementation, the changing field of view is overcompensated during the excitation pulse and then balanced by phase encoding. The amount of phase accumulated during the frequency sweep must be precisely tuned to apply a uniform amount of phase to the XY plane of the slices to be imaged. In other words, the amount of phase in each slice needs to be precisely tuned to represent the changing field of view. Similarly, the object scale in each slice must be adjusted so that all slices have the same object at the same scale. For example, tuning can be done by adjusting the gradient pulse power applied during the frequency sweep pulse while acquiring a 2D image along the XZ or YZ axes. The gradient power can be increased until the object size no longer changes along the Z axis.The cuts can then be combined into a high-quality slab image without any blurring resulting from the combination. Figure 14 shows a representative 1000-degree graph of a sweep frequency pulse, or chirp pulse, where the sweep direction is set from low to high. A chirp excitation pulse, with the sweep direction set from low to high, is an example of a sweep frequency excitation pulse. The frequency of a chirp pulse with the sweep direction set from low to high starts at a low frequency, and the frequency increases over time during the pulse's duration. The pulse can start at the lowest desired frequency and end once the maximum desired frequency is reached. The pulse frequency on the 1000-degree graph can be a negative-to-positive frequency offset relative to the baseband frequency. In other words, the frequency goes from negative to positive plus the baseband frequency.For example, for a frequency sweep of + / -100 KHz, the sweep is from the baseband frequency less than 100 KHz to the baseband frequency plus 100 KHz. The frequency of a chirp pulse can vary from a desired minimum (lowest) frequency to a desired maximum (highest) frequency. The pulse sweep speed is the difference between the highest and lowest pulse frequencies divided by the time it takes to travel between the highest and lowest frequencies. In one respect, the frequency range covered by the sweep frequency pulses used in the 900 sweep frequency pulse sequence can be from -20 kHz to 20 kHz, that is, a 40 kHz range, with a center frequency that varies from slab to slab. For example, a slab could be centered at 2.62 MHz, 2.75 MHz, 2.65 MHz, 2.72 MHz, 2.79 MHz, 2.69 MHz, and so on. For a slab centered at 2.62 MHz, the chirping pulse would sweep from 2.60 MHz to 2.64 MHz, i.e., a range of 40 KHz.In other aspects of this description, bandwidths as low as 10 kHz to as high as 200 kHz can be used in the frequency sweep pulse. Furthermore, the sweep interval can be less than 40 kHz in several cases. With reference again to Figure 9, fo may correspond to the lowest frequency of the chirping pulse and fn may correspond to the highest frequency of the chirping pulse. The chirping pulse excites the tissue farthest from the permanent magnet assembly first, such as the tissue at the slice location, and excites the tissue closer to the permanent magnet assembly later, such as the tissue at the slice location. In other words, adjacent slices comprise a proximal slice and a distal slice, where the proximal slice is positioned closer to the magnetic imaging apparatus than the distal slice, and a target in the distal slice is excited before a target in the proximal slice. The frequency range of the chirping pulse may correspond to the slices of the slab from which images are acquired. Referring again to Figure 13, the first pulse 902 is a chirping excitation pulse with the sweep direction set from low to high. This pulse excites the tissue in slices farther from the permanent magnet assembly before exciting the tissue in slices closer to the permanent magnet assembly. Through phase encoding during chiral excitation, different amounts of phase accumulate at different frequencies. Specifically, slices farther from the permanent magnet assembly accumulate more phase than slices closer to the permanent magnet assembly. In other words, the target in slices that are more distal to the permanent magnet assembly accumulates more phase than the target in slices that are more proximal to the permanent magnet assembly.Phase encoding during the frequency sweep excitation pulse, along with adjustment of the accumulated phase in each slice, can represent the phases in each slice and prevent the echo from straying outside the acquisition window (Figure 12). After considering the changing field of view in slices along the Z-axis, the slices can be combined into a slab to produce a high-quality axial image, where the object scale in each slice is the same size. Figure 15 is a flowchart 1100 for the steps in a pulse sequence to represent the changing field of view in slices along the Z-axis. In 1110, the process begins with the generation of an inherent gradient magnetic field extending from one side of a magnetic imaging device relative to the Z-axis (Figure 1) into the field of view. Next, in 1120, a frequency sweep excitation pulse is transmitted, comprising a low-to-high frequency sweep. This pulse excites the tissue in locations / slices farther from the MRI scanner on one side first, and the tissue in locations closer to the MRI scanner last. In 1130, phase encoding begins during the frequency sweep excitation pulse in 1120. Phase encoding can be performed during the frequency sweep excitation pulse to accumulate different amounts of phase at different frequencies of the frequency sweep.The slices are frequency-related, and frequencies farther from the magnetic imaging device accumulate more phase than slices closer to the device. Finally, at 1140 Hz, the amount of phase accumulated during the frequency sweep excitation pulse is adjusted to apply a uniform amount of phase to the XY plane along the magnet's Z-axis. In other words, the amount of phase accumulated in the slices during the frequency sweep is adjusted so that the changing field of view can be tuned for each slice. For example, tuning can be performed by adjusting the gradient pulse power applied during the chirping pulse while acquiring a 2D image along the XY or YZ planes. The gradient power can be increased until the object size no longer changes along the Z-axis. After the tuning stage, the signal is read using a chirping echo train.For example, the purpose of accounting for the changing field of view is to ensure that the object in each slice has the same scale. Without accounting for changes in the field of view, the object in adjacent slices would appear larger or smaller due to the gradient affecting the field of view. Combining slices with different fields of view results in a blurry axial image or a slab. Representing the change in field of view along the Z-axis allows the slices to be combined into a high-quality axial image or slab. By encoding images in this way, several problems with single-sided MRI systems can be resolved, allowing for their wider application. Encoding in this manner can prevent spin echoes from being deflected, thus keeping them from straying from the acquisition window. This can further prevent the k-space from being truncated, thereby enabling the single-sided MRI system to collect higher-resolution images. The field of view can also be prevented from shifting along the Z-axis, making the combination of image slices along the Z-axis more efficient, resulting in a higher signal-to-noise ratio (SNR) and shorter scan times. Figures 16A to 16F show a collection of 1200 image slices. Figures 16A, 16B, and 16C in the top row (1210) show an axial slice of a 3D image collected with X and Y gradients that also vary along the Z axis. When the gradients vary significantly, as shown in Figures 16A and 16B in the top row (1210), the axial slice appears blurry. When the gradient variation is reduced, as shown in Figure 16C in the top row (1210), the image appears sharper. Images with a changing field of view limit the maximum slice thickness that can be used without drastically reducing image quality, since combining slices with different fields of view results in a blurred axial image. The bottom row 1220 shows three coronal slices taken from the same 3D images as the top row 1210. The phantom clearly changes size along one axis for figures 16D and 16E.The change in size is due to the variable field of view. Figure 16F shows the object when the variable field of view is accounted for through the process described in Figure 15. I Similarly, Figure 17 shows a collection of 1300 image slices whose field of view was represented by the process described in Figure 15. Images acquired using the flowchart process 1100 result in a consistent field of view across different slices. This allows slices to be combined without blurring the image. Images acquired using the flowchart process 1100 also align echoes in time, preventing them from drifting outside the acquisition window, thus increasing resolution. The above processes and techniques can also be used with other single-sided scanners and / or inhomogeneous magnetic fields, to allow faster data and / or image acquisition. EXAMPLES Several aspects of the topic described in this description are illustrated in the following numbered examples. Example 1 - A method for imaging a slab having at least two cuts with a single-sided magnetic imaging apparatus, wherein an inherent gradient magnetic field extends from the magnetic imaging apparatus into a field of view, the method comprising: transmitting a frequency sweep excitation pulse comprising a low-to-high frequency sweep; phase encoding during the frequency sweep excitation pulse; and adjusting the amount of phase accumulated during the frequency sweep excitation pulse of adjacent cuts in the slab. Example 2 - The method of Example 1, wherein the adjacent slices comprise a proximal slice and a distal slice, wherein the proximal slice is positioned closer to the magnetic imaging apparatus than the distal slice, and wherein a target in the distal slice is excited before a target in the proximal slice. Example 3 - The method of Example 2, wherein the method is configured to compensate for the inherent gradient magnetic field so that the target in the distal slice accumulates the same phase as the target in the proximal slice. Example 4 - The method of any of Examples 1, 2 and 3, where a different amount of phase is applied at different frequencies in the frequency sweep. Example 5 - The method of any of Examples 1, 2, 3 and 4, wherein phase coding during the frequency sweep excitation pulse prevents an echo from straying out of an acquisition window. Example 6 - The method of any of Examples 1, 2, 3, 4, and 5, wherein the high-resolution images are collected with the single-sided magnetic imaging apparatus without k-space truncation. Example 7 - The method of any of Examples 1, 2, 3, 4, 5 and 6, where the magnetic field strength in the field of view is less than 1 Tesla. Example 8 - The method of any of Examples 1, 2, 3, 4, 5, 6 and 7, where the inhomogeneity of the magnetic field is between 200 ppm and 200,000 ppm. Example 9 - A magnetic imaging apparatus comprising: a permanent magnet; a set of gradient coils; an electromagnet; a radio frequency coil, wherein an inherent gradient magnetic field extends from the magnetic imaging apparatus relative to a first axis into the field of view, wherein the first axis is perpendicular to the permanent magnet; and a control circuit configured to image a slab having at least two slices, wherein the imaging comprises: transmitting a frequency sweep excitation pulse comprising a low-to-high frequency sweep; phase encoding during the frequency sweep excitation pulse; and adjusting the amount of phase accumulated during the frequency sweep excitation pulse of adjacent slices in the slab. Example 10 - The magnetic imaging apparatus of Example 9, wherein the adjacent slices comprise a proximal slice and a distal slice, wherein the proximal slice is positioned closer to the magnetic imaging apparatus than the distal slice, and wherein a target in the distal slice is excited before a target in the proximal slice. Example 11 - The magnetic imaging apparatus of Example 10, wherein a different amount of phase is applied at different frequencies. Example 12 - The magnetic imaging apparatus of Example 11, wherein the target in the distal slice accumulates the same phase as the target in the proximal slice. Example 13 - The magnetic imaging apparatus of any of Examples 9, 10, 11 and 12, wherein phase coding during the frequency sweep excitation pulse prevents an echo from straying out of an acquisition window. Example 14 - The magnetic imaging apparatus of any of Examples 9, 10, 11, 12, and 13, wherein high-resolution images are collected with the single-sided magnetic imaging apparatus without k-space truncation. Example 15 - The magnetic imaging apparatus of any of Examples 9, 10, 11, 12, 13 and 14 wherein the magnetic field strength in the field of view is less than 1 Tesla. Example 16 - The magnetic imaging apparatus of any of Examples 9, 10, 11, 12, 13, 14 and 15, wherein the inhomogeneity of the magnetic field is between 200 ppm and 200,000 ppm. Example 17 - The magnetic imaging apparatus of any of Examples 9, 10, 11, 12, 13, 14, 15 and 16, wherein the radiofrequency coil comprises a radiofrequency transmitting coil and a radiofrequency receiving coil. Although several forms have been illustrated and described, it is not the Applicant's intention to restrict or limit the scope of the appended claims to such detail. Numerous modifications, variations, changes, substitutions, combinations, and equivalents to these forms can be implemented and will be produced for those skilled in the art without departing from the scope of the present description. Furthermore, the structure of each element associated with the described forms may alternatively be described as a means of providing the function performed by the element. In addition, when materials are described for particular components, other materials may be used. Therefore, it should be understood that the foregoing description and the appended claims are intended to cover all modifications, combinations, and variations that fall within the scope of the described forms.The attached claims are intended to cover all such modifications, variations, changes, substitutions, alterations and equivalents. The preceding detailed description has established various forms of the devices and / or processes through the use of block diagrams, flowcharts, and / or examples. To the extent that such block diagrams, flowcharts, and / or examples contain one or more functions and / or operations, it shall be understood by those within the art that each function and / or operation within such block diagrams, flowcharts, and / or examples may be implemented, individually and / or collectively, by a wide range of hardware, software, microprograms, or virtually any combination thereof.Those skilled in the art will recognize that some aspects of the forms described in the present description, in whole or in part, can be equivalently implemented on integrated circuits, as one or more computer programs running on one or more computers (for example, as one or more programs running on one or more computer systems), as one or more programs running on one or more processors (for example, as one or more programs running on one or more microprocessors), as a microprogram, or as practically any combination thereof, and that the circuit design and / or the writing of code for the software and / or microprogram would be well within the skills of a person skilled in the art in light of this description.Furthermore, those skilled in the art will understand that the mechanisms of the subject matter described herein are capable of being distributed as one or more program products in a variety of forms, and that an illustrative form of the subject matter described herein applies regardless of the particular type of medium supporting the signal used to actually carry out the distribution. The instructions used to program the logic to perform the various aspects described can be stored in system memory, such as dynamic random-access memory (DRAM), cache memory, flash memory, or other storage. Additionally, the instructions can be distributed over a network or through other computer-readable media.Therefore, a machine-readable medium can include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computer), including, but not limited to, floppy disks, optical discs, compact discs, read-only memory (CD-ROM), and magneto-optical discs, read-only memory (ROM), random access memory (RAM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM); magnetic or optical cards, flash memory, or a tangible product, machine-readable storage used in the transmission of information over the Internet through electrical, optical, acoustic, or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.).Accordingly, non-transient computer-readable media includes any type of tangible machine-readable medium suitable for storing or transmitting electronic instructions or information in a form readable by a machine (e.g., a computer). As used in any aspect herein, the term control circuit may refer to, for example, hardwired circuits, programmable circuits (e.g., a computer processor including one or more individual instruction-processing cores, processing unit, processor, microcontroller, microcontroller unit, controller, digital signal processor (DSP), programmable logic device (PLD), programmable logic array (PLA), or field-programmable gate array (FPGA)), state machine circuits, a microprogram storing instructions executed by programmable circuits, and any combination thereof. The control circuit may, collectively or individually, be incorporated as a circuit forming part of a larger system, e.g., an integrated circuit (IC), an application-specific integrated circuit (ASIC), a system-on-a-chip (SoC), desktop computers, laptops,Tablet computers, servers, smartphones, etc. Accordingly, as used herein, control circuit includes, but is not limited to, electrical circuits having at least one discrete electrical circuit, electrical circuits having at least one integrated circuit, electrical circuits having at least one application-specific integrated circuit, electrical circuits forming a general-purpose computing device configured by a computer program (e.g., a general-purpose computer configured by a computer program that at least partially carries out the processes and / or devices described herein, or a microprocessor configured by a computer program that at least partially carries out the processes and / or devices described herein), electrical circuits forming a memory device (e.g., forms of random-access memory),and / or electrical circuits that form a communications device (for example, a modem, communications switch, or optical-electrical equipment). Those skilled in the art will recognize that the subject matter described herein can be implemented in analog or digital form, or any combination thereof. As used throughout this description, the term "logic" may refer to an application, software, microprogram, and / or circuitry configured to perform any of the operations mentioned above. Software may be incorporated as a software package, code, instructions, instruction sets, and / or data recorded on a non-transient, computer-readable storage medium. A microprogram may be incorporated as code, instructions, instruction sets, and / or data that are hard-coded (e.g., non-volatile) in memory devices. As used in any aspect herein, the terms component, system, module, and the like may refer to a computer-related entity, whether it be hardware, a combination of hardware and software, software, or running software. As used throughout this description, an algorithm refers to a self-consistent sequence of steps leading to a desired result, where a step refers to a manipulation of physical quantities and / or logical states that may, but do not necessarily, take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It is common to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, or the like. These and similar terms may be associated with the appropriate physical quantities and are simply convenient labels applied to these quantities and / or states. A network may include a packet-switched network. Communication devices can communicate with each other using a selected packet-switched network communication protocol. An example of a communication protocol might be an Ethernet communication protocol that enables communication using a Transmission Control Protocol / Internet Protocol (TCP / IP). The Ethernet protocol may comply with or be compatible with the Ethernet standard published by the Institute of Electrical and Electronics Engineers (IEEE) entitled IEEE 802.3 Standard, published in December 2008, and / or later versions of this standard. Alternatively or additionally, communication devices may be able to communicate with each other using an X.25 communication protocol.25 may comply with or be compatible with a standard promulgated by the Telecommunication Standardization Sector of the International Telecommunication Union (ITU-T). Alternatively or additionally, the communication devices may be able to communicate with each other using a Frame Relay communications protocol. The Frame Relay communications protocol may comply with or be compatible with a standard promulgated by the Consultative Committee on International Telegraphy and Telephone (CCITT) and / or the American National Standards Institute (ANSI). Alternatively or additionally, the transceivers may be able to communicate with each other using an Asynchronous Transfer Mode (ATM) communications protocol. The ATM communications protocol may comply with or be compatible with an ATM standard published by the ATM Forum entitled Automated ATM-MPLS NetWork Interworking 2.0 published in August 2001 and / or later versions of this standard. Of course, this description also covers connection-oriented network communication protocols that are different from and / or later than this standard. Unless otherwise specifically indicated as evident from the foregoing description, it is understood that throughout the foregoing disclosure, analysis by using terms such as processing, computation, calculate, determine, display, or similar, refers to the action and processes of a computer system, or a similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the registers and memories of the computer system into other data similarly represented as physical quantities within the registers or memories of the computer system or other similar information storage, transmission, or display devices. One or more components may be referred to in this description as configured to, configurable to, operable, adapted, capable of, conformable, etc. Those skilled in the art will recognize that configured to generally may encompass active state components and / or inactive state components and / or standby state components, unless the context otherwise requires. The terms proximal and distal are used in this description with reference to a clinician manipulating the handle, or housing, of a surgical instrument. The term proximal refers to the portion closest to the clinician and / or the robotic arm, and the term distal refers to the portion located farther from the clinician and / or the robotic arm. It will also be appreciated that, for convenience and clarity, spatial terms such as vertical, horizontal, above, and below with respect to the drawings may be used in this description. However, robotic surgical tools are used in many orientations and positions, and these terms are not intended to be limiting or absolute. Those skilled in the art will recognize that, in general, the terms used in the present description, and especially in the appended claims (e.g., the bodies of the appended claims), are generally understood as open terms (e.g., the term IVIA / a / ZUZZ / UI 1190 The phrase "includes" should be interpreted as "includes but is not limited to," "has" should be interpreted as "has at least," "includes" should be interpreted as "includes but is not limited to," etc.). It shall be further understood by those within the art that if a specific quantity of an introduced claim recitation is intended, such intention shall be explicitly stated in the claim, and in the absence of such a recitation, such intention is not present. For example, as an aid to understanding, the following appended claims may contain the use of the introductory phrases "at least one" and "one or more" to introduce claim recitations.However, the use of such phrases should not be interpreted as implying that the introduction of a claim quotation by the indefinite articles a or an limits any particular claim containing such an introduced claim quotation to claims containing only one such quotation, even when the same claim includes the introductory phrases such as a or an (e.g., a and / or an should typically be interpreted as at least one or one or more); the same applies to the use of definite articles used to introduce the quotations in the claim. Furthermore, even if a specific number of an introduced claim is explicitly recited, those skilled in the art will recognize that such recitation should typically be interpreted as meaning at least the number recited (e.g., the bare recitation of two recitations, without any other modifiers, typically means at least two recitations, or two or more recitations). Moreover, in those cases where a convention analogous to "at least one of A, B, and C, etc." is used, such a construction is generally intended in the sense that a person skilled in the art would understand the convention (e.g., a system having at least one of A, B, and C would include, but not be limited to, systems having A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, and C together, etc.).In general, such a construction is intended to mean that a person skilled in the art would understand the convention (for example, a system having at least one of A, B, or C would include, but not be limited to, systems having A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, and C together, etc.). It will further be understood by those within the art that a disjunctive word and / or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should typically be understood to include the possibilities of one of the terms, any one of the terms, or both terms, unless the context indicates otherwise. For example, the phrase A or B will typically be understood to include the possibilities of A or B or A and B. With regard to the appended claims, those skilled in the art will appreciate that the operations mentioned therein can generally be performed in any order. Furthermore, although several operational flowcharts are presented in a sequence(s), it should be understood that the various operations can be performed in orders other than those illustrated, or can be performed simultaneously. Examples of such alternative orders may include overlapping, interleaved, interrupted, reordered, incremental, preparatory, supplementary, simultaneous, reverse, or other variant orders, unless the context indicates otherwise. Moreover, terms such as "in response to," "related to," or other past-tense adjectives are generally not intended to exclude such variants, unless the context indicates otherwise. It is important to note that any reference to an aspect, an aspect, an example, an example, and the like means that a particular feature, structure, or characteristic described in relation to that aspect is included in at least one aspect. Therefore, the appearances of the phrases in an aspect, in an aspect, in an example, and in an example in various places throughout the description do not necessarily refer to the same aspect. Furthermore, particular features, structures, or characteristics can be combined in any appropriate way within one or more aspects. Any patent application, patent, non-patent publication, or other disclosure material mentioned in this description and / or listed in any Application Data Sheet is incorporated by reference into this description, to the extent that the incorporated materials are not inconsistent with this description. As such, and to the extent necessary, the description as explicitly set forth herein supersedes any conflicting material incorporated herein by reference. Any material, or portion thereof, that is said to be incorporated by reference into this description, but which conflicts with the definitions, statements, or other existing descriptive material set forth herein, shall be incorporated only to the extent that no conflict arises between that incorporated material and the existing descriptive material. In summary, numerous benefits resulting from the use of the concepts described herein have been outlined. The preceding description of one or more forms has been presented for illustrative and descriptive purposes. It is not intended to be exhaustive nor to limit the exact form described. Modifications or variations are possible in light of the foregoing teachings. The one or more forms were chosen and described to illustrate the principles and practical application, thereby enabling a person skilled in the art to use the various forms and with various modifications as deemed appropriate for the particular use. The claims presented herein are intended to define the general scope.

Claims

1. A method for imaging a slab having at least two cuts with a single-sided magnetic imaging apparatus, wherein an inherent gradient magnetic field extends from the magnetic imaging apparatus into a field of view, the method comprising: transmitting a frequency sweep excitation pulse comprising a low-to-high frequency sweep; phase encoding during the frequency sweep excitation pulse; and adjusting the amount of phase accumulated during the frequency sweep excitation pulse of adjacent cuts in the slab.

2. The method of claim 1, wherein the adjacent slices comprise a proximal slice and a distal slice, wherein the proximal slice is positioned closer to the magnetic imaging apparatus than the distal slice, and wherein a target in the distal slice is excited before a target in the proximal slice.

3. The method of claim 2, wherein the method is configured to compensate for the inherent gradient magnetic field so that the target in the distal slice accumulates the same phase as the target in the proximal slice.

4. The method of claim 1, wherein a different amount of phase is applied at different frequencies in the frequency sweep.

5. The method of claim 1, wherein phase coding during the frequency sweep excitation pulse prevents an echo from straying out of an acquisition window.

6. The method of claim 1, wherein the high-resolution images are collected with the single-sided magnetic imaging apparatus without truncation of the k-space.

7. The method of claim 1, wherein the magnetic field strength in the field of view is less than 1 Tesla.

8. The method of claim 1, wherein the inhomogeneity of the magnetic field is between 200 ppm and 200,000 ppm.

9. A magnetic imaging apparatus, comprising: a permanent magnet; a set of gradient coils; an electromagnet; a radio frequency coil, wherein an inherent gradient magnetic field extends from the magnetic imaging apparatus relative to a first axis into the field of view, the first axis being perpendicular to the permanent magnet; and a control circuit configured to image a slab having at least two cuts, wherein the imaging comprises: transmitting a frequency sweep excitation pulse comprising a low-to-high frequency sweep; phase encoding during the frequency sweep excitation pulse; and adjusting the amount of phase accumulated during the frequency sweep excitation pulse of adjacent cuts in the slab.

10. The magnetic imaging apparatus according to claim 9, wherein the adjacent slices comprise a proximal slice and a distal slice, wherein the proximal slice is positioned closer to the magnetic imaging apparatus than the distal slice, and wherein a target in the distal slice is excited before a target in the proximal slice.

11. The magnetic imaging apparatus according to claim 9, wherein a different amount of phase is applied at different frequencies.

12. The magnetic imaging apparatus according to claim 11, wherein the target in the distal slice accumulates the same phase as the target in the proximal slice.

13. The magnetic imaging apparatus according to claim 9, wherein phase encoding during the frequency sweep excitation pulse prevents an echo from straying out of an acquisition window.

14. The magnetic imaging apparatus according to claim 9, wherein the high-resolution images are collected with the single-sided magnetic imaging apparatus without k-space truncation.

15. The magnetic imaging apparatus according to claim 9, wherein the magnetic field strength in the field of view is less than 1 Tesla.

16. The magnetic imaging apparatus according to claim 9, wherein the inhomogeneity of the magnetic field is between 200 ppm and 200,000 ppm.

17. The magnetic imaging apparatus according to claim 9, wherein the radiofrequency coil comprises a radiofrequency transmitting coil and a radiofrequency receiving coil.

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