Rayleigh or Abbe? Origin and naming of the resolution formula of microlithography

Advanced biomedical engineering technologies are continuously changing the medical practices to improve medical care for patients. Needle insertion navigation during intravenous catheterization process via Near infrared (NIR) and camera-projector is one solution. However, the central point of the problem is the image captured by camera misaligns with the image projected back on the object of interest. This causes the projected image not to be overlaid perfectly in the real-world. In this paper, a camera-projector calibration method is presented. Polynomial algorithm was used to remove the barrel distortion in captured images. Scaling and translation transformations are used to correct the geometric distortions introduced in the image acquisition process. Discrepancies in the captured and projected images are assessed. The accuracy of the image and the projected image is 90.643%. This indicates the feasibility of the captured approach to eliminate discrepancies in the projection and navigation images.

Summary form only given. Magnetic Particle Imaging (MPI) commonly utilizes a Field Free Point (FFP) magnetic field gradient to localize magnetic nanoparticles [12]. With the benefits of two orders of magnitude reduced acquisition time or one order of magnitude signal-to-noise ratio (SNR) improvement, a gradient called a Field Free Line (FFL), which localizes particles to a line instead of a point, has been theoretically developed [3-6], and experimentally demonstrated [4,6]. In this work, we use a FFL with sample rotation and projection reconstruction to demonstrate experimental images with a 20 fold improvement in acquisition time compared to the first projection reconstruction (PR) MPI results [6]. To gain this 20 fold speed up, we implement a z direction focus field coil configuration instead of the previously utilized translation stage. Our imaging system included a 2.3 T/m permanent magnet FFL, a solenoidal drive coil, two focus field x and z direction electromagnet pairs with Helmholtz configurations, a solenoidal receive coil with a gradiometer configuration, and a motor driven rotary table (see Figure 1). The system drive coil was excited to create a 22.9 kHz drive field with a 1.3 cm z partial field of view (FOV). The x slow shift (focus) field operated with a 3.3 Hz triangle wave, which produced a 5 cm x FOV. A linear ramp z focus field traversed 6 cm in 3 s, once per projection image. The drive and z shift fields summed, producing a 7.3 cm z FOV. There were 20 x axis traversals (10 cycles) per projection image. With this sequence, we acquired 40 images at linearly spaced angles over 180 degrees. The image acquisition time was 2.1 min. We collected all the necessary projection data to produce a MPI tomographic 3D volume using the above parameters. Images were reconstructed using x-space reconstruction with filtered backprojection (FBP) [5-6]. The final imaging volume was limited by bore size and the z slow shift magnets to a 4.8 cm by 4.8 cm by 7.3 cm 3D volume. The 3D volume was exported in DICOM file format and subsequently imported to Osirix (Pixmeo, Switzerland) where maximum intensity projection (MIP) images were rendered. To test our imaging sytem, we have designed a phantom with a 3D distribution of magnetic nanoparticles (see Figure 1). Polyurethane tubing with inner diameter 1.6 mm (outer diameter 3.2) filled with 43 mM Fe Micromod Nanomag-D-spio was wrapped around a cylindrical piece of acrylic with a 3.4 cm outer diameter. Resulting MIP images illustrate the ability of the FFL imager to accurately resolve nanoparticle distributions in 3D. The MIP image can be rotated to any orientation, and two such views are shown in Figure 1. In previous work, an image with a similar FOV would have taken 39 min using a translation stage [6]. The two minute acquisiton time using electromagnetic z shift demonstrates an approximately 20 fold improvement in acquisition time.

Certain experimental questions in molecular imaging can be answered with projection imaging systems rather than tomographs. Accordingly, we have designed, assembled and are now testing a projection imaging system able to visualize the whole-body distribution of positron-emitting compounds in mouse-size animals. When completed, this positron projection imager (PPI) will plug into the MONICA portable dual gamma camera system to provide the user with a positron projection imaging capability and all of the data acquisition and analysis features available with MONICA for single photon projection imaging.

Near infrared (NIR) fluorescence imaging technique can provide precise and real-time information about tumor location during a cancer resection surgery. However, many intraoperative fluorescence imaging systems are based on wearable devices or stand-alone displays, leading to distraction of the surgeons and suboptimal outcome. To overcome these limitations, we design a projective fluorescence imaging system for surgical navigation. The system consists of a LED excitation light source, a monochromatic CCD camera, a host computer, a mini projector and a CMOS camera. A software program is written by C++ to call OpenCV functions for calibrating and correcting fluorescence images captured by the CCD camera upon excitation illumination of the LED source. The images are projected back to the surgical field by the mini projector. Imaging performance of this projective navigation system is characterized in a tumor simulating phantom. Image-guided surgical resection is demonstrated in an ex-vivo chicken tissue model. In all the experiments, the projected images by the projector match well with the locations of fluorescence emission. Our experimental results indicate that the proposed projective navigation system can be a powerful tool for pre-operative surgical planning, intraoperative surgical guidance, and postoperative assessment of surgical outcome. We have integrated the optoelectronic elements into a compact and miniaturized system in preparation for further clinical validation.

We developed and investigated a scanning sampled measurement (SSM) technique for scatter measurement and correction in cone beam breast CT imaging. A cylindrical polypropylene phantom (water equivalent) was mounted on a rotating table in a stationary gantry experimental cone beam breast CT imaging system. A 2-D array of lead beads, with the beads set apart about ~1 cm from each other and slightly tilted vertically, was placed between the object and x-ray source. A series of projection images were acquired as the phantom is rotated 1 degree per projection view and the lead beads array shifted vertically from one projection view to the next. A series of lead bars were also placed at the phantom edge to produce better scatter estimation across the phantom edges. Image signals in the lead beads/bars shadow were used to obtain sampled scatter measurements which were then interpolated to form an estimated scatter distribution across the projection images. The image data behind the lead bead/bar shadows were restored by interpolating image data from two adjacent projection views to form beam-block free projection images. The estimated scatter distribution was then subtracted from the corresponding restored projection image to obtain the scatter removed projection images.Our preliminary experiment has demonstrated that it is feasible to implement SSM technique for scatter estimation and correction for cone beam breast CT imaging. Scatter correction was successfully performed on all projection images using scatter distribution interpolated from SSM and restored projection image data. The resultant scatter corrected projection image data resulted in elevated CT number and largely reduced the cupping effects.

The use of X-ray computed microtomography (PCT) has increased in biomedical research and industrial applications. The inherited high quality of synchrotron radiation (SR) X-rays including high flux, collimation, and coherence, has been used recently to produce radiographic images with high spatial resolution and contrast. A simple and stable imaging system using an unmonochromatized SR source based on the principle of phase contrast X-ray imaging consists of a charge-coupled device (CCD) detector coupled with an optical lens system at the Pohang Light Source (PLS) 5C1 beamline. The spatial resolution of the imaging system was determined using the modulation transfer function (MTF), which was measured by step-by step calculations obtained from sharp edge images. Projection image data were obtained at 250 steps over 180 degrees of rotation with an acquisition time, depending on the imaged object materials, of 30 to 150 ms per projection image. The tomographic images were reconstructed using a simple filtered backprojection algorithm to reconstruct two-dimensional (2-D) images using projection data which may include characteristics of beam collimation and phase contrast. Although the use of a monochromatic X-ray beam has previously demonstrated to provide high resolution and enhanced contrast, our approach uses an unmonochromatized SR X-ray beam and shows similar image capability, without the needs for sophisticated X-ray optics, in an exposure time which is significantly less, by two orders of magnitude, than that for the monochromatic SR system. The current PLS 5C1 SR imaging system can produce projection images at a spatial resolution of 8.3 /spl mu/m over a field of view of about 5 mm at an exposure time of 30 ms per projection image for 1.5 /spl times/ optical magnification. This study presents the results of SR /spl mu/CT images of cancerous human breast tissue containing microcalcifications, mouse lumbar vertebra, and mouse coccygeal vertebra. The unmonochromatized SR /spl mu/CT imaging system provides an effective means of evaluating microstructures, not only in biomedical specimens but also in inorganic samples.

This paper presents the use of the gramian as an aid in defining the degrees of freedom (DOF) in projection imaging systems. The gramian is developed for a general continuous-discrete imaging model and is then applied to the specific case of projection imaging. The theoretical development shows the general structure of the gramian to be quite well behaved and indicates where redundant data are achieved and the best ways of increasing the degrees of freedom with a minimum sample increase. The experimental development shows these inherent limitations on gramians up to 32 768 by 32 768 and is experimentally confirmed by reconstructing a series of projection images.

Four-dimensional (4D) computed tomography (CT) can be used in radiation treatment planning to account for respiratory and organ motion. Current 4D CT techniques have limitations in either spatial or temporal resolution. In addition, 4D CT increases the radiation dose to the patients. The purpose of this study is to accurately predict images using 4D CT scan with the contour and projection imaging system.

The aim of this work was to propose system sharpness parameters for digital breast tomosynthesis (DBT) systems that include the influence of focus size and focus motion for use in quality assurance protocols. X-ray focus size was measured using a multiple pinhole test object, while detector presampling modulation transfer function (MTF) was measured from projection images of a 10 cm × 10 cm, 1 mm thick steel edge, for the Siemens Inspiration and Hologic Selenia Dimensions DBT systems. The height of the edge above the table was then varied from 1 to 78 mm. The MTF expected from theory for the projection images was calculated from the measured detector MTF, focus size MTF and focus motion MTF and was compared against measured curves. Two methods were used to measure the in-plane MTF in the DBT volume: a tungsten wire of diameter 25 µm and an Al edge 0.2 mm thick, both imaged with a 15 mm thick poly(methyl methacrylate) (PMMA) plate. The in-depth point spread function (PSF) was measured using an angled tungsten wire. The full 3D MTF was estimated with a 0.5 mm diameter aluminium bead held in a 45 mm thick PMMA phantom, with the bead 15 and 65 mm above the table. Inspiration DBT projection images are saved at native detector resolution (85 µm), while the Dimensions re-bins projections to 140 µm pixels (2 × 2 binning); both systems used 2 × 2 binning of projection data before reconstruction. The 50% point for the MTF (MTF0.50) measured in the DBT projection images for the tube-travel direction fell as a function of height above the table from 3.60 to 0.90 mm−1 for the Inspiration system and from 2.50 to 1.20 mm−1 for the Dimensions unit. The maximum deviation of measured MTF0.50 from the calculated value was 13%. MTF0.50 measured in-plane (tube-travel direction) fell as a function of height above the table from 1.66 to 0.97 mm−1 for the Inspiration system and from 2.21 to 1.31 mm−1 for the Dimensions system. The full-width half-maximum for the in-depth PSF was 3.0 and 5.9 mm for the Inspiration and Dimensions systems, respectively. There was no difference in the 3D MTF curves, sectioned in the tube-travel direction, for bead heights of 15 and 65 mm above the table. A 25 µm tungsten wire held within a 15 mm thick PMMA plate was found to be a suitable test object for measurement of in-plane MTF. Evaluation of MTF as a function of height above the table, both in the projection images and in the reconstructed planes, provides important information on the impact of focus size and focus motion on the DBT system's imaging performance.

Purpose: To develop a software to derive the intrinsic geometric parameters of a cone‐beam‐CT (CBCT) system from its projection images, for studying geometric variations in linac‐based CBCT. Methods: The projection images were taken with an IsoCal phantom, which has 16 steel ball‐bearings (BBs) with known geometry, using a Varian on‐board imaging system. The computational pipeline includes 4 components: 1) extraction of each BB position in the projection image with sub‐pixel precision using a progressive thresholding method followed by ellipse contour fitting; 2) computation of a 3‐by‐4 matrix which transforms each 3D‐phantom coordinates of BB into its corresponding 2D‐image coordinates; 3) derivation of a complete set of CBCT geometric parameters from the matrix in a phantom coordinate system; 4) distinguishing the effect of phantom setup by defining a new coordinate system intrinsic to the tractories of the moving gantry and minimizing the discrepancy between the transformed and nominal coordinates. The software was used to study the repeatability of CBCT geometric variations in a 2‐month period. Results: The source and imager showed repeatable 0.3–0.5 mm sine‐like variation patterns with random noise in both U and V directions during a 360° gantry rotation, consistent with our knowledge that the gantry‐head sagging may induce gantry‐angle dependent variation. The noise levels for the source‐U, source‐V, imager‐U, imager‐V were about 0.3, 0.1, 0.2 and 0.15 mm, respectively, suggesting the detection limits of the method. The source‐to‐imager axial direction variation for the source and imager showed ∼2 mm periodic noise patterns, possibly due to the fact that projection positions of BBs in the imager are not sensitive to the axial variation. Conclusion: We have developed a software module to derive geometric parameters of the CBCT system. The method has accuracies of 0.1–0.3 mm in the U− and V− directions, but is not as accurate in the axial direction. The study is supported by NIH Grant Number 5 R01 CA166948‐02.

Gamma tomography technique can provide cross-sectional visualization of an object that needed for investigating pipe scale in geothermal power plants. Parallel beam tomography has advantages such as a simple system so that it is easier to apply in the field, but the scanning duration is relatively long. This paper discusses the effect of projections number on the reconstructed images quality and proposes the number of most effective projections for pipe scale investigation. Geothermal pipe sample (OD = 275 mm, t = 10 mm) with scale has been scanned with a parallel beam gamma tomography system. The system consists of a gamma radiation source (137Cs, 80 mCi), scintillation detector, motorized gantry, control module, data acquisition, and computer. The images were reconstructed with six different projections: 128, 64, 32, 16, 8, and 4 projections and the scanning duration: 530.8, 258.9, 127.9, 63.5, 31.7, and 15.8 minutes, respectively. Visually, the 128 projections data produces the smoothest image, whereas 64 and 32 projections images look almost the same. The 16 and 8 projections images are still able to distinguish between the pipe wall, scale, and void even though the 8 projections image looks very blurry. Then, the 4 projections image is not able to visualize the shape of the object. The gaps between the average pipe wall and void gray-scale pixels value of 128, 64, 32, 16, 8 and 8 projections images are 175, 174, 167, 153, 106, and 45, respectively. Based on the scanning duration, visualization, and the gray contrast, then the number of most effective projections is 32.

Aiming at the scatter problem in Cone Beam Computed Tomography (CBCT) system, an improved scatter correction method based on Beam Attenuation Array (BAA) was proposed. In this method, BAA and filter plate are used as the scatter detection devices to scan 3 times and acquire 3 sets of projection images. The scatter values on the projection centers of the small ball array of BAA are calculated by using of the characteristic of a part of the ray attenuation caused by BAA, and then, the whole scatter intensity distribution covered the projection image, that is, the scatter image, is obtained by fitting these discrete scatter values on the projection centers of the small ball array. To complete the scatter correction, the final projection image is got by subtracting the corresponding scatter image from the original projection image. The experimental result shows that the improved method is practical and effective to correct the scatter in CBCT imaging systems, and the slice image quality is enhanced.

To accomplish accurate irradiation to a target, image information about the target is very useful in radiotherapy. A kilo-voltage cone-beam computed tomography (kV-CBCT) system mounted on a linear accelerator can verify the accuracy of the set-up position and the size and location of the target on each treatment day. However, the gantry of the CBCT system is heavy and so requires a long data acquisition time. As a result, image distortion occurs in the case of a moving target. In this study, we proposed a method to reconstruct a target less affected by any motion of the target, and evaluated the proposed method with a moving phantom. In our method, CBCT images of the moving phantom were acquired, and the target position in two directions was detected with a template matching method using these projection images. And we selected data acquisition angles of the projection images in which the target was located in predefined regions in the projection images, and made a sinogram with the projection image of selected angles. A less blurred image was reconstructed with a filtered-backprojection method from the sinogram. The results of experiments showed that the blurring caused by the movement of the phantom was reduced with our proposed method.

Purpose: Most tomographic imaging systems available today use a single x‐ray source and multiple projection images are obtained by rotating the x‐ray source around the object. Therefore the data acquisition rate is limited by the gantry rotation speed, which is approaching the physical limit. We proposed to develop a novel stationary scanning x‐ray imaging system based on carbon nanotube field emission x‐ray (FEX) technology. Instead of a single x‐ray source the proposed system is based on a multi‐pixel FEX source. The new scanner promises a dramatically faster data acquisition rate by reducing or totally eliminating the mechanical motion. Method and Materials: We have constructed a prototype stationary scanning x‐ray imaging system with an array of 9 individually addressable x‐ray source pixels, each of which can produce a different projection image of the object. The core of this novel x‐ray imaging technology is a gated carbon nanotube field emission cathode array. By programming the gate voltage of the cathode array, the multi‐pixel x‐ray source can generate an electronically triggered scanning x‐ray beam and produce multiple projection images from different viewing angles without mechanical motion. A Hamamatsu C7921 flat panel x‐ray sensor was used to collect all 9 projection images. Results: Tomosynthesis images of a mouse and a standard breast‐imaging phantom (Stereotactic Needle‐biopsy Tissue Equivalent Phantom, Nuclear Associates, NY) using the prototype stationary scanning x‐ray imaging system are acquired. Tomosynthesis reconstructions were applied to the breast phantom. The slice images reconstructed using an iterative reconstruction algorithm clearly show the internal structures of the breast‐imaging phantom at different depths. Conclusion: We have developed a stationary scanning x‐ray imaging system using a carbon nanotube based multi‐pixel FEX source. The mechanical motion free approach can lead to a faster and simplified tomographic imaging system.Conflict of Interest: Research partially supported by Xintek Inc.

Optical Computed Tomography (OCT) was developed as a 3D imaging system for measuring radiotherapy dose delivered to radiochromic dosimeters. The imaging system reconstructs dose distributions delivered to a radiochromic dosimeter such as PRESAGE that changes its colour when irradiated. Current optical CT systems in the market are based on CCD image sensor and have slow imaging speed. The study exploited recent advances in CMOS image sensor (CIS) technology to improve the imaging speed of the OCT system. The study characterised the components in the in-house developed CMOS-based Optical CT (CMOS-OCT) imaging system and investigates the feasibility of the system for imaging 3D radiochromic dosimeters. A green dye solution of various concentration was used to mimic colour variation in a PRESAGE radiochromic dosimeter from its response to radiation dose. The solution was filled in a plastic cylinder to study the linearity and uniformity of the system. A rotary stage was constructed using a stepper motor to hold and rotate the dosimeter between the CIS and a large area LED. The components of the imaging system were integrated and controlled using LabVIEW (National Instrument, Austin, TX). A graphical user interface (GUI) was also developed to acquire projection images of the dosimeter. The measured field of view (FOV) of the CIS is 125 mm by 90 mm that can cover the whole PRESAGE dosimeter. A projection image is captured at every 1.8 degree rotation of the dosimeter, at every second, that amounted to 200 projection images for a 360 degree rotation. Current limitation of the imaging speed is the rotation speed of the motor of 1.8 degree per second which can be improved with upgrading the stepper motor. At an imaging speed only limited by the maximum sensor frame rate of 28.5 fps, the scanning time will be reduced to 7 s compared to 200 s. The results show that the system is capable of capturing the projection images of a 3D translucent object with good linearity and uniformity. Further experiments will be carried out to optimise the development of the system to reconstruct dose distributions in 3D from a PRESAGE dosimeter.