2017 West Coast Educators Conference Orlando. Projection Geometry. 1. Review hierarchy of image qualities (amplified version):

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1 Spatial Resolution in the Digital Age: NOTES Quinn B. Carroll, MEd, RT 2017 West Coast Educators Conference Orlando Projection Geometry 1. Review hierarchy of image qualities (amplified version): a. Maximum Visibility: Optimum brightness, balanced gray scale, minimum noise i. Noise: Anything that obscures visibility of details b. Maximum Recognizability: Maximum spatial resolution, minimum magn. and distortion 2. Spatial Resolution: The most important component of the recognizability (geometrical integrity) of an image 3. Def: c/o ARRT: The sharpness of structural edges recorded in the image Def. Sharpness: The abruptness with which the edges of an image detail stop Implies moving through space, hence spatial resolution i.e., How quickly the edge of a detail transitions from a light (foreground) density to a dark (background) density; Quick transition = sharp image, gradual transition = unsharp image 4. Components of an Image Detail: Shadow (image) projected from a hypothetical point source of light perfectly sharp edges Projected from an area source of light (sun) partial shadows develop at edges from being projected at several different angles from various points of origin for the light Like the sun, the focal spot on an x ray tube anode is an area source of radiation 5. Umbra = pure or complete shadow (NOT sharp part of image as in some references) Penumbra = partial shadow at edges which gradually fades into the background Diagram: What varies are those rays which are subject to absorption by the object Within this measurable width, there is a transition from total penetration to the total absorption the object is capable of =Definition for geometrical penumbra 6. Umbra characterized by its homogeneity Penumbra is transitional in its density It is what is happening to the density or brightness which defines these two regions 7. Some publications have recently defined the umbra as the sharp portion of an image detail

2 This is false: Both sharpness and unsharpness refer to the width of the penumbra at the edge Physicists refer to the penumbra as the edge spread It can be measured and quantified 8. Unsharpness = Extent of penumbra; Sharpness = lack of penumbra 9. Wide penumbra = unsharp image Narrow penumbra = sharp image 10. It is possible to project two images such that their umbras are precisely the same size, yet their penumbras are different. Therefore, sharpness is unrelated to the umbra. 11. When penumbra spreads, it grows not only outward, but also inward, invading the umbra a. When a detail is sufficiently smaller than the FS, umbra may disappear misdiagnosis 12. Penumbra = scientific term for unsharpness or blur of image edges; It s width can be diagrammed, predicted, and measured directly Sharpness = Can be measured only indirectly as the opposite of measured unsharpness, then expressed as a relative number 13. Unsharpness: Controlled ONLY by SOD, OID and FS When FS size is known, we can calculate the exact spread of penumbra, and plot it using penumbra diagrams, (Simply extend a projected line from each end of the focal spot through each edge of the object to the IR.) 14. Penumbra (Unsharpness) follows the laws of similar triangles, formed by the SOD and the OID, (not the SID). [Not to be confused with diagrams for magnification: Apices of triangles are at edge of object, not at FS.] By inverting and flipping the SOD triangle, we see it is similar to OID triangle :: Ratios of base to height must be equal: _Base _ = FS = Penumbra Height SOD OID Relative Sharpness Cross multiplying, we find the formula for geometrical Unsharpness OR Penumbra = _FS X OID_ SOD 15. By inverting formula for unsharpness, we can derive a formula for relative sharpness: Relative sharpness = SOD/OID (Focal spot size is left out because there is no unit for sharpness) a. Useful in comparing techniques Variables Affecting Spatial Resolution 16. Scatter radiation can reduce the contrast at the edges of an image detail, thus reducing their visibility, but is unrelated to the formation of penumbra at the edges of the image a. Scatter radiation is NOT related to spatial resolution 17. Scatter cannot affect spatial resolution because it is not part of the projection geometry of penumbra formation a. Example: Penumbra Diagram showing penumbra measuring mm, unchanged by the of presence of a nearby scattering object (B)

3 18. The effects of scatter and blur are often confused, but they are separate in their origin, nature and effects: Scatter Blur Completely random Geometrically predictable Affects image visibility Affects image recognizabilityi Affects general area Affects only detail edges Emanates from patient Emanates from x ray tube (focal spot) 19. Scatter affects all 3 visibility functions in the latent image reaching the IR: (exposure, contrast, and noise), but NONE of the geometrical functions: a. For this reason, we can encourage the use of high kvp techniques; Benefits: i. Sufficient penetration to produce subject contrast ii. Reduced patient dose iii. Lengthened gray scale = more information 20. Conventional means of maximizing spatial resolution: Small FS, Max SID, Min OID, Min motion 21. Motion Penumbra: Movement of the x ray tube, object, or recording surface spreads penumbra laterally, expanding its width 22. Spatial resolution is destroyed by 1) Geometrical (projection) penumbra, 2) Motion penumbra, 3) Absorption penumbra (see below) Analyzing Resolution in the Latent Image 23. Exposure trace diagrams help visualize these effects: Thickness of trace = exposure For a particular detail: a. Depth of trace = contrast of detail b. Width of slope at detail edges = penumbra: The steeper the slope, the sharper the edge 24. Geometrical penumbra: Defined as partial absorption that the object is capable of Assumes uniform object thickness However, the real shapes of most objects vary in thickness, also causing a partial absorption of x rays This is called absorption penumbra

4 25. Absorption penumbra: When an object s thickness tapers at its edges, the visible effects of partial absorption can be indistinguishable from geometrical penumbra a. Absorption penumbra caused by the change in projected thickness of the object toward its edges b. Sharpest object shape = trapezoid; square some AP; spherical worst AP 26. Total penumbra = Absorption penumbra forms inner portion, Geometrical penumbra forms outer portion; These two combine to form total penumbra (along with any motion pen) 27. Resolution at the Microscopic Level: Resolution: The ability to distinguish two adjacent details as being separate and distinct Requires both high visibility and optimum recognizability Overall Resolution Contrast Resolution (Vertical dimension on trace diagram) Spatial Resolution (Horizontal dimension on trace diagram) LINE SPREAD FUNCTION 28. When two blurry details are close together, their penumbras can overlap, making it more difficult to distinguish them as separate objects. Poor contrast produces the same result. 29. Overall resolution can be lost by either: a. Blurred edges resulting in poor sharpness even though contrast is high, or b. Poor contrast even though sharpness is high 30. Physicists: Visibility = Contrast Resolution

5 Recognizability = Spatial Resolution 31. Resolution at the Microscopic Level Scientific principles apply only on certain scales, from the very small to the very large. At the smallest scales of an image, where details are so fine that they approach the resolving limits of the human eye, the distinctions between sharpness and contrast become blurred, (to the point where the only relevant question is whether each detail was resolved. I.e., What meaning can sharpness have when the distance scales are smaller than the human eye can perceive? At these very smallest levels, the only question becomes Can you see the little dot? (separate from the background or other dots), not Can you recognize the little dot as a dot? 32. Resolution: Impact of Digital Technology Thus, the advance achieved by digital imaging over film/screen imaging consisted in a trade off where spatial resolution was roughly cut in half, but contrast resolution increased by an overwhelming 10 fold We could say that while the recognizability of details was halved, their visibility was multiplied by 10 The result is that, at these smallest (microscopic) levels, the overall resolution of digital images was enhance by 5 times over that of film/screen technology. These geometrical factors in the original projection control the resolution of the latent image reaching the IR, however, in the digital age, we must add to these: a. The effects of digital processing b. Display monitor resolution and settings Spatial Resolution in The Digital Image Tendency has been to talk only in terms of pixels, effectively limiting the discussion to CR We need to equally address aspects of the solid state image receptor (DR detector) and the display monitor (dels and dots ) 33. Spatial frequency: A measure of spatial resolution or image sharpness, with units of Line Pairs per millimeter (LP/mm) Ex: A row of 10 pixels extending across one millimeter can resolve 5 LP/mm 34. Slow speed film/screen systems could once resolve LP/mm a. Digital systems resolve 4 8 LP/mm, about ½ i. Digital images could only achieve the resolution of analog images by reducing pixel size to that of a single silver bromide crystal (several molecules) 35. The poorer spatial resolution of digital systems is offset by vast improvements in contrast resolution 36. General principle: For a given physical area, the greater the matrix size, the smaller the pixels, and the greater the spatial resolution a. e.g., We already intuitively talk ab out the resolution of display monitors and cameras in terms of the total number of pixels in their entire active matrix array ( 3 megapixels, 5 megapixels, etc.) b. Here, we ll use dots to refer to the hardware pixels of a display monitor

6 i. Solid state Image Receptor (DR): Dels ii. Image being processed or displayed: Pixels iii. Display Monitor: Dots 37. For all digital systems, the maximum spatial resolution is equal to the Nyquist frequency, the sampling frequency expressed in LP/mm: a. For CR, the sampling frequency is the number of pixels scanned per mm by the laser beam in the CR reader b. For DR, the sampling frequency is the number of dels (hardware detector elements) per mm across the DR detector plate 38. Pixel pitch or del pitch is the distance between the centers of two adjacent pixels, dels or dots 39. Pixel/del/dot pitch is generally equal to pixel/del/dot width (Technically, for DR detectors, the del pitch includes any spaces between dels, but this is a minor point here) 40. The smaller the dot pitch, the less granularity (graininess) in the image, the sharper the image, the higher the spatial resolution 41. Restating the General Principle: For a given physical area, the greater the matrix size: a. The smaller the pixels, dots, or dels, and the greater the spatial resolution b. The lesser the pixel, dot, or del pitch, and the greater the spatial resolution 42. Since two pixels are required to record a line pair from a resolution template: Spatial frequency is inversely proportional to a doubling of the pixel size SF = 1/2p where p is the pixel, del, or dot size OR pitch 43. General principle: For a given physical area, the greater the matrix size, the greater the spatial resolution a. However, different areas or fields of view result from selecting different sizes of IRs or different collimated fields, or by different levels of magnification on a display monitor b. There are different types of matrices: 1. Hardware matrix array of dels for DR detector: Fixed del size 2. Hardware matrix array of pixels in a display monitor: Fixed pixel size 3. Light image matrix created by CR reader sampling of the PSP plate: Pixel size may be variable 4. Displayed image matrix: a. For some modalities, may be selected by the operator b. Is changed when zoom (magnification) is applied at the monitor 44. Size of Pixel, Del or Dot Vs. Resolution: Ultimately, it is the size of the pixel, del or dot that determines spatial resolution (sharpness) in the image Any effect that field of view or matrix size have on SR must be due to their effect on pixel, del or dot size If it doesn t change pixel size, it doesn t affect resolution! 45. Field of view Vs. Resolution: a. Inherent resolution for hardware arrays is unaffected by field of view: i. Collimation for a DR detector ii. Zoom feature for a display monitor b. Because the del or hardware pixel (dot) size is unchanged

7 46. For DR systems SR and the size of dels is consistent regardless of detector plate size or field size a microns b. A 100 micron del produces SR of about 5 LP/mm, (much less than old 200 speed film) 47. For CR systems: For light image matrix created by CR reader sampling of PSP plate: Depends on reader: SR is fixed for some, varies for others 48. Spatial resolution for CR: a. Upper limit that can be produced is equal to the scanning Nyquist frequency b. Due to light spread between the PSP plate and the light guide, the net Spatial frequency actually produced is slightly less than the Nyquist frequency c. The upper limitations set by the Nyquist frequency and light spread can override and reduce the sharpness achieved by good x ray beam geometry during the original projection, but d. It is still important to maximize sharpness in the remnant beam signal reaching the IR so that a sharpness level less than the digital processing factors impose does not result. 49. Displayed image field of view Vs. spatial resolution: a. For the field of view of the displayed image, there is a matrix size relative to the level of zoom (magnification) applied at the monitor b. Magnification of the displayed image using monitor controls can only be accomplished by magnifying each image pixel c. The pixel value for an original single pixel is spread out across a four pixel square d. Further magnification spreads this value out over a square of nine hardware pixels 50. Since image pixel size is increasing, spatial resolution is lost and the image becomes pixelly as individual image pixels become more apparent a. Even though the spatial resolution of the hardware pixels of the monitor itself is consistent, here we are talking about the relative pixel size of the displayed image, the image pixels Example: CT scan reconstructed at 7mm Vs 3mm pixels 51. All digital detail processing operations actually enhance the visibility of small details (local contrast resolution), NOT the spatial resolution (Details become more visible, but NOT sharper) These are all adjustments to the contrast of fine details, which are then re inserted into the final image (local contrast resolution) 52. The Display Monitor: The weakest link in the imaging chain a. More limited resolution than digital processing system or original projection geometry b. Expensive Class 1 monitors required for radiologists diagnosis station c. Technologists must be careful about judging images on Class 2 display monitors 53. A poor quality display monitor can effectively destroy the spatial resolution already achieved during image acquisition and processing 54. Understanding the Monitor Image as Frequencies: On a display monitor, any row of pixels can be sampled such that the values of the pixels along its length form a sine wave graph Compared to alternating black and white pixels, a row of alternating gray and white pixels results in a graph with less amplitude (lower height of the sine waves) 55. Wavelength on the graph represents the size (width) of the pixels, (also of pixel pitch)

8 56. On a monitor, for a single row of 10 pixels: If we define a detail as a black/white density pair: The lowest possible frequency is 1 Hertz (1 cycle) consuming 5 pixel pairs (10 pixels) per detail The highest possible frequency is 5 Hertz (5 cycles) consuming 1 pixel pair (2 pixels, one black, one white) per detail demonstrated 57. The Monitor Image: Frequency & Spatial Resolution: Higher frequency means that there are fewer pixels (or pixel pairs) per detail in the image Fewer pixels per detail translates into higher sharpness at structural edges (or a harder edge) High frequency = Fewer pixels per detail = Higher sharpness (spatial resolution) 58. Object size, wavelength, and frequency: Large objects generate Long waves Low frequency Small objects generate Short waves High frequency 59. Image Compression: a. Necessary due to huge file sizes for medical images: 4 5 megabytes each image for DR and CR 15 MG each for MRI 25 MB each for CT b. Can typically add up to 150 Gigabytes per month in storage requirements 60. Lossy compression ratios, above 10:1, result in irreversible loss of spatial resolution unacceptable for medical images 61. Lossless compression ratios, less than 8:1 have been deemed visually acceptable by radiologists 62. DICOM Viewers: Viewing software programs that should be included on any CD, DVD or flash drive along with images sent to clinical sites a. Also can be made available on password protected websites b. Preserve image qualities and manipulation features which are lost when an image is simply sent over the internet or as an attachment to an c. Without a DICOM viewer, viewing monitors and software at the clinical site can severely compromise spatial resolution 63. Final criteria for Spatial Resolution in Digital Radiography: Maximum resolution should be apparent in all digital images: a. At least 8 LP/mm for static images b. At least 6 LP/mm for digital fluoroscopy