Medical Imaging Physics, Computed Tomography (CT) QA & Radiodensity Windowing
CT Hounsfield Unit (HU) & Display Window Grayscale Formula
Calculate Calibrated Hounsfield Unit HU = 1000*(mu_x - mu_water)/(mu_water - mu_air), Lower/Upper Display Window Bounds, and 8-Bit Monitor Grayscale Intensity (0–255).
How a 5% X-ray attenuation bump maps acute brain hemorrhage from +35 HU gray matter to +52 HU bright white!
Diagnostic CT scanners reconstruct voxel X-ray Linear Attenuation Coefficients mu_x (cm^-1 at effective beam energy ~60–75 keV) and standardize them across vendors on the Hounsfield Scale anchored at Pure Water (0 HU) and Air (-1,000 HU): HU = 1,000 * ((mu_x - mu_water) / (mu_water - mu_air))! Because human vision distinguishes only ~60–100 shades of gray whereas clinical CT spans 4,096+ HU (-1,000 lung air to +3,000 cortical bone/metal), radiologists apply Display Window Level WL (center HU) and Window Width WW (span HU): every voxel below WL - WW/2 clips to pure black (0), every voxel above WL + WW/2 saturates to pure white (255), and voxels inside the window stretch linearly as Grayscale_8bit = ((HU - (WL - WW/2)) / WW) * 255!
Verify on a Non-Contrast Head CT Acute Hematoma Voxel—Voxel_Attenuation mu_x = 0.2020 cm^-1 (B2), Water_Reference mu_w = 0.1920 cm^-1 (B3), Air_Reference mu_air = 0.0002 cm^-1 (B4), Brain_Window_Level WL = 40.0 HU (B5), and Brain_Window_Width WW = 80.0 HU (B6): Voxel Radiodensity equals +52.14 HU (E2), Brain Window spans [0.00 HU, 80.00 HU] (Lower Bound = 0.00 in E3, Upper Bound = 80.00 in E4), and 8-Bit Pixel Brightness lands at 166.2 out of 255 (E5, standing out hyperdense against ~35 HU normal parenchyma)!
| CT Phantom & Brain Window KPI (mu_x=0.202, mu_w=0.192, mu_a=0.0002, WL=40, WW=80) | Formula | Verified Output |
|---|---|---|
| Calibrated CT Number (HU) | 1000 * (mu_x - mu_w) / (mu_w - mu_air) | +52.14 HU (+980.19 HU @ 0.380 bone) |
| Display Window Floor (HU) | Window_Level_WL - Window_Width_WW / 2 | 0.00 HU |
| Display Window Ceiling (HU) | Window_Level_WL + Window_Width_WW / 2 | 80.00 HU |
| 8-Bit Monitor Grayscale (0–255) | MIN(255, MAX(0, ((HU - Floor)/WW)*255)) | 166.2 (255.0 clipped @ 0.380 bone!) |
ACR Phantom Hounsfield Calibration & 8-Bit Window-Level Mapping Formula
Validate mu_x >= 0, mu_water > mu_air >= 0, and Window_Width WW >= 1 HU!
=LET(mu_x, B2, mu_w, B3, mu_a, B4, wl_c, B5, ww_s, B6, IF(OR(mu_x < 0, mu_a < 0, mu_w <= mu_a, ww_s < 1), "Invalid CT Input", LET(hu_v, 1000 * ((mu_x - mu_w) / (mu_w - mu_a)), fl_w, wl_c - ww_s / 2, ROUND(MIN(255, MAX(0, ((hu_v - fl_w) / ww_s) * 255)), 1))))Cortical Skull Bone Saturation Clipping Check (Set Voxel mu_x = 0.3800 cm^-1)
Inspect dense cortical skull bone on the same narrow 40/80 Brain Window (set Voxel_Attenuation B2 = 0.3800 cm^-1): Hounsfield Number E2 jumps to +980.19 HU, saturating 8-Bit Grayscale E5 at full 255.0 white (requiring a wide WL=400 / WW=1,800 Bone Window to resolve trabecular fractures)!
=IF(ISTEXT(E5), E5, ROUND(1000 * ((B2 - B3) / (B3 - B4)), 2))Try the example
Use the original values or change them to test your understanding.