CT Resolution Calculator

Understanding Resolution in Computed Tomography

Magnification & Voxel Size ↑ Calculator

The fundamental principle of Cone-Beam CT geometric magnification is simple: objects placed closer to the X-ray source project a larger shadow on the detector. We calculate magnification as Mag = SDD / SOD. Since the physical pixel pitch of the detector is fixed, increasing magnification spreads the image of a small detail over more pixels. The resulting "effective" pixel size at the object center is called the Voxel Size.

Nyquist Sampling ↑ Calculator

Even with perfect geometry, 3D reconstruction requires sufficient data. The Nyquist-Shannon sampling theorem dictates that to resolve a detail of a certain size, you must sample it at least twice. In CT terms, this means taking enough projection images around the 360-degree rotation. The 'Nyquist Limit' calculated above represents the minimum number of projections required to ensure the angular spacing between views at the outer edge of the object is smaller than the voxel size.

The Penumbra Effect (Geometric Unsharpness) ↑ Calculator

However, magnification is not free. The X-ray source is not a perfect mathematical point; it has a physical diameter (the 'Spot Size'). As you move the object closer to the source to gain magnification, the finite size of the spot creates a blur at the edges of the object. This shadow blur is known as the Penumbra or Geometric Unsharpness (Ug). If this blur value exceeds your Voxel Size, increasing magnification further will simply result in a larger, blurrier image without revealing more detail.

Total Effective Resolution

Ultimately, the true resolution of your scan is a combination of the digital sampling limit (Voxel Size) and the analog optical blur (Unsharpness). This calculator estimates the Total Effective Resolution using the root sum square of both values: Total = √(Voxel² + Ug²). This metric helps you identify the "weakest link" in your scan parameters—whether you are limited by the detector pixels or the X-ray spot size.