The Conoid of Sturm & Circle of Least Confusion: Astigmatic Focal Geometry

Consider an astigmatic eye with a steep vertical meridian ($F_v$) and a flatter horizontal meridian ($F_h$). As light traverses the eye:

1. The Anterior Focal Line: The more powerful vertical meridian refracts light most steeply, forming a sharp horizontal focal line closest to the lens.
2. The Expanding Vertical Ellipse: Past the first focal line, vertical rays diverge while horizontal rays continue converging, producing an ellipse with a vertical major axis.
3. The Circle of Least Confusion (CLC): At the dioptric midpoint, the vertical divergence exactly matches horizontal convergence, forming a circular cross-section of minimum blur.
4. The Posterior Focal Line: The flatter horizontal meridian finally focuses, forming a sharp vertical focal line.
5. The Expanding Horizontal Ellipse: Both sets of rays diverge into space.

The location of the Circle of Least Confusion corresponds precisely to the Spherical Equivalent ($M$) of the spherocylindrical prescription:

$$F_{\text{CLC}} = F_{\text{sph}} + \frac{F_{\text{cyl}}}{2}$$

The physical diameter of the CLC ($d_{\text{CLC}}$) is directly proportional to pupil diameter ($D_{\text{pupil}}$) and the dioptric Interval of Sturm (the difference between the two focal lines, $\Delta F = |F_v - F_h| = |F_{\text{cyl}}|$):

$$d_{\text{CLC}} = D_{\text{pupil}} \times \frac{\Delta F}{F_v + F_h}$$

Where the retina sits within Sturm's Conoid defines the five types of clinical astigmatism:

• Simple Myopic: Anterior line on retina; posterior line in vitreous.
• Simple Hyperopic: Anterior line in vitreous; posterior line on retina.
• Compound Myopic: Both focal lines sit in front of the retina.
• Compound Hyperopic: Both focal lines sit behind the retina.
• Mixed Astigmatism: The retina sits squarely between the two lines, directly slicing through the Circle of Least Confusion.

By fitting ELLASUV Precision Digital Toric Lenses, the Interval of Sturm is collapsed to zero ($\Delta F = 0$), uniting both focal lines into a single Airy disk point on the fovea.