Aberrations in optics for CV: analysis of defects

Optical Aberrations in Machine Vision Systems: Analysis and Impact

Real-world lenses produce images with flaws due to optical aberrations. An ideal lens focuses light rays from a single point on the object to a single point in the image, delivering maximum sharpness. In practice, light bundles form blurry spots, reducing contrast and detail. Third-order Seidel aberrations and chromatic effects are the main culprits affecting quality in computer vision tasks.

Aberrations fall into two main categories: those dependent on beam width (tied to entrance pupil diameter) and field aberrations (tied to field angle). Understanding them helps optimize machine vision systems for mid- and senior-level CV developers.

Wide-Beam Aberrations

These aberrations worsen as aperture size increases. Stopping down the aperture narrows the beam and reduces their impact.

Spherical Aberration

Parallel light bundles don't focus to a point but spread into a symmetric spot along the optical axis. The transverse aberration ∆y scales with the cube of the pupil diameter: doubling the diameter increases it eightfold.

For narrow beams, the spot is minimal; for wide beams, it's significantly blurred. In machine vision, this is critical for systems under varying lighting conditions.

Coma

Off-axis bundles lose symmetry, forming a comet-shaped blur spot. Coma is zero on-axis but grows toward the field edges. In astrophotography and telescopes, it turns star images into tails.

Mathematically, coma resembles the asymmetry in spherical aberration zones. Specialized optics use coma correctors.

Field Aberrations

These appear at any field angle, even with narrow beams. They degrade the edges in wide-angle systems.

Astigmatism

Off-axis bundles focus not to a point but to two astigmatic foci: tangential (t) in the meridional plane and sagittal (s) in the perpendicular plane.

• Meridional plane: t focus.
• Sagittal plane: s focus.
• t-s separation: quantifies astigmatism.

On the sensor, images shift shapes: lines at t and s, circles in between. 3D modeling tools like Zemax reveal the lack of a single focus.

Beam cross-section examples:

• Near t: line perpendicular to the plane.
• Between t and s: ellipse.
• Near s: line in the plane.

Field Curvature

The sharpest image lies on a curved surface (circle of least confusion, COC) between the tangential (TOT) and sagittal (SOS) surfaces, not the flat focal plane (FOF). Flat sensors mean blurred edges.

The COC surface approximates a sphere for small fields. It combines with astigmatism, worsening peripheral sharpness.

Chromatic Aberrations

These stem from dispersion: different wavelengths focus at different points.

• Longitudinal chromatic aberration: axial focus shift by wavelength.
• Lateral chromatic aberration: off-axis lateral shift.

Under polychromatic light, this creates color fringes, hurting quality in machine vision setups.

Overall Aberration Patterns and Correction

Combined aberrations create complex blur spots. Quality drops from center to edges: spherical and coma dominate centrally with large apertures, field aberrations at the periphery.

Correction strategies:

• Aspheric surfaces for spherical aberration and coma.
• Aspheric elements and lens combinations for field aberrations.
• Achromats (crown + flint glass) for chromatic issues.
• Multi-element systems optimized in Zemax.

In machine vision, select lenses balancing aberrations for the task: minimize coma for narrow fields, field curvature for wide ones.

Key Takeaways

• Spherical aberration scales with D³ (pupil diameter D); stop down for sharpness.
• Coma turns off-axis bundles into comet tails, critical for astro and wide-angle systems.
• Astigmatism splits foci into t and s, morphing spots from lines to circles.
• Field curvature demands curved sensors or correction for flat ones.
• Chromatic aberration is fixed with achromats; factor in lighting spectrum for CV.

— Editorial Team