Optical Aberrations in Lens Design

1. Introduction: What are Optical Aberrations?

In an ideal optical system, all light rays from a point source would converge to a single perfect image point. However, due to the nature of spherical surfaces and the dispersion of glass, real-world lenses suffer from Optical Aberrations. These are departures from ideal "Gaussian" optics that result in image blurring, distortion, and color fringing.

2. Monochromatic Aberrations (The Seidel Aberrations)

Monochromatic aberrations occur even with single-wavelength (monochromatic) light. These are traditionally categorized into the five Seidel Aberrations.

A. Spherical Aberration (SA)

Light rays passing through the edge of a lens (marginal rays) focus at a different distance than rays passing through the center (paraxial rays).

Impact: The image appears soft and lacks contrast.

Correction: Use of Aspheric Lenses or doublet designs.

B. Coma

Coma occurs when off-axis light rays do not converge at the same point, creating a "comet-like" tail on image points.

Impact: Smearing of detail at the edges of the frame.

Correction: Symmetrical lens designs (e.g., Cooke Triplet or Double Gauss).

C. Astigmatism

A defect where the lens has different focal lengths for rays in the tangential (vertical) and sagittal (horizontal) planes.

Impact: Points appear as lines or ellipses; horizontal and vertical lines cannot be sharp simultaneously.

D. Field Curvature (Petzval Curvature)

Instead of a flat image plane, the lens focuses light onto a curved surface.

Impact: If the center of the image is sharp, the corners are blurry (and vice versa).

E. Distortion

A variation in lateral magnification across the field of view.

Pincushion Distortion: Magnification increases toward the edges.

Barrel Distortion: Magnification decreases toward the edges.

Impact: Straight lines appear curved; critical in architectural and industrial imaging.

3. Chromatic Aberrations (Color Defects)

Chromatic aberrations occur because the refractive index of glass varies with the wavelength of light (dispersion).

A. Longitudinal Chromatic Aberration (LCA)

Different colors (RGB) focus at different positions along the optical axis.

Correction: Using an Achromatic Doublet (combining Crown and Flint glass).

B. Lateral Chromatic Aberration (TCA)

Different colors have different magnifications, causing color fringing at the edges of the image.

Correction: Specialized lens symmetry and Low-Dispersion (ED) glass.

4. Advanced Analysis: Zernike Polynomials and MTF

In modern lens design and testing (using tools like ZEMAX or Code V), aberrations are analyzed using:

Zernike Polynomials: A mathematical way to decompose complex wavefront errors into individual terms (e.g., Z₄ for Defocus, Z₇ for Coma).

MTF (Modulation Transfer Function): A graph showing how well a lens maintains contrast at increasing levels of detail (spatial frequency).

5. Summary Table for Lens Designers