Optics: Camera Lenses and Aberrations

Camera Lenses and Aberrations

• Using a single converging lens results in poor-quality images, especially at low f/numbers.
• Conventional ray-tracing rules only work for truly thin lenses and paraxial rays.
• Real lenses suffer from multiple "aberrations" that can be corrected using more complex combinations of spherical lenses.

Aberrations

• Coma: off-axis sources acquire a wedge-like distortion.
• Astigmatism: focal length depends on orientation in the image plane.
• Both coma and astigmatism are usually the result of imperfection in the lens.

Spherical Aberration

• Application of Snell's Law to a ray moving parallel to the optical axis of a hemispherical lens reveals that the location where it crosses the optical axis depends on how close it is to the optical axis.
• The best focus achievable is a "disc of minimum confusion".

Spherical Aberration Correction

• Adding a "stop" behind the lens to block non-paraxial and marginal rays significantly reduces aberration.
• The disc of minimum confusion is reduced in size, but less light enters the lens.
• An alternative to a stop is a combination of lenses that collectively compensate for variation in focal point, such as the Taylor-Cooke triplet.
• The Taylor-Cooke triplet consists of two converging crown glass lenses and one diverging flint glass lens in between, addressing many aberrations and distortions.

Chromatic Aberration

• The focal length of a lens depends on the index of refraction of the medium of which it's made and the surrounding medium.
• Dispersion means the focal length depends on wavelength, resulting in blurriness with a coloration at the edges.

Chromatic Aberration Correction

• A compound lens can be used to compensate for the dispersion, such as an achromatic doublet consisting of a converging crown glass element cemented to a diverging flint glass element.
• The result is a (almost) common focal length for long and short wavelengths.

Capturing Images

• The camera was of limited use until a mechanism became available to capture and preserve images.
• The first permanent(-ish) image was captured by Niépce in 1826.
• The process greatly improved by Daguerre, as shown in the 1839 "daguerreotype".
• The daguerreotype was an image on a silver-plated copper sheet, requiring an exposure time of 10-15 minutes.

Capturing Images - Black & White Film

• A plastic/cellulose backing is coated with an emulsion consisting of tiny crystals of silver-bromide suspended in gelatin.
• Each crystal is about one micron in size (varies from film to film).
• Bromine atoms can absorb visible light (mostly at the blue end of the spectrum), releasing an electron into the crystal.
• The result is a small buildup of metallic silver in the crystals that have been exposed to light.
• The buildup of metallic silver constitutes a latent image.
• Processing of the film to produce a usable image involves two separate steps: development and treatment with a developer solution.

Learn about the limitations of single converging lenses, ray-tracing rules, and common aberrations in lenses such as coma and astigmatism.