# Introduction to Aberrations, Distortion and Zoom Lenses

#### Author:

Corinne Lee # 45672003
Trinh Le       # 43474980

The study of the lens system in the fullest detail is an extremely difficult and complex in the past and maybe even now. Therefore, it was necessary to use linear approximation , first order,i.e looking at the first term of the sine and cosine function, to find equations for image formation. It assumes that the angle that exist between the optical axis and the rays are small.

Sine and Cosine Function:

First Order/ Linear Approximation:

This is consider one of the "ideal len" assumption. Since we look only at the first term in the sine and cosine function, we have eliminated the problem cause by the third order, fifth order and other orders of the sine and cosine function. Problems cause by the third order are known as the third order aberration such as spherical aberration, coma, astigmatism, curvature of field, and distortion. Additional aberration, chromatic aberration, results from the wavelength dependence of an optical system.

## Aberrations

Aberrations are faults in the lens that didn't fix problems cause by the third order of the sine and cosine function. The two main aberration we will be focusing are spherical and chromatic aberrations.

Spherical Aberration:

Definition:

-> Spherical Aberration is cause when rays from different y-distance do not converge at the same focal point.

Chromatic Aberration:

Definition:

-> Chromatic Aberration occurs when the index of refraction varies with wavelength due to dispersion.

## Curvilinear Distortions

A major problem faced with zoom lenses is the curvilinear distortions or the barrel and pincushion distortions. This is a distortion where the magnifications of different points of an image are not equal. (Langford) There are two type of distortion we are going to deal with, pincushion and barrel.

### Pincushion

->The image is less magnified at the center than at its edges

### Barrel

->The image is more magnification at the center than at ites edges.

## Zoom Lenses

Maker: Bell & Howell       Name of Lens: Filmovara      Focus: 15-25mm      Field Covered: 8 mm proj.

This is an example of a Filmovara 16mm projection lense.

Maker:Minolta     Name of Lens: Rokkor    Focus: 80-160mm    Field Covered: 24X26 mm

This is an example of a Rikkor 28-105 mm.

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