The camera and the eye

Image formation in cameras

A camera forms a real image of a scene on a sensor or film. Light from each object point passes through a lens and is focused to a corresponding image point. The image is usually inverted on the sensor, but digital processing or the brain can interpret orientation.

The thin lens equation describes focusing:

rac{1}{f}=rac{1}{d_o}+rac{1}{d_i}

For distant objects, $d_o$ is very large, so $d_iapprox f$. This is why a camera lens focuses distant scenes near its focal plane.

Aperture

The aperture controls how much light enters the camera. A larger aperture admits more light and allows shorter exposure times, but it also reduces depth of field. A smaller aperture admits less light but keeps a larger range of distances acceptably sharp.

The f-number is

N=rac{f}{D}

where $f$ is focal length and $D$ is aperture diameter. Smaller f-number means larger aperture.

Exposure and shutter

Exposure depends on aperture, shutter time, and sensor sensitivity. Shutter time determines how long light is collected. A long exposure gathers more light but can blur moving objects. A short exposure freezes motion but requires more light or higher sensor gain.

The image brightness is proportional to light power times exposure time, within the sensor's response range.

The human eye

The eye is an optical instrument that forms an image on the retina. The cornea provides most of the focusing power, while the lens fine-tunes focus. The iris adjusts pupil size, controlling light entry. The retina contains photoreceptor cells that convert light into neural signals.

The eye's lens changes shape to focus objects at different distances. This process is called accommodation.

Near point and far point

A relaxed normal eye focuses distant objects on the retina. To focus nearby objects, the lens becomes more curved, reducing its focal length. The closest distance at which the eye can focus is called the near point.

For a typical young adult, the near point is often approximated as

$25 cm$

though it varies. With age, the lens becomes less flexible, causing presbyopia and increasing the near point.

Vision correction

Nearsightedness, or myopia, occurs when distant objects focus in front of the retina. It is corrected with a diverging lens. Farsightedness, or hyperopia, occurs when nearby objects would focus behind the retina. It is corrected with a converging lens.

Lens power is measured in diopters:

P=rac{1}{f}

where $f$ is in meters. Positive power corresponds to converging lenses; negative power corresponds to diverging lenses.

Camera-eye comparison

A camera changes focus by moving lens elements or sensor position. The eye changes focus mostly by changing lens shape. A camera sensor records an image electronically or chemically; the retina begins biological signal processing immediately.

Both systems must balance light gathering, focus, resolution, and sensitivity.

Limits of sharpness

Image sharpness is limited by lens quality, diffraction, sensor or retinal spacing, motion blur, and aberrations. Even a perfect lens cannot focus light to an infinitely small point because light is a wave and diffraction occurs.

The big idea

Cameras and eyes form real images using focusing optics. Aperture controls light and depth of field, while lens shape or position controls focus. The eye adds biological accommodation and neural processing, and vision correction uses lenses to shift image formation onto the retina.