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Lec 19 Cameras, Lenses and Light Fields

Imaging = Synthesis + Capture

Field of View (FOV)

FOV

For a fixed sensor size, decreaseing the focal length increses the FOV.

\[\text{FOV}=2\,\arctan\left(\frac{h}{2f}\right)\]

Due to historical reasons, the angle of view is usually expressed using the focal length of lenses designed for 35mm format film (36 x 24mm).

  • 17mm is a wide-angle lens, with a field of view of 104°
  • 50mm is a "standard" lens, with a field of view of 47°
  • 200mm is a telephoto lens, with a field of view of 12°

Exposure

\(H=T\times E\) (Exposure = Time \(\times\) Irradiance)

Exposure time T: controlled by shutter
Irradiance E: power of light falling on a unit area of sensor. Controlled by lens aperture and focal length.

Aperture size

  • Change the f-stop by opening / closing the aperture

Shutter speed

  • Change the duration the sensor pixels integrate light

ISO gain

  • Change the amplification (analog and/or digital) between sensor values and digital image values

camera exposure

ISO (Gain)

Third vaiable for exposure

Film: trade sensitivity for grain
Digital: trade sensitive for noise

  • Multiply signal before analog-to-digital conversion
  • Linear effect (ISO 200 needs half the light as ISO 100)

F-Number (F-Stop)

Written as FN or F/N. N is the f-number.

Informal understanding: the inverse-diameter of a round aperture.

Formal definition: the focal length divided by the diameter of the aperture.

Shutter

Motion blur: handshake, subject movement.
Doubling shutter time doubles motion blur.

Rolling shutter: different parts of photo taken at different times.

If the exposure is to bright/dark, may need to adjust f-stop and/or shutter up/down.

Photograhers must trade off depth of field and motion blur for moving subjects.

High-speed photography: extremely fase shutter speed x (large aperture and/or high ISO)

Thin Lens Approximation

We consider focal length can be arbitrarily changed (in reality, yes)

Gaussian thin lens equation:

\[\frac{1}{f}=\frac{1}{z_i}+\frac{1}{z_o}\]

(Why? Draw parallel ray and focal ray)

Defocus Blur

Circle of Confusion (CoC)

When the object is not on the focal plane, the image is not on the sensor plane. Sensor recieves a circle of light.

C denotes the diameter of CoC. A denotes the diameter of lens.

CoC

\[ \frac{C}{A}=\frac{d'}{z_i}=\frac{|z_s-z_i|}{z_i}\]
\[ C=A\frac{|z_s-z_i|}{z_i}=\frac{F}{N}\frac{|z_s-z_i|}{z_i}\]

Ray tracing for defocus blur

  • Choose sensoe size, lens focal length and aperture size
  • Choose depth of subject of interest \(z_o\)

Depth of Field

Depth range in a scene where the corresponding CoC is considered small enough.

Depth of field: max depth range - min depth range