Formulas and Definitions

Optical Relationships

  • As numerical aperture increases, depth of field decreases with an increase of resolution and light gathering.
  • As magnification increases, both field of view and image illumination level decrease.
As working distance increases, field of view increases with a decrease in magnification.

Useful Formulas

Resolution in Line Pairs
Millimeters: (3,000 x N.A.)/mm
Inches: (75,000 x N.A.)/inches

Depth of Field
Millimeters: .0005/N.A.²
Inches: .00002/N.A.²

1 Inch = 25.4 Millimeters
1 Meter = 39.37 Inches
1 Micron = 0.001 Millimeters

Definition of Terms

Depth of Field (DOF)
The amount of variation in the height of the object which will be in focus at any one given time.

Depth of Focus
The allowable variation in image plane which will still produce an acceptable focus.

=M*Depth of Field Field of View
All cameras have a fixed sensor size. This means that no matter how large the image is at the sensor plane, the camera will only "look at" the portion equal to the sensor size. What the camera "sees" is called the field of view. The lens, or lens system, of the camera controls the magnification at the camera sensor. The lower this magnification, the greater the portion of the object overlaying the sensor.

Magnification
The ratio of image size to object size.

Numerical Aperture (N.A.)
The sine of 1/2 the angle of the collected light cone from the object.

Object to Image Distance (O-I)
The total distance from the object to the sensor.

Resolution
The ability of a lens system to image closely spaced points, lines and object surfaces as separate entities (see the Resolution page).

Working Distance
The clearance or distance between the object and the first physical surface of a lens system.

Lens Limited
The condition where the over-all system could display finer detail if the taking lens was capable of picking it up from the object.

Camera Limited
The condition where the over-all system could display finer detail if the camera pixels were smaller (detail must cover 2 pixels).