Formulas & Guidelines

The information on this page is a compilation of basics intended to assist you in selecting the best optical components and systems for your specific applications.

Points of Magnification
• As numerical aperture increases, depth of field decreases and resolution increases.
• As magnification increases, field of view decreases.
• As magnification increases, more light may be needed.
• Magnification is developed in two ways – different lenses create different magnifications at the camera, or camera and monitor combinations develop magnification between themselves.

Magnification at the Camera
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 of the subject 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 larger the field of view.

Magnification at the Monitor
When the camera image is displayed on a monitor for viewing, there is further magnification. The diagonal of the camera sensor is expanded to the diagonal of the monitor. Consider this example: A 1/2" camera is being used with a 13" monitor. The 8 mm diagonal of the camera will expand to 13" (330.2 mm) for a magnification of 41.3X. In practice, the camera is actually overextended in order to overfill the monitor and prevent dark edges. There is no recognized industry standard, however, a 5-10% increase in magnification resulting in a 5-10% loss in field of view can be assumed.

Camera Format Monitor Size (diagonal)

Useful Formulas
Resolution in Line Pairs
Millimeters: (3000 x N.A.)/mm
Inches: (75,000 x N.A.)/inches Depth of Field
Millimeters: ± .0005/N.A. ²
Inches: ± .00002/N.A. ² Conversion Factors
1 Inch = 25.4 Millimeters
1 Meter = 39.37 Inches
1 Micron = 0.001 Millimeters

Definition of Terms
Depth of Field: The distance allowing acceptable image definition to be maintained without refocusing
Depth of Focus: The distance along the optical axis at which the image is in focus.
Field of View The area visible through a lens or a lens system.
Magnification: A measure of the apparent differences in size between the object and the image.
Numerical
Aperture: The largest cone or number of light rays that can enter a lens system.
Working Distance: The ability of a lens system to image closely spaced points, lines and object surfaces as separate entities.
Resolution: The clearance or distance between the object and the first surface of a lens system. Affects the users’ ability to image and manipulate the sample at the same time.
Object to Image
Distance (O-I) The total distance from the object to the sensor inside the camera.