The ratio of amount of bending actual object straight line in a longitudinal direction. Expressed in percentage.
Refer to diagram 2

■Optical magnification
Refer to diagram 3

	Monitor diagonal	×　Optical mag.　＝　Monitor mag.
	Sensor diagonal

Example) VS-MS1＋10x lens for 1/2” CCD camera, imaging on 14” monitor.

	25.4×14”	×　10（x）＝　444.5x
	8（mm）

Therefore you will see 0.1mm scale on the monitor in 44.45mm.
Calculation is based on “Underscan” mode of monitor. It will be slightly different when TV monitor is on “Overscan” mode.

■Resolution
Resolution is the ability to recognize two features that are close together.
It is defined by:
0.61x wavelength(λ)/ NA=Resolution(μ)
However the distortion is not included.
※The Resolution number shown at wavelength 550nm

Resolving power is expressed in terms of the number of line-pairs per millimeter (lp/mm)－the most
number of black and white lines in one millimeter to be distinguished.

It is the figure that how the repetition of light and shade on the surface of the object was reproduced on the image side. It is shown compared with the spatial frequency and the contrast ratio.

■ＷＤ（Working Distance）
The distance between the object and front of the lens

The distance between the object and sensor

Formula 1       ２（　 Permissible COC x Working F# 　）＝DOF Optical mag. X Optical mag.         Permissible COC ＝DOF NA x Optical mag.

Depth of filed is a range of object distance, which the image appears to be sharp and focused.
Also a parameter of imaging side (CCD camera pixel side) is called depth of focus.
Tolerable level of blur is called permissible circle of confusion, or COC, and it depends on the camera
you use. The DOF numbers shown in this catalog are given by:

Distance from back focal point (H2) to the principle plane.

F# defines the brightness of lens at infinity imaging. Smaller number lens has generally brighter image.
F# = focal length/ diameter of lens aperture

Working F# defines the brightness at a certain WD.
Working F# = (1 + optical mag.) x F#
Working F# = Optical mag. / 2NA

Measure of the cone of light accepted by a lens. NA is given by:
Object side NA = sin u x n
Imager side NA' = sin u' x n'
The half angle of objective side entrance pupil is u, the half angle of image side of exit pupil is u',
and objective side refractive index is n, imaging side refractive is n'

Relative Illuminance is a ratio of brightness between center and corner of the image.
It is expressed in percentage against the center in 100%

Telecentric lens has a chief ray in parallel with the optical axis.
There are three types of telecentric lens in:
Object side, Imager side and Both sides telecentric lens system

◆Telecentricity

Telecentricity determines the amount that magnification changes with working distance. Better telecentricity means less magnification changes.
Telecentric lens has parallel chief rays to its optical axis and bad telecentricity lenses produce images with higher magnification when the object is closer and the object can be seen differently between center and field of image. The degree of telecentricity is measured by the chief ray angle in the corner of the image field. You can easily check the telecentricity using a target as shown below.
Telecentric lens is very important for gauging three-dimensional objects or objects whose working distance is not stable.

◆Depth of Field (DOF)

Depth of Field is a range of object distance, which the image appears to be sharp and focused. Also a parameter describing the distance of imaging side (sensor side) is called depth of focus.
Tolerable level of blur is called Permissible Circle of Confusion, or Permissible COC. This represents the smallest diameter of a bundle of rays when being focused on an image plane.
The diameter of Permissible COC will be defined by each application, pixel size of camera and the person who actually measures. The amount of DOF shown in this catalog is given by:
DOF = 2 x Permissible COC x Working F/# / Optical Mag.²
= Permissible COC / (NA x Optical Mag.)
(We use Permissible COC at 0.04mm in this catalog)

Even an ideal lens without any distortions cannot reproduce an object detail.
Diffraction will limit the resolution possible. The smallest achievable spot from a lens is called Airy Disk.
The radius r of the spot is given by wavelength λ and numerical aperture NA:
r = 0.61 x λ / NA
The longer wavelength of the illuminating light has larger spot.
Example)  A lens with NA0.07 at wavelength 550nm
r = 0.61 x 0.55 / 0.07 = 4.8um
The resolution on the specification sheet of VST is given by this equation.

◆MTF and resolution

The modulation transfer function MTF describes how the contrast varies with respect to spatial frequency which represents the ability of a lens to transfer information from the object to the image.

Figure 2 and 3 shows the spatial frequency against gray level at object side A and image (sensor) side B. The contrast (MTF) is given by ratio of A and B.
Resolution is the ability of lens to distinguish between two features that are close together. It is generally expressed in micrometers but it is affected by contrast, too. MTF express the relation between resolution and contrasts. Lens has lower MTF at higher frequency and MTF below 0.1 is normally not able to be resolved black and white which is usually lower resolution number than calculated.

Figure 4 shows two different lenses with different spatial frequency in each contrast level. Lens “a” has low resolution level but high contrast at low spatial frequency, however, higher resolution lens “b” has lower contrast at same level of frequency. Thus, lens “b” is higher resolution than lens “a” at high frequency level. But in actual machine vision applications, lens ability depends on different issues and it is not necessarily appropriate to suggest a lens only by resolution numbers.