- • Optical magnification
- • Monitor Magnification
- • Focal Length (ｆ)
- • Field of view (FOV)
- • W.D（Working Distance）
- • O/I（Object to Imager）
- • Image Circle , Shading
- • TV Distortion (TV.D)
- • F Number (F/#)
- • Working F#
- • Ｎ.Ａ.（Numerical Aperture）
- • Depth of field (DOF)
- • Relative Illuminance
- • Airy Disk and Resolution
- • Resolving Power
- • Floating System
- • MTF and resolution
- • Telecentricity
Magnification is a ratio between FOV and Camera sensor size.
Focal Length (ｆ)
Field of view (FOV)
*In specification tables of this catalogue, FOV is calculated by standard size of CCD sensor. To get an exact FOV of your image, please calculate by effective pixel amount and pixel size of the sensor.
The distance between the object and front of the lens.
O/I（Object to Imager）
The distance between the object and sensor.
Image Circle , Shading
A lens has the ability to support a certain sensor size to image.
The maximum sensor area that the lens can support it
defined as Image Circle.If the sensor size is too large,
it causes“ Shading” or“ Vignetting”.
TV Distortion (TV.D)
The ratio of amount of bending against actual
object straight line in a longitudinal direction.
Expressed in percentage.
※ Distortion (D) : Refer to Diagram2
F Number (F/#)
F number defines the brightness of lens at infinity imaging. Smaller number lens has generally brighter image.
F/# = Focal Length / Diameter of Entrance Pupil ( Effective Aperture )
Working F# defines the brightness at a certain magnification.
W.F/# = (1+Opt Mag.) x F/# = Opt Mag. / 2NA
Measure of the cone of light accepted by a lens. NA is given by: The half angle of objective side entrance pupil is u,
the half of image side of exit pupil is u', and objective side refractive index is n, image side refractive is n'
※ For macro lenses, NA is defined by: NA=M/2xF, NA'=1/2F, relation of NA and NA' is NA=NA'x Opt Mag.
Depth of field (DOF)
DOF 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 plan.
The diameter of Permissible COC will be definedby each application,
pixel size of camera and the person who actually measures.
The amount of DOF shown in this catalogue is given by:
DOF = 2 x Permissible COC x W.F/# / Opt Mag x Opt Mag.
DOF = Permissible COC / (Nax Opt Mag.)
※We use Permissible COC at 0.04mm in this catalogue.
Relative Illuminance is a ratio of brightness between center and corner of the image.
It is expressed in percentage against the center in 100%.
Airy Disk and Resolution
Even an ideal lens without any aberrations cannot reproduce an object detail.
Diffration 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.
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.
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. The contrast level of image has to be defined to avoid differences between individuals.
Normal lenses shift just a single group of elements for focusing. Additional floating elements (see picture below) can improve the
close-focus performance significantly. Because the floating component is separate to the focusing lens group, aberrations
caused by lens extensions are significantly reduced. Benefits are particularly great in macro lenses because they cover a wide
range of focus distances and in wide-angle.
MTF and resolution
The modulation transfer function ( MTF ) describes how the contrast varies with respect to spatial frequency. MTF represents the ability of a lens to transfer information from the object to the image.
The contrast is usually measured by a spatial frequency test target with black and white line pairs and if the intensity between black and white is perfectly described, contrast (modulation) is 100%. (Figure 1）
If the features between black and white (gray level) cannot be resolved, the contrast is too low. Higher spatial frequency is usually imaged with less contrast because of aberrations of lens.
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.
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.