# Glossary ## Performance

### Telecentric Optical System

Optical system with principal rays parallel to the optical axis of the lens. Optical systems in which the light entering the lens from the object is parallel to the optical axis (even when it is off-axis) are called "object-side telecentric optical systems". Optical systems in which the light shining from the lens to the image is parallel to the optical axis (even when it is off-axis) are called "image-side telecentric optical systems". The telecentric optical systems listed in this catalog are object-side telecentric optical systems. ### Resolution (µm)

Resolution is the closest spacing of two points (on the object) which can be distinguished by the optical system to be separate entities. For example, 1 µm resolution means two points that are 1 µm apart can be distinguished. Resolution values listed in the catalog are the theoretical resolution values of the lens.
Formula for finding the theoretical resolution value using the light diffraction of an aplanatic lens is as follows. (Rayleigh formula) ### Resolving Power (Lines/mm)

Resolving power refers to the number of black and white stripes distinguished within 1mm in an image of a black and white grid-like chart seen through the lens. Resolving power is indicated using "lp/mm". For example, 100 lp/mm means that black and white pitch 1/100 mm (10 µm) can be distinguished. The width of both the black and white lines is 1/200 mm (5 μm).

### Horizontal TV Resolution (TV lines)

The number of white and black stripes that fit inside the horizontal direction width equal to the vertical direction height of a TV monitor. The total number of stripes that fit inside the total horizontal width is equal to 4/3 times the number of stripes because the aspect ratio of regular screens is 3:4. If the horizontal TV resolution is 240 TV lines, a total of 320 stripes will fit inside the total horizontal width of the TV monitor screen. A resolving power of a lens counts one pair of black and white stripes as one line pair (lp). TV lines describe one pair as two lines.

### Distortion (%)

Lens aberration that occurs when an off-axis linear object forms an image of a curved line. If the off-axis line curves towards the center, it is called "pincushion distortion". If it curves towards the outside, it is called "barrel distortion". ### TV Distortion (%)

Image distortion on a TV monitor. The closer the figure is to zero, the better the performance. ### Aperture Efficiency Peripheral Brightness (%)

Refers to the difference in brightness (between the optical axis area and ambient area of the imaging surface) that occurs when forming an image of an object with uniform brightness using a lens. The brightness of the center area is 100, and it is indicated using percentage (%). It is one of the optical features of a lens. The peripheral brightness in this catalog refers to aperture efficiency.

"Shading" refers to the difference in brightness between the center area and surrounding area of the TV monitor when imaging an object with uniform brightness using a lens and a CCD camera. It is expressed in percent (%). Generally, the percentage is found by taking the output ratio of the light receiving element and the CCD element. Shading indicates the performance characteristics of the lens and TV camera. To reduce shading, telecentric optical systems, etc., are used.

### Chromatic Aberration

In optical systems of lenses, imaging positions, image magnification, etc., varies depending on wave length of the light. This phenomenon is called "chromatic aberration" because lights with different wavelengths will have different colors. Aberration on the optical axis is called "axial chromatic aberration". The difference in magnification is called "lateral chromatic aberration".

## Distance

### WD (Working Distance) (mm)

The distance from the tip of the lens's object-side barrel (body), etc., to the object (subject).

### Focal Point Distance f (mm) Back Focal Distance (Back Focus)/Front Focal Distance (Front Focus)

The distance from the optical system's principal point to the focal point is called the "focal distance". The distance from the lens's hindmost lens surface to the back side focal point is called "Back Focal Distance" or "back focus". The distance from the lens' frontmost lens surface to the front side focal point is called "Front Focal Distance" or "front focus".

### Depth of Field (DOF)

Depth referred here is the distance between the nearest and farthest points that appear in acceptably sharp focus when a subject is shifted back and forth from the best focal point. The object side's depth range is called the "depth of field" or "DOF".

Depth of field = 2 (Permissible Circle of Confusion × Effective Fno Magnification2)

Images created with lenses are theoretically formed as points. Acceptable blur on an acceptably clear image is called the "permissible circle of confusion".

### Depth of Focus

The range in which an image is seen with acceptably sharp focus, when CCD surface is moved back and forth from the point in which the lens focus is sharp (optimal focus position) is referred to as "depth" here. The image side's depth range is called the "depth of focus".

### Flange Focal Length (Flange Focal Distance) (mm)

The distance from the attachment side of the camera mount to the image.

### C-Mount Standard

 Nominal Designation Standard profile dimensions Threads per inch (per 25.4 mm) Flange Focal Length (Flange Focal Distance) U１ 25.400mm 32 threads 17.526mm

## Brightness

### Numerical aperture N.A.

When the half angle created by the optical system's object in the entrance pupil is "u" and the refractive index is "n", then "n ˣ sin u" is called the "object side numerical aperture, NA".
When the half angle created by the image in the exit pupil is "u'" and the refractive index is "n'", then "n' ˣ sin u'" is called the "image side numerical aperture, NA'". The NA listed in this catalog indicate object side numerical aperture. The numerical aperture is an important figure that indicates lens resolution and brightness.

NA = n ˣ sin u     NA'=n' ˣ sin u'

A lens with higher numerical aperture (NA) is brighter and has higher resolution.

### F Number F No

Figure that indicates the lens brightness. It refers to the value found when the focal point distance of the lens is divided by the effective diameter (entrance pupil diameter D mm) when seen from the object side. It can also be found from the NA and lens optical magnification (β). The lower the figure, the brighter the lens.

F No = f/D

### Effective F No

This is a figure that indicates the brightness of the lens when the position of the object is at the finite distance. Figure that indicates the lens's brightness. As the optical magnification (β) increases, the lens will become darker. Effective F No = β/(2 ˣ NA) = 1/(2 ˣ NA')

Effective F No = (1 = β) ˣ F No*
* It is an approximation used for thin-walled systems.

## Magnification

### Optical Magnification β

The ratio of the size of the image relative to the size of the object.

β = y'/y
= b/a
=NA/NA'
=Camera's image sensor dimensions ÷ actual field of view dimensions ### Electronic Magnification

Electronic magnification refers to magnification of an image on the image sensor displayed on a monitor screen.

### Monitor Magnification

Monitor magnification refers to the magnification of the subject displayed on a monitor screen through a lens.

Monitor Magnification = (Optical Magnification β) ˣ (Electronic Magnification)

(Calculation Example) If optical magnification β = 0.2 times, image sensor size = 1/2" (diagonal dimension = 8 mm), monitor = 14"
Electronic magnification = 14 ˣ 25.4 ÷ 8 = 44.45 (times)
Monitor magnification = 0.2 ˣ 44.45 = 8.89 (times) (1 inch = 25.4 mm)

### Field of View

Refers to the size of the subject that can be imaged with a CCD or CMOS camera attached to the lens.
The size of the field of view is (image sensor format dimension) ÷ (optical magnification β)

(Calculation Example) If optical magnification β = 0.2 times, image sensor size = 1/2" (vertical = 4.8 mm, horizontal = 6.4 mm)
Size of the field of view Length = 4.8/0.2 = 24 (mm)
Width = 6.4/0.2 = 32 (mm)

## CCD camera element size Type Aspect ratio Length
mm
Width
mm
Diagonal
mm
1/6" 4:03 1.73 2.3 2.878
1/4" 4:03 2.4 3.2 4
1/3" 4:03 3.6 4.8 6
1/2" 4:03 4.8 6.4 8
1/1.8" 4:03 5.3 7.2 8.9
2/3" 4:03 6.6 8.8 11
1" 4:03 9.6 12.8 16
4/3" 4:03 13.5 18 22.5

## List of Formulas

Resolution (µm) = 0.61 (Constant) ˣ 0.55 (Design Wavelength) ÷ NA
Effective Fno = Magnification ÷ 2NA
Depth of Field (mm) = 2 (Permissible Circle of Confusion ˣ Effective Fno ÷ Magnification2)
Luminous Flux Diameter (Ø) = 2NA ˣ Height from Workpiece + Field of View Size (Diagonal)

## Telecentric Optical System Features

### Non-Telecentric lens

• Lens can be miniaturized
• Lower cost due to fewer lenses than telecentric lenses.

• Workpiece size will fluctuate or the position will change if the surface of object moves up and down. ### Object side telecentric lens

• Workpiece size will not change even if the surface of object moves up and down.
• A lens - illumination system can be miniaturized when coaxial illumination is used.

• If coaxial illumination is not used, its lens - illumination system becomes larger than the typical systems. ### Double telecentric lens  