Telecentric lens required for FA and machine vision

A lens whose aperture aperture is at the focal point of the lens is called a telecentric optical system. Since the aperture stop is at the focal point of the lens, the main ray is parallel to the optical axis of the lens on the object side, image side, or both sides (angle of view 0 °). Especially for the object side and both sides telecentric lenses, the angle of view (telecentricity) is as close to 0 ° as possible, so there is no dimensional fluctuation of the image within the range of the depth of field (focus) of the lens. Even if the work is out of the depth of field and out of focus, this performance is maintained as long as the image processing measurement is possible. Ideally, the optical system with built-in coaxial epi-illumination should be a telecentric optical system.

Types of telecentric lenses

There are three types of telecentric lenses: both sides, the object side, and the image side. The features of each are described below.

Bi-telecentric lens

• ■ The main ray is parallel to the optical axis of the lens on both the object side and the image side.
• ■ Requirements for an optical system with built-in coaxial epi-illumination.
• ■ The dimensions of the image do not change within the depth of field.
• ■ The magnification does not change even if the back focus (C mount = 17,526mm) changes. However, the WD (working distance) changes. Therefore, it is convenient when you want to change only WD without changing the magnification.
• ■ Although it is an optimal optical system for image processing, it has the disadvantages of large lenses and high costs.

Object side telecentric lens

• ■ The main ray is parallel to the optical axis only on the object side.
• ■ Requirements for an optical system with built-in coaxial epi-illumination.
• ■ The dimensions of the image do not change within the depth of field.
• ■ When the back focus changes, the magnification changes. At the same time, the WD also changes. Example) For C mount (17,526mm), if the back focus is long, the magnification will be high and the WD will be short. If the back focus is short, the magnification will be low and the WD will be long.

Image side telecentric lens

• ■ The main ray is parallel to the optical axis of the lens only on the image side.
• ■ The dimensions of the image change even within the depth of field.
• ■ When the back focus changes, both the magnification and WD change.
• ■ For all CCTV lenses for color cameras with a built-in color correction filter, this type is desirable for color shift correction. (Many wide-angle CCTV lenses are telesen type on the pseudo image side)
• ■ The brightness on the image plane is uniform.

Normal lens

• ■ The main ray has an angle with respect to the optical axis of the lens.
• ■ The dimensions of the image change even within the depth of field.
• ■ When the back focus changes, the magnification and WD change.

The biggest feature of the double-sided telecentric lens

You can change the WD without changing the magnification. A finite type macro lens (non-telesen type) with a certain magnification changes the magnification when the WD is changed. It is the same with the telecentric lens on the object side. The longer the WD, the lower the magnification, and the shorter the WD, the higher the magnification. Due to the physical restrictions of the device, if you want to change the WD while keeping the magnification constant, the only optical system that can be used is a double-sided telecentric lens.

* If the amount of change in WD is large, distortion and resolution will deteriorate. Please be careful.

Depth of field of telecentric lens

Generally, the smaller the aperture of the lens, the deeper the depth of field. However, the effective F value becomes darker and the optical resolution also deteriorates. In the case of our telecentric lenses, double-sided telecentric lenses with a variable aperture can obtain a deeper depth of field by changing this. Also, in the case of fixed aperture, we will correspond with custom specifications.

Differences between telecentric lenses and general macro (magnification) lenses

As mentioned above, the telecentric lens does not change the subject dimensions within the depth of field. That is because the main ray is 0 ° with respect to the optical axis. On the other hand, in general macro lenses, the main ray has an angle of view with respect to the optical axis. Therefore, the subject dimensions within the depth of field change depending on the angle of view. In terms of cost and size, general macro lenses are generally cheaper and more compact than telecentric lenses.

Telecentric lens advantageous for image measurement

When measuring an image, if the WD between the lens and the subject does not change constantly, there is no problem with a general macro lens, but if it changes even slightly, the measured value can vary unless it is a telecentric lens. If the subject is a mirror surface, it is ideal to use a telecentric lens with built-in coaxial epi-illumination.

Different use of telecentric lens and general macro lens depending on the lighting method

Coaxial epi-illumination is required for surface pattern recognition of mirrored subjects such as wafers. Therefore, telecentric lenses are mainly used. Since there are many lighting methods for alignment of subjects that are not mirror surfaces such as metal such as iron or resin even on a flat surface or mounting substrates, ring lights or diagonal illumination methods are used, so general macro lenses are also used in addition to telecentric lenses. For edge detection, etc., the transmitted illumination method is used. Lighting includes halogen lamps, LEDs, metal halide light sources, etc., and the optimum color is selected according to the spectral sensitivity characteristics of the camera and lens system, such as general white light, ultraviolet rays, blue, red, and infrared rays.

Difference in depth of field between telecentric lens and general macro lens

Like general macro lenses, telecentric lenses do not have a deep depth of field. This is because the method of calculating the depth of field (formula) is the same for both telecentric lenses and general macro lenses. However, as mentioned above, with a general macro lens, the subject dimensions fluctuate within the depth of field, but with a telecentric lens, they do not.

Depth of field

Our way of thinking about depth of field

With the advent of 5M cameras, the pixel size of current FA cameras is becoming higher and higher. Along with this, the lens has also come to support higher NA (= higher resolution) according to the pixel size of the camera. However, recently, I have been asked by users in Japan and overseas, "I look at the catalogs of various lens manufacturers, but why is the depth of field of the lens deep in terms of specifications even though it is a high NA compatible lens?" The reason is that the formula for calculating the depth of field differs from company to company. Manufacturers of deep depth of field displays use the following formula regardless of megapixels.

Allowable circle of confusion ÷ (NA x optical magnification) or 2 {Allowable circle of confusion x effective F value ÷ (optical magnification) ² }

Then, the value of 40μ or 20μ is put in the permissible circle of confusion corresponding to the pixel size of the camera. For example, assuming the use of a 2/3 ″ 5 megapixel camera, the size of 1 pixel is 3.45μ. However, since black and white cannot be judged with 1 pixel, the value of 6.9μ for 2 pixels should be entered as 40μ or Enter 20μ. What will happen to the depth of view (DOF) if these three different numbers are calculated using the above formula?

Example) In the case of NA0.08 magnification x 1 lens compatible with 2/3 ″ 5M camera

① For 40μ 0.04 ÷ (0.08 × 1) = 0.5mm depth of field ② For 20μ 0.02 ÷ (0.08 × 1) = 0.25mm depth of field ③ For 6.9μ 0.0069 ÷ (0.08 × 1) = 0.08625 Depth of field of mm

This will make a difference in depth of field. Also, the above formula does not reflect the wavelength of the light source used. Therefore, OPTART uses the following formula so that the wavelength range used is also reflected.

DOF = R ”/ (NA × β) + {λ / (2 × NA × NA)}

R ″ =

For two camera pixel sizes ex. 2/3 ″ 5M When the camera element size is 3.45 μm, the substitution value is 0.0069.

β ″ =

magnification

λ =

Wavelength of light source ex. 600nm For a single wavelength, the substitution value is 0.0006.

NA =

Lens object NA

When the lens of the above example is calculated using the above formula, DOF = (0.0069 / 0.08 × 1) + (0.0006 / 2 × 0.0064) = 0.13 mm. 0.5mm 0.25mm 0.13mm Which of these three numbers do you recognize as the depth of field?

Our view of permissible circles of confusion and depth of field

Since the days of silver halide cameras, the depth of field has been calculated using the number of the minimum confusion circle diameter of the lens, 40 μm (size due to out-of-focus), but the pixel size of the current FA camera. Is smaller, and considering its reproducibility, it is not suitable for the actual situation. For example, when using a 5M camera with a 1-pixel size of 3.45 μm, the minimum circle of confusion must be set to 6.9 μm. We add the optical effect to the pixel size effect and use the formula below to list the depth of field closer to your environment in the catalog.

DOF = R ”/ (NA × β) + {λ / (2 × NA × NA)}

R ″ =

For two camera pixel sizes ex. 1 element size 4.65 μm, the substitution value is 0.0093

β ″ =

magnification

λ =

Wavelength of light source ex. 550nm For a single wavelength, the substitution value is 0.00055.

NA =

Lens object NA

* We define the depth of field as the range that can guarantee the optical resolution.

For more information, check on https://www.dzoptics.com/en/machine-vision/