Telecentric lens required for FA and machine vision

1-2. The biggest feature of bi-telecentric lenses

You can change the WD without changing the magnification. A finite macro lens (non-telecentric type) with a certain magnification changes its magnification when the WD is changed. The same is true for object-side telecentric lenses. Increasing the WD will lower the magnification, and shortening the WD will increase the magnification. Due to the physical limitations of equipment, the only optical system that can accommodate changes in WD while maintaining a constant magnification is a bilateral telecentric lens.

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

1-3. Depth of field of a telecentric lens

In general, the smaller the lens aperture, the deeper the depth of field. However, the effective F-number becomes darker and the optical resolution becomes worse. In the case of telecentric lenses of our products, double-sided telecentric lenses with a variable aperture can be changed to obtain a deeper depth of field. In the case of a fixed diaphragm, we will respond with custom specifications.

2. Difference between a telecentric lens and a general macro (magnifying) lens

As mentioned above, the telecentric lens does not change the subject dimensions within the depth of field. This is because the chief ray is at 0° to the optical axis. On the other hand, in general macro lenses, the chief ray has an angle of view with respect to the optical axis. Therefore, the dimensions of the subject within that 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.

2-1. Telecentric lens advantageous for image measurement

When measuring an image, if the WD between the lens and the subject is constant and does not change, there is no problem with a general macro lens. Also, if the object has a specular surface, it is ideal to use a telecentric lens with built-in coaxial epi-illumination.

2-2. Proper use of telecentric lens and general macro lens depending on illumination method

Coaxial epi-illumination is required for surface pattern recognition of specular objects such as wafers. Therefore, telecentric lenses are mainly used. Alignment illumination for non-mirror objects such as metals such as iron and resin, even if they are flat, and for mounting substrates, etc., often uses a ring light or an oblique illumination method, so a general macro lens is also used in addition to the telecentric lens. Transmitted illumination is used for edge detection, etc. Lighting includes halogen lamps, LEDs, and metal halide light sources, and wavelengths range from general white light to ultraviolet, blue, red, and infrared rays, and the optimum color is selected according to the spectral sensitivity characteristics of the camera and lens system.

2-3. Difference in depth of field between telecentric lens and general macro lens

The depth of field of a telecentric lens is basically not as deep as a general macro lens. This is because the method (formula) for determining the depth of field is the same for telecentric lenses and general macro lenses. However, as mentioned above, in the case of a general macro lens, the subject size fluctuates within the depth of field, but in a telecentric lens it does not.

3. depth of field

3-1. Our view on depth of field

With the advent of 5M cameras, etc., the pixel size of current FA cameras is becoming more and more precise. Along with this, the lens has also become compatible with higher NA (=higher resolution) to match the pixel size of the camera. Recently, however, I have been receiving questions from users both in Japan and overseas, such as, "When I look at the catalogs of various lens manufacturers, why does the lens have a deep depth of field in terms of specifications even though it is a lens that supports high NA?" The reason is that the formula for determining the depth of field differs from company to company. Manufacturers of deep depth-of-field displays use the following formula regardless of megapixels.

Permissible circle of confusion ÷ (NA x optical magnification)or2{Permissible circle of confusion × effective F value ÷ (optical magnification)²}

And we put a value of 40μ or 20μ in the permissible circle of confusion, which corresponds 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. Put 20 microns in. What is the depth of field (DOF) when you calculate these three different numbers with the above formula?

Example) NA0.08 magnification × 1 lens for 2/3″ 5M camera

①For 40μ 0.04÷(0.08×1)=0.5mm depth of field
②20μ 0.02÷(0.08×1)=0.25mm depth of field
③For 6.9μ 0.0069÷(0.08×1)=0.08625mm depth of field

This makes 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 to reflect the wavelength range used.

DOF=R”/(NA×β)+{λ/(2×NA×NA)}

R″＝

2 camera pixel sizes
ex. In case of 2/3″5M camera element size 3.45μm, substitute value is 0.0069

β″＝

magnification

λ=

wavelength of light source
ex. For 600nm single wavelength, the imputed value is 0.0006

NA =

Object NA of the lens

Calculating the lens of the above example with the above formula,
DOF=(0.0069/0.08×1)+(0.0006/2×0.0064)=0.13mm.
0.5mm 0.25mm 0.13mm
Now, which of these three numbers do you recognize as the depth of field?

3-2. Our Permissible Circle of Confusion and Depth of Field

Since the days of film cameras, the calculation of the depth of field has followed the calculation using the lens's minimum circle of confusion diameter of 40 μm (the size due to defocus), but the pixel size of the current FA camera becomes smaller, and considering its reproducibility, it is not suitable for the actual situation. For example, when using a 5M camera with a pixel size of 3.45μm, the circle of least confusion must be set to 6.9μm. We take into account the effect of the pixel size and the optical effect, and use the following formula to describe the depth of field that is closer to the customer's usage environment in the catalog.

DOF=R”/(NA×β)+{λ/(2×NA×NA)}

R″＝

2 camera pixel sizes
ex. In case of 1 element size 4.65μm, substitute value is 0.0093

β″＝

magnification

λ=

wavelength of light source
For ex. 550nm single wavelength, the imputed value is 0.00055

NA =

Object NA of the lens

*We define the depth of field as the range where optical resolution can be guaranteed.