The most efficient solution for a machine vision application is not always obvious. The characteristics of the lens influence the requirements which are placed on the image processing components located behind the lens including the processing software. Simply stated, the exposure time can be shorter if a high-quality lens is used. In addition, there is no need for processing algorithms. This is a crucial factor in high-speed measurement and monitoring applications, for example PCB inspection in electronics manufacturing where cycles times are less than 40 ms, leaving only 10 ms for image acquisition. High-speed lenses are needed to ensure correct exposure and render all of the components visible. If the brightness is uniform over the image area, the limits which have been defined can be applied to the entire image. Program loops are no longer needed to continually define new grayscale thresholds for different areas on the image. Experience has shown that this is a particularly important factor in the long-term stability of an inspection system.
To verify conformance to product specifications, telecentric lens play a key role because they provide a nearly complete, undistorted, high-resolution view of the objects. This feature differentiates them from normal photographic lenses. Because those lenses are normally entocentric, object images are subject to a greater or less extent to the perspective effect. On entocentric lenses, the center of perspectivity is located between the object and the lens (Fig. 1).
Fig. 1: The extent of the perspective effect is a major distinguishing characteristic for lenses. Because telecentric lenses are not subject to perspective errors, the surface-mounted components on the PCB are also clearly visible.
Objects which are closer to the lens appear larger than when they are further way. As a result, the rear edges of objects which have significant depth can be hidden behind the front edges or incorrect object dimensions can be derived due to variations in the object-to-lens distance. Telecentric lenses, or to be more exact object-space telecentric lenses, can eliminate the perspective effect along with the associated disadvantages. The center of perspectivity in the image space is at infinity. Through parallel projection, same-size objects appear as such in the image even if the object-to-lens distance varies. The front diameter of the lens must be at least as large as the object.
The way the lenses work is based on the position of the aperture stop.
Fig. 2: The perspective effect of a lens depends on the position of the aperture stop. The position also determines the beam's angle of incidence on the sensor.
Object imaging is not the only task for optical systems used in machine vision applications. Aperture imaging is also performed simultaneously. This determines from what direction and in what amount the rays coming from the object are captured in the image. On image-space telecentric lenses, the entrance pupil is at infinity. This design feature plays a crucial role in image uniformity as explained below. Bi-telecentric lenses combine the advantages of object-space and image-space telecentricity.
Working F-number provides a basis for comparing lens speed
Lens speed determines the correct exposure time. The working F-number Nw is used to indicate lens speed. It is defined such that at the same f-stop and same object illumination density, a lens with the same transmission properties will produce the same illuminance in the image. This number is based essentially on the solid angle projection of the illuminated surface in the sensor plane. The position of the illuminated surface is determined by the exit pupil (the sensor-side image of the aperture stop). The working F-number for an object on the optical axis and small angular aperture can be calculated using the image-side angular aperture of the lens: Nw = 1/[2∙sin(u')].
This means that essentially the image-side angular aperture determines lens speed. A larger number indicates greater light-gathering ability of the lens and hence higher speed. When the ambient medium is air, the sine of this angle is the image-side numerical aperture. The image-side numerical aperture NA' is used to describe the speed of a telecentric lens. That number can then be used to calculate the working F-number Nw: = 1/(2∙NA').
Independent lens property: telecentricity
The lens speed depends on the image-side angular aperture and consequently on the diameter of the aperture stop. It is not directly related to the telecentricity condition. However because the aperture stop influences the resolution and depth of field, it is these two parameters which determine lens speed. If only a small depth of field is needed, the aperture stop can be opened wider, increasing the resolution and lens speed. Lenses with large depth of field tend to have lower speed, so they need a longer exposure time. Because the parameters are not dependent on telecentricity, they can be determined in advance using an entocentric lens. These lenses tend to be cheaper and more readily available than telecentric lenses. This approach provides the assurance that the telecentric lens will meet the needs in practical applications. The following section explains how to compare the speed of an entocentric lens with the speed of a telecentric lens.
The f-stop setting on an entrocentric lens provides a basis for preliminary tests
Entocentric lenses are marked with an F-number to indicate the speed of the lens. In general, f-numbers between 1.0 and 2.8 indicate a relatively high speed lens and f-numbers > 16 indicate a relatively slow speed lens.
The f-number marking on an entocentric lens is only valid for objects at infinity. It can be calculated from the ratio of the diameter of the lens aperture to the focal length. This is true because the aperture stop is located close to the lens aperture and correlates with the image-side angular aperture (Fig. 2(a)). That does not work for telecentric lenses because this ratio is not related to the image-side angular aperture.
If the object is located at a finite distance from the lens as is the case with machine vision applications, the image-space angular aperture u' is reduced compared to an object at infinity (u'infinity). To determine the working f-number of an entocentric lens, the lens's magnification must be taken into consideration: Nw = N·(1+M). Real-world imaging is assumed, so magnification is always greater than 0. Conversely, it is possible to calculate the lens f-stop setting for a given working f-number.
Typical values for the image-side numerical aperture of telecentric lenses are in the 0.03 - 0.1 range. Table 1 shows the corresponding working f-numbers and the required f-stop settings on an entocentric lens for different magnification values.
Angle-dependent: image brightness uniformity
The relative illuminance on the detector is plotted against the image height to depict the progression of brightness in the image. The illumination falloff or vignetting indicates the maximum intensity decrease in percent. Ideally, maximum brightness is reached on the optical axis. Outside of the optical axis, brightness depends on the angle of incidence of the chief ray on the sensor, in other words at how large an angle the beam of light hits the sensor. This falloff can be described using the 4th power of the cosine (Fig. 3).
Fig. 3: Graph showing brightness as a function of the chief ray angle of incidence
Illumination falloff occurs because the solid angle projection of the illuminated surface in the sensor plane is reduced as the chief ray angle increases. This reduction in brightness is known as natural vignetting. Artificial vignetting can also cause loss of brightness when light beams coming from objects are partially blocked due to lens limitations. Aberrations can cause distortion of the light beam, resulting in non-uniform illumination.
The chief ray angle on object-space only telecentric lenses is typically up to 15°. Illumination falloff at the edge of the image is then around 13%. At maximum intensity in the center of the image with a grayscale value of 250, the grayscale value is only 218 at the image edge which is 32 shades of gray lower. The result can be for example that the position of the edge cannot be reliably detected because a specific threshold must be exceeded for localization.
Image-space telecentricity can help alleviate natural vignetting. Lenses which have this property are also known as anti-shading lenses. Image-space telecentricity can also be used on entocentric lenses and in combination with object-space telecentric lenses. Due to the position of the aperture stop, the exit pupil is at image-space infinity. As a result, the beams are all in parallel and all strike the sensor without loss of brightness. This type of lens must be at least as large as the sensor on the sensor side plus a bit more to avoid artificial edge shading.
The new vicotar® T42B/0.26 lens from Vision & Control combines the advantages of object-space and image-space telecentricity. Image-space telecentricity limits illumination falloff for an image circle diameter of 10 mm to 2.3% as shown in Fig. 4. Image sensors up to 2/3" can be used. 0.26-fold magnification makes the lens particularly suitable for inspection systems in the semiconductor industry.
Fig. 4: For an image circle of 10 mm, illumination falloff is less than 2.3%.
Telecentric lenses offer a complete, undistorted, high-resolution view of objects, providing the basis for high-precision measurement and reliable inspection. As described above, the speed of these lenses is not related to telecentricity. It can be estimated using the working F-number and compared with the speed of entocentric lenses. Image-space telecentric lenses can produce uniformly illuminated image areas, eliminating the need for program loops in the processing software. Overall, the measurements are more stable and reliable.
appeared in elektronikpraxis.de_11_2013