Typical sensor resolutions of 512, 1k, 2k, 4k, 8k, and 12k are available for the image acquisition. The pixel sizes on the sensor range from 5 x 5 µm, 7 x 7 µm, 10 x 10 µm to 14 x 14 µm. If possible, the camera should have preferably large pixels. A 5-µm pixel has a light-active surface of 25 µm2, yet a 14-mm pixel has 196 mm2, i.e. approximately 8 times the surface and 8 times the sensitivity to light. As the image capture time of the single lines can often only be several µs, the sensitivity to light is especially important for line scan cameras.

In order to enhance the sensitivity to light, sensors with two or more lines are used instead of those with one line, which can vertically pool the signal of several lines without losing any physical resolution like in the case of horizontal binning.

So, let’s now go back to the question. We need to identify the correct definition for the focal length of a lens. Let’s look at what our options are. Option (A) states that the focal length is the distance between the center of the lens and one of the centers of curvature. But we know that this is not correct. Although a lens does have two centers of curvature, they do not define the focal length. So, we can rule out option (A).

Which of the following is the correct definition of the focal length of a lens? (A) The focal length of a lens is the distance between the center of the lens and one of its centers of curvature. (B) The focal length of a lens is the distance between its two foci. (C) The focal length of a lens is the distance between its two centers of curvature. (D) The focal length of a lens is the distance between the center of the lens and one of its foci.

A variation of this method is to equip the system with an image trigger in order to detect single parts on a conveyor, for example. The image capture of the individual lines only starts when a photoelectric barrier is triggered by a part. This makes it possible to avoid that a part is accidentally spread over two image blocks.

Option (B) states that the focal length is the distance between the two focal points, without any mention of the center of the lens. We know that the focal length is measured from the center of the lens. And so, we know that option (B) is wrong.

If there are individual objects on a conveyor, the image acquisition can additionally be triggered: a photoelectric barrier sends a signal to the image capture hardware. Only then the lines are transmitted and it is possible to avoid that the test object spreads over two image blocks.

As the image in Y-direction is generated due to the movement of the conveyor, it is important that this is an extremely uniform motion. However, this is technically hard to realise so that the feed is synchronised by means of an encoder in order to avoid image distortions.

The transmission of smaller image blocks is also interesting. Small segments are transmitted immediately and put together in the PC. In this way the user is provided with image information at a faster pace, which can be processed. Particularly in case of continuous material which is supposed to be check completely, the processor is better working to capacity in this way. If any features (such as paint defects and scratches) are accidentally in the overlapping zone, it can be complicated to evaluate them because the information is spread over two images. However, the programmer can take this into consideration when developing the application and dynamically shift the image regions.

Finally, option (D) states that the focal length is the distance between the center of the lens and one of its focal points, or foci. That’s great because this is what we know to be the correct definition of the focal length.

From a resolution of 2048 pixels on, the sensor with 14-µm pixels has a line length of approximately 29 millimetres: the C-mount typical for industrial area scan cameras cannot be used. From a line length of over 20 mm on, the cameras have a M42 connection or Nikon bayonet, also called F-mount connection.

The CameraLink interface prevails in the image transmission for line scan cameras and has thus completely replaced the old LVDS interface. This standard serves to transmit up to 800 megabytes per second. For this purpose a CameraLink image acquisition card is required at which maximally one camera can be operated in "full configuration" or two cameras in "base configuration", depending on the data rate. It is important that the image acquisition card is adapted for the requirements of the line scan camera (bit depth, number of sensor taps, etc.). The cables are standardised, however, some important details must be observed, too, like the screwing or locking of the plugs or simply the quality of the signal lines. Cable lengths of up to 10 metres are possible without any problems using CameraLink cables, in case of longer cables repeaters or fibreglass converters must be used.

The camera only captures one image line in fast succession. For two-dimensional image acquisition, motion is required in addition to the inspection: either the object to be captured is moved by means of a conveyor ("fax principle") or the camera is moved along the stationary object ("scanner principle").

We can also rule out option (C) for the same reasons. Option (C) states that the focal length is the distance between the two centers of curvature, but we know that that’s not right.

So, we have our answer. Option (D) is the correct choice. The focal length of a lens is the distance between the center of the lens and one of its foci.

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The machine vision system is configured in such a way that always a defined number of lines are scanned. In this way, even very long image strips, e.g. with 10,000 lines, can be transmitted. Yet this very simple method does have disadvantages, too: during the transmission of the image block, this cannot be processed.

The centers of these circles are called the lens’s centers of curvature. Each lens has two centers of curvature, one on each side of the lens. Imagine now the centers of curvature are joined by a line. This line is what we call the optical axis. When parallel rays of light enter a concave lens, the lens causes them to diverge, or spread out. If we trace these diverging rays backwards, ignoring the lens, then we see that they seem to meet at a point behind the lens. We call this imaginary point the focal point of the lens.

In case of line lengths of 8k or 12k resolution, increasingly small pixel sizes are used, e.g. 7 µm, as the sensor could otherwise not be exposed using lenses with M42 or F-mount connection. The next larger standard would be optics for medium format cameras which are extremely expensive.

A peculiarity and novelty are intelligent line scan cameras. They work mainly at a line scan frequency of 12 to 18 kHz with a resolution of 1 to 2k line length. The image must no longer compulsively be transmitted to a PC, as it is immediately evaluated in the device and only the measurement results are transferred via the FastEthernet interface (100 Mbit) and I/Os. Handling these devices is also possible for less ambitious image processors, as the complexity is not that high and the modularity of the components (and number of error sources) is extremely restricted. This technology, however, has clear limits concerning camera resolution and software evaluation, as the computing power is significantly lower compared to a PC.

In practice, up to 8 sensor "taps" are operated in order to read out the sensor of a 12-megapixel line scan camera, for example, using a data rate of up to 320 MHz.

In an extreme case, so-called TDI line scan cameras (time delay integration) serve to add up to 96 lines to one overall signal in order to be 96 times more sensitive. As in this special case the large number of lines is also spatially spread, the image capture on the sensor must be synchronised very accurately with the movement of conveyor and test object in order to make both displacements (conveyor and sensor) match precisely. Only in this way the lines can subsequently be summed up without generating image blurring.

As a new, second transmission medium for bandwidths of up to 80 megabytes per second, line scan cameras with a gigabit Ethernet interface are available, too. The advantages are the omission of the image acquisition card and the long cables which can also be achieved using cheap Ethernet network cables. The overall system is therefore clearly cheaper.

Which of the following is the correct definition of the focal length of a lens? [A] The focal length of a lens is the distance between the center of the lens and one of its centers of curvature. [B] The focal length of a lens is the distance between its two foci. [C] The focal length of a lens is the distance between its two centers of curvature. [D] The focal length of a lens is the distance between the center of the lens and one of its foci.

The line scan sensor is read out in fast succession: a line scan camera with a sampling rate of 18 kHz, for instance, reads out 18,000 times per seconds, i.e. every 55 µs. In order to get the data out of the sensor, the digitalisation must happen very fast: in case of a line length of 2048 pixels, this is a frequency of 18 kHz x 2048 = 36 MHz. In order to be able to read out the sensor with even higher data rates, the sensor is read out on multiple channels:

Although the light rays don’t all actually pass through this point, it appears that the light rays exiting the lens are originating from the focal point. Now, of course, light can travel both ways through the lens. And so, there are two of these focal points, one on each side of the lens. The focal length is the distance between the center of the lens and either of the focal points. That is, the focal length of the lens is equal to either of these two distances shown in orange.

Let’s start by thinking about what we know about lenses and making sure we understand all the terms used in the question. Let’s draw a concave lens from the side. We know that the middle of a concave lens is thinner than the edges, and each side is curved. These curves are parts of circles, which we can draw in like this.