Optics Primer - F-number and Numerical Aperture - f number numerical aperture
With over 15 years of experience and 500+ unique optical systems designed, Optics for Hire specializes in advanced optical engineering. If it uses light, we've worked on it.
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.
In previous entries, we have talked about the design of scanning microscopes, infinity corrected microscopes, confocal microscope design, and Koehler illumination systems-a common illumination system in microscopes. The most essential microscope element in a borescope design is the objective lens.
There are three design variables that can help us calculate the microscope objective resolution: the system wavelength, the light cone captured by the objective (also known as numerical aperture), and the refractive index between the first lens of the objective and the sample. This can be expressed by the following formula:
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.
The simplest designs are usually called ‘achromat objectives’ and contain only a front lens and a couple of achromatic doublets to correct for aberrations. On the other hand, we have Apochromat microscope objectives in which several apochromatic doublets are used, in addition to some achromats for a better image quality. For a better explanation of the difference between achromatic and apochromatic lenses, please read the linked articles.
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.
In the previous calculation, I assumed an angle of acceptance of 72-degrees with a reasonable upper limit when working with air (that angle gives us a NA of 0.95). However, by immersing the sample and microscope in oil or another liquid, it is possible to have a larger NA. This affects not only the resolution of our image but also its brightness (the brightness is calculated as the square of its NA).
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.
Objective lenses for microscopes typically have several components, including the front lens, the rear lens, the aperture, the lens barrel, and the thread. Each component plays an important role in determining the objective’s performance. For example, the aperture determines the resolution and depth of field of the objective lens, while the thread allows the objective to be attached to the microscope.
Most off the shelf microscope objectives have several body markings to better identify them. Typical markings can be seen in Figure 2.
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:
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").
Microscope objective lenses are a crucial part of a microscope, responsible for magnifying the specimen being observed. They are used to gather light from the object being observed and focus the light rays to produce a real image. The objective lens is one of the most important parts of a microscope, as it determines the microscope’s basic performance and function [3].
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.
Another specification can be “Plan Fluor” for fluorite and “APO” for apochromatic. Next we have the magnification, numerical aperture, and the immersion medium. As mentioned before, dry objective lenses usually have a NA no larger than 0.95, but that number can be considerably higher in immerse objectives. We next have an infinity symbol, meaning that the lens is infinity corrected.
Objective lenses can have just a couple of lens elements, (an achromat and simple lens, for example) or multiple groups of elements. Even two microscope objectives with the same magnification can have a completely different design, as shown in Figure 1.
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.
The microscope objective will show the manufacturer (not shown in the figure), followed by the type of aberration correction; in our image, we have a “Plan Achromat” which produces a flat surface at the image plane and achromat for the type of chromatic aberration.
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.
In cases where the objective is not meant to be used in infinity corrected microscopes, there will be a number, usually 160) referring to the length of the microscope tube. Some microscope objectives will show the letters “DIN” which stands for “Deutsche Industrial Normen.” that sets a length of 160 mm.
In conclusion, microscope objective lenses are an essential part of a microscope and are used to magnify the specimen being observed. They consist of several components that work together to produce a clear image, and their magnification can vary depending on the intended use of the microscope.
The magnification of the objective lens can vary, depending on the intended use of the microscope. For example, objective lenses for biological applications typically range from 4x to 100x, while those used for metallurgical applications can range up to 200x or more [1].
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.
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 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 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 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.
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.
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.
With over 20 years of experience and 800+ unique optical systems designed, Optics for Hire specializes in advanced optical engineering. If it uses light, we've worked on it.
Where R is the resolution, ? is the light wavelength, n is the refractive index, and θ is the half angle of the acceptance light cone (NA is the numerical angle defined as sin(θ)). For example, a microscope objective that works with visible light, with air surrounding the sample, and an acceptance half-angle cone of 72-degrees, will have a minimum resolution of 256 nm. If we surround the sample in a liquid with a refractive index of 1.5, our resolution will improve to 171 nm.