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A vision system is generally defined as a computer based system that uses a camera and software to perform certain tasks, such as analyzing an object or scene. A system like this is most often used in quality control of manufactured parts and must be designed to resolve a minimum feature size so it is able to perform its quality control role. In addition, the field of view (FOV), camera sensor size and type, f/#, depth of field, and working distance must be specified to ensure your system meets all of your criteria. There are also other important parameters that must be addressed in your lens design, but if you are interested in these you can visit our page on specifying a custom lens. For now, here’s a description of the parameters already mentioned. We’ve put together a tool to help work out your specifications. If you’re ready, go ahead and jump to the calculator.

### Parameters

1. Working distance
2. Minimum feature size
3. Camera sensor
4. Field of view (FOV)
5. f/#
6. Depth of field

### Working Distance/Object Distance

The working distance and object distance are the same if there is nothing between the lens and the object. In some cases there are glass windows or other components between the lens and the object as seen here. If this were the case, the working distance is the distance from the front of the lens to the closest component, and the object distance is the distance from the front of the lens to the object.

### Minimum Feature Size

The minimum feature size is the smallest size feature you want your system to resolve. Depending on the system this parameter can vary significantly. For example, if a machine vision system is designed to inspect circuit boards, it may need to resolve a minimum feature size of 10 microns, but a vision system to inspect plastic containers may only need to resolve a minimum feature of 0.1mm. Specifying the minimum feature size determines the resolution of the system. In general, resolution is proportional to the price of the lens and is inversely proportional to the depth of field. It is therefore important to specify only the minimum feature size that is needed so that the cost of the lens is at a minimum and the depth of field requirement can be met.

### Camera Sensor Pixel Size

It is important to choose a sensor that will have a pixel size that will satisfy your resolution and depth of field requirements. The pixel size and the minimum feature size will determine the required magnification of the lens which is equal to the pixel size divided by the minimum feature size. Since magnification is also equal to the image distance divided by the object distance, the image distance can then be found. These values can then be used with the thin-lens formula to determine the focal length of the lens that satisfies the specifications.

### Field of View (FOV) - Camera Sensor Size

Field of view is the maximum object field that will be imaged by the system. This will be limited by the camera sensor size. Larger sensor sizes mean a greater FOV. Since cameras come in standard sizes, it’s a good idea to select the camera sensor early on in the development process and determine your other specifications from the sensor size used. Below is a table of standard 4:3 aspect ratio camera formats and their dimensions.

FOV can be specified multiple ways such as: horizontal field of view (HFOV), vertical field of view (VFOV) or just FOV which is the total diameter of the object. This means that if the object in the image above has a HFOV of 40mm and a VFOV of 30mm, then the FOV that must be specified to reflect the desired specifications would be FOV = 50mm. It’s important that your optical engineer understands what you’re specifying, so the more information the better when specifying FOV.

### F-number (f/#)

The f-number of the system defines the amount of light that can get through the lens. It’s defined as f/D, where f is the focal length and D is the entrance pupil diameter. The f/# will limit the resolution of the lens as well as the depth of field. As the f/# increases, resolution decreases, depth of field increases, and vice versa.

### Depth of Field

The depth of field is the distance the object can be moved toward or away from the lens while still meeting the resolution requirements specified by the minimum feature size. Since specifying a vision system can be a lot of work, Eckhardt Optics has made a simple calculator that will determine the important system specifications based on a few input parameters. When using the calculator, fill in the green fields and the white fields will be calculated. If some results are not what your application requires (for example, the depth of field is too small) you can change some of the parameters in the green fields (in this case the entrance pupil diameter) to meet your requirements. As always, if you have any trouble with the calculator or just need help specifying the lens, feel free to contact us.

It’s important to note that the calculator here determines the focal length of the lens while taking the object distance into consideration. We have seen many other calculators ignore the object distance and assume it’s infinity when determining the focal length, which results in the focal length calculation being equal to the image distance. Our calculator gives the focal length as calculated from the thin-lens formula.

It’s also important to note that the horizontal field of view is often used to specify a lens, but care must be taken that the optical engineer knows what is being specified. At Eckhardt Optics we design lenses based on the diagonal field of view because the full image circle must be larger than the horizontal image width as seen in the camera sensor size image above. Speaking of field of view, another important note is that one must be clear about half FOV versus full FOV. To ensure clarity, we recommend that FOV be specified using the following format: FOV (Diagonal): ± 50 mm – This specifies that a 100mm object diameter will be imaged onto the diagonal of the image sensor.

### Vision System Precision Optics

Regardless of the application, the optics used in vision systems must be designed and manufactured to a high degree of precision to obtain the best results for the system. Well designed lenses accommodate the fast inspection times often needed in assembly line type applications. To do this, a lens with a low f/# will often be specified to let more light into the system, but care must be taken that the f/# is not so low that your system’s required depth of field is not met.

When the vision system design meets all of your specifications, it is time to look into manufacturing. When lenses are specified for manufacturing, it is very important to analyze the tolerances of each optical element in the system and make the lens drawings to reflect these tolerances. Depending on the system some lenses may require very tight tolerances for manufacturing to meet the system specifications, but other designs may require looser tolerances. Since lens price increases with the specified tolerance, it is necessary to specify the tolerances appropriately to the design to get the best price for your vision system optics.

At Eckhardt Optics, we use optical design software (Zemax, SYNOPSYS, etc.) to design and tolerance our lenses. This ensures that we tolerance our optics and mechanics appropriately so we can offer you the best price for custom optics. If you are interested in our design process, or if you have any questions or comments feel free to contact us and one of our engineers will be happy to discuss your project with you.

### Machine Vision System Requiring Custom Optics

Eckhardt Optics was recently contacted by a project manager from an inspection company who requested a custom lens design for a new vision system. We were able to design a lens that satisfied all of the specifications, allowing the system to perform at the desired resolution, FOV, DOF and working distance. If you need help specifying a custom machine vision lens feel free to contact us. Our engineers are always happy to answer any questions you and walk you through the design process. If you’re not ready to start your design just yet, but are still interested in how to specify a custom lens, please visit our page on specifying a custom lens, where you can find detailed descriptions and annotated drawings explaining the most common lens specifications.