Reversing the calculation gives a required working distance of about 711.2mm (28"). If the maximum working distance available is 889mm (35"), then inverting the ratio (1:45) gives the maximum focal length of 35/45 = 19.76mm (7/9") so a focal length of 16mm will do. So, if I choose a focal length of 25mm (which is about 1") then a working distance of about 1140mm (45") is required. The ratio of working distance to focal length is 381mm/8.47mm = 45:1.
Example 4 (Using Flexible working distance): My FOV is 508mm x 381mm, my sensor size is 8.47mm (diagonal). These calculations are based on the following equation: Then once a lens is selected you can recalculate the exact working distance needed. This will allow you to use a range of working distance options to get a focal length range. If the working distance is limited, then, by inverting this ratio, we get the ratio of focal length to working distance. This will allow you to use specific lens focal lengths to determine the working distance needed. Also, it is common that the working distance is flexible, so for simple calculations start out with a ratio of working distance to focal length. Generally, lenses have fixed focal lengths. The equation can be modified to solve for any other variable so long as three variables are known. A sensor resolution of 1024X768 or 1280X1024 would be more appropriate in this case. The sensor of 640X480 will be not sufficient. Following the equation, the minimum sensor resolution is 500X600. It is generally assumed that the smallest feature is round with this 2mm diameter. Example 2: My FOV is 500mmX600mm and my smallest feature is 2mm. 
A camera with a resolution of 640x480 will work because 200 is less than the smallest dimension which is 480. Following the equation, the needed minimum sensor resolution is 200 pixel.
Example 1: My FOV is 100mm and my smallest feature is 1mm. To do the calculation for the minimum sensor resolution, multiply two (pixels/smallest feature) times the size (in real-world units) of the field of view divided by the size of the smallest feature as shown in the following equation: To make an accurate measurement on the image, you need to use a minimum of two pixels per smallest feature that you want to detect. The calculations can be done for each dimension separately but, for simplicity, this is often reduced to one dimension. This is in two dimensions for example 640X480. The resolution of an image is the number of pixels in the image.
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