A plant produces a line of translucent miniature polymer squares. Stringent qual$-$ity requirements dictate $100\%$ visual inspection, and the plant manager finds theuse of human inspectors increasingly expensive. Inspection is semiautomated.Ateach inspection station, a robotic mechanism places each polymer square over alight located under an optical system that produces a magnified image of thesquare. The image completely fills a viewing screen measuring $80$ x $80$ mm$.$De$-$fects appear as dark circular blobs, and the inspectors job is to look at the screenand reject any sample that has one or more such dark blobs with a diameter of$0\mathrm{.}8$ mm or larger, as measured on the scale of the screen. The manager believesthat if she can find a way to automate the process completely, she will increaseprofits by $50\%.$ She also believes that success in this project will aid her climb upthe corporate ladder.After much investigation, the manager decides that the wayto solve the problem is to view each inspection screen with a CCD TV cameraand feed the output of the camera into an image processing system capable of de$-$tecting the blobs, measuring their diameter, and activating the accept$/$reject but$-$tons previously operated by an inspector. She is able to find a system that can dothe job, as long as the smallest defect occupies an area of at least $2$ x $2$ pixels inthe digital image. The manager hires you to help her specify the camera and lenssystem, but requires that you use off$-$the$-$shelf components. For the lenses, as$-$sume that this constraint means any integer multiple of $25$ mm or $35$ mm$,$ up to$200$ mm$.$ For the cameras, it means resolutions of $512$ x $512$ or $1024$ x $1024$ or $2048$ x $2048$ pixels. The individual imaging elements in these cameras aresquares measuring $8$ x $8$ micrometers and the spaces between imaging elements are $2$ micromrters. For this application, the cameras cost much more than the lenses, so theproblem should be solved with the lowest$-$resolution camera possible, based onthe choice of lenses. question; what is the minimum circular diameter that would guarentee that a $2$x$2$ array of $512$x$512$ ccd chips was illuminated?