A plant produces a line of translucent miniature polymer squares. Stringent quality requir...

A plant produces a line of translucent miniature polymer squares. Stringent quality requirements dictate 100% visual inspection, and the plant manager finds the use of human inspectors increasingly expensive. Inspection is semiautomated. At each inspection station, a robotic mechanism places each polymer square over a light located under an optical system that produces a magnified image of the square. The image completely fills a viewing screen measuring 80 × 80 mm. Defects appear as dark circular blobs, and the inspector’s job is to look at the screen and reject any sample that has one or more such dark blobs with a diameter of 0.8 mm or larger, as measured on the scale of the screen. The manager believes that if she can find a way to automate the process completely, she will increase profits by 50%. She also believes that success in this project will aid her climb up the corporate ladder. After much investigation, the manager decides that the way to solve the problem is to view each inspection screen with a CCD TV camera and feed the output of the camera into an image processing system capable of detecting the blobs, measuring their diameter, and activating the accept/reject buttons previously operated by an inspector. She is able to find a system that can do the job, as long as the smallest defect occupies an area of at least 2 × 2 pixels in the digital image. The manager hires you to help her specify the camera and lens system, but requires that you use off-the-shelf components. For the lenses, assume 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 × 512, 1024 × 1024, or 2048 × 2048 pixels. The individual imaging elements in these cameras are squares measuring 8 × 8 µm, and the spaces between imaging elements are 2 µm. For this application, the cameras cost much more than the lenses, so the problem should be solved with the lowest-resolution camera possible, based on the choice of lenses. As a consultant, you are to provide a written recommendation, showing in reasonable detail the analysis that led to your conclusion. Use the same imaging geometry suggested in Problem 2.5.

2.5 A CCD camera chip of dimensions 7×7 mm, and having 1024 × 1024 elements, is focused on a square, flat area, located 0.5 m away. How many line pairs per mm will this camera be able to resolve? The camera is equipped with a 35-mm lens. (Hint: Model the imaging process as in Fig. 2.3, with the focal length of the camera lens substituting for the focal length of the eye.)

FIGURE 2.3 Graphical representation of the eye looking at a palm tree. Point C is the optical center of the lens.