They were taken using a digital camera positioned vertically above an article from Physics World. The distance between the plane of the text and the plane of the CCD device was varied and the distance recorded on the pictures.
Q1. The question you need to consider is over what range of distance does the letter F in football become resolved?
Open the Modellus model Image2. This allows you to investigate the above problem using a simple model for the CCD/lens system. You need to set the grid spacing in the model to 5 pixels per division. This ensures that the grid boxes in the animation window of the model will now represent to scale the CCD "boxes" on the device in the camera that I used to take the photos above. The animation window should look like the figure below.
This is a picture of a typical CCD imaging chip. The clear surface in the centre we model as a collection of boxes, about 10 microns square in dimension, which will charge depending on the light intensity falling on the individual box.
Try running the model and play with the u slide control. (If you are unsure about the lens equation run the lens2 model now. A screen from this is included below.)
Q2. Write down a criterion using the model to help you decide when the F is resolved. To arrive at the answer you should consider how many CCD boxes you need between non-imaged features on the F to be able to tell that you have two distinct features. Then decide if the model produces an answer consistent with the experimental data in the photographs.
To do this, work with the model changing u for example and use the edit copy window function to cut and paste into Word, producing a record to illustrate your answer.
The actual dimensions of the printed F are included above for reference.
Q3. If the focal length of the lens in the camera was 5mm, use the lens formulae m=v/u and 1/u+1/f = 1/v to estimate the size of the CCD pixel elements in the camera CCD chip. This is a tricky question, you need to reason clearly.
Download the self extracting ZIP archive. Locate the file using Windows Explorer and double click. The self extractor will then start. The default installation path is C:\AP Revision. Having set the path press the Unzip button. After the files have been extracted change directory to C:\AP Revision. To start the models double click on lmage2.mdl and Lens2.mdl.
