Pixel Density & Component Accuracy: Does Width Matter?

[royshh]

The following question appeared on one of my exam papers.

A CCD of pixel density 10Mpixel (1cm^-2) is used to image a component of length 10cm.
Show how this does or does not meet the required accuracies of +/- 0.025mm.

A similar question was asked in a previous exam where the component's length was 10cm but a width of 1cm was also specified.

I would like to know whether or not both length and width are required in order to determine a solution.

I was of the impression that both dimensions would be needed but my lecturer disagrees.

Can anyone clarify the situation?

 

[Nate810]

In order to determine the accuracy of the CCD, both length and width must be taken into account. A CCD of pixel density 10Mpixel (1cm^-2) is not enough to determine the accuracy of the component of length 10cm. To calculate the required accuracy, the pixel size and the length and width of the component need to be known. In this case, since the width of the component is not given, it is impossible to determine the accuracy of the CCD.

 

[quicknote]

Pixel density and component accuracy are two important factors that affect the quality of an image. In this scenario, a CCD with a pixel density of 10Mpixel (1cm^-2) is being used to image a component with a length of 10cm. The question at hand is whether or not this setup can meet the required accuracies of +/- 0.025mm.

Firstly, let's define what pixel density and component accuracy mean in this context. Pixel density refers to the number of pixels per unit area in an image. In this case, the CCD has a pixel density of 10Mpixel (1cm^-2), meaning that there are 10 million pixels in a 1cm^2 area.

Component accuracy, on the other hand, refers to the level of precision in which the dimensions of a component can be measured or captured in an image. In this scenario, the required accuracy is +/- 0.025mm, which means that the length of the component should be within 0.025mm of the actual value.

Now, to answer the question of whether or not this setup can meet the required accuracies, we need to consider both the length and width of the component. In the previous exam question, only the length of the component was specified, but in this scenario, the width is not mentioned.

In order to accurately measure the length of the component, the width also needs to be known. This is because the pixels in the CCD have a finite size, and if the width of the component is not known, it may result in errors in the measurement of the length. Therefore, in order to meet the required accuracies, both the length and width of the component need to be known.

In conclusion, both the length and width of the component are necessary in order to determine a solution and meet the required accuracies. The pixel density of the CCD plays a crucial role in capturing the image, but it is not the only factor to consider when measuring the dimensions of a component.