Question

Consider an imaging system with 128×128 pixels that produces a noiseless, distortion-free digital image. It is used to digitize checkerboard patterns where all squares of the pattern are in the field of view. Using this imaging system, if a checkerboard pattern with 128×128 squares is digitized, each square will be 1×1 pixel in size. What is the size of the checkerboard square in the generated digital image for which spatial aliasing is observed (measured in pixels of the imaging system)?

• A. 1
• B. 2
• C. 0.9
• D. 2.5

Hint:

Aliasing occurs when the sampling frequency is less than twice the frequency of the pattern. For a checkerboard, this happens when squares are smaller than 1 pixel.

Answer 1

The Correct Option is C

According to the Nyquist sampling theorem, to avoid aliasing, the sampling frequency must be at least twice the highest frequency in the image.

If the square size becomes smaller than 1 pixel, the frequency content exceeds the sampling capacity, leading to aliasing.
Therefore, aliasing starts when the square size is less than 1 pixel.

Hence, spatial aliasing will be observed when the checkerboard square size is approximately 0.9 pixels.

Final Answer: \(\fbox{(C)}\)