A1) Pinhole Camera

1) Sketch a diagram of the pinhole camera model (either in 2D or 3D). Include camera origin O, world point P=(x,y,z), focal length f, and image point p=(u,v) on the image plane. Inclusion of the virtual image plane is optional. Derive expressions for image coordinates p=(u,v) in terms of 3D world coordinates P=(x,y,z) and focal length f.

2) Zoe is becoming interested in photography, but currently only takes pictures using her smartphone. She is considering purchasing a full-frame 12 megapixel digital camera with a sensor size of 36mm x 36mm (square) and a focal length of 46mm. She is curious about how this compares to her smartphone, which is also 12 megapixels with a focal length of 5mm. She cant find information about the size of the sensor on her smartphone, but she knows that it is square and has the same field of view as the digital camera. That is, the digital camera and the smartphone capture an identical scene if placed at identical locations.

Using concepts from the pinhole camera model, calculate the size and area of Zoes smartphone sensor. How does this compare to the area of the camera she is considering? Show your work and include explanations so Zoe knows how to do this herself next time.

Calculate the size of a sensor pixel element for the digital camera and smartphone camera. How do they compare?