Answer:
a. An optical system capable of recovering or "processing" the original image in this scenario would consist of the following components:
Light source: A light source emitting light with a wavelength of 488 nm, which is the wavelength of the light used in the system.
Lens: A lens with a focal length of 102.5 cm, which is responsible for focusing the light onto the Fourier plane and creating the Fourier transform of the input image.
Fourier plane: The Fourier plane is the plane where the Fourier transform of the input image is displayed. The spatial frequencies between 20 and 200 lines/mm are separated by a distance of 9 cm in the Fourier plane.
Imaging system: An imaging system, such as a camera or a screen, placed at the Fourier plane to capture or display the Fourier transform of the input image.
b. To block all spatial frequencies below 160 mm^-1, a mask can be used. The mask should have a shape of a circular disk with a diameter corresponding to the spatial frequency of 160 mm^-1. The mask should be located at the Fourier plane, covering the area corresponding to spatial frequencies below 160 mm^-1. The dimensions of the mask would depend on the specific setup and requirements of the optical system.
The typical name for this type of mask is a low-pass filter, as it allows low spatial frequencies to pass through while blocking high spatial frequencies.
c. To block all spatial frequencies above 60 mm^-1, a mask can be used. The mask should have a shape of a circular aperture with a diameter corresponding to the spatial frequency of 60 mm^-1. The mask should be located at the Fourier plane, covering the area corresponding to spatial frequencies above 60 mm^-1. The dimensions of the mask would depend on the specific setup and requirements of the optical system.
The typical name for this type of mask is a high-pass filter, as it allows high spatial frequencies to pass through while blocking low spatial frequencies.
d. The effect of the low-pass filter (blocking spatial frequencies below 160 mm^-1) on the original f(x, y) image at the "object plane" at z = 0 would be to retain the low-frequency components of the image, while attenuating or blocking the high-frequency components. This would result in a blurred or smoothed version of the original image, with reduced fine details and high-frequency features.
e. The effect of the high-pass filter (blocking spatial frequencies above 60 mm^-1) on the original f(x, y) image at the "object plane" at z = 0 would be to retain the high-frequency components of the image, while attenuating or blocking the low-frequency components. This would result in an image with enhanced high-frequency details and edges, while the low-frequency components are suppressed or removed, resulting in a "sharpened" version of the original image.
Step-by-step explanation: