Multi-choice questions

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Multi-choice Quiz Module 4

1. Any arbitrary function can be analyzed as the sum of harmonic functions in Fourier Optics. Which type of waves are these harmonic functions?

a. Any optical wave that satisfies the Helmonthz equation.

b. Paraboloidal waves

c. Plane waves

2. What are the conditions that an optical imaging system must satisfy?

a. It should be linear

b. It should be invariant under displacement, (i.e., shift-invariant)

c. Both conditions should be met.

d. An optical imaging system should not be linear and space invariant.

3. True/False. The output of a linear shift-invariant optical system is the 2D convolution between the input signal and the impulse response of the system.

a. True

b. False

4. True/False. The diffraction patterns of an object are a scaled copy of the 2D Fourier transform of the object amplitude distribution t(x,y) under Fraunhofer approximation.

a. True

b. False

5. Consider that light emerging from a source with wavelength λ = 0.5 μm propagates freely between two arbitrary planes separated by a distance of 1 m. Assume that the object points lie within a circular aperture of radius 1 cm and the observation points lie within a circular aperture of radius 2 cm. Which condition is satisfied?

a. Fraunhofer approximation.

b. Fresnel approximation

c. Both Fraunhofer and Fresnel approximation.

d. None of the above

6. Select the incorrect statement regarding lenses.

a. Lenses can provide images of objects if the distances between the object-lens (z₁) and the image-lens (z₂) satisfy the lens’ imaging equation, \( \frac{1}{z_1} + \frac{1}{z_2} = \frac{1}{f} \).

b. Lenses can perform real-time Fourier transforms of objects if objects are located at the front focal plane of the lens and the observation plane (i.e., Fourier plane) is located at the lens’ back focal plane.

c. Only converging lenses can provide images and Fourier transform of an object.

7. Select the incorrect statement regarding 4f imaging systems.

a. The impulse response of a 4f imaging system is the scaled copy of the Fourier transform of the mask transmittance.

b. The transfer function of the system is a scaled copy of the mask transmittance.

c. If no mask is inserted at the Fourier plane, the system is not an imaging system.

8. Consider a 4f imaging system whose object and image are shown below.

Object

Image

Select the mask of the 4f imaging system used to obtain the above image.

9. Consider a 4f imaging system whose object and image are shown below.

Object

Image

Select the mask of the 4f imaging system used to obtain the above image.

10. Select the most restrictive approximation in Fourier Optics.

a. Helmholtz

b. Fresnel

c. Fraunhofer

11. You are hired to build a system that operates under the Fraunhofer approximation using a 589-nm light source. Assuming that the maximum lateral extent of the input signal is 2 cm. How many football fields should be between the light source and observation planes? A football field is 91 meters long,

a. 2

b. 1

c. 10

d. 300

12. Consider that you have two identical lenses separated by the sum of their focal length. If an object is placed at the front focal plane of the first lens, what is the resulting image in the back focal plane of the second lens?

a. The original object

b. The inverted object

c. A shrunken image of the object

d. A magnified image of the object

13. Which one of the below masks would act as a high-pass filter when inserted into the middle of a 4f imaging system?