06232015_Problems and questions for Fourier Optics - 副本

Problems and questions for Fourier Optics_06232015

1.What is the Fourier transform of a two-dimensional function g(x,y)? What is the

inverse Fourier transform of a function of two independent variables fx and fy?

2. The properties of the Fourier transform, including the Fourier transforms of

separable functions and functions with circular symmetry.

3.Why is it possible to fully describe light field by a single scalar wave equation?

4. What are the Kirchhoff boundary conditions?

5.What is the first Rayleigh-Sommerfeld solution of the diffraction by a plane screen?

6.How can we analyze a nonmonochromatic light diffracted by an aperture in an

opaque screen?

7. What is the angular spectrum of plane waves? How can we determine the angular

spectrum of the light field? What is the effect of the propagation over distance z in

terms of the angular spectrum?

8. How can we calculate the propagation of the angular spectrum of the disturbance

from one plane to another?

9. Why does the propagation of light from one plane to a parallel plane act a linear

space-invariant system?

10. What is the effect of a diffracting aperture on the angular spectrum of the

disturbance incident on it?

11.What are meanings of the positive and negative phases?

12. What are the general properties of the OTF? What is the relationship between the

OTF and the pupil function of the system?

13. From the wave optics point of view, what are the effects of a thin lens on the light

incident on its surface?

14. What is the relationship between the amplitude transfer function H of an optical

system and its pupil function P under the coherent illumination?

15. What is the phasor of the monochromatic scalar light field given by

,cos2uPtAPtt,

where A(P) and Pare the amplitude and phase, respectively, of the wave at

position P, while  is the optical frequency..

16. What is the transfer function of the wave propagation phenomenon in free space?

17. In the Fraunhofer diffraction region, please give the expression for the light field

and explain it in terms of Fourier transform.

18. How can we model general optical imaging systems in terms of the exit pupil or

entrance pupil?

19. For the polychromatic light field, how can we represent it in terms of the phasor?

How can we obtain the quantity?

20. What is the effect of the diffraction phenomenon on the image generated by an

optical imaging system?

21. The Fourier transform properties of a positive lens.

22. Under what condition is a linear imaging system space-invariant (or equivalently,

isoplanatic)? 23. What is the wave equation or the Helmholtz equation that satisfies by the complex

amplitude of any monochromatic optical disturbance?

24. What are the properties of the secondary sources predicted by first Rayleigh –

Sommerfeld solution?

25. Frersnel diffraction integral is an expression for the field distribution near the

optical axis. Please give the expressions of the Fresnel diffraction integral in three

forms.

26. Give a geometrical interpretation of the optical transfer function (OTF) of a

diffraction-limited optical imaging system under incoherent illumination?

27. Definitions of the frequently used functions and their Fourier transforms.

28. In the optical region of the spectrum, what quantity does a photodetector respond

directly?

29. What are the Fourier transform properties of a positive lens? What are the

differences between the cases when the input is placed in front of, against and

behind the lens?

30. What is meaning of the impulse response of a positive lens in the case of imaging?

Please give the expression for this impulse response.

31.What is the image predicted by geometrical optics? Please give the expression for

this image.

32. What are the differences between the spatially coherence and incoherent object

illumination?

33. What is the mutual intensity of the light?

34.What is the amplitude transfer function of an optical system? What is the

relationship between the amplitude transfer function and the structural parameters

of the optical system?

35. How can we represent the effects of the aberrations on the performance in the

frequency domain?

36. All the homework.

2-1. Prove the following properties of 6 functions:

(a) @x, by) = &S(x, y).

2-2. Prove the following Fourier transform relations:

(a) F{rect(x)rect(y)) = sinc(fx) sinc(fy).