Holographic Methods
Midterm exam.

Solve four problems only and state which four. Show all your logic.
1 Observe the hologram shown at the examining table.
(a) For each visible object, is the image virtual, real, or part each?
(b) Is there any restriction on the range of angles over which you can see the image? Why?
(c) Where does the color in the image come from?

2 The fringe position for a zone plate pattern is xn = R(2n[[lambda]]ff) , with [[lambda]]f as the wavelength used during formation of the pattern and n as the fringe order. Show that the zone plate acts as a lens in focusing collimated light of wavelength [[lambda]], and determine the focal length.

3 (a) Sketch the optics for making a Fresnel off-axis hologram. Identify each component. What is the function of each component? What is the role of the optical table?
(b) Explain how such a hologram can give rise to a three-dimensional image.

4 Consider a convex lens of focal length f. An object is placed a distance 2f/3 from the lens.
(a) Find the position of the image by ray tracing. Use a straight-edge or ruler.
(b) Find the position of the image by use of the appropriate lens equation.
(c) Is the image inverted or erect?
(e) What is the practical use of a lens in such a configuration?

5 Observe the hologram shown at the examining table.
(b) Sketch an optical system which would give rise to this kind of hologram, and explain the role of the components.
(c) Tilt the hologram in each of two orthogonal directions. Describe your observations and explain the cause.

Holographic Methods
Final exam

Solve five problems (20 pts each) only, and state which five. #1 is required. Show all your logic.
1 Observe holograms A and B shown at the examining table.
(a) Explain all colors in images A and B. Give equations.
(b) Is there any restriction on view angle? If so, describe it. View from 0.1 m and from 2 m.
(c) Sketch the optical setups used for hologram formation for each image. Give logic based on observations.
(d) Block the illuminating spotlight and view with ambient room light. Describe and explain what you see.

2 Observe the fringe pattern shown. The object is an in vitro tibia, fractured and fixed.
(a) What interpretation methods are applicable to a photograph of holographic fringes? Why?
(b) Give your interpretation of this image.
(c) What laser or lasers do you recommend for making such an image?
(d) How are lasers used to treat diabetic retinopathy? What laser or lasers are appropriate? What wavelengths are involved?

3 (a) Sketch an experimental configuration for lens image plane reflection holography with a magnification of 5. Show all components.
(b) How do magnified images differ from images produced with a magnification of 1? Can you envisage any problem areas? What about holographic microscopy of biological samples?

4 Consider an object undergoing a displacement field u = 0.001i. A double exposure holographic interferogram is made at 488 nm; the light upon the object is in the direction
(- k/[[radical]]2 + i/[[radical]]2), independent of position on the object. The developed hologram is viewed in the direction k, independent of position on the object. x is horizontal, y is vertical. Answer the following.
(a) Sketch the fringes. Label your axes and show units.
(b) Move your eye horizontally 0.1 rad with respect to a point on the object. How do the fringes move? Be quantitative.
(c) Move your eye vertically 0.1 rad with respect to a point on the object. How do the fringes move? Be quantitative.
(d)What does the displacement field represent?
(e) What color is the light? What laser generates it? What surgery is that laser used for?

5 (a) Show that [[Delta]]n[[lambda]] = u.(kobs,1 - kobs,2), assuming n[[lambda]] = u.(kobs - hillum).
(b) How is this [[Delta]]n[[lambda]] equation used in the lab? What does it reveal?

6 Consider an embossed hologram made from a Benton hologram which was formed with light at 633 nm. Consider an object ray incident normal to the film at 0deg., and a reference beam at 45deg.
(a) What is the spacing of fringes formed in the direction perpendicular to the plane of the reference beam and the normal to the film?
(b) At what angles are rays diffracted from the hologram at 633 nm, 500 nm, and 400 nm?
(c) Is your inferred vertical angle of view reasonable?
(d) What color is the light used for formation? What laser was used? Give some other uses for that laser.