1. Use Eq. (7-14) for the superposition of two unequal beams to show
that the irradiance pattern of a Gabor zone plate (the hologram of a
point source) is given approximately by I = A + D cos2(ar2)where ...,
..., and a = π/(2sλ). Here, I1 and I2 are the irradiances due to the
reference and signal beams, respectively, s is the distance of the
object point from the film, and λ is the wavelength of the light. For
the approximation, assume the path difference between the two beams is
much smaller than s, so that we are looking at the inner zones of the
hologram.Figure 1... Get solution
2. a. Show that if the local ratio of reference to subject beam irradiances is a factor N at some region of a hologram, then the visibility of the resulting fringes is ....b. What is the fringe visibility in a region where the irradiance of the reference beam is three times that of the subject beam? Get solution
3. A conventional 1-mm-thick compact disc (CD) can store 1 Gb of information in the form of digital data, with all of the data stored in the top 1-μm-thick layer of the CD. How much information could be stored in the 1-mm-thick CD if the data could be stored holographically throughout the entire CD at the same information density? Get solution
4. The angle between the signal and reference beams during construction of a hologram is 20°. If the light is from a He-Ne laser at 633 nm, what is the fringe spacing? Assume a refractive index of 1 for the emulsion. (See Example 16-1.). Get solution
5. Suppose a hologram is to be made of a moving object using a 1-ns laser pulse at a wavelength of 633 nm. What is the permissible speed such that the object does not move more than λ/10 during the exposure? Get solution
6. During the construction of a hologram, a beam splitter is selected that makes the amplitude of the reference beam eight times that of the signal beam at the emulsion. What is the maximum ratio of beam irradiances there? Get solution
7. Let us suppose that as a theoretical limit, 1 bit of information can be stored in each λ3 of hologram volume. At a wavelength of 492 nm and a refractive index of 1.30, determine the storage capacity of 1 mm3 of hologram volume. Get solution
9. Two beams of planar wavefront, 633-nm coherent light, whose directions are 120° apart, strike a photographic emulsion of index 1.6.a. Sketch the arrangement, showing the orientation of the planes of constructive interference within the emulsion.b. Determine the planar spacing of the developed volume hologram.c. At what angle of incidence relative to the silver planes is a wavelength of 450 nm reinforced? Get solution
10. Suppose that the blue component of a white-light hologram is formed as in Figure 16-5, using light of 430-nm wavelength. If emulsion shrinkage is 15% during processing, what wavelength is reinforced by the blue-light fringes on reconstruction? How does this affect the holographic image under white-light viewing? Get solution
11. A hologram is constructed with ultraviolet laser light of 337 nm and viewed in red laser light at 633 nm.a. If the original reference beam and the reconstructing beam are both collimated, what is the magnification of the holographic image, compared with the original subject?b. What magnification would result if coherent X-rays of 1 Å wavelength were available to construct the hologram? Get solution
12. a. Verify that the reconstructed wavefront from the hologram of a point source produces both the real and virtual images shown in Figure 1. First, find the irradiance at the film due to the superposition of a plane and a spherical wave. Then, find the amplitude of the light transmitted by the developed film when irradiated by the reference beam. Interpret the terms as done in the discussion of a hologram of a three-dimensional subject.b. Show that the phase delay of the diverging subject beam, at a point on the film a distance y from the axis, is given by πy2/λd, where d is the distance of the point source from the film. This result follows when y ≪ d. Show also that reversal of the phase angle produces a converging spherical wavefront associated with the real image on reconstruction.Figure 1... Get solution
2. a. Show that if the local ratio of reference to subject beam irradiances is a factor N at some region of a hologram, then the visibility of the resulting fringes is ....b. What is the fringe visibility in a region where the irradiance of the reference beam is three times that of the subject beam? Get solution
3. A conventional 1-mm-thick compact disc (CD) can store 1 Gb of information in the form of digital data, with all of the data stored in the top 1-μm-thick layer of the CD. How much information could be stored in the 1-mm-thick CD if the data could be stored holographically throughout the entire CD at the same information density? Get solution
4. The angle between the signal and reference beams during construction of a hologram is 20°. If the light is from a He-Ne laser at 633 nm, what is the fringe spacing? Assume a refractive index of 1 for the emulsion. (See Example 16-1.). Get solution
5. Suppose a hologram is to be made of a moving object using a 1-ns laser pulse at a wavelength of 633 nm. What is the permissible speed such that the object does not move more than λ/10 during the exposure? Get solution
6. During the construction of a hologram, a beam splitter is selected that makes the amplitude of the reference beam eight times that of the signal beam at the emulsion. What is the maximum ratio of beam irradiances there? Get solution
7. Let us suppose that as a theoretical limit, 1 bit of information can be stored in each λ3 of hologram volume. At a wavelength of 492 nm and a refractive index of 1.30, determine the storage capacity of 1 mm3 of hologram volume. Get solution
9. Two beams of planar wavefront, 633-nm coherent light, whose directions are 120° apart, strike a photographic emulsion of index 1.6.a. Sketch the arrangement, showing the orientation of the planes of constructive interference within the emulsion.b. Determine the planar spacing of the developed volume hologram.c. At what angle of incidence relative to the silver planes is a wavelength of 450 nm reinforced? Get solution
10. Suppose that the blue component of a white-light hologram is formed as in Figure 16-5, using light of 430-nm wavelength. If emulsion shrinkage is 15% during processing, what wavelength is reinforced by the blue-light fringes on reconstruction? How does this affect the holographic image under white-light viewing? Get solution
11. A hologram is constructed with ultraviolet laser light of 337 nm and viewed in red laser light at 633 nm.a. If the original reference beam and the reconstructing beam are both collimated, what is the magnification of the holographic image, compared with the original subject?b. What magnification would result if coherent X-rays of 1 Å wavelength were available to construct the hologram? Get solution
12. a. Verify that the reconstructed wavefront from the hologram of a point source produces both the real and virtual images shown in Figure 1. First, find the irradiance at the film due to the superposition of a plane and a spherical wave. Then, find the amplitude of the light transmitted by the developed film when irradiated by the reference beam. Interpret the terms as done in the discussion of a hologram of a three-dimensional subject.b. Show that the phase delay of the diverging subject beam, at a point on the film a distance y from the axis, is given by πy2/λd, where d is the distance of the point source from the film. This result follows when y ≪ d. Show also that reversal of the phase angle produces a converging spherical wavefront associated with the real image on reconstruction.Figure 1... Get solution
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