Holography

1. Holography Mon. Dec. 2, 2002

2. History of Holography • Invented in 1948 by Dennis Gabor for use in electron microscopy, before the invention of the laser • Leith and Upatnieks (1962) applied laser light to holography and introduced an important off-axis technique

3. Conventional vs. Holographic photography • Conventional: • 2-d version of a 3-d scene • Photograph lacks depth perception or parallax • Film sensitive only to radiant energy • Phase relation (i.e. interference) are lost

4. Conventional vs. Holographic photography • Hologram: • Freezes the intricate wavefront of light that carries all the visual information of the scene • To view a hologram, the wavefront is reconstructed • View what we would have seen if present at the original scene through the window defined by the hologram • Provides depth perception and parallax

5. Conventional vs. Holographic photography • Hologram: • Converts phase information into amplitude information (in-phase - maximum amplitude, out-of-phase – minimum amplitude) • Interfere wavefront of light from a scene with a reference wave • The hologram is a complex interference pattern of microscopically spaced fringes • “holos” – Greek for whole message

6. Hologram of a point source Construction of the hologram of a point source Any object can be represented as a collection of points Photographic plate • Photosensitive plate • Records interference pattern (linear response) • Emulsion has small grain structure () Reference wave - plane x z Object wave - spherical y

7. Point object hologram construction: Intensity distribution on plate • Reference wave • Object wave • Intensity distribution on plate

8. Hologram construction Gabor zone plate Maxima for kr=2m or r=m i.e. if the OPL difference OZ – OP is an integral number of wavelengths, the referencebeam arrives at P in step with the scattered (i.e. object) beam.

9. Hologram • When developed the photographic plate will have a transmittance which depends on the intensity distribution in the recorded plate • tb – backgrond transmittance due to |R|2 term • B – parameter which is a function of the recording an developing process

10. Hologram reconstruction • When illuminated by a coherent wave, A(x,y), known as the reconstruction wave, the optical field emerging from the transparency is, • i.e. a superposition of 4 waves • If A(x,y)=R(x,y), i.e. reconstruction and reference waves are identical,

11. Hologram reconstruction • Three terms in the reconstructed wave Direct wave – identical to reference wave except for an overall change in amplitude Object wave – identical to object wave except for a change in intensity Conjugate wave – complex conjugate of object wave displaced by a phase angle 2 

12. Hologram reconstruction • Three terms in the reconstructed wave of the point hologram Direct wave – identical to reference wave (propagates along z) except for an overall change in amplitude • Conjugate wave – spherical wave collapsing to a point at a distance z to the right of the hologram • a real image • displaced by a phase angle 2kz Object wave – Spherical wave except for a change in intensity B|r|2 i.e. reconstructed wavefront

13. Direct, object and conjugate waves Object wave Reference wave Real image Virtual image Direct wave Conjugate wave -z z z=0

14. Hologram :Direct, object and conjugate waves • Direct wave: corresponds to zeroth order grating diffraction pattern • Object wave: gives virtual image of the object (reconstructs object wavefront) – first order diffraction • Conjugate wave: conjugate point, real image (not useful since image is inside-out due to negative phase angle) – first order diffraction • In general, we wish to view only the object wave – the other waves just confuse the issue

15. Off-axis- Direct, object and conjugate waves Use an off-axis system to record the hologram, ensuring separation of the three waves on reconstruction Reference wave Object wave Direct wave Conjugate wave Virtual image Real image

16. Hologram – Reflection vs. Transmission • Transmissionhologram: reference and object waves traverse the film from the same side • Reflection hologram: reference and object waves traverse the emulsion from opposite sides View in Transmission View in reflection

17. Hologram: Wavelength • With a different color, the virtual image will appear at a different angle – (i.e. as a grating, the hologram disperses light of different wavelengths at different angles) • Volume hologram: emulsion thickness >> fringe spacing • Can be used to reporduce images in their original color when illuminated by white light. • Use multiple exposures of scene in three primary colors (R,G,B)

18. Hologram: Some Applications • Microscopy M = r/s • Increase magnification by viewing hologram with longer wavelength • Produce hologram with x-ray laser, when viewed with visible light M ~ 106 • 3-d images of microscopic objects – DNA, viruses • Interferometry • Small changes in OPL can be measured by viewing the direct image of the object and the holographic image (interference pattern produce finges  Δl) • E.g. stress points, wings of fruit fly in motion, compression waves around a speeding bullet, convection currents around a hot filament