Holography and resolution of recording media
How much resolution is needed to record holograms?
Fringes are formed according to n lambda = 2 d sin (theta) with lambda as the wavelength of light and theta as the angle between reference and object beam; d is the fringe spacing and n is the fringe order.
For a typical transmission hologram of a three dimensional solid object, d is about one micron, 10-6 m or 10-3 mm. There are (103)2 such fringes per square millimeter. For an image 316 mm (about a foot) square, there are some 1011 fringes. Allowing 4 pixels per fringe the image requires 400 giga-pixels. Holographic film actually has even more storage capacity since the film is about ten microns thick, allowing selection of viewing beam direction according to Bragg's law, so that there can be several three dimensional images stored simultaneously on the same film.
For reflection holograms, the fringe spacing is about 1/3 micron since the reference and object beams interact from an angle approaching 180 degrees. To record a reflection hologram, the recording medium must have a corresponding fine resolution. Since reflection holograms make use of Bragg diffraction, it is necessary to record multiple fringes through the depth of the medium, so for 10 micron thick film, the effective number of "pixels" for an image 316 mm (about a foot) square is
3 x 3 x 400 x 109 3 x 10
, about 1014 pixels or 100 tera-pixels.
High resolution film or plate material is typically used to record holograms. Standard photographic film is insufficient since its resolution is at best on the order of ten microns. The sensor in a digital camera or cell phone camera also has insufficient resolution. There is a trade-off between resolution and sensitivity. Holographic film and plate materials require considerable light to attain adequate exposure.
A digital camera that captures ten mega-pixels is sufficient to produce a photographic print 316 mm (about a foot) square in which the pixels are just barely detectable (0.1 mm across after enlargement) by the eye at near point. A transmission hologram this size would require at least 400 giga-pixels.
The digital camera resolution is far insufficient for a transmission hologram of the same size as the corresponding photograph. Lacking depth, the digital sensor is unsuitable for a reflection hologram.
Viewing of a transmission hologram is done by diffracted light from micron-size heterogeneity in the developed film or plate. To emulate this via a digital display, one would need micron size luminous pixels in which the phase of coherent light emitted by the pixels is controllable. Present digital displays cannot do this. There are other 3-D technologies that do not involve holography. For example, an array of tiny cylindrical plastic lenses can direct a different image to each eye, providing a stereo effect and a sense of depth. Such methods do not allow measurement of deformation and they do not provide full 3-D.
If the reference and object beams are separated by a sufficiently small angle, then the resolution requirements for a transmission hologram are reduced as is the capability for full three dimensional rendition of the object. Such small angles occur in "in-line" holograms of particles suspended in a fluid. The interference pattern, whether recorded on film or on a digital camera, looks nothing like the original object. Reconstruction (viewing) of the image can be done by diffraction of light in the case of film, or digital processing in the case of a digital picture.
There are other optical methods for measuring deformation: moire, digital correlation, photo-elasticity, differential thermography, speckle, electronic speckle pattern interferometry; they are outside the scope of the present discussion.