In short
Match the mean path lengths of object and reference beam first. The coherence length then only has to cover the spread of path differences across the scene, not the whole setup.
Laser power does not buy a brighter hologram. It buys a shorter exposure, and a shorter exposure is what makes the stability requirement achievable.
A single longitudinal mode source is the practical requirement. A mode hop during the exposure wipes out the recording.
Holography records the interference pattern between light scattered from an object and a reference beam that never touched it. Everything that makes the technique demanding follows from that one sentence: the two beams have to stay coherent with each other, and the pattern they form has to hold still long enough to be recorded. This article works through what that means for the laser.
How much coherence length a hologram needs
The requirement is usually stated as “coherence length greater than the object depth”, and that shorthand hides the actual mechanism. What has to stay within the coherence length is the optical path difference between the reference beam and the object beam, measured at each point on the recording plate.
That difference has two parts. There is a constant offset, set by how the two beams were routed from the splitter, and there is a variation across the scene, because light from the near side of the object travels a shorter route than light from the far side. The constant part you can remove by measuring the two paths and equalising them. The variation you cannot, and that is where the object depth enters.
The practical order of operations
1. Equalise the mean paths. Measure along the beam, with a string if nothing better is to hand. In practice a path mismatch is a frequent reason for a first attempt producing nothing, more often than anything in the laser.
2. Then size the coherence length against the remaining spread. That spread is of the order of the scene depth, and depending on the geometry up to roughly twice it. Moving a point of the object closer to the plate shortens both the leg from the source to that point and the leg from the point to the plate, so the two shortenings add. Choose a coherence length comfortably beyond the resulting spread. That makes the whole alignment forgiving, which is worth more in practice than the theoretical minimum.
| Source | Rough coherence length* | What it supports |
|---|---|---|
| Multi-mode diode | order of a millimetre | effectively nothing, unless paths are matched to a fraction of a millimetre |
| Single longitudinal mode diode, hundreds of MHz | order of tens of centimetres | shallow scenes and well equalised paths |
| Narrow line DPSS, around 10 MHz | around 10 m | deep scenes, several objects, relaxed alignment |
| Below 1 MHz | about 100 m and above | large-format and multi-object work |
*Figures use the 1/e field-correlation definition for a Lorentzian line. Other conventions give values that differ by roughly a factor of two to three, depending on which definition is used, so a number from a datasheet only means something once you know which one it assumes. The conversions are in laser linewidth and coherence length explained.
Contrast also does not stop abruptly at the coherence length. It falls off gradually as the path difference grows, which in a hologram shows up as the far parts of the scene recording more weakly than the near parts rather than vanishing outright.
Why the beam ratio is deliberately unequal
Fringe visibility is highest when both beams carry the same intensity at the plate. Written as a function of the intensity ratio r = Iobject / Ireference:
V = 2√r / (1 + r)
Maximum visibility at r = 1, falling away in both directions
| Reference-to-object ratio | Visibility V | Why it is used anyway |
|---|---|---|
| 1 : 1 | 1.00 | maximum contrast, but strong object-to-object interference adds noise to the recording |
| 4 : 1 | 0.80 | a ratio in this region is frequently used with silver halide emulsions, though published recommendations vary |
| 10 : 1 | 0.57 | a stronger reference keeps the recording closer to linear |
The reason for giving up contrast on purpose is that recording materials do not respond linearly to exposure, and light scattered from one part of the object interferes with light from another part. That intermodulation carries no useful information and prints as noise. Raising the reference beam above the object beam pushes the recording into a more linear regime and suppresses it.
Which ratio is right depends on the material and on the object, and the usable range is wide. Treat the numbers above as orientation and take the recommendation from the material datasheet.
Long coherence, green
532 nm Lambda Beam Narrow Line
DPSS green with narrow line variants · linewidth and coherence length stated per variant
See specs
Power, exposure time and stability
Recording materials are specified by the energy per unit area they need, not by irradiance. Exposure time therefore follows directly:
t = H / E
H is the required exposure in µJ/cm², E the irradiance at the plate in µW/cm²
Worked through: a material needing 100 µJ/cm², illuminated at 1 mW/cm², exposes in 0.1 s. Halve the irradiance and the exposure doubles. Published sensitivities differ by orders of magnitude between material families, so take the figure from the datasheet of the plate or film you are actually using rather than from a general table.
This is the real argument for laser power in holography. More power does not make the hologram brighter, because the recording saturates at its specified exposure either way. What it does is shorten the time during which everything has to hold still.
And the stability requirement is severe. The fringe spacing being recorded is of the order of the wavelength, so any relative movement between object, optics and plate during the exposure smears the pattern. The working rule in the holography literature is to keep the movement to a small fraction of a fringe, commonly quoted as something like a tenth of a wavelength, which at 532 nm is in the region of 50 nm. Treat that as a rule of thumb rather than a derived limit, because how much smearing a given recording tolerates depends on the material and on the fringe spacing in your geometry. Over a one second exposure it is an exacting requirement for a table, an object and a mount. Over a tenth of a second it becomes much more reachable, and that is what the extra milliwatts are buying.
Choosing the wavelength
| Wavelength | Where it is used | Note |
|---|---|---|
| 532 nm | the common single-colour choice today | Matches green-sensitised and panchromatic materials, and good narrow line DPSS sources are available |
| 633 nm | the classical holography wavelength | The historic helium-neon line, with a long tail of red-sensitive materials and literature |
| Violet and blue, roughly 440 to 460 nm | as the third channel in full-colour work | Combined with a green and a red line on panchromatic material |
Two things decide the choice, and neither is the physics of interference: what your recording material is sensitised for, and what a reconstruction is supposed to look like. Full-colour holography needs three wavelengths that together span the visible, recorded on a material that responds to all of them.
What the source has to deliver
| Parameter | Why it matters | What to ask for |
|---|---|---|
| Longitudinal mode behaviour | A hop during the exposure changes the wavelength and shifts the fringe pattern. The recording is lost, and nothing in the result tells you why | Stable single longitudinal mode operation, with the conditions under which it is guaranteed |
| Coherence length | Covers the spread of path differences across the scene once the mean paths are equalised | A figure with its convention, compared against your scene depth with margin |
| Beam quality | A clean fundamental mode expands into an even, structure-free illumination. Higher order content prints itself into the hologram as fixed pattern | M² and the beam mode |
| Polarization | Only matching polarization components interfere. Setups commonly use polarization perpendicular to the plane of incidence, so that both beams keep the same polarization direction regardless of the angle at which they meet | A defined, stable polarization with a stated extinction ratio |
| Power | Sets the exposure time and therefore how hard the stability requirement is to meet | Work backwards from material sensitivity, beam expansion and the exposure time you can hold |
| Power stability | Drift during a long exposure changes the effective exposure and the beam ratio | With a stated period, matched to your exposure time |
Frequently asked questions
What laser is used for holography?
A single longitudinal mode source with a coherence length comfortably larger than the depth of the scene. Historically the helium-neon laser at 633 nm, today most often a narrow line DPSS module at 532 nm, with violet and red lines added for full-colour work. The technology matters less than the mode behaviour and the coherence length.
Can I use a laser pointer or a laser diode module?
A free-running multi-mode diode has a coherence length of the order of a millimetre, which is not workable for a scene of any depth. Single longitudinal mode diode modules exist and are used for holography, and they shift the difficulty into equalising the two path lengths carefully. If you want alignment to be forgiving, a long coherence length is the thing that buys it.
How much power do I need?
Work it out from the exposure your material needs, the area you illuminate and the exposure time your setup can hold still for. Power does not make the hologram brighter, it shortens the exposure. If your table and mounts are good enough for a multi-second exposure, a modest source is enough. If they are not, power is the cheaper half of the solution.
Why is my hologram dim or only partly visible?
In rough order of likelihood: the two path lengths are not equalised, so contrast is low or absent in part of the scene; something moved during the exposure; the exposure or the development was off; or the beam ratio does not suit the material. The pattern of the failure is informative. A hologram where the near part of the object shows and the far part fades points at coherence length. One that is uniformly weak points at exposure or processing.
Does the laser need to be frequency stabilized?
Not usually in the sense required for metrology. What matters is that the source stays on one longitudinal mode for the duration of the exposure. Slow drift of the centre wavelength between exposures has little effect on a single recording, though it can matter for reconstruction geometry and for multi-exposure techniques.
Setting up for holography?
Tell us your scene depth, the recording material and the area you need to illuminate. We will work out the coherence length and the power the setup actually calls for.