Path Length Matching

The minimum coherence length needed for holography is the twice depth of the scene unless Multiple Coherence Volumes are used. In order to preserve your coherence length you need to make sure the distance from the laser to the film is with in the coherence length of your laser. This is extremely important with inexpensive HeNe lasers with a coherence length of only a few inches and not so important on lasers that have 50M or so of coherence length like the Coherent C315.

In a complicated set up you can end up with 5 or more laser beams. Every one of the beams needs to be traced and measured. There two methods in common use.

Method 1

The easiest way is to use a piece of string. Since the distance from the laser to the first beam splitter is the same for all paths we can start our measurements from the first beam spliter. Hold the end of the string against the beam splitter mount at a place that is the same distance as the reflective surface. Then hold the string to the next mirror or optic and keep your finger on that place of the string. Then starting where your finger was on the string continue down it to the next optic or plate and mark this on the string. Continue this until you reach the film plane. Now, mark film plane intersection on the string with a piece of tape (the edge facing the starting end of the sting). This is your path length. Now repeat the same for the second beam path again starting at the beam splitter. Adjust one of the optics to gain or lose distance such that both path lengths are the same. Do this for all paths from the beam splitter. If a second beam splitter is used then each path from that splitter needs to be matched but independenly of the total length from the first beam splitter as stated above the path to the second beam spliter will be the same for each of the split beams. This method may require two people depending on geometry and table size.

This is a little confusing, it is important to make sure that when going to the second beamsplitter thet the first path measured not be shifted. It is only the unmeasured path that needs to be changed. I'll think of how to reword it...

Tips

• Use a rigid string and not a stretchy one like nylon. Test the string by holding one end the pull it just taught against a wall or table. Then add additional pulling tension. If the string stretches easily and continuously DO NOT USE IT. If it does seem to stretch a little but then a lot of force is needed to stretch it more, it can be used and note the pressure needed to get past the original stretchyness of the string. You will need this pressure when using it on the holographic table.
• A piece of fishing thin wire and most fishing lines do not have stretch are are preferable.
• Make sure to include the distance from the object to the film for object beams!
• Unless your laser is single longitudinal mode, you want to make sure your path length is even multiples of 2L where L is the length of between resonator mirrors in your laser. So for a HeNe that is 12 inches long you want to make sure the path length is either 24,48,etc multiples of 24 inches. Odd multiples is where the beam intensity will be it's lowest.
• In Pulse lasers don't forget it's the distance from the oscillator so you need to know the laser's internal path length as well.
• Finally don't forget about polarization. If you use a standard optical table mounted setup with mirrors all the same height as the object then a vertical polarized laser orientation gives a brighter image than a horizontal one.

Method 2

Another method it to use a carpenters retractable rule, the metal kind that roll up into a casing (Tape Measure). Most of these rules are designed with a curve such that you can be at the casing end of the rule, pull it out and hold it at just the casing end and the extended end will support its own weight and remain rigid. Thus using this method has two benefits. One, longer lengths can be done by just one person. Second, there is no error of trying to hold the string and mark it with one hand and keep the mark for the next set of optics.

• Simply extend the rule from the beam splitter to just past the first optic.
• Then hold the rule such that the extended end is at the optic surface then measure to the beam splitter surface.
• Write down the length.
• Do this for each segment until the film plane.
• Add up the lenghts and that will give you a final length from the beam splitter to the emulsion surface.
• Then do the same for each beam after the beam splitter.

But the disadvantage is as follows. Say that you have a beam splitter then one mirror in each path and then the film. With the string simply find the length from beam splitter, to mirror to film and mark the string. Now with the second path simply hold the end of the string at the beam splitter and the marked end at the film and pull the center of the string out so that it makes a "V" this is where you can place the second transfer mirror. The rigigidity of the tape make this difficult.

It may be advantageous to use the string to get approximate optic placements, then use the tape method to be more precise.

Tips

• Be careful not to scratch the optics!
• The wider the tape, the longer distance it can remain unsupported.

Example Diagram

In the following diagram you can see that each path (green, red and blue) are all equal to one another starting at the first beam splitter. It is important, especially if your coherence length is low, to be precise in your measurements. Measure from the exact plane of the emulsion (in this example the emulsion is on one side of a glass plate), from the reflection side of the beam splitter for both beams and from the center of the depth of the object.

Split Beam Reflection Diagram.

Note: All of the beams are of one color and from one laser. The different colors are shown to represend different path lengths.

Red Object beam 1.

• 4.5+4+4.25+3.5+1.25=17.5

Green Reference beam.

• 1.5+5+5+6=17.5

Blue Object beam 2.

• 4.5+4+4.25+3.5+1.25=17.5

Note: Using this method (using center of object) the coherence length of your laser will very nearly dictate the depth of your object.