Coherence Length

[Alan Sailer]

I set up a basic interferometer* to try and measure the coherence length (CL) of a CrystaLaser 532nm unit. Much to my surprise it seems to work.
But I still have a few questions.

1) the interference pattern looks like newtons rings. I was expecting parallel lines. I moved the sliding mirror for maximum visibility and number of concentric circles. Then I move it until the rings are almost gone. The difference is a distance of about 100mm.

The rings disappear with any vibration.

Is this correct?

2) On some forum entries people have said this difference in distance is the CL. However in Saxbys text, he says that this length is 1/4 the CL and that the practical CL is half that new number. So in my case the CL would be 200mm.

Which is right?

Cheers.

* two mirrors, one stationary the other sliding. A beam splitter and a 20X microscope objective beam expander. All on a nice little optical breadboard.
The mirrors have quality x-y mounts. The splitter is a half reflecting mirror. Everything else is tape and glue

[Din]

I set up a basic interferometer* to try and measure the coherence length (CL) of a CrystaLaser 532nm unit. Much to my surprise it seems to work.
But I still have a few questions.

1) the interference pattern looks like newtons rings. I was expecting parallel lines. I moved the sliding mirror for maximum visibility and number of concentric circles. Then I move it until the rings are almost gone. The difference is a distance of about 100mm.

The rings disappear with any vibration.

Is this correct?

Yes, correct. The reason you got rings instead of the (more common) lines is that you'll get rings if the two beams are exactly co-linear; if there's any variation from co-linearity, you'll get lines. Since it's extremely difficult to make the two beams co-linear to a few wavelengths, you almost always get lines. As an aside, my wife, Joy, got rings in a Michelson about 20 years ago and stared at it for half an hour! "Look at that!, exactly co-linear!" Concerning the lack of vibration, you get vibration if the beams move in relation to each other. If the mirror is moved smoothly, you'll get no vibration. Having said that, once you get the maximum contrast, if you tap the table, or either mirror, lightly, you'll get vibration. The quicker the vibration stops, the more stable is your set-up.

2) On some forum entries people have said this difference in distance is the CL. However in Saxbys text, he says that this length is 1/4 the CL and that the practical CL is half that new number. So in my case the CL would be 200mm.

Which is right?

Cheers.

* two mirrors, one stationary the other sliding. A beam splitter and a 20X microscope objective beam expander. All on a nice little optical breadboard.
The mirrors have quality x-y mounts. The splitter is a half reflecting mirror. Everything else is tape and glue

You're right, the coherence length is about 100 mm. Saxby may have misunderstood, or you may have misread, two different kinds of mirrors. It is often said (or used to be) that the coherence length was twice the distance of the laser tube in a gas laser - most holographers in the 70's - 80's used either HeNe's or Argon's, both being gas lasers. However, the coherence length is actually twice the distance between the mirrors* inside the tube. These mirrors, inside the tube, are not the same mirrors as the Michelson mirrors. In practice, this idea of the coherence length being twice the inter-mirror distance is not usually true, it's only true if the laser beam consisted of a single wavelength, such as, eg 532nm. This is impossible, all light sources - even lasers - have a bandwidth consisting of a band of wavelengths. The coherence length is then a function of the bandwidth, the narrowerr the bandwidth, the longer the coherence length. Some people put etalons inside the tube to narrow the bandwidth and so extend the coherence length.

*Mathematically, if you can follow the maths, there exists 'modes' inside a laser tube that determine which wavelengths the laser tube can support - the modes are quantised and depend on the inter-mirror distance. The condition for a specific frequency to exist is given by f(n) = n* [c/(2d)], where f is the frequency of a specific mode, c is the speed of light, n is the mode number and d is the inter-mirror distance. If you replace f(n) = c/L(coh) (where L(coh) is the coherence length), and use n = 1 (TEM00 or Single Longitudinal Mode - SLM), then you get L(coh) = 2d, or, twice the inter-mirror distance. But, I stress, this is the distance between the mirrors inside the laser, not the mirrors on a Michelson.

Hot glue and tape! My own first foray into holography, 40 years ago, was at the studio of Edwina Orr, in London. Edwina used to say that hot glue and tape were a holographers best friend.

[Alan Sailer]

Din,

Thank you very much. This answers all my questions.

After I wrote this question I put another CryataLaser in the set-up. I was able to find data on this laser (unlike the other) and it was described as multi-mode. I was unable to get any fringes.

So everything looks fine for me to make either a HeNe or 532nm hologram. Just waiting for the film...

The tapping shows I have a stable set-up. The fringes go still in a few seconds.

Another optical tool I still have in reserve is a small tube of very hard red wax. We used it in an optical set-up I did in college. It's between the hardness of Museum Wax and paraffin.

By the way, this forum is great. Some forums I've been on are very snooty to noobs. You guys are very generous. Thanks again.

ADDEN: I tried the set-up with a 25 inch long HeNe. Once again getting fringes was easy, about 10 minutes of fiddle time. I adjust the two mirrors so that the two back reflected beams all go into the "mouth" of the laser. You get a fun speckle pattern in the beam when this happens. The put in the expander and boom, fringes. The HeNe has less CL, about 75mm. I'm surprised at how rewarding it feels...

Cheers.