The Why, When, and How of Fringe Locking
In any holographic recording set up there is a finite probability that the relative phases of the two or more interfering waves will be perturbed during the time necessary to complete the exposure. Any perturbation at all can affect the final uniformity, brightness and viewing aperture of the recording. Our success as holographers literally depends on how well we can reduce the probability of an untimely relative phase error. In other words we have to stop everything on the table from resonating, creeping, shrinking, distorting, buckling, flowing, rocking, sinking, expanding, bowing, settling, slipping or waving in the breeze. We have to stop the breeze and all its gradients too. Two ways around the problem are to always make only contact copies in thick glass or to only use a Q switched laser source or both. For virtually all other tasks we must do what we can to eliminate any and all sources of air, component or table movement.
A wise holographer does his best to stabilize the environment, block drafts and use rigid robust components and then tests the table with a Michelson interferometer. Let me suggest that you test your table by setting up an interferometer with longest possible arms and display the fringes on a screen with a grid on it or if possible place a pair of photovoltaic cells over a fringe and watch the differential voltage change. Do your best to block all sources of error and let everything settle for an hour then watch for fringe drift over 1 to 5 minutes.You may be surprised to see that your best efforts could not prevent the measurable displacement of a fringe over that much time. If you are working with a steel table, try holding your hand an inch or two away from the surface and watch the fringes drift slowly across the screen as the table heats up. A few experiments like this will convince you that there is often a good reason to go to the trouble to electronically stabilize your set up.
WHEN TO LOCK
Persons involved in production transfer type copying can benefit from stabilized setups to get more consistently good copies. Exposing in polymers and resists often takes so long that you would likely get nothing at all if a locker were not used. In less severe cases the use of a locker for exposures of more than a few seconds will always result in a recording of maximum fringe contrast which usually means highest possible signal to noise ratios and highest efficiency. I found that I could not make 8 by 10 reflection transfers into DCG from transmission masters without a locker on line.
Most of my experience is with reflection transfers in dichromated gelatin as shown in fig 1 or with the fabrication of first generation HOE elements in sizes up to 16 inches square and exposures up to 20 minutes,(above which time uncompensatable distortion tends to wipe me out in large formats). Fringe lockers are best at compensating for simple linear thermal growth or contraction of a table. They also do well with common vibration problems but cannot do much for a flimsy drafty arrangement. In other words, probably nothing can compensate for incompetence or ignorance of mechanical and optical principles but when all else fails they can make the difference that counts.
The Stabilock II fringe locker is available from Odhner Holographics, PO Box 841, Amherst, New Hampshire (PH;(603) 673-8651 or FAX: (603) 673-8685 (Jeff Odhner: <a href="mailto:email@example.com"> firstname.lastname@example.org</a>)." Jeff now has an RS-232 option for the Stabilock II Fringe Locker with a LabView driver. It is great for hands-off fringe locking applications. The driver will not only allow total control of zero, gain, and damping from the computer ("manual control via mouse") but will also enable the fringe locker to go into an "auto-lock" setup before every exposure so that the system is always optimized.
Figure 1a. Reflection Transfers Using a Locker
Figure 1b. Transmission Transfers Using a Locker
Some of the problems a locker will not help much with include distorting plates or components, uneven heating of components by absorbed light, random graded air drafts,large drifts in laser frequency and large amplitude vibrations or transients. If you have arranged geometries so that fringes sensed by the locker were generated very near the film plane then a hologram will be formed in the local area in spite of the severe movements mentioned but the rest of the plate will likely be blank, banded or dim.
<span style="line-height: 1.5em;" />The allowable movement to get a good recording varies with the kind of recording being made and is best described in terms of a % of a fringe. At 100% fringe movement we get total cancellation but even 10% is going to be noticeable, so our goal should be 1 or 2% max allowable which translates to .004 microns of path length change in the worst case reflection geometry but may only translate to 1 micron in a narrow angle transmission set up. In general the benefits of a locker will be most noticeable when making reflection holograms which tend to be several times more sensitive to path length changes than transmission holograms. Stabilization over many minutes with tolerances of under a hundredth of a micron seem unlikely and unrealistic but that is what is required and that is about what you can get from a well made and properly employed Fringe Locker.
HOW TO LOCK
<u The first step in fringe locking is to get a good look at the fringes that are to be locked onto. They can be magnified at the film plane at the expense of available energy or simply generated near the film plane for easy viewing and sensing electronically. It is very gratifying to be able to easily see with your eyes what is going on in real time so I always have chosen the fringe generation method rather than direct sensing and sampling. I place a beam splitter behind or to the side of the film holder and orient it so that one of the input beams is reflected to be collinear with the other beam. A small cross scratched into the surface of the splitter helps to align the two beams on a screen placed on a distant separate table. Everything is adjusted to get the biggest brightest fringes possible by inserting filters and lenses or picking different ratio splitters as necessary to get the best contrast and size. The locker will do fine with only a 1 mm fringe but I like to have a few fringes blown up to several inches wide on a cross hatched white screen so I can watch even the tiniest quiver or catch a fluttering mode or a mode hop during the exposure.
Another very useful method of generating fringes is to make a small hologram in a holder near the film plane and lock onto the moire fringes that result in placing it back in the set up slightly off its original angle. This method presupposes that the set up is stable enough to make at least a weak hologram without a locker so if it isn't then it can be very frustrating. It is a very general method otherwise and can be used with available diffuse image light rather than the strictly locally available specular light needed for the beamsplitter method. I always opt for the beamsplitter when it is possible to get light where I need it but have resorted to the hologram / moire method when I couldn't and find it only slightly more cumbersome. One pleasant benefit is that it always produces straight fringes over a large area whereas the splitter may only yield the distorted center of a zone plate with a single pair of fringes to lock onto and view.
The next step may have preceded the first step but not necessarily so. A transducer capable of introducing an optical path length change has to be introduced into one leg of the set up. The common choice is to reflect off a mirror mounted on a piezo bimorph or a speaker coil. Some drivers such as the STABILOK II move a bimorph far enough to be used in transmission mode by translating a wedge or prism to introduce a relative phase shift or optical path length difference, (OPD). If two prisms are used it is not necessary to include the transducer in the original set up prior to finding or generating fringes, the assembly may be pushed into place after the fact with only minor adjustments to prior alignments .
The two methods are illustrated in Fig 2. Before making the choice of mounting wedges on your bimorph consider that it moves over about 6 microns which may represent 30 fringes using a mirror at reasonable angles but will be only 7 or 8 fringes when used with a 45 degree prism of refractive index equal to 1.5. OPD equations are given for each configuration where L = the max bimorph travel and n = the index of refraction of the prism.
Fig 2. Mirror and Prism Configurations
SETTING UP THE STABILOK
The final step is connecting and adjusting the electronic hardware. The electronics of the STABILOK II consist of a simple but subtle differential amplifier with a few tweaks for fine tuning. The amp is required to be both stable and high gain, it must not drift over very long periods of time while responding to slowly drifting inputs and an occasional sharp transient or harmonic oscillation. In order to lock with a 20th of a fringe or better tolerance, the gain has to be as high as it can go without running the whole system into instability. The gain control is turned up until the fringes fuzz out and then it is backed off to where they are first clearly visible and solidly locked. The frequency response or damper control may be left up all the way or if vibration is not likely may be reduced or "rolled off" so that gain can be increased even higher to correct even tinier slow drift corrections.
I like to tweak all the controls liberally to see how the set up is going to respond. Each set up has its own peculiar resonances and weaknesses which can all be observed if you have generated an easy viewing port away from the set up with large bright fringes. After I get it all tuned up as best I can I stomp on the floor and tap the table and a few suspect components to find and fix any problems with the locker off and then on. Next I let everything settle for a few minutes to half an hour and then begin rapid fire shooting,relying on the locker to compensate for about a fringe worth of movement in every shot. The locker will allow you to significantly increase your throughput as it cuts settling time dramatically in a production set up.
I have used by now 6 different fringe locker designs and I really like the newest unit from MEI, the STABILOK II. It has an illuminated scale to let you know if it will work with available light and to center the bimorph travel. The same scale lets you track the action during exposure and even measure the amplitude and direction of the drift. The dynamic range is the range of usable input energies and is very large on this model.The gain is incredibly high which means it will oscillate but it will also lock on very tightly. The stability is better than the spec of a 20th of a wave when care is taken to generate large clean smooth fringes. The sensors are simple , rugged photodiodes in a balanced differential pair and the bimorph is damped and rigidly mounted. Drift is very low without feedback and essentially zero after a lock is made. Monitoring via a strip chart recorder is made convenient from a BNC output connector.
Fringe locking is often advisable or even necessary. It is only difficult for the first time or two and is usually quite simple to accomplish, requiring at times a little ingenuity and always some patience to generate fringes. The hardware is fairly rugged and laser grade dielectrics or prisms may be used by simply gluing them over the existing mirror. First timers are advised to experiment with their tables in the manner previously described to discover not only how to use the devices but to determine what is moving and what is not in any set up. Since the task is usually to compensate for table growth a separate laser and optical paths running parallel to the holographic set up with one shared mirror may work for you. And last of all, I think experimenting with lockers is even fun sometimes.
Last modified on 8/13/98