We will assume there is some familiarity with holography and that the reader has seen fringe patterns before. The Fringe Locker Applications section of this manual includes a list of literature on fringe lockers in the footnotes for those who wish to get further information on fringe locking.
Abstract
The concept of a fringe stabilization is very simple in nature. When a fringe moves its position spatially, it is simply reflecting a change in path length in either the reference or image path. Fringe stabilization depends on this inherent relationship. By use of electro-optic detectors, this path length variation can be detected. Through electronic circuitry the detected value can be scaled and amplified to drive an electronically moveable mirror, which, when used as a reflecting surface in either the image or reference path, can correct for path length variations.
Sensor geometry
To maintain a simple and cost effective detector, a minimum of two sense elements must be used. For the Stabilock II, the spatial separation is one tenth of an inch. Pinhole openings are placed over the detectors with a diameter of .032 inches. This size provides a good compromise between taking a point source sample and allowing enough energy to enter the detector.
Gain relationship between detector spacing and fringe width
It is essential to understand the gain relationship between the detector separation and the fringe width. For our purposes assume that the intensity of the recombined light in the fringes varies spatially in a sinusoidal fashion. If the spacing of the fringes (light band to light band) were equal to the spacing of the detectors, then as the fringe moves across the detector there would be no difference in the detected intensities. They would be both bright or both dim. Since the detectors work differentially, there would be no detectable signal. Consider then the alternative, where the fringe spacing is twice the detector spacing. In this case as the fringe moves, one detector would be in the bright band the other in a dark band. This condition produces the maximum detectable signal. Proper setup of the fringe size makes a large difference in the total system gain. In actuality, the original assumption of sinusoidal fringe intensity is somewhat in error and a difference signal is always generated. Also fringe locking is possible even if the fringe width is as much as an order of magnitude wider than the detector spacing.
Intensity and contrast variations
There is an additional gain relationship in the optical system caused by intensity variation and contrast. If where the light recombines destructively the result is zero energy, then where it combines constructively the amplitude is dependent on the optical energy launched into the system. The brighter the light, the greater the optical gain of the system. Also, in real systems there is a contrast factor. The greater the difference in intensity between the light and dark regions of the fringe, the greater the optical gain.
Detector responsivity variations
Finally, there is for the Stabilock II a variation in gain caused by the responsivity of the detectors which peak at 850 nanometers. A good rule of thumb is that the detectors are twice as responsive for helium neon as for argon lasers.
Sensitivity
Because of these optical gain or attenuation factors it is necessary that the electrical system allow the user to compensate for these variations. The Stabilock II provides two orders of magnitude variation, and is scaled for use in general holography. The base light level that adequate lock can be maintained is one micro watt per square centimeter.
System gain
By taking all the factors above into consideration the total system gain can be considered as follows.
(system gain = spacing x intensity x responsivity x elect. gain)
Modes of operation
This system gain generates the feed back signal that controls the mirror movement. It is a high gain system and falls into the category of a classical gain stability system. This classical system has three possible modes of operation: under damped, over damped, or critically-damped.
Under damped
Under damped is a condition where the system gain is so large that the system goes unstable. This is similar to squelching in audio system. With the Stabilock II an audible tone is often heard, but a more reliable determination is to observe the fringes. If fringes are visible when the Stabilock II is off but blur beyond recognition when the Stabilock II is on then an under damped condition is in progress.
Over damped
Over damped is a condition where there is insufficient system gain to effect the desired operation. For the Stabilock II system this is viewed as sloppy stabilization and weak locking, typically the fringe will move across the detectors as much as 30 degrees and de stabilizing forces break the lock with a 10% excursion of the mirror/bar graph.
Critically damped
Critically damped is the desired condition. When properly set up, the fringes in this mode will be crisp and clear, and slow de stabilizing forces will often cause the mirror/bar graph to move greater than 50% of it's travel. Total mirror deflection is approximately +/- 15 fringes for Helium Neon Lasers and +/-18 fringes for Argon.
Unstable
Systems which do not have adjustable gain and adjustable damping are unable to obtain good locking characteristics. However, adjustability requires an operator which is competent. The best way to acquire these skills is to experiment.
Stabilock II controls
We recommend that you set up a crude Michaelson style interference generator and apply the Stabilock II system. The Stabilock II has only three controls. Zero, Gain and Damp. The setup procedure is simple once the detector and mirror are in place. The fringes are adjusted to the proper spacing, and all the cables and cords are plugged in.
1. First turn on the Stabilock II.
2. Turn the gain and damping fully counter clockwise.
3. Adjust the Zero to center the position bar graph. Make sure that the intensity bar graph reads between 2 and 9 segments on. Less or more segments mean that your light levels exceed the operating region of the Stabilock II. Fringes should be visible and discernible.
4. Adjust the damping fully clock wise. If the fringes are still visible then you require additional electronic gain. If the fringes suddenly blur and don't resolve themselves as you turn the damping adjustment, then you have sufficient system gain for a lock. In this case rotate the damping adjustment counter clockwise until the fringes become stable, this should be your optimum setting and the fringes should be properly locked.
5. If the fringes are still stable after turning the damping fully clock wise, rotate the gain adjustment clockwise until the fringes suddenly blur and become unidentifiable. When this happens stop turning the gain adjust. Next adjust the damping counter - clock wise until the fringes resolve themselves, this is your optimum setting. If you turn the gain adjust fully clockwise and the fringes are still visible then simply leave both gain and damp fully clockwise. This is the best you can do with the existing optical setup. This generally occurs with very low light levels.
System modifications
There have been many attempts to generate workable systems for stabilization we have made several ourselves. Building a workable device is a non-trivial operation. Making it apply to many types of systems is even more difficult. It may be that this instrument will not work in your application, or it may require some variation of your setup. If you have a very exotic system, some consultation may be required. On occasion we have had requests for special detectors, mirrors and circuit modifications. We are willing to help with special modifications.
Get in print
We would appreciate submittal of any application notes you may feel are of value, especially new applications for the Stabilock II. Future catalog and literature updates will include these new applications with credit to the originator.