Build a Michelson Interferometer

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Albert A. Michelson was the first U.S. citizen to win the Nobel prize for science. The 1907 award was given to him for his “precision optical instruments and the spectroscope and metrological investigations conducted herewith.” Michelson was the inventor of a unique interferometer that opened up new vistas in the science of light and optics. With the interferometer, Michelson was able to determine — with unprecedented accuracy — the speed of light, the wavelength and frequency of light emitted by different sources, and the constancy of the speed of light through any given medium, among other feats.

Michelson’s apparatus (actually a modified version of it) can be reasonably duplicated in the home shop or garage using a minimum of optical components. When finished, you’ll be able to use your interferometer for many of the same experiments conducted by Michelson and others. You will learn first-hand about lightwave interference and discover some interesting and useful properties of laser light. The interferometer project presented provides an excellent springboard for a science fair project.

A SHORT HISTORY

Before launching into the construction plans for the interferometer, let’s take a moment to review Michelson and his exotic contraption.

Albert A. Michelson was born in Prussia in 1872. As with many Europeans at the time, Michelson moved at the age of two with his parents to the United States. They settled in the wide expanse of Virginia City, Nevada, which was then experiencing a mining boom. Michelson’s father was not a miner but a shopkeeper. He serviced the miners and local community with his dry goods store.

Even at an early age, Michelson showed great interest and adeptness in mathematics. His parents could not afford a private college but Michelson did manage to be accepted by the U.S. Naval Academy. After graduation and a short stint at sea, he accepted a job as instructor at the academy.

Michelson’s foray into light and light physics came after one of his instructors asked him to prepare a demonstration of the Foucault method of measuring the speed of light. After studying the Foucault device, Michelson saw several ways that it could be made more accurate, and set about building an improved homemade version himself. In 1878 he repeated Foucault’s earlier speed of light measurements and achieved results that were the most accurate to date.

A few years later, Michelson began designs on another apparatus that he believed could measure the speed of light with unmatched accuracy. Michelson also wanted to learn more about what scientists of his time called ether, an invisible and undetectable material that surrounded all matter, including space, planets, and stars. Though physical evidence of the ether had never been found, physicists knew it had to exist.

In the 1860s, James Clerk Maxwell had determined, on a theoretical level, that light consists of electromagnetic waves. Others postulated that if light really consists of waves, like water or sound waves, it must travel in some medium. That medium, though invisible, must be in every nook and cranny in the universe.

With a grant of about $500 from the Volta fund, Michelson began work on his first interferometer. The brass device, shown in the sketch in ill. 9-1, consisted of two optical bench arms, each about three feet long. The arms were positioned in an asymmetrical cross, and in the apex of the cross, a beam splitter was placed. At the four ends of the arms he positioned a light source, two mirrors, and a viewing eyepiece.

In operation, a beam of light from an Argand lamp (popular in vehicles and drinking pubs as well as in the laboratory) was passed through a slit and lens, then separated by the beam splitter. The two beams were directed to a pair of fully silvered mirrors and re-directed back through the beam splitter, arriving superimposed over one another at the eyepiece.


ill. 9-1. A preliminary sketch of the original Michelson interferometer.

The function of Michelson’s interferometer was to split the nearly monochromatic light from the lamp two ways. The two beams then traveled at right angles to one another, proceeding the same distance, and then recombined at some common converging point. As with all waves, fringes appeared as the two light beams recombined.

The fringing is the result of alternating reinforcement and canceling of the waves. Where the crests of two waves meet, the light is reinforced and Michelson saw a bright glow. Where the crest and valley of two waves meet, the light is canceled, causing a dark spot.

Though Michelson’s device worked, it was extremely sensitive to vibration. Minute disturbances such as the changing of air temperature, the tap of a dog’s tail on the floor 20 feet away, even human breathing causes the fringes to disappear. Serious experiments with the interferometer were not generally conducted until Michelson took the device to the Potsdam Astrophysical Observatory in Berlin and mounted it on the stable foundation designed for an equatorial telescope.

To test for the presence, direction, and speed of the ether, Michelson rotated the interferometer and looked for minute changes in the speed of light. If the ether existed, Michelson and others postulated, it would take longer for light waves to travel “upstream” through the medium than down or across it. By rotating the device at 90-degree intervals, Michelson hoped to find a direction where a shift in the fringes would show that the light was indeed taking longer to travel one path over the other.

Alas, Michelson could detect no differences or changes in the speed of light. Though the interferometer worked and promised many breakthroughs, he was disappointed and vowed to try again with a larger and more complex version.

It wasn’t until 1905 that Albert Einstein declared that the ether did not exist and announced that light travels at the same speed in all directions. That explained why Michelson’s interferometer detected no change. In the meantime, Michelson had devised several versions of his unpatented interferometer, including the interferential comparator for the standardization of the meter, a mechanical harmonic analyzer for testing the harmonic motions of interference fringes, and a stellar interferometer for measuring the size of stars. By the turn of the 20th Century, a number of firms regularly manufactured bench models of the interferometer, and it became common in laboratories around the world.

Even up to his death in 1931, Michelson kept busy trying to improve on his basic ideas. His last project was to measure, with greater accuracy then ever before, the speed of light through a mile-long vacuum tube. It’s a pity that Michelson was not born later, or at least that the laser was not invented earlier. Had Michelson used a laser in his interferometer experiments, he would have realized an even finer measure of accuracy. With the benefit of hindsight, it’s easy to see that modern physics owes a lot to Michelson’s pioneering work. Devices and processes such as holography and the laser gyroscope are a direct outgrowth of the interferometer.

BUILDING YOUR OWN INTERFEROMETER

Michelson was plagued by the problems of weak fringes in his early interferometers because the light source he used was not entirely monochromatic, and it was certainly not coherent. With the aid of a helium-neon laser, you can construct a complete and working interferometer that displays vivid, easy-to-see fringes. The interferometer plans provided below are a modification of the Michelson apparatus. The design presented is generally referred to as the Twyman-Green interferometer, after its creators.

As with most optics experiments, a certain level of precision is required for the interferometer to work satisfactorily. However, careful construction and attention to detail should assure you of a properly working model. The design outlined below uses commonly available components and yields a device that's moderately accurate in determining the speed of light, light frequency, rate of rotation, and other observations. You might want to improve upon the basic design by adding components that provide a greater level of precision.

Component Overview

A parts lists is included in TABLE 9-1. The interferometer consists of an acrylic plastic base. Four bolts allow you to make fine adjustments in the level and position of the base. A single piano-concave or double-concave lens spreads the pencil beam of the laser to a larger spot. This allows you to see the fringes. In the center of the base is a glass plate beam splitter, positioned at a 45-degree angle to the lens. The beam splitter breaks the light into two components, directing it to two fully silvered mirrors.

One mirror is mounted on a sled that can be moved back and forth by means of a micrometer. The second mirror, placed at right angles to the first mirror, is stationary. The final component is a ground-glass viewing screen. After reflecting off the mirrors, the two beams are re-directed by the beam splitter and are projected onto the rear of the screen. When adjusted properly, the two beams exactly coincide and fringes appear. You can conveniently view the fringes on the front side of the screen.

Constructing the Base

Cut a piece of ¾-inch acrylic plastic (Plexiglas) to 9½ by 7 inches. Keep the protective paper on the plastic until you are through with cutting and drilling to prevent chipping.

Be sure the plastic is square. Finish the edges by sanding or burnishing. Drill a series of mounting holes using the drilling guide shown in ill. 9-2. Although there is room for some error, you should be as accurate as possible. Measure twice and use a drill press to ensure that the holes are perpendicular. Remove the protective paper from the plastic and set the base aside.

Constructing the Micrometer Sled

The micrometer sled is perhaps the most complicated component of the interferometer and will take you the longest to make. Note that the sled is optional; you don’t need it if all you want to do is observe laser light fringes. The sled is required only if you wish to perform some of the more advanced experiments outlined in this section.

The sled consists of two 2½-inch lengths of 4 extruded aluminum channel stock. The channel stock serves as a guide rail for the sled and is available at most hardware and building supply stores. Cut the stock with a hacksaw and miter box (to assure a perfect right-angle cut), then finish the edges with a file.

Table 9-1. Michelson Interferometer Parts List

Base and Legs

1 9½-by-7-inch, ¾-inch-thick acrylic plastic

4 ¼-inch 20 by 2-inch hex-head machine bolt

4 ¼-inch 20 nut

4 Plastic discs (for feet)

Micrometer Sled (One-Axis Translation Table)

2 2½-inch lengths of 4 by ½-by-V16-inch aluminum channel stock

2 1 ½-by-2¾-inch, ¼-inch-thick acrylic plastic

2 8/32 by ½-inch bolts, nuts

4 #8 flat washers

2 #8 or #10 fender washers

4 6/ by ½-inch bolt, nuts

12 #6 flat washers

2 ¼-by-¾-inch metal mending plate (one flat, one bent to make an angle bracket)

1 4-inch length 2/56 threaded rod

2 2/56 locking nuts

3 2/ brass nut (one for soldering to straight metal mending plate)

1 2/56 self-tapping wood screw

1 Plastic wheel (from R/C servo; for turning rod)

Sled Mirror

1 1¼-by-i ½-inch front-surface mirror

1 Small metal bracket (Erector Set)

Side Mirror

1 1¼-by-2½-inch front-surface mirror

1 Small metal bracket (from Erector Set)

1 8/32 by ½-inch bolt, nut, flat washer

Beam Splitter

1 1-by-3-inch plate (coated) beam splitter

1 1½-inch, L-shaped metal girder (from Erector Set)

1 8/32 by ½-inch bolt, nut, flat washer

Lens

1 8 to 10 mm diameter double-concave lens, in plastic or metal holder (measuring 1-inch square)

2 2-inch flat metal strip (sheet metal, brass, or similar, from Erector Set)

1 1¾-by-¾-inch, ¼-inch-thick acrylic plastic

1 8/32 by ½-inch bolt, nut, flat washer

Screen

1 2½-by-3½-inch ground glass

1 1½-inch, L-shaped metal girder (Erector Set)

1 8/32 by ½-inch bolt, nut, flat washer


ill. 9-2. Drilling guide for the Michelson interferometer base. Note the gray hole for mounting the second mirror directly to the base.


ill. 9-3 and 9-4. Use the hardware shown to assemble the sled. (A) Assembled sled (end view); (B) exploded view showing the hardware to use; (C) Bend a small, flat metal plate (available at hobby stores) to make the angle bracket.

To avoid a mismatch, use the holes you drilled in the base as a template for marking the mounting holes for the channel stock. Place the stock on the base and mark the holes with a pencil. Drill the holes with a 5 bit. Remove the flash from the aluminum with a file.

During extrusion, the aluminum channel might develop slight ridges and imperfections along the surfaces and edges. Remove these blemishes by rubbing the top (undrilled side) and edge with a piece of 300-grit wet/dry sandpaper, used wet. The object is to make the surface as smooth as possible. Don’t use a file, grinding stone, or other coarse tool, as these introduce heavy and difficult-to-remove ridges.

Set the aluminum pieces aside and construct the sled from two ¼-inch-thick acrylic plastic pieces cut to 1½ inches by 2¾ inches. Sand and burnish the edges of the plastic to make them smooth (the exact dimensions of the plastic isn't important, so you may safely remove some of it when finishing the edges). Clamp the two pieces together and drill two holes are shown in ill. 9-3.

Finish the sled by attaching the hardware shown in ill. 9-4.The angle bracket is a flat mending plate (¼-by-¾-inch, available at most hobby stores), bent 90 degrees at the middle. Before inserting the fender washers, select two, butt them together, and check for size. The two washers should be exactly the same size and shouldn't have any ridges. Continue the selection process until you find two washers that are exactly the same size.


ill. 9-5. End view of the rails. Use flat washers as spacers. Be sure the two channels are parallel.

The mirror mount in the prototype was salvaged from an Erector Set. You can use a similar mounting bracket as long as it's sturdy yet can be bent slightly. Metal is the best choice because it prevents excessive vibration, yet heavy angle irons can’t be easily bent. If you can’t scrounge up a bracket from an Erector Set, check around a hobby shop for ideas. You are bound to find something.

Assemble the pieces of the sled using the ½-by-8/32-inch hardware as shown, but don’t tighten the bolts just yet. Mount the two aluminum rails using 6/32-by-1/2-inch bolts. Use two #6 washers stacked on top of one another as spacers. Attach nuts to each bolt but don’t tighten them. A mounting assembly detail is shown in ill. 9-5.

Carefully insert the sled between the rails and jiggle things around until everything fits. Center the sled between the two rails and tighten the rails. Be absolutely sure that the rails are parallel or the sled won’t travel properly. Once the rails are tightened in place, slip the sled back and forth until it rides evenly on both rails. Slowly tighten the nuts sandwiching the top and bottom sled pieces together.

If everything fits properly, the sled should mount on the rails with little or no side- to-side motion. If there is excessive play, loosen the nuts holding the rails and push the rails closer together, remembering to keep them parallel. After careful adjustment, you should be able to get the rails close enough together so that the sled still has freedom to move back and forth, but with no side-to-side play.

If the sled doesn’t move even when the rails are pushed apart, the washers might be too thin, causing the top and bottom plastic pieces to clamp against the rails. Try slightly thicker washers. A micrometer comes in handy at this point to accurately measure the thickness of the washers. The aluminum rail should be ‘/16-inch thick, or very close to it. The washers should be just slightly thicker.

Should you find that the sled binds at one end or another, the rails are not parallel. Loosen and readjust them as necessary. If both ends of the sled are not centered between in the rails, it might move at an angle and cause considerable problems when you attempt to use the interferometer. Assuming that the plastic pieces of the sled are square, there should be equal distance between the edges of the sled and the rails. If not, loosen the two nuts holding the sled together and readjust as necessary.

The sled is now almost complete. Pull the sled out of the rails. Attach two 2/56 locking nuts and a 4-inch length of 2/56 threaded rod to the angle bracket on the underside of the sled, as shown in ill. 9-6. Solder a 2 brass nut to a ¼-by-¾-inch flat mending iron (the same kind used to make the angle bracket above), being careful not to spill molten solder inside the threads. One or two small spots of solder tacked to the outside of the nut should be sufficient (it took me three tries to get it right, so don’t despair if your first attempt doesn’t work out).

With a small bit, drill a hole 3½ inches from either side of the base (see ill. 9-7). Thread the free end of the rod through the nut/mending iron, insert the sled between the rails, then secure the mending iron using a 2/56 self-tapping screw. Finish the sled by mounting a small pulley or plastic wheel to the end of the rod. I used a 1 diameter plastic hub designed for model airplane servos. The finished sled, mounted c the base and with mirror attached (plans below), is shown in ill. 9-8.


ill. 9-6. The micrometer screw is a 4-inch length of 2/56 threaded rod. Secure it to the angle bracket (from ill. 9-4) with two 2/56 locking nuts. ill. 9-7. Drilling guide for the micrometer screw. ill. 9-8. The finished sled.

Note that although the micrometer sled is fairly accurate and has a usable resolution of a fraction of a millimeter, it's not precise enough for some light measurement applications. Methods of improving accuracy are provided later in this section.

Mounting the Mirrors

One of the fully silvered mirrors attaches to the bracket on top of the sled. Use epoxy or a general-purpose adhesive to stick the mirror against the bracket. The prototype used Duco cement, which dries fairly quickly, cures overnight, and does not discolor or fog the mirrors. The mirror attached to the sled should measure approximately 1¼ wide by 1½ inches tall.

If you don’t use the adjustable sled, you can mount the mirror and bracket directly to the base. The drilling template for the base shows the location for the rear mirror when no sled is used.

The second fully silvered mirror is mounted along the right edge of the base, using the same kind of bracket as the one attached to the sled. The second mirror should measure approximately 1¼ by 2½ inches. Secure the bracket for the second mirror using an 8/32-by-1/2-inch bolt and matching hardware. Don't overtighten.

Mounting the Beam Splitter, Lens, and Viewing Screen

The beam splitter can be ordinary plate glass, but its thickness shouldn't exceed i/n-inch. Internal reflections in thicker glass can cause a separate satellite beam (that beam can be removed using electrical tape, as shown in Section 3, but the close distances between optics make this a difficult task). The prototype used a coated, flat, glass plate measuring 1 by 3 inches. You can get by with a piece that’s shorter, but stay away from beam splitters that are less than one inch wide.


ill. 9-9. Mount the beam splitter on an Erector Set (or equivalent) metal angle bracket.

A right-angle girder piece stolen from an Erector Set serves as an excellent mount for the beam splitter. Cut a piece of girder to a length of three holes wide, as shown in ill. 9-9, and glue the beam splitter to the outside edge. When the cement is dry, attach the beam splitter and bracket to the center hole of the base using an 8/32-by-½-inch bolt and hardware. Before tightening, position the beam splitter so that it's at a 45-degree angle to the sides of the base. Don’t overtighten.

The small beam from the laser must be expanded before passing through the beam splitter. A suitable choice is a piano-concave or bi-concave lens approximately 8 to 10 mm in diameter. Focal length isn’t a major consideration, but you might need to choose another lens if the spot on the screen is excessively small or large.

Mount the lens using one of the techniques outlined in Section 7, “Constructing an Optical Bench.” A metal or plastic frame is a good choice. Use flat girders from an Erector Set or similar toy, bent at right angles at the bottom. Cement the bottom of the bracket to a piece of 1 acrylic plastic. Drill a hole with a #19 bit in the center of the plastic and attach it to the base using %2-by-½-inch bolt and hardware.

The screen is made from a 2 ½-by-3½-inch piece of ground glass (plastic can also be used). Mount the glass on the same type of girder used for the beam splitter. Once the cement is dry, attach the glass to the base using an 8 ½-inch bolt and matching hardware. Position the screen so that it's parallel to the front edge of the base. Once more, don’t overtighten the hardware.

Attaching the Legs

Finish the interferometer by attaching the legs to the four corners. Tap the four corner holes with a ¼-inch 20 tap. Thread ¼-inch 20 with 2-inch machine bolts (threaded all the way) into the holes, and secure them into position with a ¼-inch 20 nut. You can adjust the overall height of the interferometer by loosening the nut and turning the bolt. Retighten the nut when the base is at the proper height.

Leveling discs or “feet” can be added to the tips of the bolts, as shown in ill. 9-10. The discs used in the prototype were ¾-inch-diameter by ¼-inch-deep plastic chassis spacers. You can use just about anything for the feet in your interferometer, including plastic or metal stand-offs, acrylic discs drilled and tapped for ¼-inch 20 hardware, or plastic torriod coil cores. A visit to any well-stocked industrial surplus or supply outlet should yield several good alternatives. You can compensate for slight differences in height by turning the discs one way or the other. The finished interferometer, with sled and feet, is shown in ill. 9-11.


ill. 9-10. Hardware detail for the leveling feet.


ill. 9-11. The finished interferometer, with all components attached and aligned.

Adjustment and Checkout

Now comes the fun part. Set the interferometer on a hard surface, preferably on a concrete floor or sturdy table covered with carpet or foam. Even minute vibrations will upset the fringes, so it's important that the interferometer be placed on a stable platform. Thoroughly clean all of the optics, including the lens. Smudges, dirt, and fingerprints may prevent the appearance of the fringes or make them extremely difficult to see.

Turn the wheel on the sled so that the distance between the mirrors and beam splitter is approximately the same (about 3 inches). Exact positioning of the sled isn't important. (Obviously, if you didn’t construct the sled, you can ignore this step.)

Position a laser in front of the lens and direct the beam through its center. Shim the front or back of the laser so that the beam is parallel to the base. Start out with the lens perpendicular to the left edge of the base. Tithe expanded beam doesn’t strike the center of the beam splitter, move the laser to the right or left as needed.

As depicted in ill. 9-12, one half of the beam should pass through the beam splitter and strike the side (say the #1) mirror. The other half of the beam should reflect off the beam splitter and strike the rear (#2) mirror. Tithe beam doesn’t hit the #2 mirror, adjust the angle of the beam splitter as needed.

The reflected beam from the #2 mirror should pass directly through the beam splitter and hit the rear of the screen. It should appear as a round, fuzzy, red dot. The reflected beam from mirror #1 should strike against the beam splitter and also project onto the rear of the screen. Most likely, this beam won't match up with the first one. Adjust differences in horizontal spacing by rotating the #1 mirror on its mount. You can compensate for differences in vertical alignment by carefully bending the #1 and /or #2 mirrors up or down. Bend the brackets to stress the metal only, not the mirror, or you might break the glass.


ill. 9-12. The beam from the laser should follow the path shown here. Be sure both reflected beams from the mirrors align perfectly at the frosted glass.

Continue adjusting the mirrors, lens, and beam splitter until the beams coincide on the screen. It’s vitally important that the two beams be as parallel as possible. Any slight incline, either horizontally or vertically, of one beam to the other will prevent the fringes from appearing.

After each adjustment, especially after bending the mirror mounts, wait 15 to 30 seconds for the vibrations in the interferometer to settle. Once you are satisfied that the beams are as parallel to one another as possible, wait a few minutes and see if the fringes appear. Although the fringes should have a concentric bulls-eye or ring appearance, the pattern you see may begin at the outside edges of the patch. You can center the beam with the rings simply by moving the laser. You won'te that moving the laser doesn’t disturb the rings nor their position on the screen. Moving the laser too much will cause the fringes to disappear.

Once the fringes show up on the screen, you can lightly tighten the optical components to the base. After tightening a nut and bolt, inspect the beam to make sure that the fringes are still visible. You’ll note that even a small thump on the base of the interferometer causes the fringes to disappear. Depending on where you placed the interferometer, vibrations through the ground or table can also cause the fringes to go away. Once the vibrations settle, the fringes should reappear.

The loss of distinct fringes is a nuisance in many laser projects such as interferometry and holography, but it's handy in other applications. E.g., you can detect even faint motion around a given perimeter by placing a phototransistor in front of the ground glass screen. Changes in the fringes appear as voltage or current fluctuations in the transistor, and an alarm circuit can announce a possible breach of security. You can even hear the disturbance by connecting an audio amplifier to the phototransistor.

If you built the sled, you can experiment with the effects of changing the distance of the two light paths. Slowly turn the sled wheel and watch the fringes. Even a slight movement of the wheel should cause the fringe rings to move in and out. Turning the wheel one way causes the rings to grow from the inside. Turning the wheel the other way causes the rings to shrink towards the center.

By looking at the center spot of the rings, you can move the sled in precise increments. Each change from light to dark denotes a movement of one-half of one wave length. When using a helium-neon laser, one half a wavelength is 316.4 nanometers (632.8 nm÷2), or 316.4 billionths of a meter! As you might guess, it’s hard to turn the wheel so that you see only one complete light-to-dark or dark-to-light transition. The section below shows how to increase the precision of the sled so that you can use it for accurate laboratory experiments.

If the Fringes Don’t Appear

In some instances, no amount of tweaking and adjustment can coax the fringes to appear. What now? If you have constructed the interferometer as described in the text and both beams of light are transversing the paths as indicated in ill. 9-12, above, then the fringes are bound to show up sooner or later. Continue experimenting with the position of the optics until they appear.

Misalignment isn’t the only cause of absent fringes. Excessive vibrations, even ones that you and your dog can’t feel, can mask the fringes. Be sure that the interferometer is on a solid base. I first tried the prototype on a carpeted floor and obtained adequate but frustrating results. Things got better when I took the contraption outside and placed it on the concrete in the garage.

If you suspect excessive vibration and just can’t seem to find a vibration-free spot, try planting the interferometer in a sand box. A similar type of sandbox is used for home- brew holography and is used for the same reason: to eliminate vibrations that cause the fringes to shift.

Loosely mounted optics can amplify even minute vibrations. Be sure the mirrors are securely cemented to their mounts and that the brackets are fairly tight on the base.

As you learned in Section 3, “Introduction to Optics,” air is a refracting medium. Like a lens, air causes light to bend and change speeds. If the air is moving around the interferometer, the density and therefore the index of refraction is constantly changing. Understandably, this has a dramatic impact on the appearance of fringes. Avoid placing the interferometer in a drafty place or where there may be a sudden change in temperature.

If you’ve just taken the interferometer from a cool to a warm atmosphere, the optics will slowly warm up and expand. This expansion, invisible to the eye, can also inhibit the appearance of the rings. Wait at least 15 to 30 minutes to acclimate the interferometer to a change in environment.

MODIFYING THE INTERFEROMETER

There are a number of ways to improve on the basic interferometer. By using a rod that has more threads per inch, you achieve greater accuracy over linear position. A quick bit of math, however, reveals that no single rod can be machined accurately enough to give a resolution good enough to turn the wheel precisely at ½-wavelength intervals.

E.g., with the 2/56 threaded rod used, there are 56 threads per inch. Each revolution, then, is 1/56 of an inch, or about 0.45 mm. With practice, you can move the wheel in 1-degree increments, or 0.00125 mm at a time. Smaller hardware exists with up to 160 threads per inch, equal to about 0.159 mm per revolution, or 0.00044 mm per degree of rotation. Hardware this fine is hard to get and is fragile. In order for you to “dial” in a half wavelength of time, the sled needs to have a positional accuracy of greater than 0.0003164 mm! (316.4 nm); that’s even less than you can hope for using the extremely small rods with 160 threads per inch.

An easier way to approach this accuracy is by using a gearing mechanism that reduces your movements to a snail’s pace. A suitable gearbox can be obtained by salvaging the gearing mechanism of a small stepper or dc motor. Attach the control wheel to the input of the gear box; attach the output of the gearbox to the interferometer sled using a rubber band or rubber belt. The belt helps isolate the interferometer from vibration.

Using the more commonly available 2/56 threaded rod, you can achieve a positioning accuracy of about 0.00014 mm (140 nm) using the 16:1 gear box supplied with a typical surplus dc stepper motor (the gear ratio may differ depending on the exact model).

Even with an improved gearing system, however, the sled may still not offer sufficient provision for some applications. There is a limit to what garage shop tinkering can do. A machinist can rebuild the sled using aluminum stock and a manual or numerically con trolled mill. In addition, a number of ready-made products that do the same thing are available. Industrial manufacturers sell optical bases (called translation stages) that have extremely fine precision. Similar (but generally less expensive) models with micrometer adjustment bases are available at most any machinist supply outlet.

One, other method is to use the works of a student’s micrometer. These are available for $40 or less at many hardware stores and have a measurement accuracy of 0.001 of an inch (0.0254 mm), but you can dial in smaller amounts. With proper gearing and careful control of the knob, you can obtain far greater resolution. A 16:1 gear ratio— which you can make yourself using small plastic or brass gears pulled from a small dc motor—should provide enough accuracy to move the mirror at half-wavelength steps.

Another modification of the interferometer is removing the viewing screen. By removing the screen, you can project the fringe pattern on a wall or other surface. The larger bullseye makes viewing and counting the fringes easier. Calibrate and graduate the screen for easier measurements.

Try bouncing the fringe pattern onto a separate, larger, rear-projection (frosted glass or plastic) screen. A graduated and calibrated magnifier (such as those used in the optics and publishing trades), can then be placed directly against the screen without worry of upsetting the interferometer.

The Michelson interferometer can be used with a number of light sources. If you have other lasers that operate at different wavelengths such as argon or krypton, you can compare fringe patterns and calculate the differences in wavelengths. Both argon and krypton lasers emit several strong lines of visible light; you can separate these with a prism or dichroic filter. After separation, the beam can be sent through the lens of the device.

INTERFEROMETRIC EXPERIMENTS

While the Michelson interferometer provides a wealth of hands-on experience in optics, interference, and lasers, it’s nice to be able to actually do something with the contraption. Here are some ideas.

Structural Stress

Remove mirror #2 from the slide and mount it on a wall. Position the interferometer base close to the wall but make sure the device doesn’t touch the wall. Apply pressure on the wall (anywhere) and you should see a shift in the fringes. Even a brick wall under light pressure by a child’s hand will show some movement.

If the stress on the wall isn't too great, project the fringe pattern on a larger surface. This enables you to more accurately measure the distance of travel. Each light-to-dark or dark-to-light transition of the center bullseye in the pattern denotes a change of 316.4 nanometers. You’ll find that a wood or plaster wall can bow so much that you’ll spend the greater part of the evening counting fringes!

Linear Measurement

By attaching a small pointer to the sled, you can measure the size of objects with amazing accuracy. Again, each transition of the bullseye patterns marks a change of 316.4 billionths of a meter. With an extra bit of work, it’s possible to locate the stage of a microscope on the base of the interferometer and sled. With the microscope, the pointer (such as a tungsten filament or even a strand of human hair) can be more easily seen than with the unaided eye.


ill. 9-13. Circuit schematic for counting fringes. (A) Complete circuit using the National Semiconductor 74C926 all-in-one counter chip; (B) Adding a Schmitt trigger to provide a clean square wave input for the counter chip (insert it between pin 6 of IC1 and pin 12 of IC2; (C) Pinout diagram for the 74C926.

Study Effects of Refraction

Placing any object in front of either mirror #1 or #2 causes a shift in the time it takes for light to traverse the two paths. You can study the effects of refraction in air by blowing gently through a tube. Place the end of the tube in either optical path and watch the fringes move. Try other objects like lenses, smoke, and water.

Similarly, you can explain the shimmer of a desert mirage by heating up the air around the interferometer and watching the fringes appear and disappear. Although a mirage doesn’t involve lasers, you can easily see how a rise in temperature causes a change in the refractive index of air. A “real” mirage looks like a shimmering oasis that awaits a weary traveler, but in reality, it's air set in motion by the heat. The different densities of the air cause unusual refraction effects.

Fringe Counter

Some experiments move the fringes too quickly and all you see is a blur. A counter circuit can be used to count the number of light-to-dark or dark-to-light transitions of the shifting fringe pattern, even if the fringes move several thousand times per second. See ill. 9-13 and parts list in TABLE 9-2.

Table 9-2. Fringe Counter Circuit Parts List

Full Counter

IC1 741 op amp

IC2 National Semiconductor 74C926 integrated four-digit counter IC

R1 1 k-ohm resistor

R2 250 K-ohm potentiometer

R3 10 k-ohm to 10 megohm resistor

R4 100 k-ohm resistor

R5-R12 330 ohm resistor (not required if supply voltage is under 5 Vdc)

Q1-Q4 2N2222 transistor

Q5 Infrared phototransistor

LED 1-4 Common-cathode seven-segment LED display

S1 SPST switch

Optional Wave-Shaping Electronics

1 0.01 F disc capacitor

1 1 megohm resistor

2 1N4001 diode

1 74C14 or 40106 Schmitt trigger IC

All resistors are 5 to 10 percent tolerance, ¼ watt. All capacitors are 10 to 20 percent tolerance, rated 35 volts or more.


ill. 9-14. Corner cubes can be used to make interferometers that don’t cause reflected light to re-enter the la ser. Three different approaches are shown here.

Remove the ground-glass viewing screen on the interferometer. Place the phototransistor behind a simple focusing lens (such as a 20 to 40 mm focal length bi convex lens), at least two or three feet from the interferometer. At this distance, the fringe pattern should be fairly large and the lens and transistor should be able to discriminate separate circular fringes.

Connect the counter to the output of the amplifier and reset it to 0000. Move the sled and watch the counter. It should read some number. Note that the accuracy won’t be 100 percent, but the counter should be able to read at least 90 to 95 fringe changes out of 100 (accuracy drops dramatically if the interferometer is exposed to vibrations). You can improve the count accuracy by turning out all room lights.

ill. 9-15. A Lloyd’s Mirror interferometer consists of a laser, two lenses, and microscope slide (or other piece of flat glass). Arrange the components as shown and watch the interference fringes appear at the screen.

OTHER TYPES OF INTERFEROMETERS

The Michelson/Twyman-Green apparatus is only one of many types of interferometers developed over the last 75 years or so. A variety of interferometer types are shown in ill. 9-14.These interferometer designs using corner cubes don't reflect the beam back into the laser cavity. This back-to-the-source reflection can perturb the laser wavelength, making fringe counts meaningless. Note that more accurate fringe counts can also be obtained using thick plate beam splitters or cube beam splitters, where unwanted reflections and satellite beams are either non-existent or can be masked off using black tape. (Full details on both plate and cube beam splitters, as well as corner- cube (porro) prisms, are in Section 3, “Introduction to Optics.”) the laser wavelength, making fringe counts meaningless. Note that more accurate fringe counts can also be obtained using thick plate beam splitters or cube beam splitters, where unwanted reflections and satellite beams are either non-existent or can be masked off using black tape. (Full details on both plate and cube beam splitters, as well as corner- cube (porro) prisms, are in Section 3, “Introduction to Optics.”)

Table 9-3. Lloyd’s Mirror Interferometer Parts List

1 Laser

1 Double-concave lens (10 to 20 mm in diameter)

1 Double-convex lens (20 to 30 mm in diameter)

1 Microscope slide

1 Viewing screen

Another type of interferometer is shown in ill. 9-15 (a parts list for this and the remaining experiments in this section is in TABLE 9-3). This is called a Lloyd’s Mirror interferometer and consists of a double-concave lens, a double-convex lens, and a microscope slide. By placing the components as shown in the figure, it’s possible to calculate the wavelength of the light using the formula for double-slit diffraction (see the previous section for more details). Note that the double-convex converging lens is re moved from the light path in order to see the fringes on the viewing screen.

One interesting interference effect can be used to dazzle an audience during a light show. Simply shine a laser beam onto a front-surface mirror and position the mirror so that the beam strikes a wall or ceiling. Dip a cotton swab in rubbing alcohol and spread the alcohol over the mirror. As the alcohol dries, you see constantly moving light-forms swirling on the wall or ceiling. Tilt the mirror at an angle and some of the alcohol will run down the mirror producing more effects.

Other effects of interference can be demonstrated using a microscope slide. Hold the slide up to a slightly expanded laser beam, as shown in ill. 9-16. Some of the light is internally reflected inside the slide until it finally exits and strikes the screen. Interference fringes appear on the screen because of the many reflections of light inside the glass.

Another experiment shows the effects of interference caused by heat expansion. Spread the beam slightly with a double-concave lens and shine it through a microscope slide. Touch a hot soldering iron to the glass and watch the fringes appear around the point of contact with the iron.


ill. 9-16. An expanded beam passed through a microscope slide shows interference fringes when the beam spots are projected on a screen.

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