Measuring opaque layers using two-beam, several-beam, and multiple-beam interferometry

Often in the course of laboratory work it becomes necessary to measure the thickness of opaque coatings, very thin mineral sections, paint layers, etc. In my case, I wanted to be able to measure the thickness of metallic layers electrodeposited on various substrates. Trying to do this by calculating the increased weight of the substrate and measuring the deposit's area is woefully inaccurate for a whole bunch of reasons. Besides—it's no fun doing it that way! One could employ various profiling techniques, such as running a stylus across the surface while measuring its displacement or using an optical profiler. Nice techniques all but not realistic for the impecunious researcher. However, there are approaches that are both practicable and affordable, if not actually easy. The remainder of the page is devoted to discussing them. And this includes my homemade interference microscope (a.k.a. pseudo optical profiler).

Some background

In 1943, Samuel Tolansky, a professor of physics at the London University in the UK, wrote an initial paper about the use of multiple-beam interferometry for the topographical measurements of surfaces. Even before that, scientists used two-beam interferometric techniques for evaluating the surfaces of optical components. If you have seen Newton's rings produced by pressing a long focal length lens against a very flat glass surface, then you've seen two-beam interferometry in action. Interferometry is so useful in fields ranging from astronomy to quantum physics that it should be a mainstay of the scientific researcher's armamentarium. (Please have a look at the References section for some suggested reading. You'll encounter the name Tolansky again and again in the earlier works on interferometry, and his groundbreaking work is acknowledged even in the most recent publications.)

To gain familiarity with Tolansky's interferometry, take a sample of mica and cleave off a very thin sheet. Place a piece of the mica sheet on a microscope slide. Drop a thin (approximately 1 mm thick) optically flat glass plate on top of the mica, sandwiching it tightly against the slide. Examine under narrow-band monochromatic light in an incident-light microscope using a 5X or 10X objective. (In an optical filter, the narrower the passband, the greater the coherence length. That translates into more fringes visible within the specimen.) With any sort of luck, given sufficient pressure, interference or Fizeau bands will appear. That's two-beam interference. A step-up with regard to reducing fringe thickness is to use a continuous variable density filter (the linear type with a gradient coating on what looks like a microscope slide) with its metallic coating side facing down on the mica. Very carefully slide the filter back and forth until the bands are sharpest and exhibit highest contrast. You are beginning to approach the multiple-beam realm. I call this method several-beam interferometry. Be very careful with the variable filter. Though it probably has a protective dielectric film, it can still be easily scratched. Accordingly, only place it on smooth surfaces. The variable filter must be within several wavelengths of the surface being explored in order for interference bands to show. I use small balance weights to weigh down the filter once I find an area of interest. WARNING: THIN GLASS BREAKS EASILY AND EXPENSIVE THIN GLASS BREAKS EVEN EASIER! Wear thin latex gloves to protect the glass surfaces and your fingers. Only use thin specimens so the filter isn't overly stressed.

You will quickly find out that using a microscope slide as the support for your specimen is quite restrictive. In fact, I remove the X-Y mechanical stage from the microscope and place a 3/8" thick flat glass plate with polished edges on the platform. On this plate, I position my test specimen along with the variable filter or other reference plate. It's much easier to work with though you have to move things around yourself without the convenience of the rack and pinion x-y adjustment. Generally, you will be using low power (5X or 10X objectives) so this does not present much of a problem. Before placing small weights on the reference plate, I apply finger pressure and gently teeter-totter the plate on the specimen as I hunt for the sometimes elusive fringes. After a while, you feel like you're part of the microscope!

Tolansky recommended vacuum coating the surface being evaluated with a highly reflective coating of silver. Doing this, coupled with employing an optically flat and highly reflective (>90%) reference plate, propels you into the realm of multiple-beam interferometry. The problem with silver is that it quickly tarnishes. So a protective coating, such as magnesium fluoride, needs to be deposited over the silver. Now aluminum, even enhanced aluminum, is not quite as reflective as silver, but as the following pictures demonstrate it will do nicely for most work. As can be seen below, the more reflective the coating the sharper the fringes. (The balance between film reflectivity as related to the coefficient of finesse and the film's absorption affect the fringe width. Be sure to read Tolansky's books for an explanation of how and why this happens.) And the sharper the fringes, the finer the details that can be seen on the surface. Tolansky assures us that by using multiple-beam interferometry under absolutely ideal conditions (~95% reflectivity and very low absorption) and high magnification, surface features as small as 10 Å in height or depth can be detected. Many atoms are around 3 to 4 Å in diameter. These nearly atomic scale elevations and depressions can be detected only in the up/down directions. An otherwise standard light microscope is still limited to an approximate half-wavelength of light resolution laterally.

More on the mechanics of the techniques

I mentioned the mineral mica. Other smooth-surfaced materials and minerals, such as (cleaved) calcite, selenite, quartz, silicon carbide crystals, metallic coatings, etc., can also be easily explored. If you can't coat the specimens with silver or aluminum, then just use the variable filter to hunt for the best interference fringes. In lieu of the filter, having a good set of thin beamsplitters (20/80, 30/70, 40/60, 50/50, etc.) will do and is less expensive. Remember to place the coated side against the surface being explored and use an incident-light microscope with a suitable narrow-band interference filter. Try different beamsplitters until you're happy with the results. The one you use will depend heavily on the reflectivity of the surface under study. I use a 546 nm (10 nm FWHM; coherence length ~ 30 microns) narrow-band interference filter for much of my work except where noted below. Start by examining the mineral section at its edges. It's easier to spot interference fringes there. Also, be sure to examine your mineral specimen under monochromatic light without using a reference plate. In many instances, especially with mica, you will note interference fringing due to the uncleaved or partially separated layers or lamellae acting as built-in reference plates. Though interesting, this phenomenon probably reveals very little about the topography of the external surface.

The distance between black fringes is one-half the wavelength of the light used to produce the fringes. This is approximately 10 microinches for visible light. You can use that to extract information about the topography of the surfaces shown. In some cases, I used two or three different interference filters to produce interference fringing with different spacing. Doing this helps reduce or eliminate ambiguities in interpreting shifts in fringes. In a way, it's almost like having a built-in vernier scale. Sometimes what looks like a shift of, say, 1/3 fringe could really be 1-1/3 or 2-1/3 fringes, etc. Again, the fringes are referenced against a, hopefully, flat reference that is placed on top of the surface being explored. Otherwise, the images are very much like the contour maps obtained from planes and satellites and can be similarly interpreted.

I used Adobe Photoshop to aid in producing these photos. In all instances except for the very first image photographed through my FluorEVER microscope (see page 3 of the LED Fluorescence section) a b&w video camera was used to record the fringes. For pictures where multiple filters were used with a halogen bulb light source, I took a separate photo through each filter mentioned. These individual photos were layered one on the other after first assigning an appropriate primary color (or colors) to the layer. Each layer was then inverted to produce a negative image, and the brightness and contrast were adjusted. The layers were then flattened into a single photo, and an unsharp mask was applied if needed. If a final positive was desired, I inverted the final flattened image. As you can see from some of the photos, in addition to the three primary colors, yellows, oranges, magentas, etc., were created from overlapping primaries.

Finally, I produced an anaglyphic stereo photo of the mica surface using an extremely crude tilting stage for my microscope. Though there are two colors in that picture, it was taken with only a single filter (620 nm) but tilted for left- and right-eye views. You will need red/blue glasses with red over the left eye.

Vertical scanning white-light interferometry

While multiple-beam interferometry is great for measuring very small features, defects, or blemishes on appropriate surfaces, there are a number of limitations. It is absolutely essential to work with surfaces that are inherently highly reflective or that can be vacuum coated. If the details being sought approach 5-10 microns in height/depth or more, it gets increasingly difficult to measure the contours. For surfaces that do have multi-micron or millimeter scale details, a device called a vertical scanning white light interferometer (VSWLI) can be applied. It is an optical profiler and is prohibitively expensive—unless you built one yourself. In that case, it's just very expensive. However, if you are willing to settle for the bare bones (i.e., no software and no automatic vertical scanner) interference microscope that lies at the heart of optical profiling, it's not too difficult to construct. I assembled mine in one day. But beware! These homemade systems can be exasperating, frustrating, and debilitating—not to mention tricky to set up. The optics have to be initially positioned to within an error not to exceed the diameter of a human red blood cell. The microscope, or at least the interferometer components, should be isolated from vibrations. Often as not, every time I get ready to toss the unit out the window the sought-after fringes suddenly pop into view. Maybe that's the secret!



This section is a catchall for techniques I work with that are not discussed elsewhere on this Web site. All the special methods described here were either modified or developed from scratch for my experiments. They were originally intended to allow certain measurements to be performed or to produce certain effects but were not the experiments themselves. In at least one case, the techniques discussed simply laid the groundwork for a series of experiments yet to be completed. I hope that they may be of sufficient interest to other experimenters to warrant collecting them into a separate section. Each page will describe a different technique. Part of the fun of getting to a particular destination are the side trips.
Measuring opaque layers using two-beam, several-beam, and multiple-beam interferometry Often in the course of laboratory work it becomes necessary to measure the thickness of opaque coatings, very thin mineral sections, paint layers, etc. In my case, I wanted to be able to measure the thickness of metallic layers electrodeposited on various substrates. Trying to do this by calculating the increased weight of the substrate and measuring the deposit's area is woefully inaccurate for a whole bunch of reasons. Besides—it's no fun doing it that way! One could employ various profiling techniques, such as running a stylus across the surface while measuring its displacement or using an optical profiler. Nice techniques all but not realistic for the impecunious researcher. However, there are approaches that are both practicable and affordable, if not actually easy. The remainder of the page is devoted to discussing them. And this includes my homemade interference microscope (a.k.a. pseudo optical profiler).
Some background In 1943, Samuel Tolansky, a professor of physics at the London University in the UK, wrote an initial paper about the use of multiple-beam interferometry for the topographical measurements of surfaces. Even before that, scientists used two-beam interferometric techniques for evaluating the surfaces of optical components. If you have seen Newton's rings produced by pressing a long focal length lens against a very flat glass surface, then you've seen two-beam interferometry in action. Interferometry is so useful in fields ranging from astronomy to quantum physics that it should be a mainstay of the scientific researcher's armamentarium. (Please have a look at the References section for some suggested reading. You'll encounter the name Tolansky again and again in the earlier works on interferometry, and his groundbreaking work is acknowledged even in the most recent publications.) To gain familiarity with Tolansky's interferometry, take a sample of mica and cleave off a very thin sheet. Place a piece of the mica sheet on a microscope slide. Drop a thin (approximately 1 mm thick) optically flat glass plate on top of the mica, sandwiching it tightly against the slide. Examine under narrow-band monochromatic light in an incident-light microscope using a 5X or 10X objective. (In an optical filter, the narrower the passband, the greater the coherence length. That translates into more fringes visible within the specimen.) With any sort of luck, given sufficient pressure, interference or Fizeau bands will appear. That's two-beam interference. A step-up with regard to reducing fringe thickness is to use a continuous variable density filter (the linear type with a gradient coating on what looks like a microscope slide) with its metallic coating side facing down on the mica. Very carefully slide the filter back and forth until the bands are sharpest and exhibit highest contrast. You are beginning to approach the multiple-beam realm. I call this method several-beam interferometry. Be very careful with the variable filter. Though it probably has a protective dielectric film, it can still be easily scratched. Accordingly, only place it on smooth surfaces. The variable filter must be within several wavelengths of the surface being explored in order for interference bands to show. I use small balance weights to weigh down the filter once I find an area of interest. WARNING: THIN GLASS BREAKS EASILY AND EXPENSIVE THIN GLASS BREAKS EVEN EASIER! Wear thin latex gloves to protect the glass surfaces and your fingers. Only use thin specimens so the filter isn't overly stressed. You will quickly find out that using a microscope slide as the support for your specimen is quite restrictive. In fact, I remove the X-Y mechanical stage from the microscope and place a 3/8" thick flat glass plate with polished edges on the platform. On this plate, I position my test specimen along with the variable filter or other reference plate. It's much easier to work with though you have to move things around yourself without the convenience of the rack and pinion x-y adjustment. Generally, you will be using low power (5X or 10X objectives) so this does not present much of a problem. Before placing small weights on the reference plate, I apply finger pressure and gently teeter-totter the plate on the specimen as I hunt for the sometimes elusive fringes. After a while, you feel like you're part of the microscope! Tolansky recommended vacuum coating the surface being evaluated with a highly reflective coating of silver. Doing this, coupled with employing an optically flat and highly reflective (>90%) reference plate, propels you into the realm of multiple-beam interferometry. The problem with silver is that it quickly tarnishes. So a protective coating, such as magnesium fluoride, needs to be deposited over the silver. Now aluminum, even enhanced aluminum, is not quite as reflective as silver, but as the following pictures demonstrate it will do nicely for most work. As can be seen below, the more reflective the coating the sharper the fringes. (The balance between film reflectivity as related to the coefficient of finesse and the film's absorption affect the fringe width. Be sure to read Tolansky's books for an explanation of how and why this happens.) And the sharper the fringes, the finer the details that can be seen on the surface. Tolansky assures us that by using multiple-beam interferometry under absolutely ideal conditions (~95% reflectivity and very low absorption) and high magnification, surface features as small as 10 Å in height or depth can be detected. Many atoms are around 3 to 4 Å in diameter. These nearly atomic scale elevations and depressions can be detected only in the up/down directions. An otherwise standard light microscope is still limited to an approximate half-wavelength of light resolution laterally. More on the mechanics of the techniques I mentioned the mineral mica. Other smooth-surfaced materials and minerals, such as (cleaved) calcite, selenite, quartz, silicon carbide crystals, metallic coatings, etc., can also be easily explored. If you can't coat the specimens with silver or aluminum, then just use the variable filter to hunt for the best interference fringes. In lieu of the filter, having a good set of thin beamsplitters (20/80, 30/70, 40/60, 50/50, etc.) will do and is less expensive. Remember to place the coated side against the surface being explored and use an incident-light microscope with a suitable narrow-band interference filter. Try different beamsplitters until you're happy with the results. The one you use will depend heavily on the reflectivity of the surface under study. I use a 546 nm (10 nm FWHM; coherence length ~ 30 microns) narrow-band interference filter for much of my work except where noted below. Start by examining the mineral section at its edges. It's easier to spot interference fringes there. Also, be sure to examine your mineral specimen under monochromatic light without using a reference plate. In many instances, especially with mica, you will note interference fringing due to the uncleaved or partially separated layers or lamellae acting as built-in reference plates. Though interesting, this phenomenon probably reveals very little about the topography of the external surface. The distance between black fringes is one-half the wavelength of the light used to produce the fringes. This is approximately 10 microinches for visible light. You can use that to extract information about the topography of the surfaces shown. In some cases, I used two or three different interference filters to produce interference fringing with different spacing. Doing this helps reduce or eliminate ambiguities in interpreting shifts in fringes. In a way, it's almost like having a built-in vernier scale. Sometimes what looks like a shift of, say, 1/3 fringe could really be 1-1/3 or 2-1/3 fringes, etc. Again, the fringes are referenced against a, hopefully, flat reference that is placed on top of the surface being explored. Otherwise, the images are very much like the contour maps obtained from planes and satellites and can be similarly interpreted. I used Adobe Photoshop to aid in producing these photos. In all instances except for the very first image photographed through my FluorEVER microscope (see page 3 of the LED Fluorescence section) a b&w video camera was used to record the fringes. For pictures where multiple filters were used with a halogen bulb light source, I took a separate photo through each filter mentioned. These individual photos were layered one on the other after first assigning an appropriate primary color (or colors) to the layer. Each layer was then inverted to produce a negative image, and the brightness and contrast were adjusted. The layers were then flattened into a single photo, and an unsharp mask was applied if needed. If a final positive was desired, I inverted the final flattened image. As you can see from some of the photos, in addition to the three primary colors, yellows, oranges, magentas, etc., were created from overlapping primaries. Finally, I produced an anaglyphic stereo photo of the mica surface using an extremely crude tilting stage for my microscope. Though there are two colors in that picture, it was taken with only a single filter (620 nm) but tilted for left- and right-eye views. You will need red/blue glasses with red over the left eye.
Mica surface, uncoated. Observed under 450 nm filtered LED light on FluorEVER microscope at 50X. Several-beam interferometry (SBI) used. Note thicker fringes obscuring some details.	Calcite surface, uncoated. Observed under 546 nm light on Leitz Metalloplan at 100X using SBI.	Mica surface, aluminized. Observed under 546 nm light at 100X. Note sharp fringes characteristic of multiple-beam interferometry (MBI) revealing discontinuities as small as 1/10 wavelength of light.
Mica surface, aluminized. Observed under 467 nm, 500 nm, and 620 nm at 100X. Positive MBI image produced by Adobe Photoshop.	Mica surface, aluminized. Filtration as in previous image at 100X. Negative MBI image.	Mica surface, aluminized. Observed under green and red at 100X. Negative MBI image.
Mica surface, aluminized. Observed under 467 nm, 500 nm, and 620 nm at 100X. Negative MBI image.	Mica surface, aluminized. Observed under 500 nm and 620 nm at 100X. Negative MBI image.	Anaglyph l(Please put on your 3D glasses.) Mica surface, aluminized. Observed under 620 nm at 100X. Right- and left-eye negative MBI images.
(You may now remove your 3D glasses.) Up next is my homemade pseudo optical profiler (a.k.a. interference microscope). This device overcomes some of the problems encountered with two-beam, several-beam, and multiple-beam interferometry. Needless to say, it introduces plenty of its own problems. A commercial instrument with its accompanying software is truly state-of-the-art and priced to match.
Vertical scanning white-light interferometry While multiple-beam interferometry is great for measuring very small features, defects, or blemishes on appropriate surfaces, there are a number of limitations. It is absolutely essential to work with surfaces that are inherently highly reflective or that can be vacuum coated. If the details being sought approach 5-10 microns in height/depth or more, it gets increasingly difficult to measure the contours. For surfaces that do have multi-micron or millimeter scale details, a device called a vertical scanning white light interferometer (VSWLI) can be applied. It is an optical profiler and is prohibitively expensive—unless you built one yourself. In that case, it's just very expensive. However, if you are willing to settle for the bare bones (i.e., no software and no automatic vertical scanner) interference microscope that lies at the heart of optical profiling, it's not too difficult to construct. I assembled mine in one day. But beware! These homemade systems can be exasperating, frustrating, and debilitating—not to mention tricky to set up. The optics have to be initially positioned to within an error not to exceed the diameter of a human red blood cell. The microscope, or at least the interferometer components, should be isolated from vibrations. Often as not, every time I get ready to toss the unit out the window the sought-after fringes suddenly pop into view. Maybe that's the secret!
I assembled my VSWLI test system around a stereo microscope only because of its long working distance. The glowing green square in the center is a 1" cube polarizing beamsplitter I had lying around. The optical components on the platform are an implementation of a Michelson interferometer. Commercial instruments have interferometers (i.e., Michelson, Mirau, Linnik) integrated within the microscope objectives. This makes the setup far more stable. With the VSWLI device, there is no need to place a reference plate in contact with the specimen. (Move the mouse pointer into the picture area for a description of the component layout.) For commercial instruments, the specimen being examined doesn't need to be highly reflective. In my setup, however, examining a transparent specimen necessitates placing it on a first-surface mirror. If the specimen is not transparent or is very thick, it must have a metallic coating; otherwise, no fringes form. The two photos at the extreme right are that of a multi-layered mica fragment that is uncoated but is resting on a mirror as described above. The photo was taken at 15X under 500 nm using a filter with a passband of 80 nm. So where does white light come in? The filters used for "white light interferometry" usually have very broad passbands, sometimes on the order of 80 nanometers. The coherence length for the filter is on the order of 4 microns. White light has an even shorter coherence length (on the order of 1 micron) and, though the results are pretty to look at, is very tricky to set up. With either a broadband filter or white light, there is the need to vertically scan a specimen in order to detect all the interference fringes and features. In effect, you are optically sectioning the specimen looking for peak fringe intensities. You can get the feel of this from the photos. The vertical scanning is not a limitation but rather the essence of the technique. Commercial instruments are accompanied by powerful software that allows autoscanning the specimen and converting the accumulated fringe information into an image that often resembles a scanning electron micrograph.	Home-brewed manual vertical scanning white light interferometer. The center cube beamsplitter divides the LED light to illuminate both specimen and reference mirror. The two images combine to produce an interferometric image as seen at right. The polarizer can be used to increase/decrease the amount of light channeled to the video camera. The CCD camera is sitting atop the microscope and is not visible in the photo. I adjust the reference mirror position and tilt to locate the fringes on the specimen. In the case of mica, moving the mirror to the right pushes the fringes further away toward the lowest layer of the specimen. Mirror tilting controls the number and inclination of fringes that appear. This gives me a manual vertical scanner. Recently, I added a homemade piezoelectric scanner to move the specimen vertically. It uses a piezoelectric transducer (PZT) of the type used in inexpensive, solid-state buzzers.	Mica, uncoated. Observed at 15X under 500 nm LED filtered light. Passband of filter is 80 nm. Vertical scanning white light interferometric setup. Positive image. No reference plate was placed on the surface of the mica and the depth revealed in this image is substantial. The fringes were set at the top layer of the mica in the top photo and at the lowest level of the mica in the lower photo. The broadband filter paints the image with a very shallow layer of fringes that need to be scanned vertically, as seen here.
As I mentioned, the VSWLI microscope I constructed is only a test version. If I wanted to convert it into a true optical profiler, special software and software-controlled vertical scanning hardware would be needed. However, the following photos, with the exception of the PZT setup, were taken with the existing unit. Each photomicrograph was captured with a b&w CCD video camera and input to an Argus 20 image processor. The Argus 20 allows me to subtract out dust on the optics and variations in light intensity. Also, the image of the specimen itself can be removed. If I do that, any fringes that form as I manually scan the reference mirror are isolated and visible. (The view that most closely demonstrates the appearance of this is the picture below of oil on a metallized cover slip.)
A small piece of a silicon wafer with dozens of ICs was placed on the specimen stage and examined at 35X. Two images were exposed: first, one of the IC circuits and then the interference fringes. After assigning a red color to the otherwise black fringes, the images were combined by overlaying. All photomicrographs in this section were taken with a 520 nm filter with a 10 nm passband unless otherwise indicated.	There was a small scratch on the gold-plated unpolished back surface of the piece of silicon wafer. Viewed at 35X. Again, two images were taken and combined. Apparent details on the surface appear that were invisible under standard microscopic examination.	A small, stamped-out steel tool examined at 30X. Looking like a bowl of bumblebee soup, the two separate images combine to reveal a surface bristling with details and dimensions otherwise unavailable. A side-by-side comparison with an SEM photo would be ideal. This also applies to the previous photo.
Nose oil on metallized cover slip. Viewed at 38X. A volunteer generously pressed my...I mean, his nose against a cover slip that had been vacuum coated with metal. For obvious reasons, you cannot get this kind of view with multiple-beam interferometry. Instead of oil droplets, slime mold amoebae crawling across the surface would also prove very interesting.	PZT on microscope platform. When operated in the range of 0 to 100 VDC, the PZT can move samples up/down by 4.6 microns. This will vary depending on the particular PZT. Displacement as minute as the span covered by 45 helium atoms sitting (or standing) side-by-side can readily be detected by slight fringe movement. Mica sample and environs seen under 532 nm LED illumination. STM anyone?	Mica surface, aluminized. A small scratch on the mica is observed at 34X illuminated by the 546.1 nm line emitted by a shortwave mercury pen lamp. (For this lamp and line, I measured a coherence length of 1.2 millimeters or so.) My piezoelectric scanner, operating with a sine waveform modulating the PZT driving voltage, was used to move the mica fragment approximately 2.2 microns up and 2.2 microns down. The mica experienced a round-trip displacement equivalent to slightly more than half the width of a human red blood cell.
I hope that you find this discussion of multiple-beam interferometry tempting enough to begin applying its methods in your research. The methods discussed here are both easy to implement and remarkably powerful. Up next, measuring transparent films with reflectometry.


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