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Modern Interferometry

Newsletter – Teaching Modern Interferometry
Instruction Manual Excerpt
Conceptual Introduction – Modern Interferometry

Modern Interferometry Brochure

Experiments

TeachSpin's Modern Interferometry experiments follow current laboratory practice in table-top optics by starting with an optical breadboard onto which students mount carefully crafted components. In addition to standard commercial components, the kit includes proprietary high stability mirror mounts with only one degree of freedom and a proprietary ± 1 mm monolithic-flexure translation stage which allows position control on the order of 0.1 µm.

The first few pages of the Student/Instructor manual, including the Table of Contents and the first introduction to the apparatus are provided here as a pdf. The sections below describe a few of the wide variety of experiments can be done in each of the three interferometer configurations, Michelson, Sagnac and Mach-Zehnder.

A Sampling of Possible Experiments from a very long list:

Michelson Configuration

Sagnac Configuration Mach-Zehnder Configuration



EXPERIMENTS IN THE MICHELSON CONFIGURATION

Introduction to the Apparatus
The Student Manual starts with an introduction to the Michelson Interferometer and guides the student through the process of setting up a system with the basic components of the kit. They then build and align a basic Michelson interferometer using the proprietary mirrors.

Measuring the Wavelength of Light with a Micrometer
The base of one of the fixed mirrors of the basic Michelson is replaced with the proprietary flexure-translation stage driven by a differential micrometer. After investigating the fringes manually, students then connect the differential micrometer to the included motor drive.


This photograph shows the 'drive train' connecting a synchronous motor, via a differential micrometer, to TeachSpin's flexure translation stage. How can you tell that this picture wasn't taken while running the apparatus?

Using the motor drive creates a slow and controlled change in path-length difference which produces 'fringes in time' patterns such as those shown. A mechanical measurement of the wavelength of the laser source comes from matching these fringes to the displacement measured by the micrometer, The source use for this experiment is a red diode-laser module included with the kit, which has the advantage of lacking a 'book value' for the wavelength.
Fringes in time, from a motor-driven Michelson interferometer.


Measuring Indices of Refraction Interferometrically
The sensitivity of a Michelson interferometer to optical phase delay not only makes it easy to see that the index of refraction of air is not exactly one but also to measure that value (about 1.000273 at STP) to good precision.


The Gas manifold

Cell and transducer interconnected

The 100 mm internal length precision gas cell is placed into the optical path of one of the arms of the interferometer. Both the gas and the gas pressure in the cell can then be varied using the TeachSpin gas-handling manifold. An electronic pressure transducer with high-resolution analog output, allows students to observe, in detail, the pressure variation of index of refraction. The user does need to supply a forepump to evacuate the cell.

The index of refraction of plane slab samples of solid transparent materials can also be measured using the TeachSpin interferometry system. In this case, there is no way to interpolate continuously from vacuum to sample conditions. Instead, using a miniature rotation stage, the sample is rotated away from the face-on condition to allow oblique transmission of the light in one arm of the interferometer. The counting of fringes as a function of tilt angle, together with some modeling for refraction, allows the index of refraction of the sample to be deduced.

Using Dielectric Beamsplitters to find the "missing energy" in destructive interference
Where is the energy of the light going in an interferometer adjusted for destructive interference? Below is a schematic diagram showing a way to detect the non-standard output of a Michelson interferometer—the light heading back toward the laser source. In the initial investigation, students use familiar dielectric beam-splitters and move mirror MA1 with a micrometer or the piezoelectric actuator. Quantitative detection demonstrates that the standard and non-standard outputs of the interferometer are complementary. That is, when interference is destructive at the standard output, it is constructive at the non-standard output.


Schematic diagram for sampling the non-standard output of a Michelson interferometer. The position of the right hand mirror, MA1, can be manipulated with a variety of included accessories.

Exploring Quadrature Detection
As indicated in the schematic, a specially-selected metal-film beamsplitter plate, which is deliberately "lossy", can be substituted for the dielectric one. With this single change, the standard and non-standard outputs of the interferometer are no longer 180 out of phase. Rather, they are very nearly in quadrature—90 degrees out of phase. The traces below were produced by using the piezoelectric actuator to vary the location of MA1.


These figures show Michelson Data Comparing Standard and Non-Standard Outputs when a Metal-film Beamsplitter has created a phase difference. The fringe signals X(t) and Y(t) and the X-Yare plots of the same data.

The traces on the left show the two outputs as a function of time. The X-Y display on the right is the trace of a dot which follows an elliptical locus. The direction of motion of the signal point around the locus reverses when the direction of motion of the end mirror reverses. The counting electronics is arranged to make reversible (up-down) counting of fringes possible.

Up-down counting can bring amazing vibration immunity to an interferometer. It is tell-tale that the apparent noise in the X(t) and Y(t) signals shown on the left, does not cause the dot in the (X,Y) display to wander about in the plane. Rather, the dot is confined to the locus shown. Hence, we can infer that the apparent noise is in fact signal, a measure of the instantaneous optical phase of the interferometer. And since the up-down counting system keeps track of the 'winding number' of that dot around the locus, it is easy to count thousands of fringes, even in the face of vibration.
Examining Magnetostriction Using Quadrature Detection
The configuration below is the one used at exhibits to show how bi-directional counting can be used to explore magnetostriction. In this case, the position of one of the end mirrors of the quadrature Michelson interferometer is controlled by the length of a polycrystalline nickel sample. The change in the length of the sample during its magnetization cycle can be followed, even as it undergoes reversals, by the up-down counting that quadrature interferometry uniquely makes possible. This length measurement has sub-wavelength resolution, bi-directional capability, superb linearity, and a precisely-known scale factor.


Photograph of exhibit layout for demonstrating magnetostriction. (The exhibit breadboard is smaller than the one supplied with the apparatus.)

Deformations in Thermal Expansion and Piezo-electric Materials
The Michelson configuration, especially in its quadrature mode, makes it easy to keep track of the position of a moving mirror; and the flexible and modular TeachSpin kit allows many possible ways to control the position of that mirror. One set of investigations shows students how to assemble samples with heater coils and temperature transducers, and then to use interferometry to monitor their changes in length with temperature. The samples provided include an Invar rod, to make clear the exceptional properties of this material.

Another way to move the end mirror is via 'converse piezoelectricity', and the kit includes a piezoelectric actuator which can move the mirror by a few µm under dc excitation in the -10 to +110 V range. The manual also describes the procedure by which motions much smaller than a wavelength of light can be detected and quantified. With ac excitation of the piezo drive and a bit of signal averaging, motions of order 1 nm can be readily detected. With a bit of lock-in detection, motions of 0.1 nm (about the diameter of a single atom!) can be detected.

White-Light Interferometry in the Michelson Configuration
Plenty of textbooks will tell you that interferometry requires 'coherent light', but the TeachSpin kit will allow students to see that coherence is a matter of degree, not kind, of light. Thus it's possible to use the TeachSpin interferometer to find the interference fringes that result not just from laser light, but also from LED sources, and even from a halogen lamp.

The art of white-light interferometry is to achieve equal lengths in the two arms of the interferometer, not just for one wavelength but over a broad range. This requires the use of a compensator plate along with a way to equalize the arm lengths to a tolerance of not just mm but µm. Using the variable-temperature laser-diode source with the quadrature interferometer, the equal arm length condition can be approached systematically.

Success is this procedure allows the direct visual detection of white-light fringes, and the use of two narrow-band filters in the light path allows students to see the trade-off between spectral bandwidth and coherence length.


White-light fringes viewed in TeachSpin's interferometer: on the left, in full optical bandwidth; on the right, for green light of 10-nm bandwidth)

Measuring the Thickness of Solid Samples - Gage Blocks
As another illustration of the power of bidirectional counting in quadrature interferometry, students can measure the mechanical thickness of a solid metal sample (up to 2 mm thick) to a resolution on the order of 0.1 µm. This process involves keeping track of the position of the moving mirror while a gap is opened in the mechanical train controlling that position, and then filling that gap with one of the Invar 'keepsake' samples included with the kit.

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EXPERIMENTS IN THE SAGNAC CONFIGURATION

The Sagnac interferometer continues to be a valuable topology for interferometry, and the TeachSpin kit makes it straightforward to set up and align this interferometer. The novelty of the Sagnac interferometer is that the two separated beams travel simultaneously, but in opposite directions, around the same rectangular path. Since both beams reflect off the same optical elements, motion of these elements is (to first order) in common in both beams. This makes the Sagnac interferometer uniquely insensitive to vibration, and because of this, uniquely low-noise in its detection capability.


Schematic Diagram of a Sagnac Configuration

Though the Michelson interferometer is famously unable to detect the absolute translational motion of the earth through the 'ether', Sagnac interferometers have been used to detect the absolute (?) rotational motion of the earth on its axis. In fact, the Sagnac topology is the basis of optical gyroscopes. The student manual includes a section on Interferometry and Relativity to explore the implications of these surprising facts.

The TeachSpin Sagnac configuration makes use of modern techniques of polarization, and the two beams in the interferometer are perpendicularly polarized. The also makes possible an ingenious 'polarimetric detection' capability of enormous sensitivity, low noise, and zero offset.

The Electro-Optic Effect, Detected Interferometrically
One illustration of the powers of this interferometer is to pass the overlapped but perpendicularly-polarized beam through a sample of material displaying electro-optic effects. The application of a transverse static electric field to a material like lithium niobate will change its indices of refraction, causing its index for vertically (vs. horizontally) polarized light to change. This index change is small, and causes a phase shift of 180° (π radians) only for kiloVolts of potential difference. Yet such is the sensitivity of Sagnac interferometry that the consequences can be seen a just a few Volts. Phase changes under a milli-radian are easily seen in real time.

Other Sagnac applications
The SRL design of the Sagnac topology also allows the two counter-propagating beams in the interferometer to be displaced laterally by order 1 cm, so that access to one beam (vs. the other) is now possible. Yet the ingenious polarimetric detection capability and most of the common-mode vibration rejection remain. Thus any sample placed in one beam can have its phase shift, relative to the other beam, quantified. This permits another way of measuring the index of refraction of gas, or transparent-slab, samples.

Astute readers will no doubt think of more experiments, not included in the TeachSpin kit, but permitted by the open-table and modular geometry of the apparatus. Who will be the first to measure the Fizeau effect, or optical effects of flowing liquids? Who will be the first to put the whole apparatus on a rotating table, and to detect its rotation interferometrically?

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EXPERIMENTS IN THE MACH-ZEHNDER CONFIGURATION

The Mach-Zehnder interferometer is another configuration famous for its applicability to optical testing, but also uniquely suited to provoking thoughtful reflection on the nature of light. In this geometry, light is split at one corner of a rectangular layout, and made to travel along the edges of the rectangle and recombine at the opposite corner. The widely separated beams and the one-way light travel make possible a unique set of experiments.

In particular, the TeachSpin kit allows this interferometer to be set up using either non-polarizing, or polarization-sensitive, elements at the input and output corners of the interferometer. In the case of the polarized Mach-Zehnder interferometer, there is plenty of room to place polarizing elements in either of the beams of the interferometer. Rotatable Polaroids are included in the kit to make the investigation of both beams easy for the student, and the manual includes a section on Interferometry and Quantum Mechanics to provoke questions about how the observations can be reconciled with a photon picture of the light passing through the interferometer. This topology is a favorite ''thought experiment' for reflection on 'welcher Weg' or 'which-path' questions in quantum mechanics. With the TeachSpin apparatus, the experiments can actually be done!

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