Interferometery Study Notes for Instrumentation Engineering

In this article, you will find the Study Notes on Interferometry which will cover the topics such as Introduction, Interference of Light, Light sources for interferometry, Interferometry Applied to Flatness Testing, Interferometers and Laser Interferometers.

1. Introduction

• Light is considered as an electromagnetic wave of sinusoidal form. When two monochromatic light beams combine they undergo the phenomenon of interference. Therefore, the resultant light rays carry the characteristics of both the monochromatic light sources. The amplitude and hence the brightness of the resultant beam also becomes different from the original ones.
• By analyzing differences in phase, which also corresponds to the difference in wavelength (length), the distance between the two lights sources can be calculated. The phenomenon of light used in this way has given rise to the branch of dimension metrology called Interferometry.
• Interferometry involves testing of flatness, surface contour, and determination of the thickness of slip gauges, etc. Interferometers are commercially available instruments for calculating small differences, constructed on the basis of principles of interferometry.

2. Interference of Light

• Let us consider two virtual sources S1 and S2 derived from the same primary source. Since both are equidistant from the source S, the secondary wavelets emerging from S1 and S2 are in the same phase and have equal amplitude.
• Let the source slit S be illuminated with a monochromatic light of wavelength λ. The identical light waves diverging from S1 and S2 at an instant t may be represented by

• where E₀ is the amplitude, T is the period, and c is the velocity of light. In travelling from S₁ to P, the wave travels a path of x₁ = S₁ P. Hence, on reaching P, the wave that emerged looks like

• Similarly, on reaching P, the wave emerged from S₂ is given by

• where x₂ = S₂ P and is the phase of the wave.

• The phase difference between the two sources is

• where the path difference 
• the condition for maximum and minimum of intensity is

• This maxima and minima constitute the bright and dark fringes.
• To calculate the position of the bright and dark fringes:

• Since we have assumed that y < < D, d < < D, we can expand the term binomially. Hence,

• Now for bright fringes:

• In the above relation, the value of y_m gives the position of m^th bright fringe. For the central fringe at P₀, m = 0 and y₀ = 0 and the next bright fringe will be at Y₁ = 
• For the (m – 1)^th bright fringe, we have

• The fringe width:

• Similarly, the dark fringes satisfy the relation

• The separation between two consecutive dark fringes is 

3. Light Sources for Interferometry

A variety of light sources are available for interferometry work but the selection of proper sources for any application depends on the requirements or results to be obtained by the interferometer, cost and convenience. Characteristics of various light sources are summarized below:

• Mercury: It is less expensive source having high intensity, and the green line can be easily isolated with filters. Since natural mercury contains several isotopes, each isotope emits light whose wavelength is slightly different from other. As a result, natural mercury light source radiates a mixture of slightly different but close to each other wavelengths that can be treated as monochromatic light.
• Mercury 198: It is pure isotope produced by neutron bombardment of gold. It is considered to be one of the best sources of very sharply defined wavelengths, and fringes are visible with path difference up to 500 mm. Light is emitted when mercury 198 is excited by microwave produced electric field. It is the international secondary standard of wavelength.
• Cadmium: It is the only natural material producing a spectral line (red) almost completely monochromatic. It can be conveniently used up to a path difference of about 200 mm. Cadmium 114 is the official secondary international standard of length. 
• Krypton: It is used in some instruments for its advantage of being easily excited. It is not as monochromatic as krypton-86 because Krypton is a mixture of isotopes. It can be used up to the path difference of 375 mm.
• Krypton 86: Krypton-86 lamp produces spectral lines of different wavelengths and, therefore, an elaborate monochromator is required to separate them. Further, its excitation takes place at very low temperature. So this lamp is used only in standardizing laboratories. It enables the fringes to be observed with maximum path differences nearing up to 800 mm.
• Thallium: As 95% of its light is emitted at one green wavelength, it can be used over a reasonable path difference without the use of the filter.
• Sodium: It is used only in applications where interference path difference does not exceed a few hundred wavelengths. Usually the yellow sodium light is used which contains two separate but closely spaced lines of equal intensities.
• Helium: Orange line of helium is used where path difference is not large.
• Gas Lasers: Lasers are highly monochromatic the light that enables the interference fringes to be observed with enormous path differences, up to 100 million wavelengths.

4. Interferometry applied to Flatness Testing

• Flatness is defined as the geometrical concept of a perfect plane. It is an important function in the construction of many technical components where accuracy is a required criterion. For example, controlled flatness is required to provide full contact with a mating part. Flatness is a precondition for the parallelism of the nominally flat surface. It is a reliable boundary plan for linear dimension. It also provides locating planes for dependable mounting or assembly of manufactured parts.
• Interferometry is one of the precise methods for calculation of flatness. In this method, monochromatic light is allowed to fall on an optical flat which in turn is placed on the surface at a small angle whose flatness is to be calculated. Optical flats are transparent, flat, circular section of small thickness usually made of clear fused quartz or pyrex.
• The optical flat is placed on the surface to be inspected in such a way as to create interference bands observable under monochromatic light. The resulting band pattern permits the object’s flatness conditions to be evaluated.

• For constructive interference, the path difference between the rays should be even multiple of where λ is the wavelength of light.

• For destructive interference, the path difference between the rays should be odd multiple of 

5. Interferometers

• Interferometers are optical instruments used for measuring flatness and determining minute differences in length by direct reference to the wavelength of light.
• Basically, an interferometer is constructed using the same principle as of an optical flat. The disadvantages of optical flats are overcome here by some refined arrangements.
• The fringes formed can be oriented to the best advantage in interferometers. Also, there is an arrangement to view the fringes directly from the top, thus avoiding any distortion due to incorrect viewing. This makes their uses easier and faster than the optical flats.

• There are a number of interferometers available. But most of them are designed employing slightly different methods to accomplish the same result.
• The light sources from a single colour light source are collimated into parallel by a lens. When these rays reach the partially silvered surface of mirror A, about half of the light is reflected towards mirror B, and the other half passes through the silvered surface towards the workpiece and table surface.
• Thus, the light rays are divided and directed along two different paths. These divided light rays fall on the surface and the mirror B and are then reflected back to mirror A.
• Since they are of the same wavelength and emerge from the same source, they will show the phenomenon of interference.
• Some light from the mirror B passes through the partially silvered surface towards the eye, and some light from the workpiece and table surfaces also are reflected towards the eye.
• If the path difference of these two rays is even multiple of the half of the wavelength of the light source, they undergo constructive interference and the light rays reinforce each other, and the workpiece and the table surface appear to be ordinarily illuminated. However, if the path of the light reflected from the workpiece surface differs in length from that of the light reflected from the mirror B by odd multiples of half wavelength, the workpiece surface appears to be dark because of destructive interference.
• The surface of the table also appears to be dark if the same situation is applied to it.

• In order that the operator can make a measurement with an interferometer, the table is tilted slightly by a very small angle. This causes a series of interference fringes to appear on the surfaces of the workpiece and table.
• In case, the surface of the workpiece is at certain angle with the base plate, fringe pattern will be

• Here the error is indicated by the amount by which the fringes are out of parallelism with those on the base plate.

6. Laser Interferometers

• The measuring capacity in interferometers of the lamp of single wavelength as a source of light is limited because of their low resolution and short measuring range. If the light source is replaced by a laser source, measurement can be done over a long distance because it facilitates to maintain the quality of interference fringes over a long distance. Since the laser is a highly monochromatic coherent light source that follows all the principles of light, the fringes formed due to an interference of laser are very sharp, accurate and precise.

• The uses of a laser interferometer are as given below:
  • Since laser interferometer produces very thin, straight beam, they are used for measurements and alignment in the production of large machines.
  • They are also used to calibrate precision machine and measuring devices.
  • They can also be used to check machine set ups. A laser beam is projected against the work and measurements are made by the beam and displayed on a digital readout panel.
  • Because of their very thin, straight beam characteristics, lasers are used extensively in constructions and surveying. They are used to indicate the exact location for positioning girders on a tall building or establishing directional lines for a tunnel being constructed under a river.
  • Laser interferometers can also be used in glass feature measurements.
• The main advantages of a laser interferometer are as given below:
  • Laser interferometers have high repeatability and resolution of displacement measurement.
  • They give high accuracy (0.1μ) of measurement.
  • It facilitates to maintain long range optical path (60 m).
  • Laser interferometers are easy to install.
  • There is no chance deterioration in performance due to ageing or wear and tear.

All the Best.

Team Gradeup!