INTERFEROMETRY

Interferometry

Principles of optical interference

Figure (a) represents two waves of light, which are 1800 out of phase. If these are assumed to be traveling in the same line, (fig.b) it can be seen that for every point on one wave there is an equal and opposite point on the other wave. These two will therefore cancel out and no light will be seen in the direction of propagation.

Fig.(c) and (d) represents two waves in phase, the resultant effect being a wave of double magnitude.

                             Waves 1800out of phase

1. (b)

                                

                                Waves in phase

              

                (c)                (d)

                           

Referring to figure (e), A and B are two sources of light exactly in phase.  In order that all relative components of these two sources shall be exactly in phase, it is essential for both of them to be produced  from a single initial source by some method of splitting it up,  possibly by partial reflection and partial transmission at a glass surface.

                

                                  (e)

At a point C on a screen, equidistant from both A and B, the waves from each source will have traveled equal distance and will be in phase.  At a point D, where the difference in path length is half a wavelength, the two waves will be out of phase and will cancel out, causing darkness.  At still further points, such as E on the other side of C, the paths differ by a whole wavelength and the waves are in phase again.  Thus a series of light and dark positions is seen on the screen.

These interference bands, as they are called, can appear as parallel bands or as concentric circles, according to the optical set-up.  It will be demonstrated in later chapters how these interference phenomena can be used to make measurements of high precision, by utilizing the  fact that the path difference between two dark bands or two light bands is one wavelength.  For such work it is essential to have light of a single wavelength, and, for this purpose, the light emitted by certain elements, such as mercury, sodium and cadmium, is suitable.  In metrology this light is usually obtained from an electrical discharge lamp.

Flatness testing:

Essential equipment for testing flatness using interference of light rays is a monochromatic light source and optical flat.

                          

Optical flat

Optical flat is a piece of optical glass or quartz having its two plane faces flat and parallel and surface are finished to an optical degree of flatness.  Size varies from 25 mm to 300 mm diameter.

                                           

If an optical flat is placed on a flat reflecting surface under monochromatic light alternate bright and dark bands or interference fringes can be seen on the surface.

Consider a ray of light AB, which strikes the surface of the optical flat.  Part of it is reflected back from B and passes through .  At C part is reflected back and passes through to D where  D is reflected back..  Similarly rays A1, B1, A2, B2 etc.  We can ignore the reflection at

 

It is obvious that each adjacent fringe represents a change in elevation of the work surface relative to the optical flat equals ½ wavelength and total change in the elevation n x    /2 where ‘n’ is the number of fringes and the wavelength.

If the surface is perfectly wrung together then no air gap exists and no fringe pattern will be observable.

If the angle is increased then fringes  are brought closer together.

If the angle is reduced then fringe spacing increases.

If the angle is too large the fringes will be closely spaced  as to be indistinguishable.

11.2.2   Light Source:

For simple application a tungsten lamp  is used.   Light sources used are mercury, cadmium, krypton, krypton 86, thallium, sodium, helium, neon and gas lasers.  In these sources the discharge lamp is charged with one particular element and contains means to vaporize them.  The atoms of these elements are excited electrically.  So that they emit radiation at certain wavelengths.

11.3    Different fringe patterns

                             

11.4   Slip gauge interferometers

The terms "interferometry'' and "interferometer'' are both derived from the word ‘interference’. Interferometry is the use of interference phenomena for measurement purposes, either for very small angles or for tiny distance increments (the displacement of two objects relative to one another). An interferometer is a device to make such measurements.

NPL gauge interferometer:

In this either a cadmium or mercury 198 discharge lamp is used for the monochromatic source.  Each of these sources gives 4 wavelengths, in cadmium red, green, blue and violet and in mercury 2 yellows, green and violet.  The constant deviation prism can be rotated to bring each wave length into operation.  The slip gauge to be measures is wrung to the platen, which is rotated by remote control to bring any gauge into optical path below the optical flat.

  

Light from the discharge lamp passes through a condensing lens and is focused on to a narrow slit which lies at the principal focus of the collimating lens.  Parallel light from this lens passes through the  constant deviation prism and is split into its constituent wavelengths, one of them is selected at a time to travel down through the optical flat on to the gauge and platen below.  Light reflected from both gauge surface and platen returns along a path which  is slightly inclined to the first to bring  the  light to a focus hot  on  the slit  but on a small prism just beside it.  For this reason light should not fall exactly  normally on the gauge platen.  Interference takes place between the under surface the optical flat and the upper surface of the gauge and platen.  Producing alternate straight bands of dark and bright.

If the upper surface of the gauge were to lie in the plane of the platen is a gauge of zero length the fringes would go straight across both gauge and plate.  If this imaginary  gauge were now to increase its size  gradually upto one half wavelength, the fringes would move gradually relative to those on to platen and shift on pitch and go straight across.

Actually two interference  systems are produced one set is due to the upper surface of the gauge and the other due to the  base plates reflecting surface.  Generally, two fringe patterns will not be in phase and will be displaced.  The displacement observed  ‘a’ is expressed as a fraction of the fringe spacing ‘b’ i.e. f = a/b.  To find the length of the gauge an estimation is made for each of the four radiations from the cadmium lamp.  

In the figure  consider pth fringe on base plate and qth fringe on the gauge.

Then the length of the gauge     = L     =   λ (p-q+a/b)

                          2

=   λ (p-q+f)

                        2   

=  λ /2 (N+f)

                                                               2

where ‘f’ is the fraction a/b, λ the wavelength and N the difference of the no. of fringes p & q.