Principle of interference and application for measurement of microtopography
Types of interferometers for microtopography measurement
Evaluation procedures
Interference microscopes in department Nano- and Micrometrology Measuring devices and measurement standards WG 5.17

Principle of interference and application for measurement of microtopography

Everyone who has observed the iridescent colours of an oil film on a water surface or has held a CD (even an empty one!) into the light, has experienced the interference of light. The interference phenomena materialize when light reaches the observer from a light source via the surface on different ways. When the light beams superimpose, the partial beams are intensified or extinguished, depending on the path difference.

	Formation of colours on an oil film on water: On the left side, the incident white light is reflected from the top and bottom side of the oil film. The thickness of the oil film is such that after superposition of the reflected light the red components are extinguished. Consequently this area appears in the light of the complementary colour, i.e. green. On the right side area the oil film is thinner, so extinction is just complied with for a shorter, e.g. green light wavelength, so that this area appears in red light.
	Figure 1: formation of colours on an oil film on water
	In an interferometer, a beam splitter allows the areas by which the reflected light is superposed, to be arranged spatially separated from one another. In Figure 2, these are the surface of the measurement object and the reference face. An interference pattern is formed which corresponds to the difference of the two areas. Assuming that the reference mirror is almost perfectly plane and even, the interference pattern practically represents a quantitatively analyzable model of the measuring face. The interference pattern is recorded by an image sensor and transmitted for further processing to a computer
	Figure 2: Principle of interferometer

In the interference microscope, an interferometric beam path is combined with the microscopic imaging. Depending on the imaging scale between measuring face and camera, a distinction is made between:

Imaging scale > 1 (magnification): Interference microscope
Imaging scale < 1 (demagnification): Interferometer.

In the field of microtopography measurement the following types of interferometers are applied:

Fizeau interferometer	Michelson interference microscope

Mirau interference microscope	Linnik interference microscope

Figure 3: Principle beam paths of interference microscopes: In some instruments the reference plane can be adapted to the reflectivity of the measurement plane in order to improve the interference contrast. In the Fizeau-type the reference plane acts additionally as beam splitter and is hence partly transparent.

Table 1 typical features of these interferometers:

Typ	Objective magnification	Width of field in mm	Sampling-interval in µm	Remarks
Fizeau	0.03 - 1	10 - 300	25 - 750	Reference mirror = beamsplitter -> no pure two beam interference
Michelson	1	10	25	Small working distance by beam splitter in front of objective
	2.5	4	10
	5	2	5
Mirau	10	1	2	Reference mirror disturbes illumination path
	20	0.5	1
	50	0.25	0.5
Linnik	50	0.25	0.5	Not identical objectives give reason for distortion
Linnik	100	0.125	0.25	Not identical objectives give reason for distortion

For the evaluation of the interference signals the following methods are applied:


	Figure 4: Interference pattern of a groove with circular section	Figure 5: Groove tilted with respect to figure 4
Carrier frequency:	By a selectively adjusted angle between measuring face and reference plane, an interference fringe system (“carrier frequency“) is superposed as shown in Figure 5 of the topography. The topography is translated in deflection of the interference fringes. It is only required to record an interferogram. Evaluation is performed by fringe tracking or in the Fourier space.
Phaseshift:	Here, the spacing between measuring face and reference plane is shifted four times in λ/8 steps. In each phase position, an interferogram is recorded. The height of each image point is calculated from the intensity in the interferograms at that point and the known phase changed introduced. The light must have a defined wavelength with a bandwidth of approx. 50 nm.
Whitelight:	When white light (coherence length approx. 2 µm ) is used, an interferogram is formed only in a narrow range at the places at which the measuring face virtually lies at the height of the reference plane. The spacing between measuring face and reference plane is vertically scanned in adjustable steps, and at each height an interferogram is recorded. From the pattern of the interference signal in the different sectioning planes, it is determined when each image point just lies at the height of the reference plane. The interference signal has the function of a zero detector, the associated height is determined by a measuring system which records the movement of the vertical scan. In commercial devices, alternatively the counter facility in the step-motor control, incremental displacement indicators, capacitive and inductive displacement transducers or displacement interferometers are used for this purpose.

In table 2 typical specifications of the evaluation methods are summarised:

Method	Phase shift	White light	Carrier frequency
Range	Depth of focus	300 µm	Depth of focus
Resolution	0.01 nm	0.1 nm	0.03 nm
Noise	0.1 nm	1 nm	2 nm
Uncertainty	1 nm	3 nm	3 nm
Aperture correction neccessary	yes	no	yes
Main uncertainty	Aperture correction	Traceability	Aperture correction