# 3D Roughness Metrology

Working Group 5.14

### Basic principle of interference and its application in microtopography measurement

Anyone who has ever observed the iridescent colors of an oil film on a water surface or of a CD when holding it into the light has encountered the phenomenon of light interference. The interference phenomena result from the fact that light from a light source hits a surface and reaches the observer on different paths. When light beams overlap, they are amplified or extinguished, depending on the path differences between the partial beams.

 Emergence of colors on an oil film on water: The adjacent figure shows how white light (i.e. light containing all colors of the spectrum) hits a surface coated in oil and is reflected both on the upper oil surface and on the lower one. To obtain such iridescent color phenomena, the oil film must have a different thickness in the range of the wavelength (for visible light: approx. 380-640 nm).On the left-hand side  of the figure, the thickness of the oil film is exactly such that the red fractions of light of the incident white light are extinguished after  overlapping. This spot therefore looks green – the complementary color. At a thinner spot of the oil film, the conditions for the extinction of a shorter (green) light wavelength are met: this spot seems red. Figure 1: Forming of interferences in the case of an oil film on water In an interferometer, a beam splitter ensures that the light traverses different paths and is reflected on different surfaces. After that, it passes the beam splitter again, where the light beams now overlap and thus, depending on the wavelength difference, extinction phenomena occur – or not.Due to the use of the beam splitter, the reflection surfaces can be spatially separated from each other, which makes the technical setup of an interferometer possible. This is shown in Figure 2. The measuring object and the reference plane are the two surfaces on which the light beams are reflected. The dashed line is meant to outline that the light paths are nearly equally long, except for the difference in the wavelength range of the light. After the light beams have overlapped, an interference image appears after the beam splitter; this interference image corresponds to the difference between the two surfaces. Assuming that the reference mirror is nearly perfectly plane and smooth, the interference image practically represents a quantitatively evaluable model of the surface of the measuring object. The interference image can be recorded and digitally processed by an image sensor (CCD camera). Figure 2: Principle of the interferometer

In the interferential microscope, an interferometric optical path is combined with the microscopic image. Depending on the imaging scale between the measurement surface and the camera, one differentiates between:Imaging scale > 1 (magnifying): Interferential microscopeImaging scale < 1 (reduction): Interferometer.

### Types of interferometers

In the field of microtopographic measurements, one differentiates between the following types of interferometers:

 Fizeau interferometer Michelson interferential microscope Mirau interferential microscope Linnik interferential microscope Figure 3: Diagrammatic sketchOne problem that may be encountered in interference microscopy is the possible different reflectivity between the measurement object and the reference mirror. A contrast loss of the interference phenomena may occur. In certain devices, the reflectivity of the reference surface can therefore be adapted to the measurement object. In the case of the Fizeau interferometer, the reference surface also acts as a splitter surface and is therefore semi-transparent.

### Interference evaluation methods

Typical properties of interferometers are:

 Typ Objective-magnifying Measuring field width / mm Sampling interval / µm Remark Fizeau 0,03 - 1 10 - 300 25 - 750 Reference mirror = splitter-> no pure two-beam interference Michelson 1 10 25 Small working distance due to beam splitter in front of objective 2,5 4 10 5 2 5 Mirau 10 1 2 Reference mirror disturbs illumination 20 0,5 1 50 0,25 0,5 Linnik 50 0,25 0,5 Uncertainty due to non-identical objectives 100 0,125 0,25

Table 1 shows typical properties of these interferometers

To evaluate the interference phenomenon, the following interference evaluation methods are used:

 Figure 4: Interferogram of a groove with partial circular cross section Figure 5: Groove from Figure 4, tilted Carrier frequency: By deliberately setting the angle between the measurement surface and the reference plane, an interference fringe system ("carrier frequency") is overlapped over the topography (Figure 5). The topography is characterized by distortions of the interference fringe pattern that is otherwise straight and uniform. Just one single interferogram image is taken. Evaluation is carried out by fringe tracking or in the Fourier space. Phase-shifting: Der Abstand zwischen Messfläche und The distance between the measurement surface and the reference plane is displaced in four λ/8 steps. In each phase angle, an interferogram image is taken. From the change in intensity between the different interferogram images and the known phase displacement applied (λ/8 increments), the height of each image point is calculated. The light must have a defined wavelength within a bandwidth of approx. 50 nm. White light: By using white light (coherence length: approx. 2 µm), interferences only occur in a narrow area where the measurement surface is virtually at the same height as the reference plane. The distance between the measurement surface and the reference plane is traversed vertically in adjustable steps, and an interferogram image is taken at each height. From the evolution of the interference signal for each image point (pixel) at the different step levels, one can determine when it is exactly at the same height as the reference plane. The interference signal acts as a zero-point detector; the corresponding height is determined by means of a measuring system which registers the motion of the vertical displacement. For this purpose, the counting device in the step motor, incremental displacement pickups, capacitive and inductive displacement transducers or shifting interferometers are integrated into the vertical drive of commercial devices.

Table 2 lists typical specifications of interference evaluation methods:

 Method Phase-shifting White light Carrier frequency Measuring range Depth of sharpness of the objective 300 µm Depth of sharpness of the objective Resolution 0,01 nm 0,1 nm 0,03 nm Noise 0,1 nm 1 nm 2 nm Measurement uncertainty 1 nm 3 nm 3 nm Aperture correction required yes no yes Mainsource of uncertainty Aperturecorrection Traceability Aperturecorrection