**Coherence Correlation Interferometry in Surface Topography Measurements**

Wojciech Kaplonek and Czeslaw Lukianowicz *Koszalin University of Technology Poland* 

### **1. Introduction**

Assessment of surface topography can be done by various methods, especially stylus and optical methods as well as utilising scanning tunneling microscopes and atomic force microscopes (Whitehouse, 1994, 2003; Thomas, 1999; Wieczorowski, 2009). The most accurate techniques for assessing surface topography include optical methods (Leach, 2011), especially methods of interference (Pluta, 1993; Hariharan, 2007). In the last two decades, there have been rapid developments in interferometry, as a result of the new possibilities for digital recording and analysis of interference images. The fastest growing interference methods include Phase Stepping Interferometry (PSI) (Creath, 1988; Stahl, 1990; Kujawinska, 1993; Creath & Schmit, 2004) and methods based on coherence analysis of light reflected from the test and reference surfaces (Harasaki et al., 2000; Blunt & Jiang, 2003; Schmit, 2005; Blunt, 2006; Petzing et al., 2010). This second group of methods is defined in different terms in English (Petzing et al., 2010; Leach, 2011), for example:


Modern methods of interferential microscopy used for the assessment of surface topography are based on automated interference image analysis and coherence analysis (Deck & de Grot, 1994; Patorski et al., 2005; de Grot & Colonna de Lega, 2004; Niehues et al., 2007). Assessment of surface topography requires that all of the information contained in one or more interference images, be porcessed in a sufficiently brief period of time. This process was made possible by:


Coherence Correlation Interferometry in Surface Topography Measurements 3

In the methods based on an assessment of the degree of temporal coherence of two interfering beams white light or low coherence light is used. These methods are incorporated in many types of measuring instrument. One of the most commonly used is the white-light interference microscope. This instrument combines the three most important features: white- light illumination, interference objective lenses and a precision scanner. The principle of operation applied in many white-light interference microscopes is based on the

exceptional versatility for for measuring objects made from different materials.

applications of white-light interference microscopes is very wide and includes:

elements, measurements of the smooth and super-smooth surfaces),

optics (measurements of optical elements e.g. microlenses, diffractive optics).

Similarly, the modern white-light interference microscopes have a number of advantages, e.g. wide measuring range, high accuracy and short time of measurement. The range of

analysis of the surface structures of micro electro-mechanical systems (MEMS) and

The third section will focus on theoretical basis of coherence correlation interferometry. This section will also cover a discussion of partially coherent wave interference and an analysis of a dependence upon the complex degree of coherence in interfering waves from a surface

The temporal coherence of light is connected with the phase correlation of the light waves at a given point in space at two different instants of time. It is characterized by coherence length, i.e. the propagation distance over which coherence of the beam is kept. Temporal coherence is a measure of the correlation between the phases of a light wave at different points along the direction of propagation. When we deal with two light waves then mutual temporal coherence can be analysed. This is a measure of the cross-correlation between the

In coherence theory a complex degree of coherence is a measure of the coherence between two waves. This measure is equal to the cross-correlation function between the normalized amplitude of one wave and the complex conjugate of the normalized amplitude of the other:

 material sciences and engineering (analysis of structures of the polymer materials), mechanics (measurement of surface topography of the precision machined parts and

CCI technique.

**3. Theory** 

topography.

**3.1 Coherence of light** 

phases of these waves.

**2.2 Features of CCI**  Features of CCI include:

short time of measurement,

 wide measuring range and high resolution, a large measurement area on the object,

electronics (measurements of silicon wafers),

micro-opto-electro-mechanical systems (MOEMS),


PSI methods (Hariharan & Roy, 1995) consist in the analysis of the light phase distribution on the measured surface. They enable the highly accurate measuring of the height of surface irregularities. The measuring range of these methods, however, is relatively small, while methods based on tracking and analysing the degree of temporal coherence of the interfering waves offer the possibility to measure the height irregularities of the surface over a greater range. Some of the measuring instruments used have the capacity to execute both methods. The principles and use of Coherence Correlation Interferometry (CCI) in surface topography measurements are presented in this chapter.

### **2. General characteristics of CCI**

A brief introduction will present the characteristics of interference-based methods used in surface topography measurement, forming a background that highlights the advantages of CCI. The second section will include:


### **2.1 General principle of CCI**

The CCI methods are based on the cross-coherence analysis of two low-coherence light beams, the object beam being reflected from the object t, whilst the reference beams is reflected from a reference mirror. The general idea of this method is shown in Figure 1. The high-contrast interference pattern arises if the optical path length in the object arm is equal to the optical path length in the reference arm. For each object point a correlogram is recorded during the movement of the object. The position of the corresponding object point along the *x*-axis can be measured by another measuring system for the maximum of the correlogram (step B in Figure 1). An interference signal is helpful for accurate determining of this position.

Fig. 1. Principle of the coherence correlation interferometry.

In the methods based on an assessment of the degree of temporal coherence of two interfering beams white light or low coherence light is used. These methods are incorporated in many types of measuring instrument. One of the most commonly used is the white-light interference microscope. This instrument combines the three most important features: white- light illumination, interference objective lenses and a precision scanner. The principle of operation applied in many white-light interference microscopes is based on the CCI technique.

### **2.2 Features of CCI**

2 Recent Interferometry Applications in Topography and Astronomy

PSI methods (Hariharan & Roy, 1995) consist in the analysis of the light phase distribution on the measured surface. They enable the highly accurate measuring of the height of surface irregularities. The measuring range of these methods, however, is relatively small, while methods based on tracking and analysing the degree of temporal coherence of the interfering waves offer the possibility to measure the height irregularities of the surface over a greater range. Some of the measuring instruments used have the capacity to execute both methods. The principles and use of Coherence Correlation Interferometry (CCI) in surface

A brief introduction will present the characteristics of interference-based methods used in surface topography measurement, forming a background that highlights the advantages of

The CCI methods are based on the cross-coherence analysis of two low-coherence light beams, the object beam being reflected from the object t, whilst the reference beams is reflected from a reference mirror. The general idea of this method is shown in Figure 1. The high-contrast interference pattern arises if the optical path length in the object arm is equal to the optical path length in the reference arm. For each object point a correlogram is recorded during the movement of the object. The position of the corresponding object point along the *x*-axis can be measured by another measuring system for the maximum of the correlogram (step B in Figure 1). An interference signal is helpful for accurate determining

development of new algorithms for digital interference image processing,

dynamic development of photonic engineering,

development of advanced specialized computer software.

topography measurements are presented in this chapter.

presentation of the general characteristics of CCI,

Fig. 1. Principle of the coherence correlation interferometry.

an overview of the general idea of the method and its key features.

**2. General characteristics of CCI** 

CCI. The second section will include:

**2.1 General principle of CCI** 

of this position.

Features of CCI include:


Similarly, the modern white-light interference microscopes have a number of advantages, e.g. wide measuring range, high accuracy and short time of measurement. The range of applications of white-light interference microscopes is very wide and includes:


### **3. Theory**

The third section will focus on theoretical basis of coherence correlation interferometry. This section will also cover a discussion of partially coherent wave interference and an analysis of a dependence upon the complex degree of coherence in interfering waves from a surface topography.

### **3.1 Coherence of light**

The temporal coherence of light is connected with the phase correlation of the light waves at a given point in space at two different instants of time. It is characterized by coherence length, i.e. the propagation distance over which coherence of the beam is kept. Temporal coherence is a measure of the correlation between the phases of a light wave at different points along the direction of propagation. When we deal with two light waves then mutual temporal coherence can be analysed. This is a measure of the cross-correlation between the phases of these waves.

In coherence theory a complex degree of coherence is a measure of the coherence between two waves. This measure is equal to the cross-correlation function between the normalized amplitude of one wave and the complex conjugate of the normalized amplitude of the other:

Coherence Correlation Interferometry in Surface Topography Measurements 5

where: *z* – position of the scanning system of interferometer, *z*0 – position of the scanning system at which the lengths of optical paths in both arms of the interferometer are equal,

Measurement of surface topography using the CCI is based on analyzing the time delay

function *x* and *y* which is changing during the scanning process. It is possible for each point

measurement is obtained through discrete function *z* = *z*0(*x*, *y*) that describes a set of points. Each point is defined by three coordinates *x*, *y*, *z*. This imaging of the shape of the surface

Fig. 2 shows a graph of relative light intensity at some point of the interference image

0 . *c*

The graph shown in Figure 2, in fact, describes the cross-correlation function of the

of the surface to determine the position of *z* = *z*0, for which

interfering waves and the envelope of this function.

depending on the position of the scanning system. The physical quantity

Fig. 2. Relative light intensity at some point of the interference image

using CCI, are discussed.

**4. Implementation of the CCI for surface topography measurements** 

Issues related to the implementation of CCI in instruments for surface topography assessments are presented in this section. The construction and general metrological characteristics of some of them (e.g. Taylor Hobson, Veeco and Zygo) are given. This section will also consist of a description of the three main interference objective lenses (Michelson, Mirau and Linnik) used in CCI instruments, as well as relevant diagrams and technical specifications characterizing these objective lenses. In the final part of the section, selected algorithms used in the practical implementation of surface topography measurements,

1 is the average wavelength of light and can be determined from the relationship:

0

(*x*, *y*) between the interfering waves at different points of the surface. Time delay is

= 0. As a result, such a

0 shown in Figure

(5)

*c* –speed of light.

values 

possible.

$$\mathbf{y}\_{12}\left(\tau\right) = \frac{\Gamma\_{12}\left(\tau\right)}{\left[\Gamma\_{11}\left(0\right)\Gamma\_{22}\left(0\right)\right]^{1/2}} \; \; \; \tag{1}$$

where: 12() – complex degree of mutual coherence, – time delay, 12() – function of mutual coherence of light, 11(), 22() – self-coherence functions of light.

### **3.2 Use of CCI for surface topography measurements**

Typically a two -beam interferometer (e.g. Michelson's, Linnik's or Mirau's interferometer) is used in coherence correlation interferometry. The two -beam interferometer is illuminated by a light source with a low degree of temporal coherence light. The optical path length in one arm of the interferometer changes during measuring and the interference signal is then analysed.Advanced analysis of the signal is carried out on every single point of the evaluated surface. In most cases this consists in determining the interference signal's envelope maximum. The shape of the interference signal depends on the complex degree of cross-coherence of the interfering waves.

Let the two partially coherent light waves with an average frequency 0 and equal intensities *I*0 interfere in the system interference microscope. One of the waves reflected from the surface of the test with *z*(*x*, *y*), and the other from the reference mirror. The light intensity *I* in the selected point interference field is determined by the equation:

$$I = \, 2I\_0 \Big| \, 1 + \left| \mathbf{y}\_{12}(\tau) \right| \cos \, a\_{12}(\tau) \Big|\, \Big. \tag{2}$$

where: *I*0 – intensity of interfering waves, 12 – function, which defines phase difference of interfering waves.

As shown in equation (2) an interference signal depends on the complex degree of mutual coherence 12 in interfering waves. The complex degree of mutual coherence 12 can be interpreted as a normalized cross-correlation function of the light wave reflected from the analysed surface and the wave reflected from the reference mirror.

$$\mathbf{y}\_{12}(\tau) = \begin{bmatrix} \mathbf{y}\_{12}(\tau) \end{bmatrix} \exp\left\{-i \left[2\mathbf{n}\boldsymbol{\nu}\_{0}\tau - a\_{12}(\tau)\right] \right\} \tag{3}$$

where: *i* – imaginary unit, <sup>0</sup> – average frequency of interfering waves.

The complex degree of mutual coherence 12 is analyzed separately at each point of the surface. If a test surface *z* = *f*(*x*, *y*) is rough, it can be assumed that the complex degree of mutual coherence is a function depending not only on the parameter , but also on the coordinates *x* and *y*. Time delay is zero at the considered point of the surface for such position *z*0 of scanning system at which the lengths of optical paths in both arms of the interferometer are equal. The parameter value of for the position of *z* is determined from the relation:

$$
\tau = \frac{2\left(z \cdot z\_0\right)}{c},
\tag{4}
$$

 12 12 1/2 11 22

0 0 

 

*Γ Γ Γ*

Typically a two -beam interferometer (e.g. Michelson's, Linnik's or Mirau's interferometer) is used in coherence correlation interferometry. The two -beam interferometer is illuminated by a light source with a low degree of temporal coherence light. The optical path length in one arm of the interferometer changes during measuring and the interference signal is then analysed.Advanced analysis of the signal is carried out on every single point of the evaluated surface. In most cases this consists in determining the interference signal's envelope maximum. The shape of the interference signal depends on the complex degree of

*I*0 interfere in the system interference microscope. One of the waves reflected from the surface of the test with *z*(*x*, *y*), and the other from the reference mirror. The light intensity

> *I I* 2 1 cos , 0 12

As shown in equation (2) an interference signal depends on the complex degree of mutual coherence 12 in interfering waves. The complex degree of mutual coherence 12 can be interpreted as a normalized cross-correlation function of the light wave reflected from the

exp 2 <sup>12</sup> *i* π

<sup>0</sup> – average frequency of interfering waves.

The complex degree of mutual coherence 12 is analyzed separately at each point of the surface. If a test surface *z* = *f*(*x*, *y*) is rough, it can be assumed that the complex degree of

position *z*0 of scanning system at which the lengths of optical paths in both arms of the

2 - <sup>0</sup> , *z z c*

 0 12 , **γ γ** (3)

  ,

– time delay,

12(

<sup>12</sup> **<sup>γ</sup>** (2)

is zero at the considered point of the surface for such

(4)

12 – function, which defines phase difference of

for the position of *z* is determined from

, but also on the

22() – self-coherence functions of light.

(1)

) – function of

0 and equal intensities

**γ**

11(), 

**3.2 Use of CCI for surface topography measurements** 

cross-coherence of the interfering waves.

where: *I*0 – intensity of interfering waves,

interfering waves.

where: *i* – imaginary unit,

the relation:

coordinates *x* and *y*. Time delay

) – complex degree of mutual coherence,

Let the two partially coherent light waves with an average frequency

*I* in the selected point interference field is determined by the equation:

analysed surface and the wave reflected from the reference mirror.

<sup>12</sup> 

interferometer are equal. The parameter value of

 

mutual coherence is a function depending not only on the parameter

where: 12(

mutual coherence of light,

where: *z* – position of the scanning system of interferometer, *z*0 – position of the scanning system at which the lengths of optical paths in both arms of the interferometer are equal, *c* –speed of light.

Measurement of surface topography using the CCI is based on analyzing the time delay values (*x*, *y*) between the interfering waves at different points of the surface. Time delay is function *x* and *y* which is changing during the scanning process. It is possible for each point of the surface to determine the position of *z* = *z*0, for which = 0. As a result, such a measurement is obtained through discrete function *z* = *z*0(*x*, *y*) that describes a set of points. Each point is defined by three coordinates *x*, *y*, *z*. This imaging of the shape of the surface possible.

Fig. 2 shows a graph of relative light intensity at some point of the interference image depending on the position of the scanning system. The physical quantity 0 shown in Figure 1 is the average wavelength of light and can be determined from the relationship:

$$
\mathcal{A}\_0 = \frac{c}{\nu\_0}.\tag{5}
$$

The graph shown in Figure 2, in fact, describes the cross-correlation function of the interfering waves and the envelope of this function.

Fig. 2. Relative light intensity at some point of the interference image

### **4. Implementation of the CCI for surface topography measurements**

Issues related to the implementation of CCI in instruments for surface topography assessments are presented in this section. The construction and general metrological characteristics of some of them (e.g. Taylor Hobson, Veeco and Zygo) are given. This section will also consist of a description of the three main interference objective lenses (Michelson, Mirau and Linnik) used in CCI instruments, as well as relevant diagrams and technical specifications characterizing these objective lenses. In the final part of the section, selected algorithms used in the practical implementation of surface topography measurements, using CCI, are discussed.

Coherence Correlation Interferometry in Surface Topography Measurements 7

parameters are a necessary source of information for determining the requirements for the purchase and later operation of instruments. A description of the selected metrological

 Vertical resolution (*z* axis) is the ability of the CCI instrument to resolve a surface profile vertically (in z axis). Vertical resolution for commercial instruments is in the

 Lateral resolution (*x* and *y* axis) is defined as one-half the spatial period for which the instrument response (measured height map compared to the actual surface topography map) falls to 50 %. Lateral resolution for commercial instruments depends on the

 Repeatability is the ability of an instrument to provide similar indications for repeated evaluation of the same measurement under the same conditions of measurement. Repeatability for commercial instruments is between 0.002 nm to 50 nm. For example: for the white-ligt interference microscope TMS-1200 TopMap μ.Lab produced by Polytec (Germany) repeatability (at 10 nm sampling increment) is 0.25 nm (smooth surface) as well as 2.5 nm (rough surface) and (at 87 nm sampling increment) is 0.5 nm

 Instrument noise is typically a small random error term superimposed on the measurement data. The source of this noise can be electronic components and devices mounted on the instrument (e.g. amplifiers, stabilizers, detectors). Some manufacturers

Selected metrological parameters, which characterize some of the commercially interferential microscopes available on the market are presented in Tab. 1. Similar metrological parameters for selected four instruments of the Talysurf CCI line manufactured

> Vertical range (mm)

MarSurf WS1 Mahr SWLI 0.1 0.1 1.6 × 1.2

In.Line Polytec SWLI 0.5 <0.55 18.6 × 13.9

Wyko NT1100 Vecco PSI/VSI 1 0.01 8.24 × 8.24

WLI MRC VSI 0.15 1 0.25 × 0.25

The CCI instruments are a large group of advanced optical measurement systems currently used in many fields of modern science and technology. There are a number of commercial CCI instruments available on the market. They are produced by Fogale, Mahr, MRC, Phase Shift, Polytec, Taylor Hobson Ltd., Vecco, and Zygo. Some examples of commercially

Table 1. Selected metrological parameters of commercially available interferential

available white-light interference microscopes are shown in Fig. 4.

Vertical resolution (nm)

Measurement area (max.) (mm)

parameters is given below.

range from 0.01 nm to 0.5 nm.

magnification and can be between 0.5 μm to 7 μm.

(smooth surface) and 20 nm (rough surface).

by Taylor Hobson Ltd., are presented in Tab. 2.

Instrument Producer Method

TMS-300-214 TopMap

microscopes.

provide software procedures, which neutralise this effect.

### **4.1 Construction of typical CCI instruments**

Typical CCI instruments are equipped with the measurement base supported on an antivibration table. The antivibration table is used for separating the instrument from external vibration sources. Usually the granite slab can fulfill the role of the anti-vibration table. In other instances more advanced solutions are used, such as active vibration isolation systems. The translating table and a vertical column are mounted upon the measurement base. The translating table enables tilt adjustment (by several degrees) around *x* and *y* axes (in some instruments also with *z* axis rotation). Tilt adjustment is one of the premeasurement procedures. This procedure is especially useful for samples, which are characterized by high angles of slope and high values of surface irregularity. Movement and adjustment of the stage can be realized manually or motorized by joystick control. The main elements of a typical CCI instrument (Talysurf CCI 6000 produced by Taylor Hobson Ltd., (UK)) are shown in Fig. 3.

Fig. 3. White-light interference microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd., (UK): a), b) front view and side view of the instrument with the main elements.

The optical interferometry and vertical scanning systems are located in a column. A source of light can be installed in compact form in the optical interferometry system or can be located outside the instrument. In this case a specially designed illuminatore was usually utilised. Light from the illuminator to the interferometer's optical system is delivered by an optical fibre.

An integral part of the CCI instrument is a stationary computer and a one or more computer monitors. Computer must be characterized by a high speed computing and adequate HDD free storage space for the archiving of recorded measurement data. In addition to controlling the CCI instrument and recording measurement data, the computer is used for processing and analysis of data. This process is realized by the use of specialist software, which is usually supplied by the producer of the CCI instrument.

### **4.2 General characteristics of the CCI instruments**

The CCI instruments are characterized by certain metrological parameters (Leach et al., 2008; Petzing et al., 2010), which are specified in the technical specifications. Metrological

Typical CCI instruments are equipped with the measurement base supported on an antivibration table. The antivibration table is used for separating the instrument from external vibration sources. Usually the granite slab can fulfill the role of the anti-vibration table. In other instances more advanced solutions are used, such as active vibration isolation systems. The translating table and a vertical column are mounted upon the measurement base. The translating table enables tilt adjustment (by several degrees) around *x* and *y* axes (in some instruments also with *z* axis rotation). Tilt adjustment is one of the premeasurement procedures. This procedure is especially useful for samples, which are characterized by high angles of slope and high values of surface irregularity. Movement and adjustment of the stage can be realized manually or motorized by joystick control. The main elements of a typical CCI instrument (Talysurf CCI 6000 produced by Taylor Hobson Ltd.,

Fig. 3. White-light interference microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd., (UK): a), b) front view and side view of the instrument with the main elements.

The optical interferometry and vertical scanning systems are located in a column. A source of light can be installed in compact form in the optical interferometry system or can be located outside the instrument. In this case a specially designed illuminatore was usually utilised. Light from the illuminator to the interferometer's optical system is delivered by an

An integral part of the CCI instrument is a stationary computer and a one or more computer monitors. Computer must be characterized by a high speed computing and adequate HDD free storage space for the archiving of recorded measurement data. In addition to controlling the CCI instrument and recording measurement data, the computer is used for processing and analysis of data. This process is realized by the use of specialist

The CCI instruments are characterized by certain metrological parameters (Leach et al., 2008; Petzing et al., 2010), which are specified in the technical specifications. Metrological

software, which is usually supplied by the producer of the CCI instrument.

**4.2 General characteristics of the CCI instruments** 

**4.1 Construction of typical CCI instruments** 

(UK)) are shown in Fig. 3.

optical fibre.

parameters are a necessary source of information for determining the requirements for the purchase and later operation of instruments. A description of the selected metrological parameters is given below.


Selected metrological parameters, which characterize some of the commercially interferential microscopes available on the market are presented in Tab. 1. Similar metrological parameters for selected four instruments of the Talysurf CCI line manufactured by Taylor Hobson Ltd., are presented in Tab. 2.


Table 1. Selected metrological parameters of commercially available interferential microscopes.

The CCI instruments are a large group of advanced optical measurement systems currently used in many fields of modern science and technology. There are a number of commercial CCI instruments available on the market. They are produced by Fogale, Mahr, MRC, Phase Shift, Polytec, Taylor Hobson Ltd., Vecco, and Zygo. Some examples of commercially available white-light interference microscopes are shown in Fig. 4.

Coherence Correlation Interferometry in Surface Topography Measurements 9

The last two of these interferometers are most commonly used in CCI instruments. In a Mirau interferometer the basic elements are a microscope objective lens, a reference surface and a beamsplitter. All the elements are on the same optical axis of the objective lens. In this configuration, there are two paths from the light source to the detector. In the first path a light beam reflects off the beamsplitter, passes to the reference mirror and then reflects back, before passing through the beamsplitter to the microscope objective lens and then on to the detector. In the second path, a light beam passes through the beamsplitter, to the reference mirror, reflects back to the beamsplitter and then reflects from the half mirror into the microscope objective lens before proceeding to the detector. The light reflected from these surfaces recombines and a fringe interference pattern is formed. The objective lenses with Mirau interferometer are usually used in applications requiring higher magnification (>10×) or numerical apertures. In such instances objective lenses can be used following

A Michelson interferometer is configured in a similar way to a Mirau with the exception that the reference mirror is in a different position (outside the optical axis). This configuration provides a longer working distance, wider fields of view and larger depth of focus at small magnifications (<5× ). The following magnification can be typically used for objective lenses

Commercial microscope objective lenses with interferometers are manufactured by Leica, Nikon, Olympus, Seiwa Optical, Veeco, Zeiss and Zygo. Availability of wide range of interference objective lenses give a great opportunities concerned with selection of the suitable lens for carrying out scientific works. Selected issues related with suitable selection of interference objective lenses were described in the work (Petzing et al., 2010). Schematic diagrams of the typical configurations of interference objective lenses are shown in Fig. 5, whereas the general characteristics of interference objective lenses produced by Nikon

Fig. 5. Schematic diagrams of the typical configurations of interference objective lenses: a) Mirau, b) Michelson, c) commercially produced microscope objective lens with Mirau

typical 10×, 20×, 50× and 100× magnification.

(Japan) are presented in Tab. 3.

interferometer (Nikon 50× CF Plan IC EPI).

with a Michelson interferometer: 1×, 1.5×, 2×, 2.5× and 5×.


\* Standard range (optional, can be extended), \*\*Square area

Table 2. Selected metrological parameters for instruments of the CCI line manufactured by Taylor Hobson Ltd., (UK)

Fig. 4. The commercially available white-light interference microscopes: a) Wyko NT1100 produced by Veeco (Vecco Instruments, 2002), b) NewView™ 7300 produced by Zygo (Zygo Corporation, 2010), c) NewView™ 600 produced by Zygo (Zygo Corporation, 2007)

### **4.3 Interference objective lenses**

Modern interference microscopes typically use standard microscope objective lenses, containing one of three types of classic two-beam interferometer, the configuration of which has been appropriately modified to enable the measurement of such instruments:


Repeatability of surface (nm)

Measurement area\*\* (mm2)

Vertical resolution (nm)

Lite CCI 2.2 0.01 0.002 6.6

<sup>9150</sup>CCI 0.1 0.01 0.003 0.25 - 7.0

<sup>6000</sup>CCI 0.1 0.01 0.003 0.36 – 7.0

<sup>3000</sup>CCI 0.1 0.01 0.003 0.36 – 7.2

Table 2. Selected metrological parameters for instruments of the CCI line manufactured by

Fig. 4. The commercially available white-light interference microscopes: a) Wyko NT1100 produced by Veeco (Vecco Instruments, 2002), b) NewView™ 7300 produced by Zygo (Zygo

Modern interference microscopes typically use standard microscope objective lenses, containing one of three types of classic two-beam interferometer, the configuration of which

Corporation, 2010), c) NewView™ 600 produced by Zygo (Zygo Corporation, 2007)

has been appropriately modified to enable the measurement of such instruments:

Mirau interferometer (Delaunay, 1953; Kino & Chim, 1990),

Vertical range\* (mm)

Standard range (optional, can be extended), \*\*Square area

Instrument Method

Taylor Hobson Ltd., (UK)

**4.3 Interference objective lenses** 

Linnik interferometer (Linnik, 1933),

Michelson interferometer (Michelson, 1882).

Talysurf CCI

Talysurf CCI

Talysurf CCI

Talysurf CCI

\*

The last two of these interferometers are most commonly used in CCI instruments. In a Mirau interferometer the basic elements are a microscope objective lens, a reference surface and a beamsplitter. All the elements are on the same optical axis of the objective lens. In this configuration, there are two paths from the light source to the detector. In the first path a light beam reflects off the beamsplitter, passes to the reference mirror and then reflects back, before passing through the beamsplitter to the microscope objective lens and then on to the detector. In the second path, a light beam passes through the beamsplitter, to the reference mirror, reflects back to the beamsplitter and then reflects from the half mirror into the microscope objective lens before proceeding to the detector. The light reflected from these surfaces recombines and a fringe interference pattern is formed. The objective lenses with Mirau interferometer are usually used in applications requiring higher magnification (>10×) or numerical apertures. In such instances objective lenses can be used following typical 10×, 20×, 50× and 100× magnification.

A Michelson interferometer is configured in a similar way to a Mirau with the exception that the reference mirror is in a different position (outside the optical axis). This configuration provides a longer working distance, wider fields of view and larger depth of focus at small magnifications (<5× ). The following magnification can be typically used for objective lenses with a Michelson interferometer: 1×, 1.5×, 2×, 2.5× and 5×.

Commercial microscope objective lenses with interferometers are manufactured by Leica, Nikon, Olympus, Seiwa Optical, Veeco, Zeiss and Zygo. Availability of wide range of interference objective lenses give a great opportunities concerned with selection of the suitable lens for carrying out scientific works. Selected issues related with suitable selection of interference objective lenses were described in the work (Petzing et al., 2010). Schematic diagrams of the typical configurations of interference objective lenses are shown in Fig. 5, whereas the general characteristics of interference objective lenses produced by Nikon (Japan) are presented in Tab. 3.

Fig. 5. Schematic diagrams of the typical configurations of interference objective lenses: a) Mirau, b) Michelson, c) commercially produced microscope objective lens with Mirau interferometer (Nikon 50× CF Plan IC EPI).

Coherence Correlation Interferometry in Surface Topography Measurements 11

The section is dedicated to some selected issues related to the applictaion of CCI for precise surface topography measurements (Conroy, 2008). A brief description of the white-light interference microscope Talysurf CCI 6000 by Taylor-Hobson Ltd., is presented. Subsequently issues related to the pre-measurements and measurements procedure, as well as processing and analysis of measurement data, are described in detail. The selected results of measurements of surface topography obtained by CCI for objects machined by various

One of the commercially available CCI instruments is a white light interference microscope produced by Taylor Hobson Ltd. The firm produces this line of instruments under the designation Talysurf CCI. One of these instruments is Talysurf CCI6000 (Conroy & Armstrong, 2005; Cincio et al., 2008; Lukianowicz, 2010). The principle of operation of this

White light generated by an external source (150 W quartz lamp installed in Fiber-Lite® DC-950 illuminator manufactured by Dolan-Jenner's Industries) is supplied to the instrument by optical fibre. In the measuring head the light beam is directed to a beamsplitter, where it is separated into two parallel beams. The first beam is directed towards the sample and the second beam is directed towards an internal reference mirror. The two beams recombine and give a local interference image, which is sent to the CCD

Fig. 6. Schematic diagram showing the principle of operation of the white-light interference

microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd.

techniques are presented and discussed in the final part of this section.

instrument, shown in Fig. 6, is based on coherence correlation interferometry.

**5.1 Interference microscope with Mirau objective lenses** 

detector.

**5. Measurements of engineering surfaces** 


CF – Chrome-Free, Plan – Flat Field Correction, IC – Infinity Corrected, EPI – Epi Illumination

Table 3. General characteristics of interference objective lenses produced by Nikon (Japan)

### **4.4 Algorithms**

The accuracy of surface topography measurements using the CCI is dependent on many factors. One of the most important factors is the algorithms used during the scan and the interference signal analysis algorithms. Analysis of signal interference generally requires the use of algorithms determining the maximum envelope of the signal (CCI mode) an the phase image-based interference (PSI mode).

An algorithm for digital envelope detection in white-light interferograms was described in the work (Larkin, 1996). It was compared with other algorithms. It was developed based on algorithms used in the PSI methods (Creath, 1988; Stahl, 1990; Kujawinska, 1993). The new algorithm was assessed in terms of accuracy and computational efficiency. It can be interpreted as a second-order nonlinear filter. Use of quadrature modulation and Hilbert transformation as a new measurement strategy, based on a direct reconstruction of the envelope of the correlogram, was presented in the paper (Hybel et al., 2008).

At work (Park & Kim, 2000) proposed the use of a new algorithm for detecting the true peak of the interference fringe. This two-step algorithm is an efficient means of computation to obtain a good measuring accuracy with greater insulation against disturbances and noise.

In order to obtain high accuracy and performance out of CCI and PSI techniques, many algorithms have been proposed (Ailing et al., 2008; Buchta et al., 2011; Kim et al., 2008). Among those algorithms analyzed were: phase-shifting, phase-crossing (Pawłowski et al., 2006), zero-crossing and Fourier-transform techniques. Algorithms that give an estimate of the envelope peak position from only a fraction of the interferogram (Sato & Ando, 2009) were also proposed.

Within the CCI techniques there were developments in scanning algorithms, merge and stitch images and error correction (Viotti et al., 2008; Kim et al., 2008), many of which have been patented and used in commercial systems (Harasaki & Schmit, 2002; Bankhead & McDonnell, 2009).

### **5. Measurements of engineering surfaces**

10 Recent Interferometry Applications in Topography and Astronomy

Working distance (mm)

Focal lenght (mm)

Weight (g)

aperture

EPI 2.5× 0.075 10.3 80 440 5× CF Plan IC EPI 5× 0.13 9.3 40 280 10× CF Plan IC EPI 10× 0.3 7.4 20 125 20× CF Plan IC EPI 20× 0.4 4.7 10 130 50× CF Plan IC EPI 50× 0.55 3.4 4 150

EPI 100× 0.7 2 2 200

Table 3. General characteristics of interference objective lenses produced by Nikon (Japan)

The accuracy of surface topography measurements using the CCI is dependent on many factors. One of the most important factors is the algorithms used during the scan and the interference signal analysis algorithms. Analysis of signal interference generally requires the use of algorithms determining the maximum envelope of the signal (CCI mode) an the

An algorithm for digital envelope detection in white-light interferograms was described in the work (Larkin, 1996). It was compared with other algorithms. It was developed based on algorithms used in the PSI methods (Creath, 1988; Stahl, 1990; Kujawinska, 1993). The new algorithm was assessed in terms of accuracy and computational efficiency. It can be interpreted as a second-order nonlinear filter. Use of quadrature modulation and Hilbert transformation as a new measurement strategy, based on a direct reconstruction of the

At work (Park & Kim, 2000) proposed the use of a new algorithm for detecting the true peak of the interference fringe. This two-step algorithm is an efficient means of computation to obtain a good measuring accuracy with greater insulation against

In order to obtain high accuracy and performance out of CCI and PSI techniques, many algorithms have been proposed (Ailing et al., 2008; Buchta et al., 2011; Kim et al., 2008). Among those algorithms analyzed were: phase-shifting, phase-crossing (Pawłowski et al., 2006), zero-crossing and Fourier-transform techniques. Algorithms that give an estimate of the envelope peak position from only a fraction of the interferogram (Sato & Ando, 2009)

Within the CCI techniques there were developments in scanning algorithms, merge and stitch images and error correction (Viotti et al., 2008; Kim et al., 2008), many of which have been patented and used in commercial systems (Harasaki & Schmit, 2002; Bankhead &

envelope of the correlogram, was presented in the paper (Hybel et al., 2008).

CF – Chrome-Free, Plan – Flat Field Correction, IC – Infinity Corrected, EPI – Epi Illumination

Designation

2.5× CF Plan IC

100× CF Plan IC

**4.4 Algorithms** 

disturbances and noise.

were also proposed.

McDonnell, 2009).

of objective lens Magnification Numerical

phase image-based interference (PSI mode).

The section is dedicated to some selected issues related to the applictaion of CCI for precise surface topography measurements (Conroy, 2008). A brief description of the white-light interference microscope Talysurf CCI 6000 by Taylor-Hobson Ltd., is presented. Subsequently issues related to the pre-measurements and measurements procedure, as well as processing and analysis of measurement data, are described in detail. The selected results of measurements of surface topography obtained by CCI for objects machined by various techniques are presented and discussed in the final part of this section.

### **5.1 Interference microscope with Mirau objective lenses**

One of the commercially available CCI instruments is a white light interference microscope produced by Taylor Hobson Ltd. The firm produces this line of instruments under the designation Talysurf CCI. One of these instruments is Talysurf CCI6000 (Conroy & Armstrong, 2005; Cincio et al., 2008; Lukianowicz, 2010). The principle of operation of this instrument, shown in Fig. 6, is based on coherence correlation interferometry.

White light generated by an external source (150 W quartz lamp installed in Fiber-Lite® DC-950 illuminator manufactured by Dolan-Jenner's Industries) is supplied to the instrument by optical fibre. In the measuring head the light beam is directed to a beamsplitter, where it is separated into two parallel beams. The first beam is directed towards the sample and the second beam is directed towards an internal reference mirror. The two beams recombine and give a local interference image, which is sent to the CCD detector.

Fig. 6. Schematic diagram showing the principle of operation of the white-light interference microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd.

Coherence Correlation Interferometry in Surface Topography Measurements 13

The process requires a sample that must be clean and free from grease, smears, fingerprints, liquids and dust. If the samples are contaminated in some way before the measurement process begins they must be cleaned. Cleaning the sample would normally require the use of alcohol based liquids, or compressed air. Cleansing the sample surface is an extremely important issue, because the accumulated contamination can be generative source of

In some cases, the reflective characteristics of a surface may hinder its measurement. This concern particularly affects those surfaces which are made of materials with relatively low reflectance. For such surfaces it may be desirable to overcoat with thin layers of vacuum

The geometry and mass of the sample are the main factors affecting their method of fixturing. Use of non-permanent adhesives (e.g. adhesive tape, gels for fixturing etc.), may cause creep, whereas use of external force may cause sample distortion. Usually a range of

The orientation of the sample may affect the results of the measurements. It is necessary to determine the proper orientation for all measured samples to obtain this same repeatability.

After the proper sample preparation the measuring procedure can begin. A typical measurement procedure (regardless of the CCI instrument) involves the following steps:

position the objective lens at its working distance from the element (adjusting the *z* axis),

A more detailed description of objective lens selection and image stitching procedures is presented below. Descriptions of other steps can be found also in (Leach et al., 2008; Petzing

table mounting points and accessories are used in the laboratory, including:

visual analysis of sample surface,

overcoating of surface (optional, if necessary),

cleaning the sample,

 fixturing the sample, orientation of sample.

measurement error.

 disk fixtures tray holders.

coated gold or chromium.

magnetic and vacuum chucks/plates,

power up the instrument and the computer,

select the objective lens for the measurement,

focus the microscope to obtain a sharp image,

adjust the test element position (*x* and *y* axes),

adjust the light intensity level to an optimum value,

minimize the number of fringes,

initiate data acquisition.

et al., 2010).

check correct software-selectable items,

run the program (for control/measurements) on the computer,

place the test element on the stage (adjusting the *x* and *y* axes),

adjust stage level or tilt to optimize fringe contrast/appearance,

**5.3 Measurements procedure** 

The optical measuring head of the microscope is coupled with precision piezo-electric actuators (PZTs). The PZTs move the measuring head vertically above the measured sample.

The CCD detector measures the intensity of the light as the interferometric lens (Mirau type, 10×, 20× and 50× magnification) is actuated in the vertical direction (*z* axis) and finds the interference maximum. The location of individual points on the test surface is determined based on the analysis of the mutual temporal coherence of the interfering waves, conducted separately for each surface point.

In this way an image is generated and acquired, before being processed on a computer manufactured by Dell, with an Intel Xenon class processor. Using this recorded data a highresolution surface topography is then generated. The instrument enables the obtainment of a vertical resolution to 10 pm (0.01 nm) at the measuring range (in the z axis) to 10 mm. Regardless of the magnification the surface topography contains more than one million data points (1024 × 1024 points).

The manufacturer of the instrument has supplied dedicated computer software. These are two applications: Talysurf CCI v. 2.0.7.3 (control elements of the system and measurements) and TalyMap Platinum v. 4.0.5.3985 (visualization and advanced data analysis). The TalyMap software uses Mountain Technology™ provided by DigitalSurf (France).

The general view of the white-light interference microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd., is shown in Fig. 7.

Fig. 7. White-light interference microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd.: a) general view of the measuring system, b) near view of the instrument.

### **5.2 Pre-measurements procedure**

The pre-measurements procedure for sample preparation usually involves:


The optical measuring head of the microscope is coupled with precision piezo-electric actuators (PZTs). The PZTs move the measuring head vertically above the measured

The CCD detector measures the intensity of the light as the interferometric lens (Mirau type, 10×, 20× and 50× magnification) is actuated in the vertical direction (*z* axis) and finds the interference maximum. The location of individual points on the test surface is determined based on the analysis of the mutual temporal coherence of the interfering waves, conducted

In this way an image is generated and acquired, before being processed on a computer manufactured by Dell, with an Intel Xenon class processor. Using this recorded data a highresolution surface topography is then generated. The instrument enables the obtainment of a vertical resolution to 10 pm (0.01 nm) at the measuring range (in the z axis) to 10 mm. Regardless of the magnification the surface topography contains more than one million data

The manufacturer of the instrument has supplied dedicated computer software. These are two applications: Talysurf CCI v. 2.0.7.3 (control elements of the system and measurements) and TalyMap Platinum v. 4.0.5.3985 (visualization and advanced data analysis). The

The general view of the white-light interference microscope Talysurf CCI 6000 produced by

Fig. 7. White-light interference microscope Talysurf CCI 6000 produced by Taylor Hobson

Ltd.: a) general view of the measuring system, b) near view of the instrument.

The pre-measurements procedure for sample preparation usually involves:

TalyMap software uses Mountain Technology™ provided by DigitalSurf (France).

sample.

separately for each surface point.

points (1024 × 1024 points).

Taylor Hobson Ltd., is shown in Fig. 7.

**5.2 Pre-measurements procedure** 


The process requires a sample that must be clean and free from grease, smears, fingerprints, liquids and dust. If the samples are contaminated in some way before the measurement process begins they must be cleaned. Cleaning the sample would normally require the use of alcohol based liquids, or compressed air. Cleansing the sample surface is an extremely important issue, because the accumulated contamination can be generative source of measurement error.

In some cases, the reflective characteristics of a surface may hinder its measurement. This concern particularly affects those surfaces which are made of materials with relatively low reflectance. For such surfaces it may be desirable to overcoat with thin layers of vacuum coated gold or chromium.

The geometry and mass of the sample are the main factors affecting their method of fixturing. Use of non-permanent adhesives (e.g. adhesive tape, gels for fixturing etc.), may cause creep, whereas use of external force may cause sample distortion. Usually a range of table mounting points and accessories are used in the laboratory, including:


The orientation of the sample may affect the results of the measurements. It is necessary to determine the proper orientation for all measured samples to obtain this same repeatability.

### **5.3 Measurements procedure**

After the proper sample preparation the measuring procedure can begin. A typical measurement procedure (regardless of the CCI instrument) involves the following steps:


A more detailed description of objective lens selection and image stitching procedures is presented below. Descriptions of other steps can be found also in (Leach et al., 2008; Petzing et al., 2010).

Coherence Correlation Interferometry in Surface Topography Measurements 15

Fig. 9. The method of measurement of surface topographies with use of an image stitching function realized by TalyMap Platinum software: a) principle of image stitching procedure, b) single interferential image of measured surface with magnification 50×, c) output surface topography as a mosaic composed from a series of single surface topographies acquired as a

Visual Basic script called Advances DataStiching v.1.2.1. In this case, the output surface topography is a mosaic composed of the 9 single surface topographies recorded as a 3 × 3

A microscope objective lens with Mirau interferometer 50× CF Plan IC EPI, produced by Nikon, was used in the acquisition of the surface topographies The area measured for each of the topographies was the same 359 × 359 μm. During the stitching procedure, the area was often reduced by an overlap to a size 288 × 359 μm, 359 × 288 μm and 288 × 288 μm. The visual interpretations of the operations of the image stitching procedure are shown in Fig. 9.

Procedures relating to processing, analysis and interpretation (Petzing et al., 2010) are an important part of the measurement process following the acquisition of measurement data. In practice, these procedures are realized by special computer software. The popular commercial softwares for processing and analysis of measurement data include: Mountains Map by DigitalSurf (France), TrueMap by TrueGage (USA) and SPIP by Image Metrology A/S (Denmark). The pre-processing of measurement data usually includes (depending on

**5.4 Processing, analysis and interpretation of the results of measurements** 

3 × 3 matrix.

software used):

matrix.

One of the important steps during the measuring process is selection of the objective lens. From a practical point of view it is most important to determine the main characteristics of the measured surface. It is on this basis that an appropriate objective lens is usually selected. General information concerning the selection of the objective lens is presented in Tab. 4, whereas general views of two types of microscope objective lenses with Mirau interferometer (used for surface roughness measurement) produced by Nikon (Japan) are show in Fig. 8.


Table 4. General information on selection of the objective lens.

Fig. 8. Two types of the microscope objective lenses with Mirau interferometer used for surface roughness measurement: a) Nikon 10× CF Plan IC EPI (field of view 1.8 × 1.8 mm), b) Nikon 50× CF Plan IC EPI (field of view 0.36 × 0.36 mm).

In some cases there is a need for measurement of a larger area than that which would constitute the field of view of the objective lens. This is when the image stitching procedure, whereby a matrix of mages are joined, or stitched, together, can be utilised. Image stitching can be realized only if the CCI instrument is fitted with a motorized stage with horizontal translation, which allows the computer program to precisely adjust the surface position. Each acquired image is precisely positioned and there is a consistent overlap of images. This is important because it allows for a comparison of neighbouring images, and enables the precise correlation of lateral position and consistent vertical range values. The typical overlap between images ranges from 0 % to 25 %.

The operations of the image stitching procedure are described below using the example of the functions implemented in TalyMap Platinum software. This function is realized by

One of the important steps during the measuring process is selection of the objective lens. From a practical point of view it is most important to determine the main characteristics of the measured surface. It is on this basis that an appropriate objective lens is usually selected. General information concerning the selection of the objective lens is presented in Tab. 4, whereas general views of two types of microscope objective lenses with Mirau interferometer (used for surface roughness measurement) produced by Nikon (Japan) are

Surface Objective lens

size Surface element Resolution Magnification Type of interference

Very Michelson

Fig. 8. Two types of the microscope objective lenses with Mirau interferometer used for surface roughness measurement: a) Nikon 10× CF Plan IC EPI (field of view 1.8 × 1.8 mm),

In some cases there is a need for measurement of a larger area than that which would constitute the field of view of the objective lens. This is when the image stitching procedure, whereby a matrix of mages are joined, or stitched, together, can be utilised. Image stitching can be realized only if the CCI instrument is fitted with a motorized stage with horizontal translation, which allows the computer program to precisely adjust the surface position. Each acquired image is precisely positioned and there is a consistent overlap of images. This is important because it allows for a comparison of neighbouring images, and enables the precise correlation of lateral position and consistent vertical range values. The typical

The operations of the image stitching procedure are described below using the example of the functions implemented in TalyMap Platinum software. This function is realized by

rough surfaces High 10×, 20×, 50×, 100× Mirau

1×, 1.5×, 2×, 2.5×, 5×

1×, 1.5×, 2×, 2.5×, 5× +image stitching procedure

objective lens

show in Fig. 8.

Small Steep slopes,

Flat and smooth

surfaces Low

Table 4. General information on selection of the objective lens.

b) Nikon 50× CF Plan IC EPI (field of view 0.36 × 0.36 mm).

overlap between images ranges from 0 % to 25 %.

Area

Large

large

Fig. 9. The method of measurement of surface topographies with use of an image stitching function realized by TalyMap Platinum software: a) principle of image stitching procedure, b) single interferential image of measured surface with magnification 50×, c) output surface topography as a mosaic composed from a series of single surface topographies acquired as a 3 × 3 matrix.

Visual Basic script called Advances DataStiching v.1.2.1. In this case, the output surface topography is a mosaic composed of the 9 single surface topographies recorded as a 3 × 3 matrix.

A microscope objective lens with Mirau interferometer 50× CF Plan IC EPI, produced by Nikon, was used in the acquisition of the surface topographies The area measured for each of the topographies was the same 359 × 359 μm. During the stitching procedure, the area was often reduced by an overlap to a size 288 × 359 μm, 359 × 288 μm and 288 × 288 μm. The visual interpretations of the operations of the image stitching procedure are shown in Fig. 9.

### **5.4 Processing, analysis and interpretation of the results of measurements**

Procedures relating to processing, analysis and interpretation (Petzing et al., 2010) are an important part of the measurement process following the acquisition of measurement data. In practice, these procedures are realized by special computer software. The popular commercial softwares for processing and analysis of measurement data include: Mountains Map by DigitalSurf (France), TrueMap by TrueGage (USA) and SPIP by Image Metrology A/S (Denmark). The pre-processing of measurement data usually includes (depending on software used):

Coherence Correlation Interferometry in Surface Topography Measurements 17

Fig. 10. Exemplary analysis of a DOE sample for measurements obtained by white-light

interference microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd.


After these procedures the file is ready to be processed, which will allow for the acquisition of:


Above nly a few select procedures are given, in practice there may be many more.

They may also be more complicated and multi-threaded. Processing leads to the analysis, which typically involves:


As a result of analysis of the measurement data obtained, numerical values of the assessed paremeters characterizing the surface features are established.Based on these parameters and the machining parameters the whole machining process can be deduced. The interpretation of results in this case is very important, because it allows for the establishment of proper conditions within which the machining process will be optimally realised.

### **5.5 Examples of measurements and analysis**

On the following pages some example results of analysis are shown, alongside collections of acquired surface topographies obtained by white-light interference microscope TalysurfCCI 6000 produced by Taylor Hobson Ltd., equipped with the TalyMap Platinum v.4.0.5.3985 software produced by DigitalSurf.

Fig. 10 presents an example analysis of a diffractive optical element (DOE) by Thorlabs, Inc. (USA).The DOEs are usually used in structured light generators. This sample has been manufactured from transparent polycarbonate. The value of light reflection coefficient for a polycarbonate surface was low, which made it a little awkward to analyse. The measurement was carried out on an area of approx. 4 sq. mm (Kaplonek & Tomkowski, 2009). Fig. 10 shows approx. 12% of the measured area (549 × 507 × 1.73 mm). The irregularities of this surface are periodical.

On Fig. 11 an example analysis of a 2.5" HDD platter, by Toshiba Corp. (Japan), is shown.The topography has been measured on an area less than 1 sq. mm (980 × 979 × 0.06 μm). The irregularities of the surface are fairly insignificant and random. For these surfaces the values of 2D (*Ra,Rq, Rp, Rv, Rt, Rsk, Rku* and *Rz*) and 3D (*Sa, Sq, Sp, Sv, St, Ssk, Sku* and *Sz*) paremeters (Lukianowicz & Tomkowki, 2009) were also calculated. The collections of

After these procedures the file is ready to be processed, which will allow for the acquisition

Above nly a few select procedures are given, in practice there may be many more.

They may also be more complicated and multi-threaded. Processing leads to the analysis,

As a result of analysis of the measurement data obtained, numerical values of the assessed paremeters characterizing the surface features are established.Based on these parameters and the machining parameters the whole machining process can be deduced. The interpretation of results in this case is very important, because it allows for the establishment of proper conditions within which the machining process will be optimally

On the following pages some example results of analysis are shown, alongside collections of acquired surface topographies obtained by white-light interference microscope TalysurfCCI 6000 produced by Taylor Hobson Ltd., equipped with the TalyMap Platinum

Fig. 10 presents an example analysis of a diffractive optical element (DOE) by Thorlabs, Inc. (USA).The DOEs are usually used in structured light generators. This sample has been manufactured from transparent polycarbonate. The value of light reflection coefficient for a polycarbonate surface was low, which made it a little awkward to analyse. The measurement was carried out on an area of approx. 4 sq. mm (Kaplonek & Tomkowski, 2009). Fig. 10 shows approx. 12% of the measured area (549 × 507 × 1.73 mm). The

On Fig. 11 an example analysis of a 2.5" HDD platter, by Toshiba Corp. (Japan), is shown.The topography has been measured on an area less than 1 sq. mm (980 × 979 × 0.06 μm). The irregularities of the surface are fairly insignificant and random. For these surfaces the values of 2D (*Ra,Rq, Rp, Rv, Rt, Rsk, Rku* and *Rz*) and 3D (*Sa, Sq, Sp, Sv, St, Ssk, Sku* and *Sz*) paremeters (Lukianowicz & Tomkowki, 2009) were also calculated. The collections of

 opening the file, levelling ,

 photo simulations, contour diagrams, mesh axonometrics, continuous axonometrics Abbot-Firestone curves, texture direction.

which typically involves:

realised.

 calculating the 2D parameters, calculating the 3D parameters.

**5.5 Examples of measurements and analysis** 

v.4.0.5.3985 software produced by DigitalSurf.

irregularities of this surface are periodical.

of:

filling non-measured points.

pseudo-colour surface maps,

Fig. 10. Exemplary analysis of a DOE sample for measurements obtained by white-light interference microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd.

Coherence Correlation Interferometry in Surface Topography Measurements 19

Fig. 12. Collection of surface topographies obtained by white-light interference microscope

Talysurf CCI 6000 produced by Taylor Hobson Ltd.

Fig. 11. Exemplary analysis of a 2.5" HDD platter sample for measurements obtained by white-light interference microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd.

Fig. 11. Exemplary analysis of a 2.5" HDD platter sample for measurements obtained by white-light interference microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd.

Fig. 12. Collection of surface topographies obtained by white-light interference microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd.

Coherence Correlation Interferometry in Surface Topography Measurements 21

topographies for different surfaces are shown in Fig. 12. and Fig. 13 (Kaplonek &

The first collection (Fig. 12) contains topographies of an engineering surface after the burnishing process. The value of the *x* axis is very high and amounts to 19.2 mm. This topography was generated using the image stitching procedure. In this same collection is a topography of a typically milled surface (measured area 366 × 366 × 10.9 μm) and a topography of a ground surface (measured area 1.83 × 5.43 × 0.07 mm) with defects in the form of scratches. These defects are typical for the surfaces of machine parts, which operate

In the second collection (Fig. 13) a polished surface is shown (measured area 0.359 × 0.359 × 7.9 μm) with a different defect, in this case taking the form of pitting. The next topography shows the surface of a grinding wheel 1-20×20×10 SG 80 M 8 V (measured area is 1.5 × 1.5 ×

On the surface different sized abrasive grains are clearly visible. The last topography of this collection shows the surface of a calibration specimen, made for glass. Calibration specimens are usually used for routine calibrating of the stylus profilometers (measured area is 2.75 ×

During the interference measurements of surface topography some errors and limitations may be generated, for a number of different reasons. The sources of these errors are most often concerned with the measuring instrument and its software, as well as with the properties of the measured surface and the conditions in which the measurement was made. The limitations of CCI, and some factors affecting the accuracy of CCI based surface

One of the major contributing factors, which favor the generation of errors (Harasaki & Wyant, 2000, Pförtner & Schwider, 2001; Gao et al., 2008) in interference measurements of surface topography, are large gradients upon the surface analyzed. For such surfaces irregularities of slope and incline are significant.Slopes are usually described mathematically using the angles of slope tangent, surface derivatives or function gradient. In many cases, a considerable gradient causes the measurement errors due to limitations caused by the properties of the measuring instrument and its software. Fig. 14 shows three typical situations that may cause limitations in the measurement of surface topography:

No signal in the interference microscope caused by irregularities of slope occurs when, the

max given by the numerical aperture

exceed the maximum value

Lukianowicz, 2010; Lukianowicz, 2010).

in industrial conditions.

0.25 mm).

2.71 × 0.004 mm).

**6. Limitations of CCI** 

**6.1 Surface properties** 

sloping recess.

slope angles of inequality

of the lens (Petzing et al., 2010):

 large slope angles of inequality, step height of surface irregularities,

topography measurements, are discussed in this section.

Fig. 13. Collection of surface topographies obtained by white-light interference microscope Talysurf CCI 6000 produced by Taylor Hobson Ltd.

topographies for different surfaces are shown in Fig. 12. and Fig. 13 (Kaplonek & Lukianowicz, 2010; Lukianowicz, 2010).

The first collection (Fig. 12) contains topographies of an engineering surface after the burnishing process. The value of the *x* axis is very high and amounts to 19.2 mm. This topography was generated using the image stitching procedure. In this same collection is a topography of a typically milled surface (measured area 366 × 366 × 10.9 μm) and a topography of a ground surface (measured area 1.83 × 5.43 × 0.07 mm) with defects in the form of scratches. These defects are typical for the surfaces of machine parts, which operate in industrial conditions.

In the second collection (Fig. 13) a polished surface is shown (measured area 0.359 × 0.359 × 7.9 μm) with a different defect, in this case taking the form of pitting. The next topography shows the surface of a grinding wheel 1-20×20×10 SG 80 M 8 V (measured area is 1.5 × 1.5 × 0.25 mm).

On the surface different sized abrasive grains are clearly visible. The last topography of this collection shows the surface of a calibration specimen, made for glass. Calibration specimens are usually used for routine calibrating of the stylus profilometers (measured area is 2.75 × 2.71 × 0.004 mm).

### **6. Limitations of CCI**

20 Recent Interferometry Applications in Topography and Astronomy

Fig. 13. Collection of surface topographies obtained by white-light interference microscope

Talysurf CCI 6000 produced by Taylor Hobson Ltd.

During the interference measurements of surface topography some errors and limitations may be generated, for a number of different reasons. The sources of these errors are most often concerned with the measuring instrument and its software, as well as with the properties of the measured surface and the conditions in which the measurement was made. The limitations of CCI, and some factors affecting the accuracy of CCI based surface topography measurements, are discussed in this section.

### **6.1 Surface properties**

One of the major contributing factors, which favor the generation of errors (Harasaki & Wyant, 2000, Pförtner & Schwider, 2001; Gao et al., 2008) in interference measurements of surface topography, are large gradients upon the surface analyzed. For such surfaces irregularities of slope and incline are significant.Slopes are usually described mathematically using the angles of slope tangent, surface derivatives or function gradient. In many cases, a considerable gradient causes the measurement errors due to limitations caused by the properties of the measuring instrument and its software. Fig. 14 shows three typical situations that may cause limitations in the measurement of surface topography:


No signal in the interference microscope caused by irregularities of slope occurs when, the slope angles of inequality exceed the maximum value max given by the numerical aperture of the lens (Petzing et al., 2010):

Coherence Correlation Interferometry in Surface Topography Measurements 23

Fig. 15. Double-reflection of light focused by interference objective lens on the surface of the

The significant instrumental limitations of CCI are limited resolution of the lens aperture and the interference microscope objective lens, as well as the limitations concerned with the source of light and the scanning system.These limitations can cause inaccurate representation of the surface topography. The reason for the additional errors may be improper calibration of the measuring system, and imperfect software. Among the limitations related to the environment in which the measurement is carried vibrations and temperature changes are particularly noteworthy, as they cause random changes to occur in the measured surface topography. Limitations of CCI methods were discussed in more

The results presented in this chapter show that coherence correlation interferometry is an advanced optical technique used for precise measurement of surface topography. The dynamic development of this technique means that it should play a dominant role in modern interference microscopy. CCI extends the scope of inferferometric techniques used in the measurement of surface topography. Especially those, which are characterized by complex structure or a relatively low reflectance (e.g. calibration specimens made from glass

The comparison between coherence correlation interferometry techniques and phase shifting methods shows that CCI has a better tolerance for variations in surface texture as well as greater capabilities for measuring surface features and structures, such as step heights. An important feature is also the fact that the point where the maximum interference occurs can be found for each single pixel of the detector. Additional advantages are concerned with large measurement ranges, high accuracy and repeatability as well as

Part of this work was supported by National Science Center of Poland. The Authors would like to thank Mr. Robert Tomkowski MSc, BSc, from the Laboratory of Micro- and Nano

**6.2 Instrumental and measuring environment limitations** 

measured wedge groove.

detail in (Petzing et al., 2010).

**7. Conclusions** 

or transparent films).

shortened times of measurement.

**8. Acknowledgments** 

$$
\theta\_{\text{max}} = \ \alpha\_o \ = \arcsin\left(\frac{N\_A}{n}\right) \ ,\tag{6}
$$

where: *NA* = *n* sino – numerical aperture of interference microscope objective lens, *n* – refractive index of medium surrounding the objective lens,o – half the maximum value of the cone vertex angle formed by the rays from the microscope objective lens (Fig. 14a).

Fig. 14. Simplified diagram which showing the reflection of light focused by interference objective lens: a) from a sloped flat surface, b) from the surface with a step height, c) from the surface with sloping recess

Strong interference and no interference signal frequently reveal those surface areas, where there are significant step heights in surface irregularities or a sloping recess. During the measurements of these surfaces the self-shadowing of some areas, or partial self-shadowing of the light beam reflected from the surface, occurs (Fig. 14b and 14c).

For an analysis of the measurement errors of surface topography by interference methods, it is necessary to consider two models of surface irregularities. The first of these, is inequality, where the lateral dimensions are larger than the transverse resolving power *d* of an interference microscope objective lens given by the equation:

$$d = \frac{\mathcal{X}}{2N\_A} \,' \,. \tag{7}$$

where: *NA* – numerical aperture of interference microscope objective lens, – average wavelength of light used to illuminate the surface. The slopes of these inequalities can be regarded as smooth.

An interference image at a location corresponding to the slope will depend upon the shape of the surface. This image can be observed, if the slope angles do not exceed the specified maximum angle max given by equation (6). However, if the slope angle of inequality as well as the slop of the surface are excessive, then the reflected radiation can be directed out of the microscope objective lens (Fig. 15a). In the second model, the transverse dimensions of irregularity are smaller than the transverse resolving power *d* of the interference microscope objective lens. Such surfaces can be considered as rough surfaces, which scatter the incidence light in a more or less diffuse way.In this case a part of the light scattered by the surface will be directed at the optical system of interfence microscope (Fig. 15b).

Fig. 15. Double-reflection of light focused by interference objective lens on the surface of the measured wedge groove.

### **6.2 Instrumental and measuring environment limitations**

The significant instrumental limitations of CCI are limited resolution of the lens aperture and the interference microscope objective lens, as well as the limitations concerned with the source of light and the scanning system.These limitations can cause inaccurate representation of the surface topography. The reason for the additional errors may be improper calibration of the measuring system, and imperfect software. Among the limitations related to the environment in which the measurement is carried vibrations and temperature changes are particularly noteworthy, as they cause random changes to occur in the measured surface topography. Limitations of CCI methods were discussed in more detail in (Petzing et al., 2010).

### **7. Conclusions**

22 Recent Interferometry Applications in Topography and Astronomy

max o arc sin , *NA*

of the cone vertex angle formed by the rays from the microscope objective lens (Fig. 14a).

Fig. 14. Simplified diagram which showing the reflection of light focused by interference objective lens: a) from a sloped flat surface, b) from the surface with a step height, c) from

Strong interference and no interference signal frequently reveal those surface areas, where there are significant step heights in surface irregularities or a sloping recess. During the measurements of these surfaces the self-shadowing of some areas, or partial self-shadowing

For an analysis of the measurement errors of surface topography by interference methods, it is necessary to consider two models of surface irregularities. The first of these, is inequality, where the lateral dimensions are larger than the transverse resolving power *d* of an

, <sup>2</sup> *<sup>A</sup>*

(7)

– average

*N* 

wavelength of light used to illuminate the surface. The slopes of these inequalities can be

An interference image at a location corresponding to the slope will depend upon the shape of the surface. This image can be observed, if the slope angles do not exceed the specified

well as the slop of the surface are excessive, then the reflected radiation can be directed out of the microscope objective lens (Fig. 15a). In the second model, the transverse dimensions of irregularity are smaller than the transverse resolving power *d* of the interference microscope objective lens. Such surfaces can be considered as rough surfaces, which scatter the incidence light in a more or less diffuse way.In this case a part of the light scattered by

the surface will be directed at the optical system of interfence microscope (Fig. 15b).

max given by equation (6). However, if the slope angle of inequality as

*d*

where: *NA* – numerical aperture of interference microscope objective lens,

of the light beam reflected from the surface, occurs (Fig. 14b and 14c).

interference microscope objective lens given by the equation:

*n* – refractive index of medium surrounding the objective lens,

where: *NA* = *n* sin

the surface with sloping recess

regarded as smooth.

maximum angle

 

*n*

o – numerical aperture of interference microscope objective lens,

(6)

o – half the maximum value

The results presented in this chapter show that coherence correlation interferometry is an advanced optical technique used for precise measurement of surface topography. The dynamic development of this technique means that it should play a dominant role in modern interference microscopy. CCI extends the scope of inferferometric techniques used in the measurement of surface topography. Especially those, which are characterized by complex structure or a relatively low reflectance (e.g. calibration specimens made from glass or transparent films).

The comparison between coherence correlation interferometry techniques and phase shifting methods shows that CCI has a better tolerance for variations in surface texture as well as greater capabilities for measuring surface features and structures, such as step heights. An important feature is also the fact that the point where the maximum interference occurs can be found for each single pixel of the detector. Additional advantages are concerned with large measurement ranges, high accuracy and repeatability as well as shortened times of measurement.

### **8. Acknowledgments**

Part of this work was supported by National Science Center of Poland. The Authors would like to thank Mr. Robert Tomkowski MSc, BSc, from the Laboratory of Micro- and Nano

Coherence Correlation Interferometry in Surface Topography Measurements 25

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B2


**2** 

*Egypt* 

**Surface Micro Topography Measurement** 

Surface topography measurement plays an important role in many applications in engineering and science. The three dimensional (3D) shapes of objects need to be measured accurately to ensure manufacturing quality. Optical methods have been used as metrological tools for a long time. They are non-contacting, non-destructive and highly accurate. In combination with computers and other electronic devices, they have become faster, more reliable, more convenient and more robust. Among these optical methods, interferometry has received much interest for its shape measurement of optical and nonoptical surfaces. Information about the surface under test can be obtained from interference fringes which characterize the surface. Two-beam interference fringes have been used to investigate the shape of optical and non-optical surfaces for a long time (Born et al., 1980). Phase distribution is encoded in an intensity distribution as a result of interference phenomena, and is displayed in the form of an interference pattern. Phase distribution should therefore be retrievable from the interference pattern. There are many methods of phase evaluation. In this chapter, we present recent developments in interferometry techniques carried out in our laboratory. In Sec. 2, the flat fielding method for coherent noise suppression is described. In Sec. 3, a combination of flat fielding and apodized apertures is presented. In Sec. 4, the phase retrieval using single-shot off-axis geometry, Zernike's polynomial fitting, Bünnagel's method, phase shifting interferometry, and two-wavelength interferometry are described. Section 5 describes a new off-axis interferometry configuration and the principle of single-shot, dual-wavelength interferometry for measuring a step height

*m* nominally. In Sec. 6, a multiple-beam interferometry technique at reflection for

The use of digital detectors in digital holography for recording a series of iterferograms is usually accompanied by dark current (thermal noise), shot noise, and scattering noise due to some dust particles, scratches, etc., on optical elements. Such coherent noise can affect the

/20 is described. Section 7

measuring the microtopography of an optical flat nominally of

gives concluding discussions and remarks.

**1. Introduction** 

of 1.34 

**2. Flat fielding** 

**Using Interferometry** 

*Engineering and Surface Metrology Laboratory,* 

Dahi Ghareab Abdelsalam

*National Institute for Standards,* 

