**2.1. Measurement principle**

in ourresearch centre on the applications of optical interferometry at a shop floor environment, which is normally subjected to environmental disturbances and vibrations. These researches mainly focus on surface measurement and inspection, and this is the main focus of the research centre. The methods discussed here may also be applied to other application areas depending

The manufacture of highly added value components in developed economies is rapidly shifted to the design and production of micro-/nano-structured and free-form surfaces. The application of the use of micro-/nano-scale and ultra-precision structured surfaces is broad and covers the optics, silicon wafer, hard disks, MEMS/NEMS, micro-fluidics and micromoulding industries. All these industries critically rely on ultra-precision surfaces. However, there is an essential factor to limit of the manufacture of these kinds of surfaces, that is to say the ability to measure the product quickly and easily within the manufacturing environment. According to the report, currently the quality of fabrication of these kinds of products depends mainly on the experience of process engineers backed up by an expensive trial-and-error approach. Subsequently, the scrap rates of these manufactured items are

Optical interferometry has been extensively studied for surface measurement due to the advantages of non-contact measurement and high measurement accuracy. Nevertheless, conventional optical interferometry techniques are exceptionally sensitive to environmental noises such as air turbulence, temperature drift and mechanical vibration. Such noises can cause errors during surface measurement and produce void measurement results. There are a number of methods to reduce the influence of these noises. While controlling the measurement environment by using a vibration isolation stage and retaining a stable temperature is an effective way to reduce noise for laboratory and offline applications, it may not be practical in manufacturing conditions, for instance, when a measurement part is too large to be

In order to extend the application of interferometry to shop floor inspection, two methods can be adapted. One method is by introducing a reference interferometer and vibration compensation system to the main interferometer to compensate the environmental disturbance [2–4]. Complete common-path interferometers such as the scatterplate interferometer are insensitive to noises as well [5–7]. These noise reduction approaches are generally used for laser-based phase-shifting interferometry, for which the applications are limited to measurement of relatively smooth surfaces due to the well-known 2π phase ambiguity problem of monochromatic interferometry. The other method is to realize the data sampling in just one image shot [8–10]. This kind of so-called one shot interferometer is immune to the environmental noise

We will discuss the above two kinds of interferometry through two case studies: the common-path wavelength scanning interferometer and the single-shot line-scan dispersive

on the optical set-up of the interferometer system and the measurement objects.

50–70% high [1].

42 Optical Interferometry

mechanically insulated.

and vibrations.

interferometer.

White light vertical scanning interferometry (WLSI) is able to overcome the 2π phase ambiguity problem and extend its application to rough surfaces and structured surfaces with large step heights [11–13]. It measures the optical path difference (OPD) by determining the peak position from the interferograms. It can be used to measure optically smooth surfaces as well as the optically rough surfaces. (The definition of an optically smooth surface is the surface height variation within the resolution cell of the imaging system is not exceed one-eighth of the wavelength of the light used. For optically rough surface which is defined as the height variations within the resolution cell of the imaging system is exceed one-fourth of the wavelength of the light used [13]). However, the need to perform a mechanical scanning of the heavy probe head or the specimen stage limits the measurement speed. In addition, the data acquisition procedure and processing are more complicated than monochromatic interferometry.

**Figure 1.** Schematic diagram of the proposed surface measurement system. AOTF–acousto-optic tuneable filter; PD– photo diode; IR SLED–inferred superluminescent light-emitting diode; DAQ–data acquisition card.

Wavelength scanning interferometry (WSI) has been reported by many researchers worldwide in areal surface measurement by using a two-dimensional CCD detector [4, 14–16]. Compared with WLSI, surface topography measurements are based on the phase shifts due to wavelength variations, thus avoiding any mechanical scanning process. Absolute optical path difference can be measured without any 2π phase ambiguity. WSI has advanced itself to dispersive white light interferometry [17, 18], measuring full field of surface instead of a single point of the surface by means of spectrometry.

We have proposed an environmentally robust fast surface measurement system by means of wavelength scanning interferometry and active servo control techniques. The basic configuration of the proposed surface measurement system is illustrated in **Figure 1**. The measurement system is composed of two Linnik interferometers that share a common optical path. The measurement interferometer is illuminated by a white light source through an acousto-optic tuneable filter (AOTF) to filter the light from the white light source to the main interferometer. This is to select a specific wavelength for the interferometer, thus producing an interferogram at the CCD sourced only by that specific wavelength. The selected light wavelength is determined by:

$$
\mathcal{A} = \Delta n \alpha \frac{\nu\_a}{f\_a} \tag{1}
$$

where Δn is the birefringence of the crystal used as the diffraction material, α is a complex parameter subject to the design of the AOTF, and *va* and *fa* are the velocity and frequency of the driving acoustic wave, respectively. The wavelength of the light which is selected by the AOFT can therefore be varied just by changing the driving frequency *fa*. Consequently, different wavelengths of light will pass through the AOTF in sequence so a series of interferograms of different wavelengths will be detected by the CCD camera. The absolute optical path difference can be calculated in real time through analyzing interferograms captured by the CCD camera. The reference interferometer, which is illuminated by an inferred superluminescent lightemitting diode (SLED), is used to observe and compensate for the environmental noise, for example, mechanical vibration, temperature drift and air turbulence. Because the two interferometers undergo similar environmental noise, the measurement interferometer will be capable of measuring surface information once the reference interferometer is 'locked' into the compensation mode.

The light beams from the AOTF and the IR SLED are combined by a dichroic mirror that is highly reflective in the inferred wavelength and transmissive in the visible light wavelength range. After passing through the dichroic mirror, the light beam is coupled into an optical fibre patch cable. By separating the light source and AOTF from the interferometers, not only the size and weight of the interferometers have been greatly reduced, but also the thermal influence from the light source has also been eliminated.

It is well known that surface measurement in the workshop/manufacturing environment has been challenging to achieve using interferometric techniques since they are very sensitive to environmental vibrations, in particular, axial (vertical) vibration [5]. In addition, measurement noise can be induced by air turbulence and temperature drift as well. In this experimental study, the reference interferometer is illuminated by a SLED, which made by EXOLES (EXS2100068–01, 850 nm centre wavelength with 50 nm bandwidth) together with a servo feedback electronic unit to compensate the environmental noise effectively. Output light from the SLED is combined with the measurement light and travels virtually the same optical path as the measurement interferometer. The interference signal of the reference interferometer is picked up by a photodiode after being filtered off by dichroic beamsplitter 2 (Thorlabs, DMSP805 short pass dichroic mirror with 805 nm cut-off wavelength). As a result of a shared optical path, it is intended that if the noise happening in the reference interferometer is monitored and compensated for; the measurement interferometer will not suffer any noise disturbance during measurement. The reference interferometer will be locked at about quadrature to maximize sensitivity to environmental instabilities through a piezoelectric transducer (PZT). The resolution of modern PZT can be up to 0.05 nm with a frequency response of 35 kHz (e.g. P-249.10, PI Company); the noise compensation can be quick and accurate provided the load is light. This technique has been tested effectively and proved in our previous research [6, 7].
