Optics and Lasers in Engineering
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techniques, a known optical fringe pattern is projected onto the surface of interest. The fringe pattern on the surface is perturbed
in accordance with the profile of the test surface, thereby enabling direct derivation of surface profile.
evidence is in the form of finely spaced micro-irregularities
of measurement, control and analysis of surface roughness
has assumed greater significance.
conventional method for measuring surface roughness is to
handled carefully in a fairly, clean environment. Another
problem with the stylus measurement technique is the size
of the stylus radius and the crevices of the surface. If the
ARTICLE IN PRESScrevices are narrow such that the stylus cannot penetrate all
the way to the bottom, the measurement will not be
accurate and cannot be a true representation of the surface.
0143-8166/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.optlaseng.2007.09.003
Corresponding author. Fax: +91 44 22575705.
E-mail address: ramoo@iitm.ac.in (B. Ramamoorthy).left by the cutting tool. Each type of cutting tool leaves its
own individual pattern which therefore can be identified.
This pattern is known as surface finish or surface rough-
ness. Surface characteristics reflect all aspects of manufac-
turing processes and have close relationship with the
functional property of engineering surface and the work
piece. Also, with improvements in machining technologies
to produce micro and nano-scale components, importance
pass a stylus probe across the surface and monitor its
movement such that the surface micro-profile can be
traced. These devices are very sensitive, and the diamond
stylus could scratch the surface particularly when the
materials are soft. A common drawback of this approach is
the small area using which the roughness is evaluated at
any one time and also the transducer is very sensitive and
the stylus tip is fragile. Therefore, the instrument must bealgorithm for machined surface (ground surface). As these fringes are too noisy, advanced filtering technique has been used so as to
reduce noise and to get improved wrapped phase map from the phase shifted fringes. A phase unwrapping software has been developed
using discrete cosine transform (DCT) to generate the three-dimensional (3-D) profiles. Finally, it is compared with Ra values measured
using a mechanical stylus instrument, showing good agreement.
r 2007 Elsevier Ltd. All rights reserved.
Keywords: Surface roughness; Interferometry; Phase shifting; Unwrapping
1. Introduction
The quality of a machined surface is characterised by the
accuracy of its manufacture with respect to the dimensions
specified by the designer. Every machining operation leaves
characteristic evidence on the machined surface. This
Until today, these measurements are usually performed
using linearly probing instruments, such as mechanical and
optical profilometers [1,2]. The results are well specified
roughness parameters, e.g. the rms-roughness Rq or the
arithmetic mean of the surface heights Ra (ISO 4287) [3],
which are calculated from the sampled surface profile. TheIn this work, an attempt has been made to assess the surface roughness using a speckle fringe analysis method of five frame phase shiftDigital speckle interferometry fo
B. Dhanasekar, B
Manufacturing Engineering Section, Department of Mechanical Engi
Received 14 August 2007; received in revised for
Available online
Abstract
In this work, the principle of interferometry is used to assess the
an interference fringe pattern when two or more light waves interac
metrology and testing. Well-known advantages of the phase s
measurement, good result even with low contrast fringes and that t46 (2008) 272–280
assessment of surface roughness
Ramamoorthy
ring, Indian Institute of Technology Madras, Chennai 600036, India
1 September 2007; accepted 21 September 2007
November 2007
face roughness of the machined surfaces. Interferometry produces
ith each other. It is one of the important tool for precision optical
ting interferometry include high measurement accuracy, rapid
polarity of the wave front can be determined. In fringe projection
www.elsevier.com/locate/optlaseng

The
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coherently at the observation plane. By tilting one of
the mirrors by an angle a (mirror M1) one can generate
a linear fringe pattern. The fringe spacing po at the
observation plane is governed by the following relation:
po ¼
l
2 sin a=2 , (1)
where l is the wavelength of the laser. The tilt angle a
controls the fringe spacing in the interferometer.
(b) Grating projection arrangement: Two methods have been
widely used in the grating projection technique.The first
method is associated with a linear grating of fixed
frequency, while in the second method the linear fringe
patterns are generated by software by a DLP projector.
The second method is suitable to control the frequency
of the grating. Figs. 2(a) and (b) show the basic lay out of
the grating projection arrangements. In this work,
Michelson interferometric arrangement as shown in
Fig. 1 for introducing the linear fringe pattern for
surface roughness measurement is used.
3. Theoretical analysis
ARTICLE IN PRESS
S
Fig.
fring
Obs
S Digital projector
To PC
Fig. 2. Grating projection system (a) set-up using a linear grating having a
fixed frequency and (b) digital grating with a variable frequency.
andattention.
Common optical methods for contouring include use of
holographic interferometry, moire´, fringe projection and
other methods [7–12]. The ease with which a diffuse surface
can be measured has been significantly increased by the
development of the moire´ and fringe projection methods.
Two-dimensional (2-D) moire´ fringe patterns are useful to
extract qualitative information but it is sometimes tedious
and time-consuming to evaluate quantitative data from the
fringe patterns. The fringe projection method that entails
projecting a fringe pattern or grating on an object and
viewing it from a different direction is gaining grounds in
many engineering applications. Use of fringe projection to
determine surface roughness was first presented by Rowe
and Welford [13] in 1967. Later, Windecker developed a
fringe projection method for surface roughness measure-
ment and topometry of engineering and biological objects
[10,11]. Zhang used the fringe projection method by using
the spatiotemporal phase unwrapping for the surface
profiling [14].
In this work, the surface profiles of the machined surface
(ground) are measured using the fringe projection technique.
The system consists of a conventional Michelson interferom-
eter with one of the arms equipped with a PZT driven mirror.
A software based on Lab VIEW has been developed to shift
the PZT and to grab and visualise the speckle correlation
fringes in real time. Experimental results are compared with
the Ra values measured using a mechanical stylus instrument.
This indicated the effectiveness of this approach of surface
roughness evaluation using fringe projection system which is
explained and analysed in this paper.
2. Basic principle of fringe projection
The fringe projection technique requires the generation
of a linear fringe pattern (grating) onto the surface of the
object. In most of the traditional fringe projection
techniques, the fringe pattern is created by using either
an interference pattern or a grating projection. The
interferometers widely used for fringe projection are
classified as (i) Michelson interferometer or (ii) Mach–
Zehnder interferometer using a collimated laser beam. The
fringes can be generated by tilting one of the mirrors in the
set-up.
(a) Michelson interferometer: Fig. 1 represents an inter-
ferometric arrangement for generating the linear fringe
pattern. It is a Michelson interferometer that uses a
collimated laser beam. The collimated laser beam splits
into two at the beam splitter (BS). The beams traveland
scatse drawbacks [4–6] explain the need and the importance
non-contact techniques for measurement of surface
ghness. With the development of lasers, modern optics,
photodiode arrays, the technique of applying light
tering for surface roughness has received a considerable
B. Dhanasekar, B. Ramamoorthy / Opticsequal distance from the BS and reflect back from the
mirrors M1 and M2. Both the beams are combined
T
imaervation plane Observation plane
Po
Grating having a
fixed frequencyM2
M1
BS
Collimated Laser
Beam
Po
α
1. Basic set-up of a Michelson interferometer for generating the linear
e pattern.Observation plane
Lasers in Engineering 46 (2008) 272–280 273he optical geometry of fringe projection and the
ging system is shown in Fig. 3. The fringe pattern