DIGITAL HOLOGRAPHIC CAMERAS FOR REMOTE MONITORING AND
MEASUREMENTS OF MECHANICAL PARTS
Aneta Michalkiewicz, Malgorzata Kujawinska
Institute of Micromechanics and Photonics, Warsaw University of Technology
8 Sw. A. Boboli Str, 02-525 Warsaw, Poland
ABSTRACT
Fast growing technology and requirements for testing of different types of materials and devices require new methods and
systems for investigation of their parameters. Among the quantities of high interest are: shape, roughness, local materials
constants, displacement and strain fields at elements under load. In the paper we present novel solutions for digital
holographic cameras, which allow remote monitoring and measurement of the above mentioned quantities at small mechanical
objects or at area of interest of big structures. The system has compact design, “black box” measurement approach and allows
fast and accurate measurements performed directly at the element and often in outdoor environment. Some of the exemplary
measurement results obtained by means of these cameras are presented in the paper.
Introduction
Digital holography provides a way to record and restore amplitude and phase of an investigated object [1]. It allows, using
amplitude information, distant monitoring of an object and its remote optoelectronic reconstruction [2,3]. Proper manipulation of
phases could provide information about shape of an object and its out-of-plane and in-plane displacements during internal or
external loading [2]. The architecture of digital holographic (DH) system which consists of two types of measurement heads,
fibre optics link and control/illumination module is presented in Fig.1. One of the measurement heads is configured to perform
out-of-plane displacement and shape measurement. The second one (with four illumination beams) allows to measure (u,v,w)
displacement fields. Due to fiber optics light delivery system the DH head is able to work in a distance from its
electronic/processing part and it allows direct access to all mechanical parts of machinery (Fig.1a). The DH head can be handheld or can be mounted directly at a machine. The data from both cameras can be transferred remotely to optoelectronic
reconstruction station based on LCOS spatial light modulator (Fg.1b)..
a)
b)
Figure 1. The scheme of DH system for mechanical parts monitoring a) measurement module,
b) optoelectronic reconstruction module.
Principles of digital holographic interferometry
Digital holography provides the convenient way to record and restore not only intensity but also phase of a given wave front.
Intensity and phase distributions can be calculated from a complex wavefront b’, which is in our system reconstructed
numerically by Fresnel approach wave (b’) [1] as:
ϕ ( x, y ) = arctan
Im(b' )
Re(b' ) (1a)
I ( x, y ) = b'⋅b'*
(1b)
For interferometric applications, which include displacement and shape measurement, the phase difference Δφ of two
reconstructed wave fields has to be calculated.
Δφ = ϕ1 ( x, y ) − ϕ 2 ( x, y )
where
Displacement vector
ϕ i ( x, y ) = calculated for waves
(2)
bi , where i=1,2
d and sensitivity vector e are connected with phase difference by the equation:
Δφ
d=
e
(3)
In order to determine out-of-plane displacement we need to determine sensitivity vector which depends on geometry of the
setup. Depending on the type of object changes and quality to be measured, the proper directions of illumination and
observation are required.
In practice two main configurations are required depending on the technical object to be measured, namely: the out-of-plane
displacement/shape measurement setup and full displacement vector (u,v,w) setup. The hardware and software solutions are
different for both setups and therefore in order to provide user friendly cameras for mechanical engineers two separate devices
had been designed and built: DH_SHAPE, DH_UVW.
Also for specific applications the camera is equipped in the remote data transfer. This may be used by the data capturing
system (computer) and both numerical or optoelectronic data reconstruction systems [2,6]. Optoelectronic data reconstruction
is performed by transferring a digital hologram (for object intensity reconstruction) or a pair of digital holograms captured in
DHI setup (for interferogram reconstruction) to computer controlling spatial light modulator for example LCOS. Spatial light
modulator illuminated by coherent light generates true image or interferogram of an object.
Holocamera for out-of-plane displacement and shape measurement
The first holocamera DH_SHAPE is designed for out-of-plane displacement measurement and shape determination and it is
shown in Fig. 2. The source is pigtailed laser with output power 7mW and operating wavelength 532 nm. The beam is
delivered by a single mode fiber SM450 and splitted by single mode fiber optic coupler in 90/10 ratio to form the object and
reference beams. The tip of object illumination fibre can be subjected to the linear shift introduced by micromotor. Reference
fiber tip is placed in the focal point of collimator lens and the plane reference beam is impinging at CCD matrix directed
through mirror and beam splitter. The light scattered from object recombine with the reference beam at beamsplitter cube and
the resultant interference field is captured by CCD matrix. The CCD is the standard microhead B/W camera JAI M536 CCIR
with pixel size 8.6 μm and resolution 752x582 pixels. Dimension of the measurement head are: diameter 50mm and length
100mm.
b)
a)
Figure 2. Measurement head for out-of-plane displacement measurement and shape determination. a) the camera head
without cover, b) the camera at work
In this configuration out-of-plane displacement is given by equation [3]:
dz =
where
λΔφ
2π (1 + cos Θ)
(4)
dz = sensitivity per fringe,
Θ = angle between illumination and reference wave directions
As the angle Θ equals 8°, the sensitivity per fringe is estimated for 42 μm.
In the setup two-sources contouring method is applied for an object shape determination. The change of sensitivity vector is
introduced by tilt of illumination beam through shifting of the fibre tip. The value of a single contour Δh is given by [4]:
λ
Δh =
2 sin
where
ΔΘ
2
(5)
Δh = depth of contouring surfaces,
λ = wavelength of laser,
ΔΘ = angle between two illumination directions.
As the angle ΔΘ introduced by the shift of fibre tip ranges from 0.05 ° to 1.5°, the values of single contours vary from 0.6 mm to
10 μm.
While the height of the object h is given by:
h = Δh ⋅
Δφ
2π
(6)
The object under study was quasi-flat silicon membrane (3.5 mm x 3.5 mm) fixed at the edges and loaded by changing
pressure. The results of out-of-plane displacement measurements performed for loads 0.1, 0.3 and 0.4kPa are shown in Fig.
3a while 3D map of membrane displacement under 0.4kPa pressure is shown in Fig. 3b.
b)
a)
Figure 3 Measurement of silicon membrane under pressure load: a) central crossections of out-of-plane displacements and
b) 3D map of out-of-plane displacement for 0.4 kPa
In the next step we checked the system capability to measure object shape. Test was perform for the same micromembrane
loaded with pressure 2 kPa. The P-V shape value after scaling according to the sensitivity vector reached 21 μm (Δh≈10 μm)
and the results are shown in Fig.3.
a)
b)
c)
Figure 4. Shape of silicon micromembrane loaded with 2.0 kPa, a) mod2π fringes, b) cross-section A-A, c) 3D shape
representation
Holocamera for arbitrary displacement vector measurement
The second holocamera designed for arbitrary displacement vector measurement is shown in Fig. 5. The source is pigtailed
laser with output power 7mW and operating wavelength 1064 nm. The beam is splitted into object and reference beams by
single mode fiber optic coupler in 90/10 ratio. The object beam goes to optical switch 1x4 and produces 4 object illumination
beams. Reference fiber tip is placed in the focal point of collimator lens and the plane reference beam is impinging at CCD
matrix directed through mirror and beam splitter. The light scattered from an object recombines with the reference beam at
beamsplitter cube and the resultant interference field is captured by CCD matrix. The CCD is the standard microhead B/W
camera JAI M536 CCIR with pixel size 8.6 μm and resolution 752x582 pixels. Dimensions of measurement head are:
diameter 46mm and length 100mm.
a)
b)
Figure 5. The holographic camera for arbitrary vector displacement determination. a) the camera head and b) the
experimental setup with the holographic camera.
Measurements of an arbitrary displacement vector are more complicated and require at least three object illumination beams.
Sensitivity vector depends on the angles between illumination directions and reference beam direction. In order to simplify the
calculations we describe DH system which provides in-plane displacement u(x,y) and out-of-plane displacement w(x,y) from
two pairs of holograms captured before and after loading [2]. The specimen is illuminated symmetrically by the beams
impinging from left Σill and right Σilr directions (Figure 6). They interfere with reference beam Σref and sequentially four
holograms are captured.
Figure 6. The scheme for an arbitrary displacement vector measurement.
The relevant phases are calculated from holograms by using conventional (Eq.1a) or phase shifting procedure. The phases
include the following information:
φl1 = k (sin(α )u1 + (cos(α ) + 1) w1 )
φ r1 = k (sin(−α )u1 + (cos(−α ) + 1) w1 )
φl 2 = k (sin(α )u 2 + (cos(α ) + 1) w2 )
φ r 2 = k (sin(−α )u 2 + (cos(−α ) + 1) w2 )
where
(5)
(6)
(7)
(8)
r = right direction of illumination,
l = left direction of illumination,
α =angle of incident light,
u,w = displacement vector components.
1,2 = states of object
In order to obtain u(x,y) and w(x,y) displacement vector components the following equations are used:
and
λ (Δφl − Δφr )
4π sin(α )
λ (Δφl + Δφ r )
w2 − w1 =
4π cos(α ) + 4π
where
Δφ r ,l = φ r1,l1 − φ r 2,l 2
u 2 − u1 =
(9)
(10)
The same procedure is applied for the holograms captured with the object beams obtained after illuminating object by beams
located in vertical direction (upper and lower beams- Fig. 5a) and as the result the (v2-v1) and (w2-w1) maps are calculated.
As 2 pairs of beams are used for displacement measurement the out-of-plane displacement (w1-w2) is calculated two times
so the systematic errors can be more easily detected. Displacement fields obtained by such phase manipulation will be correct
under assumption of flat object. In the case of 3D object studies its shape has to be known for correct displacement vector
determination [1].
The applicability of this camera had been demonstrated through performing measurements of u,v,w displacement fields
obtained during fracture test of short fibre reinforced composite specimen. The composite material employed was a phenolic
short glass fibre reinforced composite IXEF 1022 supplied by Solvay-Belgium. The samples were machined from 5 mm thick
sheets prepared by injection moulding technology. The Mode I fracture tests had been performed (Fig.7) and the the pairs of
holograms (right, left, up, down) had been captured for the series of tensile forces applied ranging from 100 N.to 620 N.
Figure 7. Specimen geometry
The phases reconstructed from the holograms were applied according to Eq. 9 and 10 and several sets of displacement maps
(u,v,w) had been obtained. This procedure is illustrated by the exemplary phase maps manipulation shown in Fig.8.
b)
a)
Figure 8 Measurement of specimen loaded with force Δ=10N for 530 N a) for v direction in-plane and out-of plane
displacements, b) u direction in plane and out-of-plane displacements.
Figure 9. Measurement of specimen loaded with force 4N for 620 N a) for v direction in-plane and out-of plane displacements,
b) u direction in plane and out-of-plane displacements
The region of very big displacements at the crack tip had been masked in order to allow the proper unwrapping precedure.
The energy had been released due to cracking process and therefore the u and w displacement values decreased.
This experiment had shown the ability of the system to provide data for complex analysis of displacement and strain fields.
However the camera still need to develop the proper calibration procedure.
Conclusions
The presented work is one of many attempts undertaken by holographic groups to built device dedicated for arbitrary
displacement measurement and shape determination. The initial tests had proven that both systems are able to measure with
high precision arbitrary displacement.
Acknowledgments
The work was performed within the project PBZ-MIN-09/T11/2003 financed by the Ministry of Scientific Research and
Information Technology. The authors acknowledge the financial support of Ministry of Education and Science within the project
no. N505 010 31/1426.
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