1 CHAPTER 1 TV HOLOGRAPHY 1.1. Introduction and Basic Theory TV Holography (TVH) also known as Electronic/Digital Speckle Pattern Interferometry (ESPI/DSPI) or Phase Shifting Speckle Interferometry (PSSI) is a reliable non-contact optical technique for quantitative measuring displacement components of a deformation vector of a diffusely scatter object under static or dynamic load [1-2]. The method is based on speckle correlation using the direct electronic/digital subtraction of the intensities in the initial and deformed state of the object. The ability to measure three dimensional surface profiles by generating the contours of constant depth of an object is yet another major achievement of TV holography. The range of the object that can be evaluated by TV Holography is the order of few hundreds microns to few meter. This technique is normally used in two modes: addition or subtraction speckle correlation mode and time average mode. Addition or subtraction mode is used in deformation analysis, means it is used to measure the displacement components and shape of the object. Time average mode is applied vibration analysis. In this project subtraction speckle correlation mode of operation is used. In this mode the diffuse surface in its initial state, one frame of the interference speckle fields (object and reference beams combined at the CCD plane) is recorded on video store. Now the object is deformed and the current frame speckle field is subtracted electronically pixel by pixel from the stored frame. The correlation spackle fringes are displayed on the monitor in real time. Here speckle pattern is a granular structure, which is formed in space when a coherent wave from a laser is reflected from or transmitted through an optically rough surface. The intensity distribution in the image of a diffused surface, when it is illuminated by a
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CHAPTER 1
TV HOLOGRAPHY
1.1. Introduction and Basic Theory
TV Holography (TVH) also known as Electronic/Digital Speckle Pattern Interferometry
(ESPI/DSPI) or Phase Shifting Speckle Interferometry (PSSI) is a reliable non-contact
optical technique for quantitative measuring displacement components of a deformation
vector of a diffusely scatter object under static or dynamic load [1-2]. The method is
based on speckle correlation using the direct electronic/digital subtraction of the
intensities in the initial and deformed state of the object. The ability to measure three
dimensional surface profiles by generating the contours of constant depth of an object is
yet another major achievement of TV holography. The range of the object that can be
evaluated by TV Holography is the order of few hundreds microns to few meter.
This technique is normally used in two modes: addition or subtraction speckle correlation
mode and time average mode. Addition or subtraction mode is used in deformation
analysis, means it is used to measure the displacement components and shape of the
object. Time average mode is applied vibration analysis. In this project subtraction
speckle correlation mode of operation is used.
In this mode the diffuse surface in its initial state, one frame of the interference speckle
fields (object and reference beams combined at the CCD plane) is recorded on video
store. Now the object is deformed and the current frame speckle field is subtracted
electronically pixel by pixel from the stored frame. The correlation spackle fringes are
displayed on the monitor in real time.
Here speckle pattern is a granular structure, which is formed in space when a coherent
wave from a laser is reflected from or transmitted through an optically rough surface. The
intensity distribution in the image of a diffused surface, when it is illuminated by a
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coherent wave also exhibits granular structure [1-2]. This speckle pattern is called a
subjective speckle pattern.
Let 1I and I2 be the irradiance distribution incident on a camera face plate before and after
the object is deformed. Then the intensity before and after the displacement can be
expressed as [1-2]
1 2 cos( )O R O RI I I I I (1.1)
2 2 cos( )O R O RI I I I I (1.2)
where OI and RI are irradiance of object wave and reference wave respectively. is the
phase of the random speckle and is the phase change due to object deformation.
Video signal are assumed to be proportional to the irradiances. So the subtracted video
signal SV will be
2 1 2 cos( ) cos( )S O RV I I I I (1.3)
Therefore the brightness B on
2 1 sin( 2)sin( 2)O RB I I C I I (1.4)
where C is proportionality constant. sin( / 2) represents the speckle noise which
varies randomly between object images, because it is sin function of . Equation (1.4)
describes the modulation of high frequency noise by a low frequency interference pattern
related to phase change .
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The condition for minimum B is that,
sin( / 2) 0 (1.5)
when ever 2n n = 0, 1, 2…….
This condition corresponds to dark fringes and denotes all of those regions where the
speckle patterns are correlated. The condition for maximum B is that,
sin( / 2) 1 (1.6)
when ever, (2 1)n n=0, 1, 2……..
This condition corresponds to bright fringes and denotes all of those regions where the
speckle patterns are uncorrelated. As a result, the speckle correlation fringes that
represent the contour of constant phase are seen in monitor. From monitor we have seen
the consecutive dark and bright fringes modulating object. The speckle fringe pattern
seen on the monitor is shown in Fig.1.1.
Fig.1.1 Speckle correlation fringe pattern observed on the Monitor using TV
holography
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The phase change is directly related to deformation vector ( , , )L u v w
; , ,u v w are the
displacement component along , ,x y z directions respectively. So we have to measure the
phase change . We can arrange the optical head of the system in several different ways
for measuring the shape and as well as the deformation. The different methods for shape
measurement of a 3-D object are described here.
1.2 Shape Measurement
TV holography is suitable for measurement of the shape of 3-D objects. It generates the
contours of constant depth of a curved object. The existing methods used for shape are
described below [1-7]
(a) Multiple Wavelength Method
In this method, two or multiple wavelength is used for shape measurement. The multiple
wavelength yields the effective wavelength and it can be directly related to the shape of
the object [3].
Consider two wavelengths 1 and 2 is used either sequentially or simultaneously for
recording. The difference between the two phases 1 2, corresponds to the wavelengths
1 and 2 respectively can be related to the surface depth of the object, „Z‟ as [3]
1 2 12
4Z
(1.7)
where, 1 2
1 2
; is the effective wavelength.
The depth contour interval depends on the effective wavelength .
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(b) Changing of Refractive Index Method
In this technique the 3-D object is placed inside an immersion tank filled with a
transparent liquid of refractive index „n1‟. A change in the refractive index of the liquid
„n2‟ between the two frames introduces a relative phase change 12 . The subtracted
frame represents the relative phase change 12 as [1-2, 4]
1 2 12 2 1
4( )n n Z
(1.8)
The depth contour interval depends on the refractive index term 2 1( )n n .
(c) Two Beam Illumination Method
In-plane sensitive two beams symmetrically illumination configuration in TV holography
is used for shape measurement [1, 5-7]. The 3-D object is illuminated by two beams
incident at equal angles θ on both sides of the optical axis. The interference at the CCD
plane results from the superposition of the individual fields generated from the two beam
illuminated beams. The object is rotated (tilted) by an amount ξ about an axis
perpendicular to the plane containing the two illumination beams. The in-plane motion of
the object represents the surface variation of the object. The relative phase change
introduced in the setup as result of this rotation ξ is given as
1 2 12
4sin sinZ
(1.9)
The sensitivity of the method is dependent on the angle θ. From the Equation (1.9) it can
be noticed that the accuracy of the shape measurement is dependent on the measurement
of the rotation angle ξ given to the object between the recordings at the CCD plane.
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In this project work, we propose to develop a three beam illumination configuration in
TV holography for the measurement of object rotation angle ξ that is required for precise
evaluation of the shape of the 3-D object. The in-plane sensitive configuration is
combined with an out-of-plane sensitive arrangement for measurements. The three beam
illumination TV holographic setup is discussed in Chapter 2.
1.3 Phase Shifting Technique for Speckle Fringe Analysis
The phase shifting method is well established for phase evaluation in speckle metrology
[1-2]. The concept of the phase shifting techniques [8] is described briefly here.
In a two beam interference pattern, the intensity distribution is given by [8]
0( , ) ( , ) 1 cos( ( , )I x y I x y V x y (1.10)
where ( , )x y the phase difference distribution and V is the modulation of fringes. V and
I0 are given by V 1 2
1 2
2 I I
I I
and 0 1 2I I I , where 1I and 2I are the intensity of two
interfering beam.
Since CCD camera can measure only intensity of speckle pattern. But we have to find the
phase difference. The equation (1.10) has three unknowns 0, , ( , )I V x y . A minimum
three equations is necessary to find the interference phase ( , )x y . Therefore, a known
phase is introduced by shifting one of the interfering light waves against the other. This
can be done by several different ways [8].
(a) Three Step Method
In three step method we introduce three phase steps such as ,0, in reference wave.
The intensity equations are [8]
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1 0 1 cos( )I I V (1.11)
2 0 1 cos( )I I V (1.12)
3 0 1 cos( )I I V (1.13)
From this three above equation we may write
1 3
2 1 3
1 costan
sin 2
I I
I I I
(1.14)
This is the general equation to find .
For a phase step / 2 and phase values of / 4, / 4,3 / 4 and the intensity equations
are [8]
1 0 1 cos( / 4)I I V (1.15)
2 0 1 cos( / 4)I I V (1.16)
3 0 1 cos( 3 / 4)I I V (1.17)
From these three equations, we can get
2 1
3 2
tanI I
I I
(1.18)
But, the three-step method is not self calibrating and it is also the most sensitive to
system errors.
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(b) Four Step Method
In the common four-step method a phase step / 2 and phase values of 0, / 2, ,3 / 2
are used. The four intensity patterns are [8]
1 0 1 cos( )I I V (1.19)
2 0 1 cos( / 2)I I V (1.20)
3 0 1 cos( )I I V (1.21)
4 0 1 cos( 3 / 2)I I V (1.22)
The phase is given by [8]
4 2
1 3
tanI I
I I
(1.23)
(c) Five Step Method
This is most useful technique to find phase difference . For a phase change / 2 and
phase value of 0, / 2, ,3 / 2,2 and the intensity equations are [8]
1 0 1 cos( )I I V (1.24)
2 0 1 cos( / 2)I I V (1.25)
3 0 1 cos( )I I V (1.26)
4 0 1 cos( 3 / 2)I I V (1.27)
5 0 1 cos( 2 )I I V (1.28)
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From this above five equations we get phase as
2 4
3 5 1
2( )tan
2
I I
I I I
(1.29)
In the present work a five-step method as described above is used for the measurement of
the shape of a 3-D object. The five step algorithm is useful as it acts as a self-calibration
for phase shifting and if there is no miss-calibration of phase shifter for 2 phase shift,
then 5 1( )I I .
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CHAPTER 2
TV HOLOGRAPHIC SYSTEM AND THEORY
2.1. Experimental Arrangement
The schematic of the three beam illumination arrangement is shown in Fig.2.1. The
narrow beam from a continuous wave 20mW He-Ne laser is divided into two beams
using a beam splitter (BS1). One beam (Beam-1) falls on a mirror (M) and after reflecting
it passes through a spatial filtering set up (SF1) to expand the beam. Similarly the second
beam (Beam-2) also expanded using the spatial filtering setup (SF2). The diffusely
reflective surface is symmetrically illuminated with two expanded beams (Beam-1 and
Beam-2) inclined at an angle θ with respect to the surface normal. A smooth reference
wave (Beam-3) is added at the CCD plane using a beam splitter (BS2) and a cube beam
splitter ( BS3) in one of the object beam illumination (Beam-1) A lens (f=50mm) is used
to image the object on to the Sony XC-ST70CE CCD. A PZTM Mirror (Piezo-Mechanik
– STr 25/150/6) in Beam-2 is used for introducing the desired phase steps. The PZTM is
interface with a PC with a digital-to-analog card (NI6036E). The neutral density filter
(NDF) in the setup allows to controlling the intensity ratio between the object and
reference beams. The CCD camera is interfaced to a PC with an NI1409 frame grabber
card. The frame grabber is a device that interfaces with a camera to capture and stores a
complete video frame and converts into a digital image. The shutters S1 and S2 in the
setup allow for sequential recording using two beams at a time for shape and the
corresponding object rotation (tilt) measurements. LabVIEW programs have been used
for (i) visualization of real time speckle correlation fringes, and (ii) storing the phase
shifted frames for fringe analysis.
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2.1.1 Hardware Used for the Three Beam Illumination Arrangement: