measurement of thin film thickness by electronic speckle pattern interferometry

Optics Communications 234 (2004) 269–276

www.elsevier.com/locate/optcom

Measurement of thin film thickness by electronicspeckle pattern interferometry

Canan Karaalio~glu, Yani Skarlatos *

Department of Physics, Bo~gazic�i University, Bebek 80815, Istanbul, Turkey

Received 2 June 2003; received in revised form 20 September 2003; accepted 6 February 2004

Abstract

The surface profile of an Al thin film and its thickness have been observed by electronic speckle pattern interfer-

ometry (ESPI). The Michelson interferometer was used as our basic interferometric system to obtain interference

fringes on a CCD camera. These interference fringes, arising from the path differences due to the surface contours of the

thin film, were analyzed with three different techniques: fast Fourier transform (FFT), phase shifting, and digital image

subtraction; and the results were compared with each other. We also derived a new formula for the image subtraction

method, which is only valid in one-dimensional calculations. An unwrapping procedure was used to obtain a contin-

uous phase in the FFT and phase shifting methods. Results on thickness measurements are presented and are found to

be in good agreement with each other.

� 2004 Elsevier B.V. All rights reserved.

1. Introduction

When an optically rough surface is illuminated

by a beam of coherent laser light and the light

scattered from the surface is observed on a plane

some distance away, then at any point P on this

plane, the electric field is the vector sum of all the

elementary fields which reach the point P after

being scattered by different portions of the entire

rough surface. Since the surface is optically rough,the total electric field and intensity around point P

change randomly with position on the observation

* Corresponding author. Fax: +90-212-287-24-66.

E-mail address: [email protected] (Y. Skarlatos).

0030-4018/$ - see front matter � 2004 Elsevier B.V. All rights reserv

doi:10.1016/j.optcom.2004.02.025

plane. These random fluctuations in intensity are

known as laser speckles. Laser speckles carry in-formation about the rough surface which produces

them and have found many applications, which

are known generally as speckle methods. One of

these methods is electronic speckle pattern inter-

ferometry (ESPI) and it is the most practical and

powerful one among the existing optical tech-

niques for deformation and vibration analysis [1].

Contour measurement by interferometry is usedwidely to determine the shape of a surface. Infor-

mation about the surface of a static object can be

obtained from interference fringes, whose contour

lines characterize the surface on which they are

formed. There are two basic methods for mea-

surement of surface shape or height profile by

ed.

mail to: [email protected]

270 C. Karaalio~glu, Y. Skarlatos / Optics Communications 234 (2004) 269–276

optical contouring. These are phase shifting and

Fourier transform. A third, less frequently used

method is called digital image subtraction.

The fast Fourier transform (FFT) method has

been used by many researchers, such as de Angelis

et al. [2] to measure the focal lengths of lenses andthe index of refraction of transparent liquid ma-

terials [3], Spagnolo et al. [4,5] to obtain surface

topography of ancient stone artworks or to ana-

lyze microclimate variation on artworks [6], and

Wu et al. [7] to quantify immunoreactive terminal

area apposed to nerve cells. The phase shifting

method has also been used by many researchers.

The studies of Tay et al. [10], He et al. [11], L€ucket al. [12], Quan et al. [13] and Hobson et al. [14]

are some recent examples for this method; while

Abedin et al. [1,15] have employed the digital

subtraction method.

Thin film thickness is an important parameter

in many applications. In this paper, we obtain a

surface topography for thin films by using three

different shape construction methods: FFT, phaseshifting, and digital subtraction. Previously, we

had used the FFT method to measure the thick-

ness of a thin film [16]. In this paper, we derive a

new formula for the subtraction method in one-

dimensional case. Finally, the results of those three

techniques are compared with each other. The

fringe patterns were captured by a CCD camera.

The deformed surface information is encoded intothese fringes. Contour fringes were displayed on

a monitor and then analyzed with the above

methods.

2. Principle of the methods

2.1. Digital speckle subtraction method

The incident plane wavefront is divided into

two plane wavefronts of equal intensity by a beam

splitter, BS. The plane waves fall on the two rough

surfaces D1 and D2, which produce two indepen-

dent, random speckle distributions. These speckle

distributions are imaged by the camera lens L in its

image plane. The system is essentially equivalent toa Michelson�s interferometer, where the two mir-

rors are replaced by two rough surfaces. Let

E1 ¼ e1 expði/1Þ and E2 ¼ e2 expði/2Þ be the com-

plex amplitudes of these wavefronts in the image

plane, where e1; e2 and /1;/2 correspond, respec-

tively, to randomly varying amplitudes and phases

of the image plane speckles. The total intensity fcat a given point P ðx; yÞ in the image plane must beproportional to the square of the sum of E1 and E2,

i.e.

fcðx;yÞ¼ f1ðx;yÞþ f2ðx;yÞþ2½f1ðx;yÞf2ðx;yÞ�1=2 cos/;ð1Þ

where f1ð¼ E1E�1Þ and f2ð¼ E2E�

2Þ are the intensity

distributions of the two speckled wavefronts,

/ð¼ /1 � /2Þ is their phase difference, f1ðx; yÞþf2ðx; yÞ ¼ aðx; yÞ, and 2½f1ðx; yÞf2ðx; yÞ�1=2 ¼ bðx; yÞ.Therefore, we can write the intensity equation as

fcðx; yÞ ¼ aðx; yÞ þ bðx; yÞ cos/: ð2ÞSurface D2 is now deformed by some mechani-

cal or thermal disturbance, while surface D1 is left

undisturbed (E2 can be considered as the ‘‘object’’

wavefront, and E1, the ‘‘reference’’ wavefront). In

our experiment, D2 and D1 are the Al surfaces with

and without a thin Al strip on top respectively. Let

zðx0; y0Þ be the displacement of any given point of

Surface D2 in the normal direction (known as out-of-plane motion in the literature), then the corre-

sponding phase change for this point is

D/ðzÞ ¼ 4pzk

: ð3Þ

Due to this phase change, the intensity distri-

bution at the image plane will change to a new one,f 0cðx; yÞ, given by

f 0cðx; yÞ ¼ aðx; yÞ þ bðx; yÞ cos½/þ D/ðzÞ�: ð4ÞWe have two different images with mirror–

mirror and object–mirror reflectivity surfaces in

Fig. 2. The image obtained by mirror–mirror sur-faces, i.e. fcðx; yÞ is subtracted from the image

obtained by object–mirror surfaces, i.e. f 0cðx; yÞ.

The intensity distributions fcðx; yÞ and f 0cðx; yÞ are

captured (photographically) by the digital camera,

which produces electrical signals ultimately stored

in the computer memory in the form of digital

JPEG image files . After the image files are ac-

quired and stored, image fcðx; yÞ is subtracted fromf 0cðx; yÞ in the computer and the subtracted image

C. Karaalio~glu, Y. Skarlatos / Optics Communications 234 (2004) 269–276 271

is displayed on the monitor. This subtraction is

performed pixel by pixel. If we assume that the

displayed brightness is proportional to the differ-

ence between f 0cðx; yÞ and fcðx; yÞ, then

B / ½f 0cðx; yÞ � fcðx; yÞ�; ð5Þ

B / ½f1ðx; yÞf2ðx; yÞ�1=2

�fcos½/þ D/ðzÞ� � cos/g: ð6Þ

If, for some points on D2, z is such that

D/ðzÞ ¼ 2pn, then B ¼ 0, and dark fringes occur

on the computer monitor. On the other hand, for

some other points, if z is such that

D/ðzÞ ¼ ð2nþ 1Þp, then B has maximum values

and bright fringes occur. Using Eq. (3), theseconditions mean

• z ¼ nðk=2Þ for dark fringes.

• z ¼ ðnþ 12Þðk=2Þ for bright fringes.

The dark and bright fringes on the computer

monitor will therefore map the displacements

zðx0; y 0Þ of the different parts of the surface D2.

Successive dark or bright fringes on the computer

monitor will indicate displacement differencesof ðk=2Þ of the corresponding areas of surface D2,

or about 0.32 lm if a He–Ne laser is used for the

illumination.

The presence of the factor ½f1ðx; yÞf2ðx; yÞ�1=2 in

Eq. (6) means that the dark and bright fringes on

the computer monitor are accompanied by some

random speckle ‘‘noise’’ due to the speckle distri-

butions f1ðx; yÞ and f2ðx; yÞ. The presence of this‘‘noise’’ is however unavoidable in ESPI, since it is

this speckle noise which encodes and carries the

essential phase information D/ðzÞ into f 0cðx; yÞ in

Eq. (4) [1].

We derived a new formula for this method, but

it is valid only for one dimensional calculations.

By considering an interference pattern like in

Fig. 3, if we plot the intensity values of one row ofthe surface without an Al strip on it, this plot

corresponds to a sinusoidal curve for a flat surface.

In a similar way, if we plot the intensity values of

one row of the surface with an Al strip on it, this

should still correspond to a sinusoidal curve; but

this plot should have a shifting at the edge of the

strip because of the height difference. When we

plot one row intensity distributions from deformed

and flat interference patterns, this shifting amount

gives us the desired information

/d ¼ 2pDxx

�þ n

�: ð7Þ

Dx is the shifting amount in the deformed case

plot and x is the amount of one full period in the

flat case plot. If there is no shifting, i.e. Dx ¼ 0,then /d ¼ 2p and no shifting. n is an important

integer here and we should have an idea about the

order that we are looking for. n is determined from

the order of the height. If we know the height

value approximately, we can determine the value

of n. The height value can be obtained for each

row separately and then two-dimensional surface

profile can be obtained by plotting all these heightvalues next to each other in this technique.

2.2. Phase shifting method

Three or more phase shifted images are required

to produce a wrapped phase map; this map

indicates the contour of the surface under exami-

nation. Using the unwrapping technique, a con-

tinuous phase distribution is obtained from which

the required measurement parameter can be cal-

culated [10].

The light intensity, f ðxÞ of a digital specklefringe pattern can be expressed in the form

f ðxÞ ¼ aðxÞ þ bðxÞ cosð/þ d/Þ; ð8Þwhere a; b are constants, / is a phase angle intro-

duced due to object deformation, and d/ is a

subsequent additional phase change. Four differ-

ent f ðxÞ equations are obtained corresponding tofour different d/ values. If we solve these four f ðxÞequations, the following is obtained:

tan/¼ ½ðf3� f1Þðcosd/4� cosd/2Þ�ðf4� f2Þ�ðcosd/3�1Þ�=½ðf3� f1Þðsind/4� sind/2Þ�ðf4� f2Þsind/3�; ð9Þ

where f1ðxÞ, f2ðxÞ, f3ðxÞ, and f4ðxÞ represent the

light intensities corresponding to phase angles of

/, /þ d/2, /þ d/3, and /þ d/4, respectively.

The phase angle / of a deformed object can

thus be obtained using Eq. (9). For additional

Fig. 1. Schematic of the Al thin film.


phases of d/2 ¼ p=2, d/3 ¼ p, d/4 ¼ 3p=2, Eq. (9)would appear in its simplest form

/ ¼ arctanf4ðxÞ � f2ðxÞf1ðxÞ � f3ðxÞ

: ð10Þ

Even though we have used a 4-frame phase shift

algorithm to find phase shifting amount, the

choice is not unique. The reason for chosing this

particular algorithm is that it is very common and

easy to apply on our set-up, as there is no error

coming from phase shifting increments other than

the manufacturing error. In the literature, there

are algorithms from 3-frame to 12-frame as well asFourier transform methods of phase-shift deter-

mination [8,9].

Since arctan function is mathematically defined

from �p to p, the phase distribution is wrapped

into this range and, consequently, has disconti-

nuities with 2p phase jumps for variations larger

than 2p. These discontinuities can be corrected

easily by adding or subtracting 2p according to thephase jump involved.

The height of the surface z follows from the /0,

i.e. unwrapped phase, according to

z ¼ k4p

/0; ð11Þ

where k is the wavelength of the light source

[10–13].

The phase shifting algorithms used are less

complicated than the Fourier transform analysis

and hence greatly simplify the computational me-

dium. Errors might come from estimating thevalues of the experimental parameters [10].

2.3. FFT method

If structured light consisting of parallel stripes,

or fringes, is projected onto a surface, then the

surface acts as a phase modulator, with the

amount of modulation at any point dependingupon the height of the surface at that point.

In various optical measurements, we find a

fringe pattern of the form

f ðx; yÞ ¼ aðx; yÞ þ bðx; yÞ cos½2pu0xþ /ðx; yÞ�;ð12Þ

where the phase /ðx; yÞ contains the desired in-

formation and aðx; yÞ and bðx; yÞ represent un-

wanted irradiance variations arising from the

nonuniform light reflection or transmission by a

test object [17].The Fourier transform method for fringe pat-

tern analysis requires an added high spatial carrier

frequency. In this case, the distinct and equally

spaced sinusoidal fringes serve as the carriers. If

the spatial carrier frequency is properly selected,

the contour can be reproduced using the inverse

Fourier transform and phase unwrapping tech-

niques. The method has the advantage of usingonly one interference pattern during processing.

The resulting fringes are analyzed with automatic

phase unwrapping, and the background intensity

variations and speckle noise can be reduced [18].

This method is exhaustively explained in [16],

which is based on [18].

3. Experiments

3.1. Description of the experimental setups

We evaporated Al as a thin film onto a glass

substrate. Then, a second Al evaporation was

performed through a stainless steel mask approx-

imately 0.2 mm from the substrate to obtain a thinstrip on the first Al layer. A schematic diagram of

the Al thin strip is shown in Fig. 1. Since every

material induces a phase shift depending on its

index of refraction, we used the same material for

the surface and the thin strip on top of it, in order

not to cause different phase shifts and not to find

incorrect height values at the boundary. We per-


formed the experiments to measure the second

strip�s thickness. When we measured its thickness

by a commercially available interferometric

thickness monitor (Varian Ascope* Interferometer

Model No. 980-4006), we found that it changed

approximately from 284.7 to 261.2 nm dependingon the exact location. Naturally this method was

not a non contact as the Fizeau plate of the

thickness monitor presses against the sample dur-

ing measurement. A schematic diagram of the ex-

periment is shown in Fig. 2.

We used a He–Ne laser with a wavelength

k ¼ 632:8 nm as our light source. The distances

between object–beam splitter and mirror–beamsplitter are not important in our experiment since

the main point is just to obtain the interference

pattern caused by the Al strip. The pictures were

taken of the film surface of size 1.260 cm� 0.945

cm. We obtained reference and deformed states by

sliding the glass substrate which was mounted to a

microblock. When we illuminated an area which

included the part of Al strip�s part, the resultantinterference pattern was our ‘‘deformed state’’.

We used a commercial digital still camera

(SONY, CVX-V18NSP) to directly capture digital

images of the speckle fields. A schematic diagram

of the experiment is shown in Fig. 2. Light from

the laser is expanded by the beam expander BE

and is incident on the beam splitter BS. The two

beams from BS then fall on the object and themirror. The speckle fields created by the object and

MirrorBS

Object

BE

ND filter

Serial cable

PC

CCD Camera

Laser

Fig. 2. Schematic diagram of the experimental setup for FFT

method (BS: beam splitter, BE: beam expander, ND filter:

neutral density filter, PC: personal computer).

the mirror travel in opposite directions and inter-

fere with each other in the image plane of the

digital still camera after passing through the

camera lens. The digital still camera has a

576� 768 pixel charged couple device(CCD) array

as its recording element. A neutral density filter(THORLABS Mounted Metallic ND Filter

D ¼ 0:4; 0:5) was placed in front of the camera to

reduce the intensity of the incoming light, and thus

enhance the images. The aperture and shutter

speed of the camera were selected appropriately to

have the maximum light intensity without satu-

rating the camera. The exposure time of the cam-

era was set at 1/150 s. The image acquisition cardconverts the images directly into PNG image files,

which are in turn converted into JPEG images

since the latter require much less memory space in

the hard disc of the computer. Subsequently, a

special software is used to convert the images from

RGB color mode to gray-scale mode. We thus

have 576� 768 pixel images, where each pixel is

represented by 1 byte of data (256 gray levels). Onesuch image is shown in Fig. 3. Three phase shifted

images are produced by the use of quarter wave

plates (THORLABS WPQ05-532). The sub-

sequent additional phase changes are p=2, p, and3p=2.

3.2. Plots and numerical results from the experi-

ments

The fringe patterns were digitized with an 8-bit

gray scale, corresponding to 256 levels.

Fig. 3. Interference pattern obtained from the Al thin film.


For the digital image subtraction method,

Fig. 3 is our interference pattern which is obtained

and used in this part of our experiments. When we

illuminated an area which included the part of Al

strip�s part, the resultant interference pattern was

our ‘‘deformed state’’, i.e. f 0cðx; yÞ. When the area

which did not include the Al strip was illuminated,

the resultant interference pattern was our ‘‘refer-

ence state’’, i.e. fcðx; yÞ. The subtraction was made

by using a software program, MATLAB. By

considering the explanations in Section 2.1 and

from Fig. 4, we can find the results as

Dx ¼ 27 pixels; x ¼ 32 pixels:

Fig. 4. One-dimensional plots from the interference pattern of

Fig. 3.

Assuming n ¼ 0, we find the height value to be

approximately z ¼ 267 nm by using Eq. (7) with a

wavelength k ¼ 632:8 nm. As we know from the

interferometric measurement, the film thickness is

to be between 285 and 261 nm. This value is also

checked by measuring with a thickness monitor(Varian Ascope). We cannot accept taking n ¼ 1

since in this case the thickness is found to have an

out of range value of nearly z ¼ 583 nm. The error

on z comes from reading the plots of Fig. 4. This

error in reading the plot is 1 pixel and this corre-

sponds to �10 nm error on z.For the phase shifting method; by considering

the explanations in Section 2.2, if we take thephase value as /0 ¼ 6:15 rad from the right hand

plot of Fig. 5, the thickness value is found to be

z ¼ 261 nm by using the formula /0 ¼ 4pz=k,where k ¼ 532:5 nm is the wavelength of the laser.

Fig. 5. Wrapped phase mesh and one-dimensional unwrapped

phase plot of row100 for the phase shifting method.


By plotting one-dimensional unwrapped phase

plots for each row, this method can give infor-

mation on the surface profile on both coordinates

ðx; yÞ. The error on z value comes from the phase

value which is obtained from the right hand plot of

Fig. 5. The error reading the phase value is 0.01rad and this corresponds to �1 nm error on z.

For the FFT method, we found the thickness

261� 2 nm between pixel values from 280 to 420.

We used a He–Ne laser with a wavelength

k ¼ 632:8 nm as our light source. Since phase

values can be measured with a depth (z) resolutionis greater than k=200 with the FFT method [16],

our error is �3 nm. By using the Varian thicknessmonitor mentioned above on the same location,

we found this value to be 261� 3 nm. The plots

and explanations of them can be found in [16].

4. Discussion and conclusion

Our work represents a new formula for imagesubtraction technique for one-dimensional case,

and the comparison of a new application of a well

known FFT technique [16], image subtraction

method, and phase shifting method. We have

measured the thickness of an Al thin film with a 2

nm accuracy by using three different image con-

struction methods. In all methods, the fringe pat-

terns obtained contain information on whether thesurface of an object is flat or deformed.

In the phase shifting method, the phase steps

were chosen such that the phase of the speckle

pattern at each pixel could be extracted by arith-

metic operations on the data. In this method, we

saw that the path difference values could be found

with good accuracy when we compared it to a

known result. In addition to this high accuracy ofthe thickness value, all surface contours can be

obtained in detail. This method is quite powerful,

at the cost of taking four records rather than just

one. Unlike the FFT method, as noise cannot be

separated from the signal, the plot in Fig. 5 is not

as smooth as the unwrapped phase plot of FFT

method [16].

The subtraction image is proportional to thedifference between the undeformed and deformed

images. The difference images contain intensity

fringes located at points where the difference is a

multiple of the quantity d, i.e. displacement. These

intensity fringes are, of course, speckled. The dig-

ital image subtraction method is best when the

deformed area is to be seen. Subtraction enhances

the visibility of the deformed spot; however, it isnot as effective as the FFT or phase shifting

methods if the amount of deformation is to be

measured.

We can summarize all these explanations as:

1. To minimize environmental noise effects, FFT

is preferred to the phase shifting technique since

the time required for fringe acquisition is much

shorter [19].2. The subtraction method results in better accu-

racy than the FFT method. The FFT method

utilizes shifting of the Fourier spectra, and

hence its accuracy is dependent on the digital

frequency resolution [20].

3. The surface acts as a phase modulator of the

fringe pattern, and the first stage in the evalua-

tion of surface shape is the demodulation of theobserved fringe pattern. Phase stepping is not a

true demodulator since it yields total signal

phase rather than the required phase deviation,

while Fourier transform techniques are complex

and are best used by researchers experienced in

their applications [14].

4. There are problems with both fringe phase step-

ping and Fourier transform analysis. Fringephase stepping requires the capture of at least

three images, with the restriction that the object

must remain stationary while the fringes are

moved. On the other hand, Fourier transform

profilometry requires complex processing, and

the effects of signal filtering in the frequency do-

main are difficult to predict. Indeed, frequency

domain filtering has been the subject of exten-sive research [14].

The image subtraction and phase shifting

methods as well as the new application of FFT are

important in the area of thin film thickness mea-

surements for the following reasons: They are easy

to perform and understand; all apparatus used in

the experiments is standard and relatively inex-

pensive; finally, these measurements do not causeany extra deformation on a thin film�s surface sincethese methods are absolutely non-contact. In the


future, better results can be obtained with im-

proved CCD cameras and new software. Larger

powers of 2 for the FFT method can be included in

the calculations, and larger surface topographies

can be obtained with higher resolution.

Acknowledgements

We would like to thank Pietro Ferraro for his

helpful suggestions.

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measurement of thin film thickness by electronic speckle pattern interferometry

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