White-light digital speckle photography in free convection

D. Ambrosinia,*, D. Paolettia, G. Schirripa Spagnolob

a INFM – Dipartimento di Energetica, Universit�aa di L’Aquila, Localit�aa Monteluco di Roio, Roio Poggio (AQ) 67040, Italyb INFM – Dipartimento di Ingegneria Elettronica, Universit�aa Roma Tre, Via della Vasca Navale 84, Roma 00154, Italy

Received 2 August 2001; received in revised form 2 October 2001; accepted 29 October 2001

Abstract

A digital white-light speckle system is proposed for measurements in free convection. White-light speckle photog-

raphy has certain advantages with respect to traditional speckle photography. Theory of the method and its application

to free convective flows in liquids are presented. � 2002 Elsevier Science B.V. All rights reserved.

PACS: 42.30.Ms; 44.25.+f; 02.30.N

Keywords: White light; Speckle photography; Electro-optic systems; Digital image processing; Free convection; Fluid mechanics

measurements

1. Introduction

Flows having a variable fluid density can bevisualized with optical methods [1–3]. A number ofoptical techniques have been used for measure-ment of heat transfer and/or temperature profilesin thermal layers such as interferometry [1], holo-graphic interferometry [4], sandwich holography[5], schlieren methods [6,7], moir�ee deflectometry[8], electronic speckle pattern interferometry [7,9],digital shearography [10,11] and speckle photog-raphy [7,12,13].

In speckle photography, the information is ob-tained from the geometrical displacement of a

speckle pattern generated by the interaction ofcoherent light beam with a diffusing surface. Thespeckle displacement is traditionally recorded on aphotographic film, while the evaluation of thespecklegrams is performed by probing the devel-oped negative with a narrow laser beam [12]. Thisprocedure produces Young’s fringes from whichthe displacement can be determined. The obviousdrawbacks of the traditional technique (need forphotographic film processing, time and materialsconsumption, difficulty to fully automate) werealleviated by several authors introducing electronicspeckle photography, in which data treatment andspeckle pattern recording are performed digitally[12,14]. Recently, the digital recording of thespeckle patterns was proposed in heat transfermeasurements [15,16], thus extending to trans-parent media the full digital approach to specklephotography.

1 January 2002

Optics Communications 201 (2002) 39–44

www.elsevier.com/locate/optcom

*Corresponding author. Tel.: +39-086-243-4336; fax: +39-

086-243-4303.

E-mail address: dario@ing.univaq.it (D. Ambrosini).

0030-4018/02/$ - see front matter � 2002 Elsevier Science B.V. All rights reserved.

PII: S0030-4018 (01 )01674-1

The white-light speckle method [17–19] relies onthe random pattern, artificially created or natu-rally present, on the test object. The methodevolved from moir�ee and laser speckle techniques.Because of its simplicity and versatility, it wasapplied to deformation measurements [18] and tovelocimetry in fluid mechanics [20–22]. In a white-light speckle pattern, speckle decorrelation is lesssevere, which makes the method much robust.Therefore, in many cases, white-light speckle pat-terns provide more accurate results than do laserspeckle patterns [23].

In this paper we propose to study the temper-ature gradients in liquids by using white-lightdigital speckle photography.

The system is based on a recorded speckle pat-tern illuminated by a white-light source. The light isthen passed through a transparent test section. Twodifferent exposures, recorded on a CCD photosen-sor, are taken. The first of the non-refracted pat-tern, obtained with the test fluid in thermalequilibrium with the surrounding ambient, and thesecond of the refracted pattern obtained with atemperature gradient in the test cell. Fast Fouriertransform based algorithms are applied to obtainfringe patterns of Young’s type and/or digital cor-relation. An automated measure of the magnitudeand orientation of in-plane displacement can thenbe made. The proposed technique can be consid-ered an evolution of digital speckle photographyapplied to buoyancy-induced flows monitoring.

2. The principle of the method

White-light speckle photography, like tradi-tional speckle photography, is a two-step process:recording of the specklegram and reconstruction(or filtering) of the same specklegram to obtaininformation on the displacement undergone by thetest object.

As white light is not coherent, speckles must beartificially created. In this work, speckle patternswith different speckle sizes were created by ex-posing holographic plates to a speckle patternobtained by illuminating a diffuse glass plate witha laser beam. In this way, we obtained a truerandom pattern.

The electro-optical system used in this work isshown schematically in Fig. 1.

The light source is a white lamp of 150 W witha green filter (not shown). An artificial specklepattern is placed in front of the test cell. Thisspeckle pattern is visualized on the photosensorof a TV camera. If the test object has a non-uniform refractive index, the rays through the testobject will be deflected. In other words, if therefractive index changes, the deflection angle willalso change. The change of the deflection anglecan be regarded as a local translation of the ar-tificial speckle pattern. In strict analogy withtraditional speckle photography [12], this speckledisplacement is proportional to the temperaturegradient.

Fig. 1. Experimental setup.

40 D. Ambrosini et al. / Optics Communications 201 (2002) 39–44

Generally speaking, a phase object, with a non-uniform refractive index distribution, has two ba-sic effects on a light beam:

(a) a change in phase (which can be measuredand visualized by optical interferometers);(b) a deflection of the beam from its original di-rection.

The latter is the physical effect involved in ourmeasurement. Beam deflection becomes negligiblein speckle interferometry if the ground glass is onthe viewing side and it is imaged on the CCD [24].Therefore, in our system the speckle picture (whichpractically acts as a ‘‘frozen’’ speckle pattern) mustbe on the illumination side, see Fig. 1. The specklepictures were recorded on Agfa Holotest 8E56HD, developed according to the standard proce-dure [25].

It can be shown (see [16] and references therein)that, for a stratified medium, the following relationholds:

oT ðxÞox

����x¼x0

¼ Dx x0ð Þ n x0ð Þ‘2

onðT ÞoT

� ��1

; ð1Þ

where oT ðxÞ=ox is the temperature gradient in thedirection perpendicular to the propagation axis, ‘represents the thickness of the test cell, Dxðx0Þ isthe vertical shift of the speckle pattern, induced bytemperature difference, as seen from the TV cam-era and nðx0Þ is the value of the refractive index atthe location at which the ray enters the medium(x0).

The values of n and onðT Þ=oT are calculatedfrom the following equation, valid for the refrac-tive index of water at 514.5 nm [4]:

n� 1:337253 ¼ � 2:8767T�

þ 0:14825T 2�� 10�5;

ð2Þwhere T is in degrees Celsius.

Reference speckle pattern (no temperaturegradients in the test cell) and deformed specklepattern (temperature gradients in the test cell) aredigitized into an array of (512� 512� 8) bit-data,and stored in the computer.

One of the key features of digital speckle pho-tography development and success is the possibil-ity to perform computerized fringe analysis. Indigital speckle photography the speckle displace-

ments can be obtained both with the traditionalauto-correlation approach (Young’s fringes) andwith the cross-correlation approach [12]. Thepresence of periodic structures changes the corre-lations, therefore random pattern is needed.

Auto-correlation is digitally performed by sim-ulating the Fraunhofer diffraction of a speckle-gram, which is the sum of the reference image withthe deformed image, by a fast Fourier transform.This yields [16,18]

~IIðg; nÞ ¼ 2~IIRðg; nÞ � 1½ þ cos 2pd � xð Þ; ð3Þwhere I is the specklegram intensity, IR is the in-tensity of the reference image, denotes the

Fourier transform and jxj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðg2 þ n2Þ

q, and

cosð2pd � xÞ is a term that contains the informa-tion of the speckle translocation (d).

In laser speckle photography, the fringe visi-bility in Eq. (3) is always less than 1, dependingprincipally on the speckle decorrelation. In white-light speckle photography, decorrelation is lesssevere. Therefore the fringe visibility is increased.

In speckle photography techniques involvingthe detection of Young’s fringes, two approachesare commonly used: whole-field filtering techniqueand pointwise filtering technique [12].

As was shown previously [16], a digital proce-dure, which involves segmenting the image into aseries of small subimages and Fourier transform-ing each subimage, provides both enhanced sensi-tivity (as in pointwise filtering technique) and anoverall view of the deformation (such as whole-field filtering technique). Cross-correlation ispreferable to auto-correlation because the latterintroduces a sign ambiguity and carries decorre-lation into the final results. However, auto-corre-lation can be useful in gaining a bird’s eye view ofthe deformation.

In the cross-correlation approach, subimagesare extracted from the reference image IR and thedeformed image ID. The cross-correlation betweenthese two subimages is calculated according to thefollowing relation:

cðDx;DyÞ ¼ F�1~IIR~II�D~IIR~II�D��� ���

264

375; ð4Þ

D. Ambrosini et al. / Optics Communications 201 (2002) 39–44 41

where F is the Fourier transform operator, Dxand Dy are the displacement components and theasterisk means the complex conjugate. The peaklocation in the correlation surface gives the relativedisplacement between the two subimages.

As a rule of thumb one can think that thesharper the correlation peak, the more reliable theestimation of its position. This is not completelytrue, because also noise tolerance is very important[23]. In particular, the digital correlation filtershown in Eq. (4), the so-called phase-only filter(POF) is a good compromise between peaksharpness and noise tolerance [26]. Furthermore,the coarse structure and finite size of the CCDlimit the accuracy in determining the peak posi-tion. An alleviation of this problem may be ob-tained by subpixel analysis [12,27–30].

3. Experimental results and discussion

In this work, white-light digital speckle pho-tography was demonstrated in free convection in

Fig. 2. Computer-aided Young’s fringes, obtained by white-

light digital speckle photography, on a central region of a

horizontal plate with upper surface cold. Undisturbed water

temperature was 21:8 0:1 �C while the plate cooled at

12:8 0:1 �C.

Fig. 3. Cross-correlation, codified in grey values and as a 3D plot, of two selected subimages from Fig. 2: (a) C8; (b) E1.

42 D. Ambrosini et al. / Optics Communications 201 (2002) 39–44

water. The flow facility (see Fig. 1) is a high-quality glass rectangular tank, filled with distilledwater. The bottom of the tank is a 7 mm thickaluminum plate, with dimensions 45 mm� 58mm, which can be cooled or heated by a Peltierdevice. This flow facility assures a good approxi-mation of an isothermal plate.

Before the experiment was started, the undis-turbed water in the tank was in thermal equilib-rium with the plate, at room temperature21:8 0:1 �C. Then the plate was cooled at12:8 0:1 �C. Fig. 2 shows Young’s fringes, ob-tained by white-light speckle photography. Each

subimage is of size 64� 64 pixels. The cross-cor-relations, relative to two selected subimages, nearand far from the plate, are shown in Fig. 3. Thepeak correlation value is about 0.27. This rela-tively low peak is due to the using of Eq. (4), andto the stooping and towering effects, which occurwhen looking through media with a gradient of therefractive index [31].

Fig. 4 shows Young’s fringes obtained with theplate cooled at 9:8 0:1 �C. The relative dis-placements, in pixels, are summarized in Table 1.The indetermination in each displacement is 0:1pixel.

In our experiment, 1 pixel � 30 lm and conse-quently, see Eq. (1), 1 pixel shift represents agradient temperature of 1:8� 10�1 �C mm�1. Us-ing a procedure able to provide a subpixelaccuracy of one-tenth of a pixel width, the mini-mum detectable gradient temperature is 1:8 �10�2 �C mm�1.

It was concluded earlier [23] that white-lightspeckle photography can give high accuracy, witha high-quality white-light speckle pattern, andshould be used whenever possible.

The application of white-light digital specklephotography to heat transfer studies in transpar-ent media has some remarkable features. First ofall, we can apply the technique in the transmissionmode. Using very high-quality speckle pictures, wefulfill the first condition for obtaining high accu-racy.

The sensitivity of white-light speckle method isgenerally considered lower than that of laserspeckle method [18]. The two main reasons for thisare that artificial speckles are usually larger than

Fig. 4. Computer-aided Young’s fringes, obtained with an

undisturbed water temperature of 21:8 0:1 �C and a plate

temperature of 9:8 0:1 �C.

Table 1

Speckle displacements (pixels), relative to Fig. 4, computed by the cross-correlation approacha

8 3.0 2.9 3.1 3.0 3.0 2.9 3.0 3.1

7 3.5 3.3 3.4 3.3 3.5 3.3 3.4 3.3

6 3.8 3.9 3.8 3.9 3.8 3.9 3.7 3.8

5 4.1 4.1 4.0 4.1 4.1 4.0 4.0 4.1

4 4.5 4.6 4.5 4.6 4.6 4.6 4.5 4.5

3 4.9 5.0 4.9 4.9 4.9 5.0 5.0 4.9

2 5.0 5.0 5.0 4.9 5.0 4.9 5.0 5.0

1 4.9 5.0 4.9 4.9 5.0 5.0 4.9 5.0

A B C D E F G H

aThe indetermination on each displacement is 0:1 pixel.

D. Ambrosini et al. / Optics Communications 201 (2002) 39–44 43

laser speckles and that even a small defocusingreduces the high frequency content. Both theseshortcomings are alleviated in our system. In fact,as our speckle picture is a photograph of a laserspeckle pattern, speckle size is practically the same.There is only a loss in flexibility, as to change thespeckle size one needs to change the speckle pic-ture.

As regards defocusing, speckle size is no longerdependent on the aperture of the camera. There-fore small apertures (high f#) can be used, thusassuring a high depth of field.

In conclusion, white-light full digital specklephotography can be considered as an improve-ment of digital speckle photography, featuring asimpler setup and better performances.

The major limitation of the proposed technique,as was with its laser counterpart, arises from theCCD camera, not only as regards spatial resolu-tion but also in terms of image quality [23].

4. Conclusions

In this paper, white-light full digital specklephotography was proposed for measurements offree convection in water. White-light specklephotography has certain advantages with respectto traditional speckle photography, which makes ita more robust method. Fast Fourier transformalgorithms were used to compute the speckledisplacement through the location of the cross-correlation peak.

The proposed system has the potential toovercome some shortcomings inherent in tradi-tional laser and white-light speckle photography.

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