**4.1.1 Choice of laser and colour base**

The following points have to be addressed to show the feasibility of real-time colour holographic interferometry. Firstly, a laser has to be found that will supply the three primary wavelengths forming as extensive as possible a base triangle2. It is an Innova

<sup>2</sup> The three wavelengths chosen define the three vertices of a triangle chromaticity diagram (MacAdam, 1985).

Spectrum 70 ionized gas laser (mixed argon and krypton) that produces approximately 10 visible lines with a total power of 4.7 W. The three wavelengths retained are 647 nm for the red line of krypton and 514 nm and 476 nm for the green and blue lines of argon. All three exhibit a TEM00 mode because thee laser is equipped with a Fabry-Perot etalon to increase the coherence length of the three lines selected. The etalon is treated on both faces to get 66% transmittance for the blue line, 63% for the green line and 61% for the red line. This treatment increases the blue line's coherence length 2 or 3 centimetres at a range of several tens of centimetres. This is sufficient because, in our study, the reference and measurement paths can be roughly equalized and the optical path variations to be measured are no greater than a few microns. In the other hand, a large light energy is needed to record the studied phenomena at ultra-high speed (35,000 f/s with an exposure time of 750 10-9 s).

### **4.1.2 Panchromatic holographic plates**

6 Advanced Holography – Metrology and Imaging

*Transmission hologram Reflection hologram*

**RO GO BO**

Holographic plate Holographic plate

*Transmission hologram*

**ROD GOD BOD**

variations will thus be visualized in real time behind the hologram (Step 4, Fig. 2).

**4. Real-time colour transmission holographic interferometry** 

**ROC GOC BOC**

**ROD GOD BOD**

4) Restitution with the three reference waves and the three object waves

transmitted ROC, GOC and BOC. The profiles of the ROD and ROC, GOD and GOC waves, and the BOD and BOC waves are strictly identical to each other if no change has occurred between the two exposures and if the hologram gelatine has not contracted during development. So there will be three simultaneous interferences among the object waves constructed by the hologram and the live object waves. In this case, a flat uniform colour can then be observed behind the hologram. If a change in optical path is created in the test section of wind tunnel, the three live waves will deform and adopt the profiles 'ROC, 'GOC and 'BOC while the waves reconstructed in the hologram, ROD, GOD and BOD, remain unchanged. Any colour variations representing optical path

The following points have to be addressed to show the feasibility of real-time colour holographic interferometry. Firstly, a laser has to be found that will supply the three primary wavelengths forming as extensive as possible a base triangle2. It is an Innova

2 The three wavelengths chosen define the three vertices of a triangle chromaticity diagram (MacAdam,

**RR GR BR**

 **'ROC 'GOC**

Holographic plate

Recording

Holographic plate

Fig. 2. Formation of colour interference fringes

**4.1 Laboratory study of feasibility 4.1.1 Choice of laser and colour base** 

1985).

**RO GO BO**

**RR GR BR**

**RR GR BR**

**ROC GOC BOC**

> **RR GR BR**

1) Recording : 1st exposure, 2) Development of hologram and resetting 3) Restitution with only the three reference waves

Holographic plate

Holographic plate

**'BOC 'ROC**

**RR GR BR**

**RR GR BR**

**ROD GOD BOD**

> **ROD GOD BOD**

 **'GOC 'BOC**

Since Russian panchromatic plates came on the market twenty years ago, progress has been made in true colour holograms (Hubel, 1991; Bjelkhagen & Vukicevic, 1991; Bjelkhagen et al., 1996). The various chemical treatments applied to these plates are explained in detail by several authors (Bjelkhagen, 1993; Sasomov, 1999). The plates used are silver-coated singlefilm PFG 03C plates from the Slavich company in Moscow. Their chemical treatment first includes a hardening of the gelatine, development, bleaching, a series of rinses in alcohol and slow drying. The hologram's spectral characteristics were analyzed by taking a double exposure holographic interferogram and placing a small mirror near the object to be analyzed, in order to make a spectral analysis of the reconstructed light waves. The spectrograms of the reconstructed waves in our very first validation tests showed that the three peaks corresponding to the reconstructed colours are slightly shifted by a few nanometres, which corresponds to the contraction of the gelatine thickness:


These differences are reduced practically to zero in wind tunnel tests when the hologram is placed normal to the bisector of the angle formed by the object and reference beams.

### **4.1.3 Laboratory results**

Fig. 3 shows the feasibility setup implemented in the laboratory. The Innova Spectrum laser emits eleven lines in the visible simultaneously. The red, green, and blue lines we want are diffracted by an acousto-optic cell in which are generated three frequencies f1, f2 and f3 appropriate to the three wavelengths 1, 2 and 3. A beamsplitter cube splits the reference beams and three object beams. The three reference beams are collimated onto the holographic plate by an achromatic lens located a focal length from the pinhole (diameter 25 m) of a spatial filter having a microscope objective lens (x60). The three object beams are collimated the same way to form three parallel light beams between two large achromatic lenses and illuminate the test section.

The hologram is thus illuminated on the same side by the three parallel reference beams and the three convergent measurement waves. A diaphragm is placed in the focal plane just in front of the camera in order to be able to filter out any parasitic interference. The hologram is first illuminated in the absence of flow and is then developed and placed back in exactly its original position. When the hologram is illuminated with the reference beam, nine diffraction images are seen. They are clearly visible in Fig. 4. Of the nine, three coincide and

Real-Time Colour Holographic Interferometry (from Holographic Plate to Digital Hologram) 9

pattern can be formed. The achromatic central white fringe can be made out very clearly. One also can see the deformation due to an microscope plate and a small jet at two different instants. Lastly, the diffraction efficiency was measured behind the hologram. The hologram exhibits a diffraction efficiency of about 0.8% for the red and green lines and 0.5% for the

The optical setup for testing the feasibility of the technique had to be modified and adapted around ONERA's wind tunnel at Lille centre. For reference, this wind tunnel is equipped with a 2D test section 200 mm high and 42 mm wide. The Mach number can be varied from 0.3 to 1.1. The flow studied was the unsteady flow downstream of a cylinder 20 mm in

The optical setup is shown in Fig. 5. The beam power as it leaves the laser is 1.80 W when the etalon is set perpendicular to the laser beam axis and 1.20 W when it is tilted. The polarization of the three beams rotates 90° at the exit from the acousto-optic modulator, so that the polarization vectors lie parallel to the reflecting surfaces of the mirrors. This arrangement makes it possible to have beams of the same polarization interfere on the hologram. The three wavelengths downstream of the acousto-optic cell are split into a reference beam and object beam by a beam splitter cube. A right angle prism is used to adjust the reference and object path lengths on the hologram. A spatial filter is used to expand the beam for its passage through the test section. A pair of achromatic lenses converts the beam into parallel light in the test section and then focuses it on the hologram. The reference beam passes over the test section, and then another achromatic lens is used to illuminate the hologram with a parallel light beam. For reference, the object beam diameter is 40 mm at the hologram and that of the reference beam is 60 mm. At the acousto-optic cell, the power of the three light waves is practically the same (of the order of 70 mW per channel). The beam splitter cube distributes 85% of this power to the reference path and 15%

> Holographic Plate

Camera

Mirror

Spatial Filter

blue line. Although these values are very low, they do allow a good visualization.

**4.2 Wind tunnel adaptation of the method** 

diameter D placed crosswise in the test section.

**4.2.1 Optical setup around the wind tunnel** 

to the measurement path.

1 2 3

Acousto Optical Cell

Right angle Prism

Beamsplitter Cube

Filter

Spatial Objet

Fig. 5. Optical setup implemented around the wind tunnel

Achromatic Lenses

At the hologram, one measures 250 W/cm² in the red and blue lines and 280 W/cm² in the green line for the reference beam, while the object beam powers are 30 W/cm² in the

Mirror

Fig. 3. Real-time colour holographic interferometry setup (Transmission mode)

focus exactly at a single point if the setup is perfectly achromatic. These three images correspond to the diffraction of the blue image by the blue beam, that of the green image by the green beam, and that of the red image by the red beam. They are exactly superimposed. The other six images are parasitic and have to be filtered out. They correspond to the diffraction of the blue image by the green and red lines, that of the green image by the blue and red lines, and that of the red image by the blue and green lines. Fig. 4 shows how all the images are diffracted behind the hologram, and the spatial filter system that is used to select only the focal point of interest to us.

Fig. 4. Real-time colour holographic interferometry setup (Transmission mode)

Moreover, an adjustable neutral density filter made it possible to balance the power of the measurement beams with that of the reference beams. For reference, the power of the three lines at the acousto-optic output is 50 mW for the red line and 90 mW for the green and blue. In the hologram plane, the reference beam powers are 240 W/cm² for the red line, 270 W/cm² for the green, and 290 W/cm² for the blue. For the object beams, one measured 100 W/cm² for the red and green lines and 330 W/cm² for the blue. The hologram exposure time for the first exposure was 4 s. Fig. 4 shows some images obtained. First, the uniform background colour was obtained over the entire surface of the test section, which shows that it is possible to re-position the three live waves simultaneously with the three waves contained in the hologram. The tint is the purple of the first order of interference, which is one of the most sensitive. The interference pattern is obtained by slightly displacing one of the two large achromatic lenses. So a horizontal, vertical, or even circular fringe pattern can be formed. The achromatic central white fringe can be made out very clearly. One also can see the deformation due to an microscope plate and a small jet at two different instants. Lastly, the diffraction efficiency was measured behind the hologram. The hologram exhibits a diffraction efficiency of about 0.8% for the red and green lines and 0.5% for the blue line. Although these values are very low, they do allow a good visualization.

### **4.2 Wind tunnel adaptation of the method**

8 Advanced Holography – Metrology and Imaging

Fig. 3. Real-time colour holographic interferometry setup (Transmission mode)

Spatial filter

Fig. 4. Real-time colour holographic interferometry setup (Transmission mode)

only the focal point of interest to us.

Hologram

Diffracted waves

Parasitic images in the focal plane

Reference waves

focus exactly at a single point if the setup is perfectly achromatic. These three images correspond to the diffraction of the blue image by the blue beam, that of the green image by the green beam, and that of the red image by the red beam. They are exactly superimposed. The other six images are parasitic and have to be filtered out. They correspond to the diffraction of the blue image by the green and red lines, that of the green image by the blue and red lines, and that of the red image by the blue and green lines. Fig. 4 shows how all the images are diffracted behind the hologram, and the spatial filter system that is used to select

Uniform background

Deformation induced by a microscope plate

Moreover, an adjustable neutral density filter made it possible to balance the power of the measurement beams with that of the reference beams. For reference, the power of the three lines at the acousto-optic output is 50 mW for the red line and 90 mW for the green and blue. In the hologram plane, the reference beam powers are 240 W/cm² for the red line, 270 W/cm² for the green, and 290 W/cm² for the blue. For the object beams, one measured 100 W/cm² for the red and green lines and 330 W/cm² for the blue. The hologram exposure time for the first exposure was 4 s. Fig. 4 shows some images obtained. First, the uniform background colour was obtained over the entire surface of the test section, which shows that it is possible to re-position the three live waves simultaneously with the three waves contained in the hologram. The tint is the purple of the first order of interference, which is one of the most sensitive. The interference pattern is obtained by slightly displacing one of the two large achromatic lenses. So a horizontal, vertical, or even circular fringe

Flow jet at two different instants

Achromatic fringe

The optical setup for testing the feasibility of the technique had to be modified and adapted around ONERA's wind tunnel at Lille centre. For reference, this wind tunnel is equipped with a 2D test section 200 mm high and 42 mm wide. The Mach number can be varied from 0.3 to 1.1. The flow studied was the unsteady flow downstream of a cylinder 20 mm in diameter D placed crosswise in the test section.

### **4.2.1 Optical setup around the wind tunnel**

The optical setup is shown in Fig. 5. The beam power as it leaves the laser is 1.80 W when the etalon is set perpendicular to the laser beam axis and 1.20 W when it is tilted. The polarization of the three beams rotates 90° at the exit from the acousto-optic modulator, so that the polarization vectors lie parallel to the reflecting surfaces of the mirrors. This arrangement makes it possible to have beams of the same polarization interfere on the hologram. The three wavelengths downstream of the acousto-optic cell are split into a reference beam and object beam by a beam splitter cube. A right angle prism is used to adjust the reference and object path lengths on the hologram. A spatial filter is used to expand the beam for its passage through the test section. A pair of achromatic lenses converts the beam into parallel light in the test section and then focuses it on the hologram. The reference beam passes over the test section, and then another achromatic lens is used to illuminate the hologram with a parallel light beam. For reference, the object beam diameter is 40 mm at the hologram and that of the reference beam is 60 mm. At the acousto-optic cell, the power of the three light waves is practically the same (of the order of 70 mW per channel). The beam splitter cube distributes 85% of this power to the reference path and 15% to the measurement path.

Fig. 5. Optical setup implemented around the wind tunnel

At the hologram, one measures 250 W/cm² in the red and blue lines and 280 W/cm² in the green line for the reference beam, while the object beam powers are 30 W/cm² in the

Real-Time Colour Holographic Interferometry (from Holographic Plate to Digital Hologram) 11

Lastly, the colours of each interferogram were analyzed using the "MIDI" software3, which models the light intensity and experimental interference fringe colours as a function of the path difference (Desse, 1997a). The gas density measured under free stream conditions is the same as that measured at the outer flow of the wake (measured in the vicinity of the wind

If *e* is the test section width and *n* the refractive index, the optical thickness *E* can be

*<sup>n</sup> <sup>K</sup>*

Dale constant (296.10-6), the relative gas density variation is written :

the orders of interference, and thereby the measurement precision.

**5. Real-time colour reflection holographic interferometry** 

3 Modelling of Luminous Interferences and Analysis of Interferograms

*s*

*s* is the gas density under standard conditions (1.29 kg/m3) and *K* the Gladstone-

*<sup>0</sup>* the stagnation gas density. Starting from a point external to the wake, one

<sup>0</sup> <sup>0</sup> . 

can work back to the gas density at the stagnation point (at the nose of cylinder) and measure the gas densities at the centre of the vortices. The graph of Fig. 6c shows how

varies for the vortices emanating from the upper and lower surfaces. The trend curves plotted show the same variations. For *0.5 < x/D < 1*, the vortices are in a formation or agglomeration phase because the gas density decreases at their centre. Then, when *x/D > 1*, the vortices enter a dissipation phase because the gas density increases again at their centres. The drop in gas density is large, reaching about 20% 0. A rather large dispersion may nonetheless be noticed in the data. This is due mainly to our determination of the vortex centre locations, which are not very easy to determine when the vortices are in the dissipation phase. Moreover, taking the hologram transfer function into account in the exact modelling of the interference fringes should greatly improve the modelled colours between

Since transmission holograms are used, the diffraction efficiency of holograms just reaches between 10% and 20%, which limits the quality and the contrast of interferences fringes. On the other hand, if reflection holograms are used, the theoretical diffraction efficiency can reach 100% with a monochromatic light. The development of real-time true colour reflection holographic interferometry also offers two important advantages. The first one concerns the analysis of the three-dimensional (3D) flows and the second one lies in the comparison with digital colour holographic interferometry. In fact, ONERA is looking towards analyzing unsteady 3D flows, and the optical setup to be designed must be based on several crossings

 *s Ke <sup>E</sup>*

)1(

).1( *enE* (1)

(2)

(3)

*0*

being the gas density measured under free stream

tunnel's upper and lower walls).

Knowing the Gladstone-Dale relationship :

and *EEE* ,

expressed by :

where 

with 

conditions and

red line and 40 W/cm² in the green and blue lines. These proportions can be used to obtain a perfect balance among the powers of the three waves diffracted by the hologram when repositioning it, and the three live waves. For reference, the hologram diffracts 70 W/cm² in the red line, 65 W/cm² in the green line, and 90 W/cm² in the blue line. The first exposure lasts 2 s. The holograms are then subjected to treatments to harden the gel, develop it, and bleach it. When the hologram is put back in place, the light power at the camera entrance is 1.5 10-3 W at the focal point, which is sufficient to record interferograms at an ultra-high speed of 35,000 frames per second with an exposure time of 750 ns per shot.

## **4.2.2 Results and analysis of interferograms at Mach 0.37**

Figure 6a gives a sequence of six interferograms of the flow around the cylinder at Mach 0.37. The time interval between each picture is 100 s. One can see that each vortex is represented by concentric rings of different colours where each colour represents an isochoric line. The vortex formation and dissipation phases can be seen very clearly while the fringes oscillate between the upper and lower surfaces of the cylinder. Several types of measurements were made by analyzing a sequence of some 100 interferograms. First, the vortex centre defined by the centre of the concentric rings was located in space for each interferogram, which made it possible to determine the mean paths for the vortices issuing from the upper and lower surfaces. The results of this are shown in Fig. 6b. The "o" symbols represent the positions of the vortex centres from the upper surface, and the "•" symbols those of the lower surface. Remarkably, the two paths exhibit a horizontal symmetry about the x = 0 axis passing through the cylinder centre. One may also point out that even at x/D = 4 downstream of the cylinder, the upper and lower vortex paths do not come together and line up.

Fig. 6. Unsteady wake flow around the cylinder -Results and analysis – Mach 0.37

Lastly, the colours of each interferogram were analyzed using the "MIDI" software3, which models the light intensity and experimental interference fringe colours as a function of the path difference (Desse, 1997a). The gas density measured under free stream conditions is the same as that measured at the outer flow of the wake (measured in the vicinity of the wind tunnel's upper and lower walls).

If *e* is the test section width and *n* the refractive index, the optical thickness *E* can be expressed by :

$$E = (n - l).e\tag{1}$$

Knowing the Gladstone-Dale relationship :

10 Advanced Holography – Metrology and Imaging

red line and 40 W/cm² in the green and blue lines. These proportions can be used to obtain a perfect balance among the powers of the three waves diffracted by the hologram when repositioning it, and the three live waves. For reference, the hologram diffracts 70 W/cm² in the red line, 65 W/cm² in the green line, and 90 W/cm² in the blue line. The first exposure lasts 2 s. The holograms are then subjected to treatments to harden the gel, develop it, and bleach it. When the hologram is put back in place, the light power at the camera entrance is 1.5 10-3 W at the focal point, which is sufficient to record interferograms at an ultra-high

Figure 6a gives a sequence of six interferograms of the flow around the cylinder at Mach 0.37. The time interval between each picture is 100 s. One can see that each vortex is represented by concentric rings of different colours where each colour represents an isochoric line. The vortex formation and dissipation phases can be seen very clearly while the fringes oscillate between the upper and lower surfaces of the cylinder. Several types of measurements were made by analyzing a sequence of some 100 interferograms. First, the vortex centre defined by the centre of the concentric rings was located in space for each interferogram, which made it possible to determine the mean paths for the vortices issuing from the upper and lower surfaces. The results of this are shown in Fig. 6b. The "o" symbols represent the positions of the vortex centres from the upper surface, and the "•" symbols those of the lower surface. Remarkably, the two paths exhibit a horizontal symmetry about the x = 0 axis passing through the cylinder centre. One may also point out that even at x/D = 4 downstream of the cylinder,

> -1.5 -1 -0.5 0 0.5 1 1.5

0.75

0.8

0.85

**o**

Fig. 6. Unsteady wake flow around the cylinder -Results and analysis – Mach 0.37

0.9

0.95

**y/D**


**b) Vortices trajectories**

01234 **x/D**

**c) Vortices gas density**

speed of 35,000 frames per second with an exposure time of 750 ns per shot.

**4.2.2 Results and analysis of interferograms at Mach 0.37** 

the upper and lower vortex paths do not come together and line up.

**4**

**5**

**6**

**a) High speed holographic interferograms recorded by transmission – t = 100s**

**1**

**2**

**3**

$$K = \frac{(n-1)}{\mathcal{P}\big\triangleright\_s} \tag{2}$$

where *s* is the gas density under standard conditions (1.29 kg/m3) and *K* the Gladstone-Dale constant (296.10-6), the relative gas density variation is written :

$$\frac{\Delta\rho}{\rho\_0} = \frac{\Delta E}{e.K} \frac{\rho\_s}{\rho\_0} \tag{3}$$

with and *EEE* , being the gas density measured under free stream conditions and *<sup>0</sup>* the stagnation gas density. Starting from a point external to the wake, one can work back to the gas density at the stagnation point (at the nose of cylinder) and measure the gas densities at the centre of the vortices. The graph of Fig. 6c shows how *0* varies for the vortices emanating from the upper and lower surfaces. The trend curves plotted show the same variations. For *0.5 < x/D < 1*, the vortices are in a formation or agglomeration phase because the gas density decreases at their centre. Then, when *x/D > 1*, the vortices enter a dissipation phase because the gas density increases again at their centres. The drop in gas density is large, reaching about 20% 0. A rather large dispersion may nonetheless be noticed in the data. This is due mainly to our determination of the vortex centre locations, which are not very easy to determine when the vortices are in the dissipation phase. Moreover, taking the hologram transfer function into account in the exact modelling of the interference fringes should greatly improve the modelled colours between the orders of interference, and thereby the measurement precision.
