**6.3 Results obtained in subsonic wake flows**

Again, near wake flow downstream from a circular cylinder has been studied at Mach 0.45. Here, one used a ORCA-3CCD Hamamatsu camera with 3 chips of 1344x1024 pixels, 6.45 m x 6.45 m in size. The framing rate is 9 f/s and the filters of RGB camera are very narrowband and centred on the three laser wavelengths. As the framing rate is very slow compared to the frequency of the vortex street, a transducer has been implemented in the cylinder at an azimuth of 90° (perpendicular to the flow axis) in order to synchronize the

Achromatic lenses

Fig. 14. Generation and micro-fringes formation by the phenomenon studied

Again, near wake flow downstream from a circular cylinder has been studied at Mach 0.45. Here, one used a ORCA-3CCD Hamamatsu camera with 3 chips of 1344x1024 pixels, 6.45 m x 6.45 m in size. The framing rate is 9 f/s and the filters of RGB camera are very narrowband and centred on the three laser wavelengths. As the framing rate is very slow compared to the frequency of the vortex street, a transducer has been implemented in the cylinder at an azimuth of 90° (perpendicular to the flow axis) in order to synchronize the

**6.3 Results obtained in subsonic wake flows** 

Fig. 13. Digital colour holographic interferometer – Formation of spatial carrier frequencies interference fringes are introduced into the field of visualization. These micro fringes are recorded on the CCD in order to calculate the three reference phase maps. Then the wind tunnel is started and the three object waves are distorted by the aerodynamic phenomenon. Micro-fringes interference is again recorded by the 3CCD sensor to enable calculation of the phase maps related to the object. For maps of phase difference, the reference phase is

cube

Camera

Acousto optical cell

1 2 3 Mask

Spatial

Micro-fringes

subtracted from the phase object.

Diaphragm

Filter Beamsplitter

Concave mirror

**MR MG MB**

**RR RG RB**

Flat mirror

*a) Digital optical bench b) Micro-fringes recording*

Object

**3** CCD sensor

interferogram recording with the signal of the unsteady pressure measurement. The cycle of the vortex street was decomposed in eight different instants shifted by 76 s and at each instant, five interferograms were recorded from several cycles to average the unsteady maps. First, Fig. 15 shows two micro fringes images recorded with and without the flow in order to constitute reference and object interferograms. It can be seen in the zoomed image that micro-fringes are deformed by the shear layer of the upper side.

Fig. 15. Micro-fringes recording for the reference and object images

The three Fourier transforms are calculated from each image in order to reconstruct the phase maps with the +1 order (the zero order and the -1 order are filtered). An example of reference and measurement spectra is given in Fig. 16 for the green line. One can see that the spectrum only exhibits a spot corresponding to the green spatial carrier frequency. No parasitic frequencies due to the blue and red lines are found. By subtracting the reference phase maps from the measurement phase maps, one obtains the modulo2 phase difference maps. After unwrapping, it possible to compute the refractive index maps and the gas density field assuming the Gladstone-Dale relation.

Fig. 16. FFT reference and object spectra and difference phase map for the green line

Real-Time Colour Holographic Interferometry (from Holographic Plate to Digital Hologram) 25

can then be compared to that obtained using the reflection holographic plates. After locating an interferogram recorded at a phase very similar to that of digital interferogram, Fig. 18

So, in image colour holographic interferometry, a reflection panchromatic holographic plate (7,000 to 10,000 lines per mm in spatial resolution) has to be illuminated with a total energy of 600 J and the resetting of holographic plate is very sensitive and delicate. In digital technique, energy of 1J is sufficient to illuminate the sensor (155 lines per mm in resolution). The implementation is easy enough and the phase difference is entirely estimated with a computer. The coherence lengths of the three lasers must be more 2 meters in the two optical setups. In image holographic interferometry, about 220 successive frames of the phenomenon can be recorded at high framing rate (35,000 images per second with an exposure time of 750 ns for each). Each image has to be digitalized and processed. Also, it is important to obtain a reference hologram of about 50% diffraction efficiency for the three lines. In digital holographic interferometry, the framing rate is limited to 9 frames per second, full size and a synchronized triggering of interferograms recording has to be used to

The possibilities of image and digital colour holographic interferometry have been demonstrated. Colour holographic interferometry using panchromatic plates will continue to be used due to the high resolution of holographic plates. In near future, digital threewavelength holographic interferometry seems the best candidate to characterize the future complex flows. Although CCD resolution and size are not as good as that of holographic plates, the digital approach is more accessible and versatile since the time for the hologram processing is greatly reduced and the processing is purely numerical. On the other hand, the value of using colour has been demonstrated as the zero order fringe can be easily determined and the variation in the background colour due to disturbances can be quantified. The limitations of the digital method seem to lie in the wide spectral sensitivity of the sensor which produces light diffusion in each monochromatic hologram. Work is currently in progress for removing the colour diffusion using a segmentation approach. Success in this strategy will allow increasing the spatial resolution in the reconstructed object. Future work will focus on the extension of the proposed technique for analyzing 3D

shows that the correspondence is very good.

analyze unsteady phenomena.

**7. Conclusion** 

Fig. 18. Comparison between image and digital interferogram

Colour interferences fringes and gas density field are shown in Fig. 17 for the first three images of one cycle of the vortex street.

Fig. 17. Evolution of colour interference fringes and gas density field – Mach 0.45

The intensity of the interference fringes is computed on the three channels R, G, B from the phase maps with following the following relationship :

$$\mathbf{I}\_{\boldsymbol{\lambda}} = \mathbf{A}\_{\boldsymbol{\lambda}} (\mathbf{1} + \cos(\boldsymbol{\Delta} \boldsymbol{\phi}\_{\boldsymbol{\lambda}}) \tag{10}$$

The gas density measured to the cylinder nose is particular as the gas density is equal to the stagnation gas density though the position of the vortex street, that means the colour found at this point has to be the same on each interferogram. Here, the intensity of colour interferences fringes is computed by imposing the white colour ( = 0 m) on each interferogram. Note this shifting is only made possible by the use of colour in the experiments. The time evolution of the gas density fields shows that the gas density decreases to 73% of *io* in the vortex core. Then, the averaged field of one cycle is calculated by averaging the 8 maps of instantaneous gas density field.

### **6.4 Comparison between holographic plate and digital holograms**

As regards previous results obtained, silver-halide plate and digital holographic interferometry can be compared. The only possibility to compare plate and digital interferograms is to compare the interferograms displaying the interference fringes. Indeed, the technique of holographic interferometry in real time using panchromatic plates directly displays the colour density variations of the flow. It's a light intensity information that is obtained. With digital holography, the three monochromatic intensity maps are superimposed to obtain a colour map of the intensity of the interference fringes. This map can then be compared to that obtained using the reflection holographic plates. After locating an interferogram recorded at a phase very similar to that of digital interferogram, Fig. 18 shows that the correspondence is very good.

Fig. 18. Comparison between image and digital interferogram

So, in image colour holographic interferometry, a reflection panchromatic holographic plate (7,000 to 10,000 lines per mm in spatial resolution) has to be illuminated with a total energy of 600 J and the resetting of holographic plate is very sensitive and delicate. In digital technique, energy of 1J is sufficient to illuminate the sensor (155 lines per mm in resolution). The implementation is easy enough and the phase difference is entirely estimated with a computer. The coherence lengths of the three lasers must be more 2 meters in the two optical setups. In image holographic interferometry, about 220 successive frames of the phenomenon can be recorded at high framing rate (35,000 images per second with an exposure time of 750 ns for each). Each image has to be digitalized and processed. Also, it is important to obtain a reference hologram of about 50% diffraction efficiency for the three lines. In digital holographic interferometry, the framing rate is limited to 9 frames per second, full size and a synchronized triggering of interferograms recording has to be used to analyze unsteady phenomena.
