**2. Fundamental**

Digital holography has been widely developed for analysing diffusive objects since the digitally reconstructing of the optical wavefront was shown by Goodman and Lawrence [9]. But, in fluid mechanics, the objects under analysis are very often transparent because it is the field of refractive index of the flow which is measured. There are two ways to measure variations in the refractive index by digital holography. The first one, presented in **Figure 1**, is comparable to the technique used for measuring diffusive objects in structural mechanics.

**Figure 1.** Fresnel holography for measuring transparent objects.

For example, if three different wavelengths are considered, ∑MR for the red line, ∑MG for the green line and ∑MB for the blue line, the wavefronts of measurement which cross the trans‐ parent object in the test section can be sent on a ground plate and each point of the plate diffracts and interferes on the sensor with the three reference waves, ∑RR, ∑RG and ∑RB. In this case, the sensor can be a Bayer mosaic, a stack of photodiodes or a 3CDD. The recorded image is a speckle image which can be processed using Fresnel transform and the field (, , ) diffracted at the distance and at the coordinates (, ) of the observation plane is given by the propagation of the three object waves to the recording plane. The second technique is shown in **Figure 2**. The three wavelengths ∑MR, ∑MG and ∑MB interfere directly onto the sensor with the three reference waves, ∑RR, ∑RG and ∑RB. As the three measurement waves are smooth waves, the interferences with the three reference waves on the sensor produce three gratings of interference micro‐fringes which can be used as spatial carrier frequencies, one for each wavelength. By using direct and inverse 2D Fast Fourier Transform (FFT), the amplitude and the phase of the analysed field is obtained.

**Figure 2.** Fourier holography for measuring transparent objects.

been obtained for visualizing convective flows induced by the thermal dissipation in a tank filled with oil [6]. Quantitatively, the feasibility of three‐wavelength digital holographic interferometry has been demonstrated for analysing the variations in the refractive index induced by a candle flame [7] and the technique has been applied in wind tunnel on two‐ dimensional unsteady flows where the time evolution of the gas density field has been determined on the subsonic near wake flow downstream a circular cylinder [8]. But, when the flow regime reaches the transonic or supersonic domain, problems appear because refractive index gradients become very strong and a shadow effect is generated by the shock waves, for instance, superimposes to the micro‐fringes of interferences. Phase shifts appear and limit the interferogram analysis.In orderto solve these different problems, the authors propose to study three different cases of flows presenting high‐density gradients using specific optical techni‐ ques based on digital holography. The first one concerns a small supersonic jet analysed by Michelson colour digital interferometry, colour holographic interferometry using Wollaston prisms and monochromatic digital holography without reference wave. The second case is to compare Michelson and Mach‐Zehnder interferometers for analysing the unsteady wake flow around a circular cylinder at transonic Mach number. And finally, digital and image holo‐ graphic methods are presented to visualize and measure the refractive index variations, convection currents or thermal gradients occurring inside a transparent and strongly refract‐ ing object. In the case of image holographic interferometry, a comparison with transmission

Digital holography has been widely developed for analysing diffusive objects since the digitally reconstructing of the optical wavefront was shown by Goodman and Lawrence [9]. But, in fluid mechanics, the objects under analysis are very often transparent because it is the field of refractive index of the flow which is measured. There are two ways to measure variations in the refractive index by digital holography. The first one, presented in **Figure 1**, is comparable to the technique used for measuring diffusive objects in structural mechanics.

For example, if three different wavelengths are considered, ∑MR for the red line, ∑MG for the green line and ∑MB for the blue line, the wavefronts of measurement which cross the trans‐ parent object in the test section can be sent on a ground plate and each point of the plate diffracts

and reflection holograms is provided.

292 Holographic Materials and Optical Systems

**Figure 1.** Fresnel holography for measuring transparent objects.

**2. Fundamental**

All details and basic fundamentals of these two techniques can be found in the study of Picart et al. [10].
