Multi-pass probing for high-sensitivity tomographic interferometry

Abstract

Optical probing is an indispensable tool in research and development. In fact, it has always been the most natural way for humankind to explore nature. However, objects consisting of transparent materials with a refractive index close to unity, such as low-density gas jets, are a typical example of samples that often reach the sensitivity limits of optical probing techniques. We introduce an advanced optical probing method employing multiple passes of the probe through the object to increase phase sensitivity, and relay-imaging of the object between individual passes to preserve spatial resolution. An interferometer with four-passes was set up and the concept was validated by tomographic characterization of low-density supersonic gas jets. The results show an evident increase of sensitivity, which allows for the accurate quantitation of fine features such as a shock formed by an obstacle or a barrel shock on the jet boundary in low ambient gas pressures. Despite its limitations in temporal resolution, this novel method has demonstrated an increase in phase sensitivity in transmission, however, it can also be employed to boost the absorption or polarization contrast of weakly interacting objects in both transmission and reflection setups, thus, upgrading the sensitivity of various optical characterization methods.

Figure 1

Schematics of the double-pass setup (a) and four-pass setup (b) for interferometric gas jet characterization. The first reflections of the beam on the beam splitters and their beam blocks are not shown.

Figure 2

Comparison of spatial phase distributions obtained at a different number of passes of the probe beam through the gas jet generated by a cylindrical nozzle for backing pressure of 1.6 bar Ar (a–c) and 7 bar He (e–g). For the phase maps from left to right single-pass, double-pass, and four-pass. Phases at two different heights above the nozzle in the single-pass and the four-pass configurations are shown for Ar (d) and He (h) jets.

Figure 3

Comparison of density profiles calculated using the inverse Abel transform of an axisymmetric gas jet with backing pressure of 1.6 bar Ar (a, b) and 7 bar He (c, d) at 1.5 mm (a, c) and 0.75 mm (b, d) above the nozzle exit. The profiles for single-pass (dotted blue lines) and four-pass (solid red lines) probing configuration calculated from the phase maps shown in Fig. 2 are compared to the profiles from the hydrodynamic simulations (dashed black line).

Figure 4

Tomographic density reconstructions of Ar (a, b) and He (c, d) gas jets obstructed by a razor blade placed 1 mm above the nozzle at a backing pressure of 1.6 bar and 7 bar, respectively. Gas distribution is represented by density isosurfaces with values shown in the legend. The z-coordinate describes the height above the nozzle. Vertical cross-sections of the density profiles in the middle of the gas jet (plane y = 0) is shown in the insets (b) and (d) for Ar and He, respectively.

Figure 5

(a) Phase map of Ar with backing pressure of 1.6 bar and ambient pressure of 1.0 mbar showing the clear barrel shock formed on the edge of the jet. (b) Gas density distribution of Ar gas jets (backing pressure 1.6 bar) during expansion in ambient gas pressure in the range of 0–3 mbar at the height of 2 mm above the nozzle exit.

Figure 6

(a) Part of the raw interferogram with bent fringes due to the shock front from the blade. (b) Raw interferogram with schematics showing the positions of the nozzle and the blade.

Figure 7

(a) Phase map with second Wollaston copy visible as a dark blue region in the right of the jet (Argon, backing pressure 1.6 bar). The area marked by the dotted line is the extension with a size corresponding to the shear vector $\mathit{s}$. (b) Corrected phase map of the same interferogram.