Direct Comparison of Quantitative Shadowgraphy with Interferomery for Plasma Density Measurements

Summary form only given. Though based on the geometrical optics approximation, quantitative refractive shadowgraphy can be a reliable alternative to interferometry for sensitive optical measurements of electron densities in under-critical plasmas. We carried out a careful comparison of the two methods arranging an optical set-up capable of taking simultaneously and in single-shot a shadowgram and an interferogram of laser-produced plasma bubbles in air. In the range of electron densities 0.2-1.5times10¹⁹ cm^-3 and plasma bubble diameter between 30 and 60 mum, the results of both methods were virtually identical. We reported slightly better sensitivity and spatial resolution for the shadowgraphy channel. Signal-to noise estimates assigned a density sensitivity of 0.05times10¹⁹ cm^-3 for shadowgraphy and 0.2times10¹⁹ cm^-3 for interferometry. The smallest detected details were measured to be of 20 mum in shadowgraphy, and 30 mum in interferometry. Apart from diffraction effects, limitations to the quantitative shadowgraphy arise mainly from inverse bremsstrahlung absorption in the probed plasma. Just a 10% absorption induces a 50% systematical error in the evaluation of the peak phase-shift of the retrieved shadow graphic data. Our simulations pointed out that appropriate calibration of the shadowgram with absorption measurements can retrieve accurately density profiles even with absorptions up to 20%. Additionally, this procedure will provide information on inverse bremsstrahlung coefficients, thus opening the possibility to estimate simultaneously density and temperature profiles in under-critical plasmas.