On the application of background oriented schlieren for wavefront sensing

Abstract

The concept of utilizing a background oriented schlieren (BOS) imaging system to measure the distortion of a wavefront is presented and analyzed. It is shown that the fundamental equations characterizing the image distortion measured using BOS and the distortion of a wavefront are based on the same physical phenomena and can be easily related to one another. An analysis is performed to consider the influence of practical considerations, such as the field-of-view (FOV) and depth-of-field (DOF) on the sensitivity of the BOS measurement. It is found that when the FOV of the schlieren object is held constant and placement of both the medium and background is constrained to the DOF of the imaging system, the sensitivity of the BOS measurement is independent of the focal length of the imaging lens and overall length of the system, both of which are dependent on the FOV and DOF. An equation is derived that expresses the BOS sensitivity as a function of imaging lens f-number and the circle of confusion as these parameters are used in practice to determine the FOV and DOF. It is shown that allowing the background to be slightly out of focus can significantly increase the sensitivity of the measurement. The analysis is tested and confirmed using both computer generated model images and experiments performed to measure the wavefront distortion induced by a plano-convex lens. An uncertainty analysis is performed showing better than 0.1 pixel resolution in the image distortion, which results in an absolute error of the reconstructed wavefront that is better than 5% for the case considered here.

A review of recent developments in schlieren and shadowgraph techniques

“…A recent survey of the topic by Raffel [24] cited 115 references, and the numbers continue to grow. A selection of recommended BOS reading is given here in [24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

“…If the BOS camera has a sufficient depth-of-field, the background B should be at the far end and the schlieren object S at the near end of it, rather than centering the depth-of-field on the background. Further discussion of this issue is found in [37].…”

High-speed videography of transparent media using illumination-based multiplexed schlieren

“…The effect of object position on sensitivity. One of the main drawbacks with a BOS system is that the image plane of the textured background (or modulated illumination) must not coincide with the object plane of the sample under study 4,48 . As the analysis of the displacement relies on visualizing fine distortions in the background pattern, the object inevitably needs to be placed out-of-focus from the cameras perspective.…”

Practical Approach for Absolute Density Field Measurement Using Background-Oriented Schlieren

“…The basic principle behind visualizing the density gradient field using the refractive index is given by the Gladstone-Dale relationship, which relates density (ρ) with the refractive index (n) as follows [1,7,10]:…”

“…To date, numerous studies have been undertaken to improve the BOS technique since the late 1990s [1]. Specifically, quantitative BOS measurement [6,7], three-dimensional applications [8,9], sensitivity evaluation [9,10], applications related to high-speed propulsion flowfields [11][12][13], and large-field outdoor measurements [1][2][3]14,15] have been demonstrated. Furthermore, an actual flight demonstration called Background-Oriented Schlieren in Celestial Objects (BOSCO) has recently emerged [14,15].…”