Out-of-focus effects on microscale schlieren measurements of mass transport in a microfluidic device

The microscale schlieren technique provides a means for a non-invasive, full-field measurement for mixing microfluidics with excellent sensitivity and resolution. Nevertheless, an out-of-focus effect due to microscopic optics may lead to undesirable errors in quantifying the gradient information at high degrees of magnification. If the channel in the microfluidic device under study is too deep, light deflection caused by inhomogeneity located far from the focal plane may contributes little to the intensity change on the image plane. To address this issue, we propose the use of a weighting function that approximates a Gaussian profile with an optical-system-dependable width. We assume that the resultant intensity change is proportional to a weighted sum of the gradient across the channel depth and acquire microschlieren images of fluid mixing in a T-junction microchannel at various positions along the optical axis. For each objective, the width of the weighting function is then determined iteratively by curve fitting the ratio of changes in grayscale readouts for out-of-focus and focus micro-schlieren images. The standard deviation in the Gaussian distribution facilitates the quantification of the out-of-focus effect. In addition, we measure the sensitivities of a microscale schlieren system equipped with different objectives and compare the values to the model. Despite its better resolution, we find that an objective with higher magnification suffers from a more severe out-of-focus effect and a loss of sensitivity. Equations are proposed for estimations of the standard deviation and the sensitivity of microscale schlieren measurements. The outcome will facilitate the selection of proper microchannel depths for various microscale schlieren systems or vice versa, thus improving the precision of micro-schlieren measurements in microfluidic devices.