One of the main approaches for contact angle determination using sessile drops with a missing apex (e.g., because of the presence of the needle tip) is the polynomial drop-profile fitting method. The major disadvantage of this fitting procedure is that the derived contact angle is highly sensitive to the polynomial order and the number of pixels involved in the actual fit. In the present work, an easily implementable method is introduced to effectively tackle these drawbacks. Instead of fitting the drop-profile itself, the polynomial fitting is applied to the difference between the drop profile and the circumcircle, independently for both sides of the drop. The derivative value of this difference at the contact point is used to correct the slope obtained analytically from the circumcircle. It is shown that this approach allows the robust determination of the contact angle with high (≤0.6°) accuracy in a straightforward manner, and the results are not affected by the actual contact angle, drop volume, or the resolution of the captured image. Validation of this new approach is also given in the contact angle range of 20°-150° by comparing the results to the values calculated by the Young-Laplace fit.
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