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Recently, reflection interference fringe (RIF) and transmission fringe (TIF) techniques have been introduced to investigate the origin of far-field interference fringe (IF) formation and to determine a droplet's contact angle and thickness by measuring the fringe radius. In this study, characteristics of the IF technique are analyzed based on the RIF and TIF by varying the schematics, such as configuration (transmission/reflection), the droplet's side (left-hand side/right-hand side), and the substrate types (flat/prism). The analysis also investigates the refraction effect at the droplet edge and the maximum incidence and contact angles. The schematic variation shows that the widest contact angle range can be measured in a transmission configuration with droplet's right-hand side, and that the fringe radius decreases with incidence angles on a prism substrate, consistent with the recent observation. Refraction at the droplet edge causes the fringe radius to increase or decrease depending on the degree of refraction. Based on the characteristics study, it is revealed that the IF technique can determine nanometer-scale thicknesses below 100 nm on droplets, corresponding to ultra-small contact angles of less than 0.01°, with an extended working distance of 3000 mm and an optimized incidence angle, assuming a spherical profile. This finding is significant, as it demonstrates that the nanoscale thickness can be determined in situ under ambient conditions using a simple optical configuration, without requiring a sophisticated setup, such as a microscope. It is anticipated that the IF technique can be combined with other nanoscale thickness measurement techniques to enhance its measurement reliability. 

The transmission interference fringe (TIF) technique was developed to visualize the dynamics of evaporating droplets based on the Reflection Interference Fringe (RIF) technique for micro-sized droplets. The geometric formulation was conducted to determine the contact angle (CA) and height of macro-sized droplets without the need for the prism used in RIF. The TIF characteristics were analyzed through experiments and simulations to demonstrate a wider range of contact angles from 0 to 90°, in contrast to RIF's limited range of 0–30°. TIF was utilized to visualize the dynamic evaporation of droplets in the constant contact radius (CCR) mode, observing the droplet profile change from convex-only to convex-concave at the end of dry-out from the interference fringe formation. The TIF also observed the contact angle increase from the fringe radius increase. This observation is uniquely reported as the interference fringe (IF) technique can detect the formation of interference fringe between the reflection from the center convex profile and the reflection from the edge concave profile on the far-field screen. Unlike general microscopy techniques, TIF can detect far-field interference fringes as it focuses beyond the droplet-substrate interface. The formation of the convex-concave profile during CCR evaporation is believed to be influenced by the non-uniform evaporative flux along the droplet surface. 

We show that the reflection interference fringe (RIF) is formed on a screen far away from the microdroplets placed on a prism-based substrate, which have low contact angles and thin droplet heights, caused by the dual convex–concave profile of the droplet, not a pure convex profile. The geometric formulation shows that the interference fringes are caused by the optical path difference when the reflected rays from the upper convex profile at the droplet–air interface interfere with reflection from the lower concave profile at oblique angles lower than the critical angle. Analytic solutions are obtained for the droplet height and the contact angle out of the fringe number and the fringe radius in RIF from the geometric formulation. Furthermore, the ray tracing simulation is conducted using the custom-designed code. The geometric formulation and the ray tracing show excellent agreement with the experimental observation in the relation between the droplet height and the fringe number and the relation between the contact angle and the fringe radius. This study is remarkable as the droplet's dual profile cannot be easily observed with the existing techniques. However, the RIF technique can effectively verify the existence of a dual profile of the microdroplets in a simple setup. In this work, the RIF technique is successfully developed as a new optical diagnostic technique to determine the microdroplet features, such as the dual profile, the height, the contact angle, the inflection point, and the precursor film thickness, by simply measuring the RIF patterns on the far-field screen.