Interference Colors Research Articles

First-Generation Radiolabeled Cyclic Peptides for Molecular Imaging of Platelet-Derived Growth Factor Receptor α.

Occult nodal spread and metastatic disease require longstanding imaging and biochemical assessments for thyroid cancer, a disease that has a propensity for diffuse, small-volume disease. We have developed a 64Cu-labeled platelet-derived growth factor receptor α (PDGFRA) antibody for immuno-PET of PDGFRA in metastatic papillary thyroid cancer (PTC). The present work describes the discovery of small cyclic PDGFRA-targeting peptides, their binding features, and radiolabeling with positron emitter gallium-68 (68Ga) for in vitro and in vivo characterization in thyroid cancer models. Phage-display technology with two separate libraries and seven different cell lines was used through three rounds of biopanning as well as flow cytometry and comparative analysis with recombinant protein to select specific peptide sequences. Phenotypic binding analysis was completed by using phosphorylation and cell migration assays. In vitro protein binding was analyzed with thermophoresis and flow cytometry using the fluorescent-labeled PDGFRA peptide. Peptide candidates were modified with the NOTA chelator for radiolabeling with 68Ga. In vitro cell uptake was studied in various thyroid cancer cell lines. In vivo studies of 68Ga-labeled peptides included metabolic stability and PET imaging. From the original library (1013 compounds), five different peptide groups were identified based on biopanning experiments with and without the α subunit of PDGFR, leading to ∼50 peptides. Subsequent phenotypic screening revealed two core peptide sequences (CP16 and CP18) that demonstrated significant changes in the level of PDGFRA phosphorylation and cell migration. Alanine scan sublibraries were created from these two lead peptide sequences, and peptides were radiolabeled using 68Ga-GaCl3 at pH 4.5, resulting in RCP > 95% within 34-40 min, including SPE purification. Cyclic peptide CP18.5 showed the strongest effects on cell migration, flow cytometry, and binding by visual interference color assay. 68Ga-labeled PDGFRA-targeting peptides showed elevated cell and tumor uptake in models of thyroid cancer, with 68Ga-NOTA-CP18.5 being the lead candidate. However, metabolic stability in vivo was compromised for 68Ga-NOTA-CP18.5 vs 68Ga-NOTA-CP18 but without impacting tumor uptake or clearance profiles. First-generation radiolabeled cyclic peptides have been developed as novel radiotracers, particularly 68Ga-NOTA-CP18.5, for the molecular imaging of PDGFRA in thyroid cancer.

Bioinspired transparent ultratough birefringent photonic films with engineerable interference colors derived from in-situ synthesis of CaCO3

Chameleons can rapidly modify their coloration by manipulating the arrangement of iridophores encompassing guanine crystals in their dermis, which enables incident light to undergo birefringence. Various biomaterials have been designed to mimic the arrangement of guanine crystals, yet instances of synthesizing bottom-up structures with anisotropy for optical functionality remain rare. In this study, we report a novel two-step gas diffusion method for in-situ synthesis of CaCO3 (Vaterite) within a hydrogel to fabricate a bio-photonic film displaying birefringence interference colors. This strategy enables the successful fabrication of an inorganic–organic photonic film with superior mechanical properties and flexibility, resulting in high transparency, superior toughness, and adjustable optical anisotropy. Through a combination of experiment and simulation results, we elucidated the critical role played by shape factor (distribution) and structural factor (particle size) in producing transmitted interference colors. Finally, the birefringent photonic films prepared using the dot-plate method can function as optical patterns accurately representing the “on”/“off” state within a binary system. This system offers high spatial resolution, excellent repeatability, and precise controllability of optical properties, making it applicable in fields such as information encryption and decrytion. Our study has successfully synthesized photonic material with anisotropic structure though in-situ method while elucidating the underlying mechanism governing their ability to generate transmission interference colors, thus opening up new avenues for transparent flexible polarized optics, imperceptible wearable devices, and advanced information encryption.

Anodic oxidation of wireless niobium electrode in bipolar electrochemistry

The anodic oxidation of a wireless niobium substrate serving as a bipolar electrode (BPE) in a direct or alternating current electric field was investigated in detail via spectrophotometry, electrochemical measurement, glow discharge–optical emission spectroscopy, and direct microscopic observation. Niobium oxide was a suitable material for the experiment because it is amorphous and can be evaluated through conventional electrochemical methods. It also has a clear interference color, enabling easy optical evaluation. The effect of the BPE configuration (e.g., vertical and horizontal alignments) in the cell on the anodic oxidation area was also investigated visually using the interference color. Transmission electron microscopy observation was also performed for an accurate measurement of the thickness of the anodic film formed on the niobium BPE. Although the basic film formation behavior and film composition were consistent with those in conventional anodization, even in wireless operation, the effective voltage directly contributing to film formation was found to be lower than the applied voltage (30%–70% of the applied voltage), depending on the electrolysis conditions.

Geology and characteristics of petrographic rocks in the region of Trepça, Kosovo

Purpose. The purpose of this paper is to accomplish a thorough identification of rock types occurring within the Mitrovica region by describing in detail all encountered varieties. The authors aim to determine the discontinuity or continuity of all inter-formational boundaries, crucial for accurate delineation on the ground and complete reflection on a 1:25000 scale map. Additionally, the objective is to identify the nature of contact between rock types and provide a detailed their description. Methods. Field exploration in the Mitrovica region was conducted for several months. Rock identification involved detailed sampling and petrographic analysis, including thin section preparation of magmatic rocks. The method included sample preparation, polarized light source interactions with minerals and observation of optical properties. Key properties observed are birefringence, interference colors, extinction angles, identification and analysis. Findings. Based on the study of stratigraphic units and geological descriptions of mineral outcrop areas, various types of rocks through petrographic microscope preparation, as well as chemical and geochemical analyses, have been differentiated. The Mitrovica area encompasses the following lithostratigraphic units: harzburgite, gabbro, diabase, metasandstone, sandstone, quartzite and grainstone with calcium (Aeolisaccus sp.; Bioclastic grainstone with dacycladal algae and small milliolides; Salpin-goporella sp.). Originality. The originality of the research lies in employing an optical microscope for the precise identification of rocks. Through the re-search carried out in the study area, we obtained a comprehensive petrographic description of mineral composition, texture, and mineralization, facilitating the assessment of the area exploitation potential. Practical implications. The petrographic exploration yielded the conclusion that the Pb-Zn mineralization is present in the study area, which is a sig-nificant finding for the advancement of the mining sector and the local community, provided that environmental preservation measures are upheld and responsible methods of area exploitation are implemented.

Tunable and Non-Invasive Printing of Transmissive Interference Colors with 2D Material Inks.

Interference colors hold significant importance in optics and arts. Current methods for printing interference colors entail complex procedures and large-scale printing systems for the scarcity of inks that exhibit both sensitivity and tunability to external fields. The production of highly transparent inks capable of rendering transmissive colors has presented ongoing challenges. Here, a type of paramagnetic ink based on 2D materials that exhibit polychrome in one magnetic field is invented. By precisely manipulating the doping ratio of magnetic elements within titanate nanosheets, the magneto-optical sensitivity named Cotton-Mouton coefficient is engineerable from 728 to a record high value of 3272 m-1 T-2, with negligible influence on its intrinsic wide optical bandgap. Combined with the sensitive and controllable magneto-responsiveness of the ink, modulate and non-invasively print transmissive interference colors using small permanent magnets are precised. This work paves the way for preparing transmissive interference colors in an energy-saving and damage-free manner, which can expand its use in widespread areas.

Tunable colors from responsive 2D materials

AbstractOne of the long‐sought‐after goals in responsive material development is to generate and tune colors for advanced and emerging applications such as dynamic displays, light‐emitting diodes, lasers, smart windows, chromic fabrics, high‐security encryption, and visual sensors. Benefiting from the atomically thin nature as well as strong optical interaction, two‐dimensional (2D) materials can serve as color‐generating centers for both chemical pigment colors and physical interference colors in solution, gels, films, and matrix interface systems, to offer new promises for color science and applications. Concerning color tunability, 2D material systems have been demonstrated as one of the ideal responsive materials to achieve the desired goals, including the change of composition, layer thickness, strain, magic angle, and thermally/photically/chemically responsive, magnetically‐responsive, electrically‐responsive, mechanically‐responsive. This makes it an attractive prospect for device applications such as optoelectronics, displays, and nanomedicine. However, to the best of our knowledge, no comprehensive review has been reported specifically on color‐centered aspects of 2D materials. In this review, we highlight experimental approaches and related applications for tuning pigment colors, reflective structural colors, and transmissive interference colors, and we refine the challenges and propose opportunities in future studies for the further development of color science in the 2D material system. Eventually, it is anticipated that this review will serve as a resource and source of inspiration for scientists, as well as open up new avenues for the advancement of color science and related fields in responsive 2D material systems.

Design and Fabrication of Biosensor for a Specific Microbe by Silicon-Based Interference Color System.

In this paper, one of the great challenges faced by silicon-based biosensors is resolved using a biomaterial multilayer. Tiny biomolecules are deposited on silicon substrates, producing devices that have the ability to act as iridescent color sensors. The color is formed by a coating of uniform microstructures through the interference of light. The system exploits a flat, RNA-aptamer-coated silicon-based surface to which captured microbes are covalently attached. Silicon surfaces are encompassed with the layer-by-layer deposition of biomolecules, as characterized by atomic force microscopy and X-ray photoelectron spectroscopy. Furthermore, the results demonstrate an application of an RNA aptamer chip for sensing a specific bacterium. Interestingly, the detection limit for the microbe was observed to be 2 × 106 CFUmL-1 by visually observed color changes, which were confirmed further using UV-Vis reflectance spectrophotometry. In this report, a flexible method has been developed for the detection of the pathogen Sphingobium yanoikuyae, which is found in non-beverage alcohols. The optimized system is capable of detecting the specific target microbe. The simple concept of these iridescent color changes is mainly derived from the increase in thickness of the nano-ordered layers.

Highly anisotropic and stretchable birefringent elastomers for multicolored strain displays

The birefringent response of elastomer materials with rich polarized interference colors is promising in the field of stretchable optical areas. Increasing the accessible change number of interference colors during stretching birefringent materials is important for optical strain display. Here, we can fabricate birefringent elastomers with multicolor response of polarized interference color via compositing with highly oriented cellulose nanocrystals (CNCs), transparent one-dimensional biomass nanocrystals with excellent birefringent properties, which exhibit sensitive, reversible, and controllable changes of interference color during stretching in perpendicular to the orientation of the CNCs. Employing a layer-by-layer shearing process of CNC aqueous dispersion, solvent exchange of monomers, and in-situ polymerization, we can produce birefringent elastomers with high optical path difference (>1500 nm) due to the high birefringence (2.81 × 10−3) and high thickness (within 1 mm). In addition, the high retardation of the birefringent elastomers is conducive to more interference color changes when stretching perpendicularly to the direction of oriented CNCs. Then, we demonstrate this birefringent material capable of fabricating a polarized-optical strain display by utilizing the multicolored responses during the stretching process.

Photo‐Arbuzov Reactions as a Broadly Applicable Surface Modification Strategy

AbstractChemical vapor deposition (CVD) polymerization is a commonly used approach in surface chemistry, providing a substrate‐independent platform for bioactive surface functionalization strategies. This work investigates the Arbuzov reaction of halogenated polymer coatings readily available via CVD polymerization, using poly(4‐chloro‐para‐xylylene) (Parylene C) as a model substance. Postpolymerization modification of these coatings via catalyst‐free and UV‐induced Arbuzov reaction using phosphites results in phosphonate‐functionalized polymers. The combination of infrared reflection‐absorption spectroscopy (IRRAS), X‐ray photoelectron spectroscopy (XPS), and time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) provides detailed insights into the reaction progress. Time‐dependent studies suggest that the non‐polar phosphites penetrate deep into the CVD films and react with the polymer film. In addition, ToF‐SIMS, scanning electron microscopy (SEM), and atomic force microscopy (AFM) confirm spatial control of the reaction, resulting in localized chemical and topographical surface modification, recognizable by changes in interference color, fluorescence, and wettability. Preliminary 3D fluorescence spectroscopy investigations indicate tunable near‐infrared emission of these polymer films. This work is the first step toward generating multifunctional polymer coatings based on chemically modifiable, CVD polymers with potential applications in biomaterials, sensors, or optoelectronics.

Influence of geographical origin and shell positions on nacre color and thickness in mabé pearl oysters Pteria penguin

To examine variations in nacre color and thickness in Pteria penguin oysters obtained from Tonga and Japan, a novel approach with a focus on their potential for mabé pearl production was used. Detailed analyses of color and microstructure revealed that the middle position of the right-valve nacre (position 1) primarily showed a reduction in yellow pigmentation. This was indicated by a decrease in the yellowness index (YI) and an increase in the whiteness index (WI). In contrast, the anterior and middle positions of the left-valve nacre (positions 2 and 3) consistently displayed a higher level of yellow pigmentation. A comparison of oysters from different geographical origin found that Tonga wild-caught oysters had significantly thicker nacre than Tonga culture-site oysters, suggesting the influence of probable genetic diversity and environmental factors on nacre formation. Notably, nacre at position 1 was generally thinner, while at positions 2 and 3 it was thicker, which would influence the resultant pearl quality and attributes. We demonstrate the significance of the nacre position on the valve for mabé pearl production: position 1 tended to produce white pearls with pronounced interference colors, whereas position 2 tended to yield gold pearls. Furthermore, our findings highlight the significant impact of the oysters' geographic origin on mabé pearl color and quality. This study emphasizes the importance of considering the position of shell nacre and the potential influences of the oysters' genetic origins and environmental factors on mabé pearl formation.

A new approach to the textural interpretation of magnetically aligned nematic and cholesteric lyotropic mesophases by using plate-λ accessory

ABSTRACT Lyotropic liquid crystals are substances formed by anisotropic micelles. Their unit structure change with the concentration and temperature and, as a consequence, the optical anisotropy changes. A measurable optical parameter, which reflects these anisotropies, is the refractive indices. Using these indices, it is possible to represent the anisotropic medium by indicatrix figures. In this sense, the indicatrix orientations will be interpreted in this work along the discotic nematic ( N D ) – biaxial nematic ( N B ) – calamitic nematic ( N C ) phases using a plate- λ accessory, from the polarized light microscopy, to modify the interference colors along the Michel-Lévy chart of the textures exhibited by the sample. Furthermore, the discotic cholesteric ( C h D ) – biaxial cholesteric ( C h B ) – N C ∗ [ unwounded calamitic cholesteric ( C h C ) ] phases are also investigated by the same methodology. The optic sign is also discussed here. In addition, we will also present a procedure that may help us to recognize the N B − N C phase transition from the microscopic textures.

Smectic and Soap Bubble Optofluidic Lasers

Soap bubbles are simple, yet very unique and marvelous objects. They exhibit a number of interesting properties such as beautiful interference colors and the formation of minimal surfaces. Various optical phenomena have been studied in soap films and bubbles, but so far they have not been employed as optical cavities. Here we demonstrate that dye doped soap or smectic liquid crystal bubbles can support whispering gallery mode lasing, which is observed in the spectrum as hundreds of regularly spaced peaks, resembling a frequency comb. The lasing enabled the measurement of size changes as small as 10 nm in a millimeter-sized, ∼100−nm-thick bubble. Bubble lasers were used as extremely sensitive electric field sensors with a smallest measurable electric field of 110 Vm−1 Hz−1/2. They also enable the measurement of pressures up to a 100 bar with a resolution of 1.5 Pa, resulting in a dynamic range of almost 107. By connecting the bubble to a reservoir of air, almost arbitrarily low pressure changes can be measured while maintaining an outstanding dynamic range. The demonstrated soap bubble lasers are a very unique type of microcavities which are one of the best electric field and pressure microsensors to date and could in the future also be employed to study thin films and cavity optomechanics. Published by the American Physical Society 2024

A highly birefringent metal-free crystal assembled by cooperative non-covalent interactions.

Birefringent crystals can manipulate the phase and polarization of light, so they are widely used as essential components in various optical devices. Common strategies to construct birefringent crystals are introducing metal cations that are either able to realize favorable coordination with functional anionic units or are susceptible to polarizability anisotropy. Herein, we report a metal-free crystal, NH4(H2C6N7O3)·2H2O, synthesized using the facile solution method. In the crystal structure of NH4(H2C6N7O3)·2H2O, (H2C6N7O3)- functional units are assembled in an optimal manner by cooperative non-covalent interactions, i.e., hydrogen bonding and π-π interactions. As a result, this metal-free crystal possesses exceptional birefringence up to 0.54@550 nm, which is larger than those of most metal-containing birefringent crystals. In addition, the interference color of this crystal does not change obviously from 243 K to 313 K, indicating that the birefringence is robust at different temperatures. This work will inspire useful insights into the role of non-covalent interactions in designing outstanding birefringent crystals for efficient polarized optical devices.

Mineralogy and Geochemical Characteristics of Scheelite Deposit at Xuebaoding in Pingwu, Sichuan Province, China

Featuring subtle lithological alterations in the host rocks and containing colossal gemstone crystals, the scheelite deposit at Xuebaoding in the Pingwu region of Sichuan Province exhibits characteristics typical of a vein-like hydrothermal-type deposit. The scheelite from the Xuebaoding region is renowned for its high saturation of color, perfect crystal shape, and pure color. In this study, its crystal structure and mineralogical, geochemical, and in situ Sr-Nd isotope characteristics are all systematically characterized. Our objective is to determine the source of ore-forming materials, the timing of the mineralization, and the chemical composition of scheelite, including major elements, trace elements, and rare earths elements (REE). The scheelite samples were analyzed with a variety of methods such as polarizing microscopy, X-ray powder diffraction (XRD), X-ray fluorescence spectrometry (XRF), electron probing, and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). In addition, conventional gemological tests were performed using instruments including gemstone microscopes, GI-UVB ultraviolet fluorescent lamps, grating spectroscopy, etc. The results demonstrate that scheelite exhibits a high refractive index, excellent crystallinity, and a granular structure. Clear color bands and ring structures are observed within the minerals, accompanied by interference colors of light blue, blue, and yellow. Additionally, the mineral components are relatively concentrated, with muscovite and illite serving as accessory minerals. Furthermore, the chemical composition of scheelite reveals a WO3/CaO mass ratio that approaches or exceeds the ideal value. Moreover, it exhibits a wide range of variations in total rare earth element (∑REE) content, which is characterized by an enrichment of light rare earths (LREE), significant negative Eu anomalies, and insignificant Ce anomalies. In addition, the metallogenic formation of scheelite can be estimated to have occurred during the Toarcian stage in the Lower Jurassic Epoch period, approximately 183 Ma. The study further revealed that A-type granite serves as the genesis type of scheelite, with most of the ore-forming materials originating from the upper crust and a few derived from younger crustal sources.

Optimized procedure for conventional TEM sample preparation using birefringence

Specimens for quality transmission electron microscopy (TEM) analyses must fulfil a range of requirements, which demand high precision during the prior preparation process. In this work, an optimized procedure for conventional TEM specimen preparation is presented that exploits the thickness-dependence of interference colors occurring in birefringent materials. It facilitates the correct estimation of specimen thickness to avoid damage or breaking during mechanical thinning and reduces ion-milling times below 30minutes. The benefits of the approach are shown on sapphire and silicon carbide cross-section samples. The presented method is equally suitable for assessing specimen thickness during dimpling and wedge-polishing, and is particularly useful at thicknesses below 20 μm, where the accuracy of mechanical techniques is insufficient. It is precise enough to be employed for a visual thickness estimation during the thinning process, but can be additionally optimized by analyzing the RGB spectrum of the occurring interference colors.

Bio-inspired structural coloration of carbon fiber based on thin film interference: Synergistically enhancing thermal durability, tensile strength and interface properties of colored fiber

Carbon fiber (CF) is inert to dyes or pigments, thus its products usually exhibit a drab black and unexciting look. The bio-inspired structural coloration may provide a dye-free method to color CF. Herein, inspired by the interference colors of the insect's wing, a dye-free structural coloration method is proposed to color CF. A layer of poly(cyclotriphosphazene-co-4,4′-oxydianiline) film is assembled on the CF surface by in situ polymerization under a mild reaction condition, creating vivid colors based on thin film interference. Moreover, the structural color shows excellent thermal durability due to the good thermo‑oxygen stability of NP heterocycles and cross-linked networks in coloration film. Furthermore, the tensile strength of colored CF and the interfacial adhesion between colored CF and resin are also synergistically improved by 17.1% and 48.7%, respectively, because of the sturdiness and surface chemical activity of coloration film. In brief, the colored CF may have potential in designing and preparing new structural and functional composites.

A Two-Dimensional Hybrid Perovskite With Heat Switching Birefringence.

Birefringent crystals that can switch light polarization have important applications in optoelectronics. In the last decades, birefringence is mostly optimizedby chemical strategies. Recently, switching birefringence by physical means has attracted much attention. Here, this work reports the observation of heat switching birefringence in a 2D layered hybrid halide perovskite (C2N3H4)2PbCl4 ([C2N3H4]+ = 1,2,4-triazolium). This heat switching birefringence leads to a significant change in the interference color for the crystal plate under the illumination of orthogonal polarized light. Structure analyses reveal a heat dependent structure transition in (C2N3H4)2PbCl4, whose birefringence is switched by the change in the distortion degree of PbCl6 octahedron. This discovery may be beneficial to the further development of stimuli-responsive polarization optical devices.

A Two‐Dimensional Hybrid Perovskite With Heat Switching Birefringence

AbstractBirefringent crystals that can switch light polarization have important applications in optoelectronics. In the last decades, birefringence is mostly optimized by chemical strategies. Recently, switching birefringence by physical means has attracted much attention. Here, this work reports the observation of heat switching birefringence in a 2D layered hybrid halide perovskite (C2N3H4)2PbCl4 ((C2N3H4)+=1,2,4‐triazolium). This heat switching birefringence leads to a significant change in the interference color for the crystal plate under the illumination of orthogonal polarized light. Structure analyses reveal a heat dependent structure transition in (C2N3H4)2PbCl4, whose birefringence is switched by the change in the distortion degree of PbCl6 octahedron. This discovery may be beneficial to the further development of stimuli‐responsive polarization optical devices.

The geochemistry and geochronology of garnet from the Jinchanghe Fe-Cu-Pb-Zn deposit, Baoshan Block, western Yunnan

The Jinchanghe polymetallic Fe-Cu-Pb-Zn deposit is located in the northern region of the Baoshan Block in western Yunnan. Using electron probe micro-analysis and laser ablation inductively coupled plasma mass spectrometry, we analyzed the major, trace, and rare earth elemental contents of garnets from the Jinchanghe deposit. Moreover, U-Pb dating was performed using the laser ablation sector field inductively coupled plasma mass spectrometry (LA-SF-ICP-MS) method to determine the direct mineralization age of the Jinchanghe deposit. Petrographic analyses revealed three garnet generations: early (GrtI), middle (GrtII), and late (GrtIII). GrtI (And55.69-64.47Gro30.28-41.21Ura + Pyr + Spe + Alm2.35-5.49) was characterized by irregular shapes and weak optical properties, and primarily comprised Fe-rich grossular. GrtII (And53.69-96.17Gro2.78-45.07Ura + Pyr + Spe + Alm0.59-2.12) was characterized by andradite, in which GrtIIa was a homogeneous body, whereas GrtIIb shows exhibited oscillatory zoning with abnormal interference colors. Fine-veined andradite aggregates were predominant in GrtIII (And70.51-90.33Gro6.34-27.80Ura + Pyr + Spe + Alm1.03-3.32). The GrtI, GrtIIa, and the rims of GrtIIb were depleted in heavy rare earth elements and enriched in light rare earth elements, with positive Eu anomalies, indicating that these garnets crystallized from mildly acidic magmatic hydrothermal fluids. However, the cores of GrtIIb had negative Eu anomalies and may have crystallized from a relatively neutral Cl-rich fluid. GrtIII was severely depleted in light rare earth elements with positive Eu anomalies, indicating the presence of a weakly acidic environment. Accordingly, owing to a decrease in temperature and an increase in oxygen fugacity, the pH of the Jinchanghe deposit may have transitioned from an early weakly acidic to neutral, then to a late weakly acidic environment. Furthermore, the ages of GrtII and GrtIII ranged from 520 to 496 Ma, which places the formation of the Jinchanghe deposit during the Late Cambrian. The deposit is closely related to the arc magmatic rocks produced by the subduction of the Proto-Tethys Ocean.

Coherence effects on the interference colors of soap films

Acquiring the thickness field of a soap film from interference colors requires an accurate relationship between color and film thickness. Throughout the literature, an interference relation derived using monochromatic waves is widely used to calculate the colors of soap films illuminated by light sources with significant frequency bandwidths by applying the relation at a number of discrete wavelengths in the source, which assumes that the interfering waves are perfectly coherent. However, since the coherence between waves is expected to decrease with increasing film thickness, it is poorly understood when interference relations derived using monochromatic waves can be applied. In this study, an interference relation incorporating the coherence between interfering waves is derived. The effects of coherence on the interference colors of soap films are then studied by comparing the colors computed using each of these two interference relations for light sources with different frequency bandwidths. As the frequency bandwidth of the light source increases, the difference in the colors computed using each interference relation increases, which implies that the accuracy of the method involving the monochromatic relation decreases with increasing frequency bandwidth of the source. The findings of this study will allow for more accurate measurements of the thickness of soap films from their interference colors.