What is Total Internal Reflection (TIR)
Total Internal Reflection (TIR)

Key Takeaways Total Internal Reflection (TIR) is a physics phenomenon where light transitions from a denser to a less dense medium, causing it to reflect back into the denser medium at a specific angle called the critical angle.  This occurs when the angle of incidence exceeds the critical angle, resulting in total internal reflection rather than refraction.  It has practical applications in optics, including creating mirages, enhancing diamond brilliance, designing prisms for image manipulation, and enabling efficient data transmission in optical fibers.  These applications exploit total internal reflection’s ability to manipulate light propagation for various technological advancements. What is Total Internal Reflection (TIR) Total internal reflection (TIR) is a phenomenon in physics where light rays travel from a more optically denser medium to a less optically denser medium. Consider the situation of a ray of light passing from water to air; the light ray is refracted at the junction of the two media, bending away from the normal due to the change in refractive indices. At a specific angle of incidence known as the critical angle, which is when the angle of refraction is 90 degrees, the incident ray is refracted in such a way that it travels along the surface of the water. Beyond the critical angle, the incident ray undergoes total internal reflection, reflecting back into the medium. In general, this phenomenon occurs when a ray of light in a medium with a higher index of refraction approaches another medium at an angle of incidence greater than the critical angle, which varies with the media involved. For a water-air surface, the critical angle is 48.5°, but it may slightly vary with wavelength and color due to the dependence of indices of refraction on these factors. At angles less than the critical angle, both refraction and reflection occur in varying proportions. Figure1. Total Internal Reflection TIR finds practical applications in various optical phenomena and technologies. Some notable applications include: Mirage: Mirage is an optical illusion caused by total internal reflection. During hot weather, the temperature difference between the ground and the air above can create conditions for TIR. Light from distant tall objects undergoes total internal reflection as it travels from denser, cooler air to rarer, hotter air, resulting in an inverted image observed by the observer. Diamond Cutting: The dazzling appearance of diamonds is attributed to the careful cutting by diamond craftsmen. By shaping the diamond to exploit total internal reflection, light entering the diamond undergoes multiple reflections. The small refractive index of diamond (approximately 24.4°) contributes to the diamond’s brilliance and sparkle. Prisms: Prisms are designed to utilize total internal reflection for various optical applications. When light enters a prism at a specific angle, it undergoes total internal reflection either at 90° or by 180°, producing an inverted image without altering the object’s size. Prisms are integral in optical systems for tasks such as dispersion and image rotation. Optical Fibers: Optical fibers, composed of glass or quartz, leverage total internal reflection for efficient data transmission. An optical fiber consists of a core and cladding, with the cladding having a lower refractive index than the core. Light signals transmitted through the optical fiber undergo repeated total internal reflections, ensuring minimal signal loss. Optical fibers are widely employed for high-speed data, signal, and video transmission, with the added advantage of maintaining data integrity even if the fiber is bent or twisted. Figure 2. Internal Reflection Understanding Total internal reflection TIR is a physics phenomenon occurring when light travels from a denser medium to a less dense medium, such as from water to air. When the angle of incidence exceeds a certain critical angle, specific to the media involved (48.5° for water-air), the light ray reflects entirely within the denser medium instead of refracting. This results in complete internal reflection rather than partial refraction. TIR has several practical applications: mirages, caused by light bending in hot air layers; diamond cutting, which uses TIR to enhance sparkle; prisms, which utilize TIR for image inversion and light dispersion; and optical fibers, where TIR allows efficient, high-speed data transmission with minimal signal loss. Related Content

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The Complete Guide to Aspheric Lens
Aspheric Lens

Product Highlights: Aspheric lens corrects spherical aberration, improving image quality. They feature varying curvature, unlike spherical lenses and spherical elements enhancing, enhancing precision.  Manufacturing methods include precision glass molding, precision polishing, and diamond turning, each with unique benefits and limitations. Material selection depends on application needs and manufacturing process compatibility.  Avantier offers comprehensive custom solutions, emphasizing precise specifications, material flexibility, and tailored designs. Selection criteria include application type and lens details.  Avantier’s manufacturing capability ensures precision, customization, and comprehensive support, vital for high-performance optics. Table of Contents The Complete Guide to Aspheric Lens Characteristics of Aspheric Lens Spherical Aberration Correction One of the most important features of aspheric lenses is their ability to correct for spherical aberration. Spherical aberration is found in all spherical lenses, such as plano-convex or double-convex lens shapes. However, aspheric lenses excel in focusing light to a precise point, resulting in minimal blur and enhanced image quality. Spherical Aberration is the consequence of the uniform curvature of the lens surface and not the result of a manufacturing error. The outer rays converge at a different focal point than the inner rays resulting in blurred or distorted images.  A spherical lens with a significant amount of aberration and an aspherical lens with almost no aberration can be seen(Figure 1). Aspherical Lenses address the issue by deviating from a perfectly spherical shape. An aspheric lens can be designed by modifying the curvature length and adjusting the conic constant and aspheric coefficients of the curved surface of the lens. By carefully shaping the lens, aspheric lenses ensure that all incoming light rays converge to a single focal point. minimizing spherical aberration and improving image quality.  Figure 1. Aspherical Lens (left) vs Spherical Lens (right) In Figure 1, the difference in focusing performance of spherical lenses and aspheric lenses is further explained by the table below.  It compares the performance of a spheric lens and an aspheric lens both with a diameter of 25mm and focal lengths of 25mm (f/1 lenses). The table presents a comparison of spot sizes, or blur sizes, for collimated 587.6nm light rays under different conditions: on-axis (0° object angle) and off-axis (at 0.5° and 1.0° object angles). The spot sizes of the asphere are significantly smaller, differing by several orders of magnitude compared to those of a spherical lens. Object Angle (°) 0.0 0.5 1.0 Spherical Spot Size (μm) 710.01 710.96 713.84 Aspheric Spot Size (μm) 71.43 3.91 8.11 Aspherical Lens Family Structure of an Aspheric Lens In various industries, ranging from automotive sensors and LED lighting systems to cutting-edge cameras and medical diagnostic devices, the significance of aspheric lenses is steadily growing. These lenses are part of the subset defined by rotationally symmetric optics with a radially varying radius of curvature. Aspheric lenses play an increasingly crucial role in various aspects of the optics, imaging, and photonics industries. This is attributed to the unique advantages they provide compared to traditional spherical optics  and spherical elements. Unlike spherical lenses, which can be specified solely by the radius of curvature that fluctuates radially from the center of the lens, aspheric lenses exhibit a surface with varying local radii of curvature. The definition of rotationally symmetric aspheres often involves a surface sagitta (the measure of the surface shape in relation to a plane), or sag, expressed through an even aspheric polynomial. Where: Z: sag of surface parallel to the optical axis s: radial distance from the optical axis C: curvature, inverse of radius k: conic constant A4, A6, …: 4th, 6th, … order aspheric coefficients When the aspheric coefficients are equal to zero, the resulting aspheric surface is considered to be a conic. The following table shows how the actual conic surface generated depends on the magnitude and sign of the conic constant, k. Additional Performance Advantages To achieve the necessary performance of an imaging lens, optical elements designers frequently resort to stopping down, or increasing the f/# of their design. Although the desired resolution goal is obtained, the approach results in a reduction in light throughput. Using aspheric lenses in the design, however, ​​improves aberration correction and enables the creation of high-throughput systems with low f/#s, while also maintaining excellent image quality. The following table compares two designs: an 81.5mm focal length, f/2 triplet lens (depicted in Figure 2) with all spherical surfaces and the same triplet with an aspheric first surface. Both designs utilize identical effective focal length, f/#, field of view, glass types, and total system length. The table provides a comparison of the modulation transfer function (MTF) at 20% contrast for on-axis and off-axis collimated, polychromatic light rays at 486.1nm, 587.6nm, and 656.3nm. The triplet lens with the aspheric surface demonstrates significantly improved imaging performance at all field angles with high tangential and sagittal resolution values, surpassing those of the triplet with only spherical surfaces by factors as high as four. Figure 2. Polychromatic light focused through a triplet lens Object Angle (°) All Spherical Surfaces Aspherical First Surfaces Tangential* Sagittal* Tangential* Sagittal* 0.0 13.3 13.3 61.9 61.9 7.0 14.9 14.9 31.1 40.9 10.0 17.3 14.8 36.3 41.5 “Tangential” and “Sagittal” units are both described as Benefit of Aspheric Lenses Unlike conventional spherical optics, aspheric lenses use less elements to enhance aberration correction. An example would be zoom lenses. Zoom lenses typically use ten or more elements while two aspheric lenses can be replaced for a handful of spherical lenses in order to achieve similar or better optical results. The system size and overall cost of production are also potentially reduced. Aspheric Surface Tolerances Surface Accuracy: Surface Accuracy is the measurement of how similar the intended shape is to the desired shape. There are many ways to measure and define surface accuracy and the errors that occur. The errors can be grouped into three categories depending on their frequency across the surface of a part: form errors, waviness, and surface roughness. Form error, or irregularity, is a low frequency variation or a larger-scale error. They are the most important and frequently specified

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