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Partial Fractions01:28

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A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
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In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
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The signs and symptoms of fever include hot and dry skin, flushed face, thirst, muscle aches, anorexia, headache, tachycardia, tachypnea, and fatigue. Elevated body temperature is reduced using two methods: pharmacological and nonpharmacological. Proper identification and treatment of the root cause of a fever is of utmost importance.
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The partial pressure of a gas is a measure of the thermodynamic activity of the gas's molecules. The pressure that a gas would create if it occupied the total volume available is called the gas's partial pressure. If two or more gases are mixed together in a container, the molecules move randomly and collide with each other, causing them to reach thermal equilibrium. When the gases have the same temperature, their molecules have the same average kinetic energy. Thus, each gas obeys the...
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Reduced distortion in high-index microsphere imaging by partial immersion.

Songlin Yang, Xiaoqing Wang, Jianguo Wang

    Applied Optics
    |November 22, 2018
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    Pincushion distortion in BaTiO3 glass (BTG) microsphere imaging is reduced when partially immersed in SU-8 resist. This partial immersion maintains super-resolution imaging of sub-diffraction features on Blu-ray disks.

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    Area of Science:

    • Optics and Photonics
    • Materials Science
    • Nanotechnology

    Background:

    • Microsphere-based imaging offers potential for super-resolution microscopy.
    • Pincushion distortion can degrade image quality in such systems.
    • The choice of immersion medium affects optical performance.

    Purpose of the Study:

    • To investigate the effect of immersion medium thickness on pincushion distortion in BaTiO3 glass (BTG) microsphere imaging.
    • To evaluate the super-resolution imaging capability of BTG microspheres under different immersion conditions.
    • To correlate optical distortion with the position of photonic nanojets.

    Main Methods:

    • Experimental imaging of Blu-ray disk sub-diffraction features using BTG microspheres.
    • Varying the immersion medium (ethanol, SU-8 resist) and its layer thickness.
    • Optical distortion analysis and simulation using ZEMAX software.
    • Calculation of photonic nanojet positions.

    Main Results:

    • Significant pincushion distortion observed when BTG microspheres are fully immersed in ethanol or SU-8 resist.
    • Distortion is strongly dependent on the immersion medium's layer thickness.
    • Partial immersion in SU-8 resist (approx. 4/5 diameter) dramatically reduces distortion.
    • Super-resolution imaging of Blu-ray disk features is maintained with partial immersion.
    • Simulations confirm reduced distortion and photonic nanojet formation outside the microsphere.

    Conclusions:

    • Partial immersion of BTG microspheres in SU-8 resist is an effective strategy to mitigate pincushion distortion.
    • This technique preserves the super-resolution imaging capabilities of BTG microspheres.
    • Understanding immersion layer thickness is critical for optimizing microsphere-based super-resolution imaging systems.