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Related Concept Videos

Active Filters01:25

Active Filters

Active filters are electronic circuits that use operational amplifiers (op-amps), resistors, and capacitors to filter out unwanted frequency components from a signal. A first-order low-pass active filter is designed to pass signals with a frequency lower than a certain cutoff frequency and attenuate frequencies higher than that cutoff frequency. The transfer function for a first-order low-pass active filter is:
Passive Filters01:27

Passive Filters

Passive filters are utilized to shape the frequency spectrum of signals across a diverse array of applications. These filters, using only passive elements like resistors (R), inductors (L), and capacitors (C), are capable of selectively allowing or blocking certain frequency ranges without the need for external power sources.
Low-Pass Filters
Low-pass filters are designed to transmit signals with frequencies lower than the cutoff frequency, ωc, and attenuate those above it. The cutoff frequency...
Law of Rational Indices01:29

Law of Rational Indices

The Law of rational indices is a fundamental principle in the field of crystallography. According to this law, the intercepts of a crystal face along the crystallographic axes (the three-dimensional axes along which a crystal is measured) can be expressed as either equivalent to the unit intercepts (a, b, c) or simple whole number multiples of them. These multiples are typically denoted as na, n'b, and n''c, where n, n', and n'' are simple whole numbers.To illustrate, consider a crystal with...
Filtration00:53

Filtration

Filtration is a physical separation process that involves passing a suspension through a porous medium to separate solids from fluids. During filtration, solids collect on the porous medium while liquids, also collectively known as the filtrate, pass through. The filtration medium is selected based on the filtration purpose, quantity, and nature of the precipitate. The general criteria for a suitable filtering medium are that it is inert, mechanically strong, nonabsorbent toward dissolved...
UV–Vis Spectroscopy: Woodward–Fieser Rules01:29

UV–Vis Spectroscopy: Woodward–Fieser Rules

UV–Visible absorption spectra of conjugated dienes arise from the lowest energy π → π* transitions. The light-absorbing part of the molecule is called the chromophore, and the substituents directly attached to the chromophore are called auxochromes. A strong correlation exists between the absorption maxima, λmax, and the structure of a conjugated π system. The Woodward–Fieser rules predict the value of λmax for a given structure by adding the contributions...
Focusing of Light in the Eye01:16

Focusing of Light in the Eye

Light rays enter the eye through the cornea, a transparent dome-shaped tissue that is the eye's outermost layer. The cornea bends or refracts, light rays traveling to the pupil. The shape of the cornea determines how much of the light is bent and whether the image will be focused correctly on the retina at the back of the eye. Once the light has passed through both refraction layers, it converges into a single focal point onto a small area. This is where photoreceptors start transforming...

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In Situ Measurement of Vacuum Window Birefringence using 25Mg+ Fluorescence
07:03

In Situ Measurement of Vacuum Window Birefringence using 25Mg+ Fluorescence

Published on: June 13, 2020

Precise and versatile formula for birefringent filters.

Z Shao

    Applied Optics
    |November 25, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study presents a precise formula for birefringent filters, improving upon approximations for extraordinary ray behavior in uniaxial crystals. The new formula enables wider laser tuning ranges, especially for filters with inclined optical axes.

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    Area of Science:

    • Optics and Photonics
    • Crystalline Optics
    • Laser Technology

    Background:

    • Existing formulas for birefringent filters often rely on approximations for extraordinary ray (E-ray) behavior and refractive index in uniaxial crystals.
    • These approximations can lead to inaccuracies, particularly concerning the optical path difference and tuning capabilities of the filters.

    Purpose of the Study:

    • To develop a precise and versatile formula for birefringent filters based on the exact construction of the optical path difference.
    • To overcome limitations of previous approximations, such as Δn = n(o) - n(e) ≤ (or n(e)) and sin(θ)sin(r(ω)) = n(e).
    • To investigate the applicability of the formula to filters with optical axes parallel (PAPS) and inclined (PAIS) to the entrance surface.

    Main Methods:

    • Derived a new formula for birefringent filters using the exact geometric construction of the optical path difference.
    • Analyzed the formula's validity for both PAPS and PAIS configurations.
    • Evaluated the tuning range capabilities of FAIS (Filter with Axis Inclined to the Surface) compared to FAPS (Filter with Optical Axis Parallel to the Surface).

    Main Results:

    • The exact construction accurately predicts the variation in position and dimension, yielding the correct optical path difference during filter tuning.
    • The derived formula is applicable to both PAPS and PAIS filters.
    • A FAIS demonstrates a wider laser wavelength tuning range compared to a FAPS, attributed to greater refractive index variation.

    Conclusions:

    • The developed formula provides a more accurate method for designing birefringent filters, especially for applications requiring precise optical path difference calculations.
    • Filters with inclined optical axes (FAIS) offer superior wavelength tunability for lasers.
    • The formula was successfully applied to design a FAIS for tuning a continuous-wave Ti:sapphire laser.