diffraction grating
Definition: Diffraction grating denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: Light incident on a periodic diffraction grating (groove spacing d) constructively interferes at specific angles θ_m for which the path-length difference between adjacent grooves equals an integer number of wavelengths: the grating equation, mλ = d(sinθ_i + sinθ_m), with m the (integer)...
Why it matters here: Lectures 01-08 covered imaging: recording an object’s brightness and broadband color. Astronomical spectroscopy, this course’s next major topic, instead records how brightness varies with wavelength in fine detail, the technique behind measuring radial velocities, chemical abundances, and physical conditions in astronomical...
Relationships: It is used with groove density to interpret the lecture model. The quantitative connection is the working relation \(m\lambda = d\left(\sin\theta_i + \sin\theta_m\right), \qquad \dfrac{d\theta}{d\lambda} = \dfrac{m}{d\cos\theta_m}\).
Boundary or common confusion: Assuming a grating disperses light only in the commonly used first order. Real gratings simultaneously produce multiple overlapping orders at different angles for different wavelengths; every practical spectrograph design must explicitly account for and, where necessary, suppress unwanted orders (with order-blocking filters) or exploit them deliberately...
groove density
Definition: Groove density denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: Every commercial spectrograph and grating monochromator specification sheet states groove density (grooves/mm) and blaze angle, and reports its dispersion (nm per mm at the focal plane, or resolving power) as a direct, computable consequence of those two numbers via the grating equation,...
Why it matters here: Lectures 01-08 covered imaging: recording an object’s brightness and broadband color. Astronomical spectroscopy, this course’s next major topic, instead records how brightness varies with wavelength in fine detail, the technique behind measuring radial velocities, chemical abundances, and physical conditions in astronomical...
Relationships: It is used with diffraction grating, grating equation to interpret the lecture model. The quantitative connection is the working relation \(m\lambda = d\left(\sin\theta_i + \sin\theta_m\right), \qquad \dfrac{d\theta}{d\lambda} = \dfrac{m}{d\cos\theta_m}\).
Boundary or common confusion: Assuming a grating disperses light only in the commonly used first order. Real gratings simultaneously produce multiple overlapping orders at different angles for different wavelengths; every practical spectrograph design must explicitly account for and, where necessary, suppress unwanted orders (with order-blocking filters) or exploit them deliberately...
grating equation
Definition: Grating equation denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: Light incident on a periodic diffraction grating (groove spacing d) constructively interferes at specific angles θ_m for which the path-length difference between adjacent grooves equals an integer number of wavelengths: the grating equation, mλ = d(sinθ_i + sinθ_m), with m the (integer)...
Why it matters here: Lectures 01-08 covered imaging: recording an object’s brightness and broadband color. Astronomical spectroscopy, this course’s next major topic, instead records how brightness varies with wavelength in fine detail, the technique behind measuring radial velocities, chemical abundances, and physical conditions in astronomical...
Relationships: It is used with groove density, diffraction order to interpret the lecture model. The quantitative connection is the working relation \(m\lambda = d\left(\sin\theta_i + \sin\theta_m\right), \qquad \dfrac{d\theta}{d\lambda} = \dfrac{m}{d\cos\theta_m}\).
Boundary or common confusion: Assuming a grating disperses light only in the commonly used first order. Real gratings simultaneously produce multiple overlapping orders at different angles for different wavelengths; every practical spectrograph design must explicitly account for and, where necessary, suppress unwanted orders (with order-blocking filters) or exploit them deliberately...
diffraction order
Definition: Diffraction order denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: Light incident on a periodic diffraction grating (groove spacing d) constructively interferes at specific angles θ_m for which the path-length difference between adjacent grooves equals an integer number of wavelengths: the grating equation, mλ = d(sinθ_i + sinθ_m), with m the (integer)...
Why it matters here: Lectures 01-08 covered imaging: recording an object’s brightness and broadband color. Astronomical spectroscopy, this course’s next major topic, instead records how brightness varies with wavelength in fine detail, the technique behind measuring radial velocities, chemical abundances, and physical conditions in astronomical...
Relationships: It is used with grating equation, angular dispersion to interpret the lecture model. The quantitative connection is the working relation \(m\lambda = d\left(\sin\theta_i + \sin\theta_m\right), \qquad \dfrac{d\theta}{d\lambda} = \dfrac{m}{d\cos\theta_m}\).
Boundary or common confusion: Assuming a grating disperses light only in the commonly used first order. Real gratings simultaneously produce multiple overlapping orders at different angles for different wavelengths; every practical spectrograph design must explicitly account for and, where necessary, suppress unwanted orders (with order-blocking filters) or exploit them deliberately...
angular dispersion
Definition: Angular dispersion denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: Differentiating the grating equation with respect to wavelength gives the angular dispersion, dθ/dλ = m/(d cosθ_m): higher diffraction order m and finer groove spacing d both increase angular dispersion, spreading a given wavelength range over a larger angle (and, at the focal plane, over...
Why it matters here: Lectures 01-08 covered imaging: recording an object’s brightness and broadband color. Astronomical spectroscopy, this course’s next major topic, instead records how brightness varies with wavelength in fine detail, the technique behind measuring radial velocities, chemical abundances, and physical conditions in astronomical...
Relationships: It is used with diffraction order, free spectral range to interpret the lecture model. The quantitative connection is the working relation \(m\lambda = d\left(\sin\theta_i + \sin\theta_m\right), \qquad \dfrac{d\theta}{d\lambda} = \dfrac{m}{d\cos\theta_m}\).
Boundary or common confusion: Assuming a grating disperses light only in the commonly used first order. Real gratings simultaneously produce multiple overlapping orders at different angles for different wavelengths; every practical spectrograph design must explicitly account for and, where necessary, suppress unwanted orders (with order-blocking filters) or exploit them deliberately...
free spectral range
Definition: Free spectral range denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: A grating’s free spectral range, the wavelength interval over which order m does not overlap order m+1, shrinks as Δλ ≈ λ/m; this means high orders give large dispersion (good for resolving power, Lecture 10) but at the cost of a narrow, order-overlapping wavelength window, which is...
Why it matters here: Lectures 01-08 covered imaging: recording an object’s brightness and broadband color. Astronomical spectroscopy, this course’s next major topic, instead records how brightness varies with wavelength in fine detail, the technique behind measuring radial velocities, chemical abundances, and physical conditions in astronomical...
Relationships: It is used with angular dispersion, blaze angle to interpret the lecture model. The quantitative connection is the working relation \(m\lambda = d\left(\sin\theta_i + \sin\theta_m\right), \qquad \dfrac{d\theta}{d\lambda} = \dfrac{m}{d\cos\theta_m}\).
Boundary or common confusion: Assuming a grating disperses light only in the commonly used first order. Real gratings simultaneously produce multiple overlapping orders at different angles for different wavelengths; every practical spectrograph design must explicitly account for and, where necessary, suppress unwanted orders (with order-blocking filters) or exploit them deliberately...
blaze angle
Definition: Blaze angle denotes the physical quantity, process, or instrument component captured by this lecture-specific statement: Every commercial spectrograph and grating monochromator specification sheet states groove density (grooves/mm) and blaze angle, and reports its dispersion (nm per mm at the focal plane, or resolving power) as a direct, computable consequence of those two numbers via the grating equation,...
Why it matters here: Lectures 01-08 covered imaging: recording an object’s brightness and broadband color. Astronomical spectroscopy, this course’s next major topic, instead records how brightness varies with wavelength in fine detail, the technique behind measuring radial velocities, chemical abundances, and physical conditions in astronomical...
Relationships: It is used with free spectral range to interpret the lecture model. The quantitative connection is the working relation \(m\lambda = d\left(\sin\theta_i + \sin\theta_m\right), \qquad \dfrac{d\theta}{d\lambda} = \dfrac{m}{d\cos\theta_m}\).
Boundary or common confusion: Assuming a grating disperses light only in the commonly used first order. Real gratings simultaneously produce multiple overlapping orders at different angles for different wavelengths; every practical spectrograph design must explicitly account for and, where necessary, suppress unwanted orders (with order-blocking filters) or exploit them deliberately...