Spectrograph

A spectrograph records the optical spectrum dispersed by an instrument. Its spectral resolving power describes which nearby wavelengths it separates.

Spectrophotometry measures received light as a function of wavelength, accounting for the instrument's wavelength-dependent response.

A sample holder providing a defined geometric light path through a chemical solution for spectrophotometry, as in the trypsin colorimetric assay.

A spectrophotometer measures radiant power in selected wavelength bands. Comparing a chemical solution in a cuvette with a reference blank gives transmittance and absorbance.

A spectral resolution element is a spectral interval at the adopted instrumental resolution. At spectral resolving power $R$, its width is $\Delta \lambda =\lambda /R$. The number of photodetector detector pixels sampling it is distinct from $R$.

Linear spectral dispersion is the derivative of the photodetector coordinate in the dispersion direction with respect to wavelength. Near the optical axis, $q=f_{\mathrm{cam}}d\beta /d\lambda$.

An integral field spectrograph records a spectrum for each of many spatial elements across a two-dimensional field, producing a spectral data cube. Field reformatters include lenslet arrays, optical fibers and image slicers.

With fixed spectral resolving power, wavelength interval, diffraction grating geometry, photodetector sampling and collimator focal ratio, a beam diameter scales as the spaxel width $\theta$, but the optical camera focal length stays fixed. A simple on-axis beam-envelope model therefore gives collimator and disperser volumes proportional to ${\theta }^3$ and optical camera volume proportional to ${\theta }^2$. With a fixed number of spaxels per photodetector, replication multiplies these volumes by $M\propto {\theta }^{-2}$. A fixed photodetector field adds transverse clearances and changes the small-$\theta$ limit; these exponents are not universal mechanical-volume laws.

A spaxel is one spatial sampling element in a spectral data cube. For a square field of angular side $\beta$ sampled at angular side $\theta$, the number of spaxels is $(\beta /\theta {)}^2$, before edge rounding.

An image slicer divides a two-dimensional image into narrow strips and optically rearranges them into a long pseudo-slit. A spectrograph then disperses each strip while preserving its position along the slit.

A spectral data cube stores intensity $I(x,y,\lambda )$ with two spatial coordinates and one spectral coordinate. The third coordinate is wavelength, not an additional spatial dimension.

Spectral resolving power is $R=\lambda /\Delta \lambda$, where $\Delta \lambda$ is the wavelength separation just resolved under the specified instrumental and source conditions.

A cross-dispersed echelle spectrograph uses an echelle grating for strong dispersion and a cross-disperser in the perpendicular direction to separate overlapping diffraction orders. It records many orders simultaneously in an echellogram.

A cross-disperser is a second dispersing element, often an optical prism or diffraction grating, oriented to separate optical spectra perpendicular to their principal dispersion direction.

An echellogram is the two-dimensional detector pattern of separated diffraction orders from a cross-dispersed echelle spectrograph.

A multi-object spectrograph records optical spectra of many selected objects simultaneously. The main designs are multi-slit spectrographs and fiber-fed spectrographs. The ESO instrumentation overview describes both arrangements.

A multi-slit spectrograph puts separate slits at target positions in the focal plane. Each slit transmits the target plus nearby sky; dispersion places its spatially resolved optical spectrum on the detector.

A fiber-fed spectrograph places optical fibers on selected targets and reformats their output into a common entrance slit. Dedicated sky fibers sample sky brightness. Fiber coupling, transmission, and output beam spreading affect throughput and resolution.