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.

Co-oximetry determines hemoglobin composition using optical measurements at multiple wavelengths. In a laboratory blood analyzer, it can distinguish oxyhemoglobin, deoxyhemoglobin, carboxyhemoglobin and methemoglobin rather than infer all hemoglobin behavior from a single oxygen-related number. A manufacturer description explicitly identifies direct optical spectrophotometry as the measurement method for its analyzer's co-oximetry parameters.^[ref]

An idealized mixture model makes the separating information explicit:where $A_j$ is measured absorbance, $\ell$ the path length, $c_i$ a species concentration, ${\epsilon }_i$ its molar absorption coefficient and $b_j$ a background term. Estimating four unconstrained concentrations requires sufficient independent spectral observations and known response coefficients; merely having four wavelength labels does not guarantee independence. An isosbestic point shared by two species supplies information about their combined amount but cannot by itself separate their proportions.

The denominator of a reported fraction matters. In a simplified four-form example, stipulate $90\%$ oxyhemoglobin, $5\%$ deoxyhemoglobin, $4\%$ carboxyhemoglobin and $1\%$ methemoglobin, all expressed on the same total-hemoglobin basis. Fractional oxyhemoglobin is $0.90$, but the functional oxygen saturation isThese differ because the second denominator excludes the other two forms. The manufacturer's parameter description distinguishes these definitions.^[ref] The chosen fractions are an explanatory example, not clinical thresholds.

A blood-sample optical assay and a noninvasive pulsatile optical measurement use different observation models. Their output labels and denominators must be established from the specific method, rather than inferred from the common word oximetry. Likewise, oxygen partial pressure describes dissolved oxygen equilibrium and is not itself a measurement of all hemoglobin fractions.

An instrument test can compare reference mixtures with independently established composition, record full spectral residuals and vary a suspected interferent. Agreement of one derived saturation number alone does not validate every inferred species concentration. Background, spectral overlap and sample handling belong in the measurement model and its uncertainty.

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 microplate reader is an optical instrument that records signals from addressed wells in a microplate, allowing many small samples, references and repeats to be measured in one arrangement. In absorbance mode it acts as a spectrophotometer: wavelength-selected illumination passes through the well and a photodetector measures transmitted light. The vertical sample geometry makes the liquid depth part of the optical path length.^[ref]

For an ideal homogeneous non-scattering solution, the Beer-Lambert law giveswhere $\ell$ is the geometric light path through the solution. For an original dye example, suppose $\epsilon c=0.60\mathrm{c}{\mathrm{m}}^{-1}$. A0.50cm depth gives absorbance0.30 and transmittance about0.501, whereas a1.00cm depth gives absorbance0.60 and transmittance about0.251. The concentration is identical. A darker well can therefore result from a longer path rather than a more concentrated sample. Microplate path-length correction is needed when comparing such readings on a common path-length basis.

A manufacturer experiment used a yellow buffer at426nm in a96-well clear plate, with volumes from75 to300µL. A1cm cuvette gave absorbance0.556. Uncorrected plate values were roughly0.17–0.53, while path-length-corrected values ranged from0.55 to0.57. The varied-volume experiment directly illustrates why the raw signal cannot be interpreted as concentration alone.^[ref]

The same instrument technology estimates path length using water's near-infrared absorbance at1000 and900nm, with plate-background subtraction preceding normalization.^[ref] In a simple independent example, a sample reading0.34 with plate contribution0.04 leaves solution absorbance0.30. At path0.50cm, normalization to1cm gives0.60. Dividing the uncorrected0.34 by0.50 instead gives0.68, incorrectly assigning the plate's contribution to the solution.

The instrument must therefore preserve well positions, wavelength settings, reference measurements and the reduction applied to each reading. Blank correction, matched sample handling and appropriate measurement calibration help distinguish optical differences from differences in concentration. A microplate reader can produce an array of precise numbers while a shared path-length or background error affects the whole array.

Microplate path-length correction expresses a solution's measured absorbance on a specified common geometric light-path basis. In a microplate reader, liquid depth varies with filling volume, unlike a fixed-width cuvette. For a homogeneous solution obeying the Beer-Lambert law, the solution contribution is proportional to geometric path length $\ell$. Normalizing to reference length $L$ therefore multiplies that contribution by $L/\ell$.

An instrument can estimate $\ell$ using a solvent absorption feature. Define $D_w$ as the corrected near-infrared absorbance difference of an aqueous well and $D_r$ as the corresponding difference for matched solvent in a reference cuvette of length $L$. If the same absorption coefficient applies,The manufacturer's method uses water measurements at1000 and900nm; the1000nm choice reduces the temperature sensitivity associated with using the water peak near977nm. A matched reference is important when solvent composition changes the near-infrared response.^[ref]

Plate background must be separated from the part proportional to liquid depth. With raw reading $A_{\mathrm{raw}}$, plate contribution $P$ and solvent blank already expressed at length $L$, a simple reduction model isFor an original example, $D_w=0.10$, $D_r=0.20$ and $L=1\mathrm{cm}$ imply $\ell =0.50\mathrm{cm}$. If $A_{\mathrm{raw}}=0.35$, $P=0.05$ and $A_{\mathrm{blank},L}=0.02$, the corrected result is0.58. Normalizing the raw value first and then subtracting the unscaled plate contribution instead gives0.63. The0.05 discrepancy is an incorrect assignment of plate background to the solution.^[ref]

The correction's interpretation also depends on what is held fixed. Different volumes of the same-concentration solution change depth and raw absorbance. For a fixed amount $n$ of a nonvolatile absorber in an ideal flat-bottom well of area $S$, however, $c=n/V$ and $\ell =V/S$, so $\epsilon c\ell =\epsilon n/S$ is volume-independent. This is microplate fill-height optical cancellation. A path-normalized result then tracks the changing concentration, rather than a changing amount of absorber. The measurement question determines which quantity is useful.

Scattering, interfering near-infrared absorption, an unsuitable solvent reference or poor blank correction can invalidate the simple model. A corrected number should retain its reference length, background treatment and source of the path estimate; normalization alone does not establish a valid concentration measurement.

A microplate is a tray containing an ordered array of small wells that keep samples physically separate while permitting repeatable handling and measurement. A microplate reader addresses wells to measure optical signals. The plate is consequently part of the measurement geometry: its positioning, well shape and material affect how illumination reaches the solution and how transmitted or emitted light is collected.

The microplate footprint is the base outline used to fit the plate into handling equipment. The primary footprint standard specifies nominal length127.76mm and width85.48mm. Its tolerances distinguish measurements within12.7mm of the corners, $\pm 0.25\mathrm{mm}$, from measurements anywhere along the sides, $\pm 0.5\mathrm{mm}$. The stated dimensions apply at $20{}^{\circ }\mathrm{C}$ unless otherwise specified.^[ref] Nominal dimensions alone therefore do not define the entire fit envelope.

For an original counting and volume example, an8-row,12-column layout has96 wells. Filling each with200µL requires19.2mL of delivered liquid, before losses in transfer equipment are included. Equal delivered volume does not itself prove equal concentration, and a plate-wide mean can conceal an individual underfilled well. Keeping the row/column address with each reading allows sample, reference and repeat locations to remain distinguishable.

For an ideal flat-bottom well, a volume estimate can be related to depth by $\ell =V/S$, where $S$ is its internal liquid-covered area. A hypothetical $S=32\mathrm{m}{\mathrm{m}}^2$ and $V=160\mathrm{m}{\mathrm{m}}^3=160\mu \mathrm{L}$ give5mm depth. Curved bottoms, taper and the meniscus alter that simple geometry. In transmission measurements the resulting depth enters the Beer-Lambert law, making microplate path-length correction relevant to comparisons across filling volumes.

The standard's foreword records dimensional variation across suppliers as a source of problems in automated instruments and describes standardization work beginning in1995.^[ref] A common footprint promotes mechanical compatibility; it does not imply identical well volumes, optical backgrounds or spectral transmission. Those properties still need to match the intended physical measurement.

The microplate footprint is the base outline used to locate a microplate in a carrier, gripper or microplate reader. It defines a mechanical interface rather than the liquid volume or the detailed geometry of individual wells. A common nominal rectangle promotes compatibility, but its dimensional tolerances and measurement locations must accompany the nominal values.

The primary footprint standard gives length127.76mm and width85.48mm. Within12.7mm of the outside corners, its specified tolerances are $\pm 0.25\mathrm{mm}$; measured anywhere along the sides, they are $\pm 0.5\mathrm{mm}$. Its default dimensional reference temperature is $20{}^{\circ }\mathrm{C}$.^[ref] Using the tighter near-corner tolerance for every location would misread the specification.

For an original rectangular-envelope calculation, take a carrier opening128.40mm long and86.10mm wide. The standard's full-side upper limits are128.26mm and85.98mm, leaving total length and width clearances0.14mm and0.12mm. If the plate and opening are centered in this simplified model, those become0.07mm and0.06mm per side. Designing only from nominal dimensions would instead suggest much larger total clearances0.64mm and0.62mm.

The calculation concerns the stated planar envelope. Corner shape, flange geometry, vertical clearance, positioning features and the carrier's own tolerances can also determine whether a real plate seats correctly. The footprint standard separately specifies a continuous base outline and corner-radius requirements, rather than reducing the entire interface to two nominal lengths.^[ref]

A footprint check can use calibrated dimensional measurements at the specified locations and conditions. It should distinguish a length measurement from a functional fit test: a plate that enters one carrier does not by that observation alone establish every standard dimension, and agreement in two measured dimensions does not establish optical suitability. Well-bottom transmission and microplate path-length correction remain separate parts of the optical measurement chain.

The standard's foreword identifies dimensional variation between suppliers as an automation problem. This supplies the practical motivation for the interface: a plate should arrive at a predictable physical location so that downstream handling and measurements can be repeatable.^[ref]

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.