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Built by André Baranne, Michel Mayor, Didier Queloz and colleagues, the ELODIE fiber-fed spectrograph carried light from Haute-Provence's 1.93-metre telescope through optical fibers. Its echelle grating dispersed light in high diffraction orders; an optical prism and grism cross-disperser separated them perpendicularly on a charge-coupled device. This cross-dispersed echelle spectrograph achieved spectral resolving power $R=42000$. A simultaneous thorium reference tracked instrumental drift. Wavelength calibration mapped detector positions to wavelengths; spectral cross-correlation combined many spectral lines into a fitted profile. A barycentric velocity correction removed the observer's motion.^[ref]

Why can a spectrograph measure a Doppler shift much smaller than one spectral resolution element? Resolution concerns separating neighbouring features, whereas locating the centre of a known profile uses information across that profile and across many spectral lines. For a chosen example, at $\lambda =500\mathrm{nm}$ a recession velocity of $60\mathrm{m}{\mathrm{s}}^{-1}$ givesAt $R=42000$, one spectral resolution element corresponds to $c/R\simeq 7.14\mathrm{km}{\mathrm{s}}^{-1}$, about $119$ times larger. A well measured centre can move by a small fraction of that width. More photons and more useful spectral lines improve the estimate, but do not remove wavelength calibration errors or stellar activity.

A simple mathematical picture of spectral cross-correlation makes the readout concrete. Define $x=c\log (\lambda /{\lambda }_0)$, with fixed reference wavelength ${\lambda }_0$, and let $d(x)$ be continuum-normalized line absorption. For small velocities, a common Doppler shift approximately translates $d(x)$. A positive absorption mask $m(x)$ then givesIf $d(x)=m(x-v_r)$, the maximum occurs at $u=v_r$; a convention correlating the received observed radiative flux instead produces a dip. A fitted correlation centre is an effective collective line position, not a claim that each individual spectral line has been resolved into a narrower feature. The lamp tracks instrumental drift, while the barycentric velocity correction removes the observer's changing line-of-sight velocity; neither removes changes in the star itself.

Spectroscopy investigates how a system emits, absorbs or scatters signals as a function of frequency, wavelength or energy. A spectrum can identify transition energies, response strengths and line shapes. In atomic spectroscopy, a photon connects two energy levels through $h\nu =|E_f-E_i|$; in inelastic scattering, both energy and momentum transfers can matter.

A simple optical experiment passes source light through a sample, disperses the transmitted light and compares it with a reference. An absorption line identifies reduced transmission over a spectral interval, but its depth also depends on the sample amount and instrumental response. Wavelength calibration and energy resolution distinguish an intrinsic feature from a shifted or broadened recording. The inference therefore uses a response model as well as a list of line positions.

Time-resolved spectroscopy measures how a spectroscopic response changes after a defined excitation or other reference event. Instead of only a time-integrated spectrum, it records a response such as $S(\nu ,t)$ as a function of frequency and delay. A changing spectral feature can distinguish population loss, changing molecular environment and motion of a resonance; a single integrated intensity need not separate them.

In pump-probe spectroscopy, a pump pulse prepares the sample and a delayed probe interrogates it. A movable mirror in a double-pass optical path provides a precise delay change:For an original displacement of 15 micrometres, the delay changes by about 100 femtoseconds. A spectrally resolved detector records the response while delay is scanned. The time resolution is set by pulse overlap, jitter and the detection scheme, rather than by mirror step size alone. Ahmed H. Zewail's lecture explains how such optical timing enabled femtochemistry.^[ref]

An original decay example assumes an isolated feature with background already removed and responseIf its intensity at 3 picoseconds is $1/e$ of its intensity at 1 picosecond, then $e^{-2\mathrm{ps}/\tau }=1/e$ and $\tau =2\mathrm{ps}$. This inference assumes the same feature is measured at both delays and that the instrument response is sufficiently short. A shifting line observed through a narrow spectral window can change intensity without following that simple population law.

Finite resolution instead produces a convolution. For a time-invariant instrument response function $R$ at a selected spectral channel,For ideal Gaussian pump and probe intensity envelopes, their cross-correlation width is the square root of the sum of their squared widths. Chosen full widths of 80 and 100 femtoseconds therefore give about 128 femtoseconds before other contributions. This original calculation describes pulse-overlap resolution, not an arbitrary material lifetime.

A motivating historical example is Zewail's discussion of the NaI/NaBr experiments reported in 1988. Delay-dependent signals probe evolving molecular motion and final fragments, supplying information absent from a static spectrum. His lecture presents the NaI dynamics in Figure 15.^[ref]

A practical experiment compares pumped and unpumped records, checks delay zero and wavelength calibration, and varies excitation strength to test whether the response remains in the intended regime. Negative-delay data, backgrounds and the measured instrument response function help distinguish sample dynamics from timing and detection artifacts.